Technical Manual, Seismic Design Guidelines for Essential Buildings

ARMY TM 5-809-10-1 NAVY NAVFAC P-355.1 AIR FORCE AFM 88-3, CHAP. 13, SEC A

a TECHNICAL MANUAL

SEISMIC DESIGN GUIDELINES FOR

ESSENTIAL BUILDINGS

This copy is a reprint which includes current I pages from Changes I 1 DEPARTMENTS OF THE ARMY, THE NAVY, AND THE AIR FORCE 27 FEBRUARY 1986

89:121402368391212 FDR WASTE WM-1 I PDC TM 5-809-10-1 /NAVFAC P-355.1 /AFM 88-3. Chapter 13, Section A C1 CHANGE DEPARTMENTS OF THE ARMY, THE NAVY AND THE AIR FORCE No. 1 WASHINGTON, DC, 15 December 1986 TECHNICAL MANUAL SEISMIC DESIGN GUIDELINES FOR ESSENTIAL BUILDINGS TM 5-809-10-1/NAVFAC P-355.1IAFM 88-3, Chapter 13, Section A, 27 Feb- ruary 1986, is changed as follows: 1. Remove and insert pages below. New or changed text material is indicated by a vertical bar in the margin. Remove pages Insertpages Cover 1 and Cover 2...... Cover 1 and Cover 2 2. This transmittal sheet should be filed in the front of the publication for reference purposes. The proponent agency of this publication Isthe Office of the Chief of Engi- neers, United States Army. Users are Invited to send comments and suggested Improvements on DA Form 2028 (Recommended Changes to Publi- cations and Blank Forms) direct to HQDA (DAEN-ECE-D). WASH DC 20314-1000.

By Order of the Secretaries of the Army, the Air Force, and the Navy:

Official: MILDRED E. HEDBERG JOHN A. WICKHAM, JR. BrigadierGeneral, United States Army General, United States Army The Adjutant General Chief of Staff CHARLES G. GABRIEL General, USAF Chief of Staff Official: NORMAND G. LEZY J. P. JONES, JR. Colonel, USAF RearAdmiral, CEC, U.S. Navy Directorof Administration Commander, Naval Facilities EngineeringCommand Distribution: Army: To be distributed in accordance with DA Form 12-34B, Requirements for Seismic Design for Buildings. AirForce: F Navy: FOREWORD

The seismic design guidelines manual was developed to meet one of the objectives for earthquake hazards reduction measures as promulgated by the Earthquake Hazards Reduction Act of 1977 (Public Law 95-124). The objective is the development and implementation of a technologi- cally and economically feasible, improved design and construction methods and practices in areas of seismic risk to provide earthquake resistant structures which are especially needed in time of disaster.

This guideline manual provides the latest seismic design concepts for earthquake resistant structures by utilizing the dynamic analysis approach. The concept is for essential buildings but also includes design provisions for high risk and irregular buildings. This manual also provides methodologies and procedures to determine site-dependent earthquake ground motions for sites anywhere in the United States. Two levels of earthquake motion are considered. At the first level, the structure will be designed to remain elastic for damage control at a moderate earthquake and at the second level, the criterion requires that the structure remains functional after a major earthquake. Also, commentary and design examples are included to provide a comprehensive applica- tions of the design methodologies for earthquake resistant facilities. The general direction and detailed development of this manual was under the supervision and guidance of the Office of the Chief of Engi- neers, Headquarters, Department of the Army, Washington, DC and necessary coordination was maintained with the Naval Facilities En- gineering Command, Headquarters, Department of the Navy, Washing- ton, DC and Directorate of Engineering and Services, Headquarters, Department of the Air Force, Washington, DC. TM 5-809-10-1 NAVFAC P.355,1 AFM 88-3, Chapter 13, Section A

TECHNICAL MANUAL DEPARTMENTS OF THE ARMY, THE NAVY No. 5-809-10-1 AND THE AIR FORCE NAVY MANUAL WASHINGTON, DC, 27 February1986 NAVFAC P-355.1 AIR FORCE MANUAL No. 88-3, CHAPTER 13, SECTION A SEISMIC DESIGN GUIDELINES FOR ESSENTIAL BUILDINGS Paragraph Page CHAPTER 1. GENERAL * Purpose and scope ...... 1-1 1-1 Backgrounda. 1-2 1-1 Preparation of project documents. 1-3 1-2 References and bibliography. 1-4 1-3 * CHAPTER 2. INTRODUCTION TO SEISMIC ANALYSIS Introduction. 2-1 2-1 General. 2-2 2-1 Ground motion caused by earthquakes . 2-3 2-1 Site effects . 2-4 2-5 Dynamic analysis of structure. 2-5 2-6 Nonstructural elements. 2-6 2-14 CHAPTER 3. SPECIFICATIONS OF GROUND MOTION Section I. Basic steps for specification of ground motion Introduction. 3-1 3-1 Definition of terms, glossary, and symbols. 3-2 3-3 General overview of seismic hazard analysis. 3-3 3-3 Section II. Procedure for site specific ground motion Determination of source seismicity. 3-4 3-11 Selection of the attenuation relation. 3-5 3-30 Site specific response spectra. 3-6 3-40 Interpretation and summary. 3-7 3-54 Section III. The ATC-3-06 method The ATC--06 method . 3-8 3-57 CHAPTER 4. CRITERIA FOR STRUCTURAL ANALYSIS Introduction. 4-1 4-1 General requirements...... 4-2 4-1 Elastic design provisions. 4-3 4-2 Post-yield analysis provisions. 4-4 4-7 CHAPTER 5. STRUCTURAL DESIGN PROCEDURE Introduction. 5-1 5-1 Preliminary design considerations. 5-2 5-1 General design procedures. 5-3 5-1 Designing for EQ-I . 5-4 5-12 Designing for EQ-I . 5-5 5-19 CHAPTER 6. NONSTRUCTURAL ELEMENTS Introduction. 6-1 6-1 General requirements...... 6-2 6-1 EQ-I provisions. 6-3 6-1 EQ-I provisions. 6-4 6-6 Architectural elements ...... 6-5 6-6 Mechanical and electrical elements ...... 6-6 6-6 Essential systems. 6-7 6-7 CHAPTER 7. STRUCTURES OTHER THAN BUILDINGS Introduction. 7-1 7-1 General requirements...... 7-2 7-1 Elevated tanks and other inverted pendulum structures. 7-3 7-1 Vertical tanks (on ground). 7-4 7-2 Horizontal tanks (on ground). 7-5 7-2 Retaining walls . 7-6 7-2 Buried structures . 7-7 7-2 APPENDIX A. SYMBOLS AND NOTATIONS . A-I APPENDIX B. REFERENCES. B-1 APPENDIX C. GROUND MOTION BACKGROUND DATA ...... C-1

I TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

SEISMIC DESIGN GUIDELINES FOR ESSENTIAL BUILDINGS Paragraph Page APPENDIX D. DESIGN EXAMPLES-GROUND MOTION ...... D-1 APPENDIX E. DESIGN EXAMPLES-STRUCTURES...... E-1 APPENDIX F. DESIGN EXAMPLES-EQUIPMENT IN BUILDINGS ...... F-1 BIBLIOGRAPHY ...... Bibliography 1 GLOSSARY ...... Glossary 1 INDEX ...... Index I

LIST OF FIGURES Figure 2-1. Recorded acceleration at ground level for three components of motion 2-2. Ground acceleration and integrated ground velocity and displacement curves 2-3. Description of acceleration response spectrum 2-4. Response spectra from recorded ground acceleration shown in Figure 2-1, transverse (north) 2-5. Single-degree-of-freedom system 2-6. Multi-degree-of-freedom system 2-7. Multi-mass system represented by a single-mass system 2-8. Design response spectra for examples in figures 2-9 and 2-10 2-9. Sample modal analysis of a 30-story building 2-10. Sample modal analysis of a 7-story building 2-11. Response of flexibility mounted equipment in buildings 3-1. Selection procedures 3-2. General flow diagram selection chart 3-3. General flow chart 3-4. Flow diagram for the Western United States 3-5. Hazard evaluation of Western United States 3-6. Flow diagram for the Eastern United States 3-7. Hazard evaluation of Eastern United States 3-8. Regional differences 3-9. Flow chart for Step 1, source identification and modeling for the Western United States 3-10. Point, line, and area sources 3-11. Dipping plane source 3-12. Flow chart for Step 1, source identification and modeling for the Eastern United States 3-13. Seismic sources after Algumissen and Perkins 3-14. Seismic sources after Hadley and Divine 3-15. Seismic sources after Tera 3-16. Flow chart for Step 11, seismicity and recurrence relationships for Western United States and Eastern United States 3-17. Linear recurrence relationship 3-18. Bilinear recurrence relationship 3-19. Recurrence relation for North San Andreas 3-20. Flow chart for Step 111, seismic forecasting model 3-21. Step IV, attenuation of ground motion from source to site 3-22. Attenuation distances 3-23. OASES attenuation 3-24. Attenuation relations 3-25. Comparison of ground motion models for Mb = 5.5 3-26. Description of sets of M and R required for a given PGA 3-27. Step V, site specific response spectra 3-28. Newmark-Hall spectrum 3-29. Statistical averaging of normalized spectra 3-30. Average acceleration spectra for different site conditions 3-31. Eighty-four percentile acceleration spectra for different site conditions 3-32. Predominant periods in rock, earthquake magnitude 7 3-33. Predominant periods for maximum acceleration in rock 3-34. Comparison of DAF from Kiremidjian and Shah to DAF from Seed et al, soil class = 0, damping = 5% 3-35. Comparison of DAF from Kiremidjian and Shah to DAF from Seed et al, soil class = 1, damping = 5% 3-36. Comparison of DAF from Kiremidjian and Shah to DAF from Seed et al, soil class = 2, damping = 5% 3-37. Factors affecting spectral shape 3-38. Envelope quality of the DAF shape 3-39. Hazard curve for site PGA with exposure time of 50 years 3-40. Contour map for effective peak acceleration ii 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Figure 3-41. Contour map for effective peak acceleration 3-42. Contour map for effective peak velocity-related acceleration coefficient 3-43. Contour map for effective peak velocity-related acceleration coefficient 3-44. Schematic representation showing how effective peak acceleration and effective peak velocity are obtained from a response spectrum 3-45. Annual risk of exceeding various peak accelerations for locations on the indicated contours of A. and A, 3-46. Tripartite representation of EQ-1i 3-47. EQ-Il spectra for A. = A, = 0.40 and i3 = 5 percent 3-48. Effective spectra] envelope 3-49. Regional shape differences 3-50. Las Vegas, Nevada, site spectra for soil type S2 3-51. Emeryville, California, site spectra for soil type S3 4-1. Definition of inelastic demand ratios for flexural members 4-2. Ductility check of steel columns 4-3. Ductility check for concrete columns 5-1. Gravity/seismic load relationships 5-2. Dynamic structural characteristics 5-3. Nonproportional relationship between peak ground acceleration and spectral acceleration 5-4. Sample EQ-I spectrum and ZICS curve 5-5. Force-displacement capacity curve 5-6. Capacity spectrum method 6-1. Design M.F. vs. period ratio 6-2. Sample roof response spectrum 6-3. Post-yield M.F. curve C-I. Earthquake source model C-2. Types of fault slips C-3. The Richter scale CG4. Relation between earthquake magnitude and intensity C-5. McCann and Shah relationship C-6. The PGA-MMI relationship with the intervals associated with each intensity C-7. Single-degree-of-freedom system C-8. Maximum dynamic load factor for sinusoidal load C-9. Judgmental averaging of empirical and analytical site spectra C-10. Relative degree of fault activity D-i. Source models and records for sources I and 2 D-2. Recurrence relation for source I D-3. Recurrence data plot for source I D-4. Source location and element properties D-5. Probability calculations for event combinations giving the hazard P (PGA > 0.20g) DU-. Site hazard curve and scaled site spectrum for EQ-I D-7. Scheme of present seismic hazard methodology U-8. General flow chart for seismic hazard analysis D-9. Earthquake listing for example 2 D-10. Output for recurrence relationship, example 2 D-lI. Recurrence relationship for example 2 D-12. Output for bilinear recurrence relationship, example 2 0-13. Bilinear recurrence relationship for example 2 D-14. Seismic sources for region of example 3 D-15. Earthquake listing for sources in example 3 D-16. Output for recurrence relationships and site PGA probability distribution for example 3 D-17. Complementary cumulative distribution function for example 3 D-18. Acceleration zone graph (AZG) for CITY 2 E-l. Sample modal analysis E-2. Building with a box system E-3. Building with steel moment-resisting frames and steel braced frames E-4. Seven-story ductile concrete frame building F-I. Cooling tower in building F-2. Unit heater-flexible brace F-3. Unit heater-rigid support '-4. Tank on a building

iii -

TM 5-809-1 0-1 /NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 LIST OF TABLES Table 3-1. Return period as a function of exposure time and probability of exceedance 3-2. OASES attenuation constants for median PGA values 3-3. Spectrum amplification factors for horizontal elastic response 3-4. Map contour and ground motion levels 3-5. Site soil profile types 3-6. Site profile coefficient 3-7. Damping adjustment factors 4-1. Damping values for structural systems 4-2. Inelastic demand ratios 5-. Seismic design procedures 5-la. Seismic design of essential facilities 5-lb. Seismic design of high-risk buildings 5-ic. Seismic design for other buildings 5-2. General modal relationships 5-3. Seven-story building-transverse direction-summary of modal analysis 5-4. Conversion of V and BN to S. and T 6-1. Example of a response amplification curve for the building's fundamental mode of vibration. 6-2. Data for the floor (roof) response spectrum example of figure 6-2 6-3. Essential nonstructural systems 7-1. Damping values for structures other than buildings C-l. Magnitude and seismic moment C-2. The Modified Mercalli intensity scale C-3. The Rossi-Forel scale CA-. Relationship between Modified Mercalli intensity (MM) and Rossi-Forel intensity (RF) C-5. Relationship between MMI and PGA C-6. Magnitude-displacement relationship C-7. Displacement-fault length relationship CG-. Magnitude-fault length relationship C-9. Magnitude-length times displacement relationship C-10. Magnitude-length times squared displacement relationship C-li. Degree of fault activity D-1. Return period vs PGA for CITY 2 E-l. Design examples-structural F-I. Design examples-equipment in buildings

iv 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A CHAPTER 1 GENERAL

1-1. Purpose and scope. are based on DOD standards; however, the risk a. Purpose. This manual prescribes criteria levels may be revised, as warranted, by approval and furnishes guidelines for the design of es- authorities. sential buildings, high-risk buildings, and other d. Classificationof structures. structures that may require analytical proce- (1) Hazardouscritical facilities. These fa- dures that are beyond the scope of TM 5-809- cilities (e.g., nuclear power plants, dams, and 10/NAVFAC P-355/AFM 88-3, chapter 13, "Seis- LNG facilities) are not included within the scope mic Design for Buildings." Methodologies and of this manual, but are covered by other publi- procedures are given for determining site-de- cations or regulatory agencies. For any facilities pendent ground motion and for the dynamic housing hazardous items not covered by criteria, analysis of buildings. These criteria apply to all advice should be sought from DAEN-ECE-D elements responsible for design of military con- (Army), NAVFAC Code 04BA (Navy), or HQ struction located in seismic regions. This man- USAF/LEEE (Air Force). ual is a supplement to TM 5-809-1O/NAVFAC (2) Essential facilities. These are struc- P-355/AFM 88-3, chapter 13, referred to herein tures housing facilities that are necessary for as the Basic Design Manual. post-disaster recovery and require continuous operation during and after an earthquake. This b. Scope. Approval from DAEN-ECE-D includes facilities where damage from an earth- (Army), NAVFAC Code 04BA (Navy), or HQ quake may cause significant loss of strategic and USAF/LEEE (Air Force) is required for the use general communications and disaster response of this manual as an alternative requirement to capability. This category also includes facilities applicable provisions of the Basic Design Man- serving an essential military function that must ual. This manual is for guidance in the design not be disrupted. Typical examples are listed in of buildings and other structures housing es- the Basic Design Manual, paragraph 3-Sa. sential mission-oriented facilities and those that (3) High-risk. This classification includes are vitally needed for post-disaster recovery that those structures where primary occupancy is for require continuous operation during and after assembly of a large number of people; where the an earthquake. This manual may also be used primary use is for people that are confined; or for guidance in the design of buildings that are where services are provided to a large area or classified in a high-risk category; buildings that large number of other buildings. Buildings in are irregular in shape, size, and configuration this classification may suffer limited damage in that require consideration of the dynamic char- a large earthquake, but are recognized as war- acteristics of the structure; and all other build- ranting a higher level of safety than the average ings as an alternative to the equivalent lateral building. Typical examples are listed in the Basic static force procedure for determination and Design Manual, paragraph 3-5b. distribution of seismic forces. These guidelines (4) All others. The provisions of this man- encompass: (1) assessment of the seismic haz- ual may be used for irregular buildings or as an ard at the site; and (2) seismic design of the option for all other buildings not covered by the structural and nonstructural systems for new above paragraphs only with the consent of the buildings and other structures. The problems approval authority. relating to earthquake-induced ground failure (e.g., liquefaction) are already stated in Basic Design Manual paragraph 2-7 and will not be 1-2. Background. covered in this manual. Alterations or evalua- a. Expectations. Current seismic design cri- tions of existing structures are not specifically teria, such as prescribed by the Basic Design covered by this manual; however, the principles Manual, consist of specified equivalent lateral and guidelines contained herein may be adapted static forces that are resisted by the designed for such use. structural systems. Structures designed in con- c. Seismic hazardrisk levels. Seismic ground formance with such provisions and principles motion input for two risk levels is specified in are expected to be able to: (1) resist minor chapter 3 for the prescribed structural perform- earthquakes without damage; (2) resist mod- ance criteria in chapter 4. The selected risk lev- erate earthquakes without structural dam- els of the two earthquakes (EQ-I and EQ-Il) age, but with some nonstructural damage; and 1-1 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 (3) resist major or severe earthquakes without occurring during the life of the building (e.g., major failure of the building or its component 10-percent chance of being exceeded in 100 years). members and equipment, and to maintain life In the first phase of the procedure, the building safety. For most structures, even in a major is structurally designed to resist the lower level earthquake, structural damage should be lim- earthquake within prescribed bounds of elastic- ited to repairable damage. It is also recognized linear procedures. In the second phase of the that for certain critical facilities, particularly procedure, the building is analyzed for its re- those essential to public safety and well-being sponse to the higher level earthquake by means in case of emergency, criteria should be avail- of procedures that account for inelastic behav- able to the designer that will permit design of ior, ductility demands, potential instability, and a facility that will remain operational during damage control. These guidelines are intended and after an earthquake. to insure that essential facilities will be capable b. Lessons learned. Recent earthquakes have of resisting the two levels of earthquake ground demonstrated that the existing seismic design motion as follows: (1) for ground motion as- requirements, as they have been implemented, sociated with the maximum probable earth- are not necessarily adequate to insure contin- quake, only minor damage, if any, will occur and ued operation of critical facilities vitally needed the facilities will not have any loss of function; after a major earthquake, such as hospitals, fire and (2) for ground motion associated with the stations, and communications centers. There- maximum theoretical earthquake, no cata- fore, there is a need for a more realistic ap- strophic failures will occur, damage will be re- proach to seismic-resistant design for buildings pairable, and essential facilities will remain that must remain continuously functional after functional. The definitions and the methodology a major earthquake. for determining these earthquakes are covered c. Recent developments. Earthquake engi- in chapter 3. The criteria and procedures for neering research and data collected from ground design are covered in chapters 4 and 5. motion instrumentations and earthquake-caused building responses during the last two decades 1-3. Preparation of project documents. have greatly increased knowledge in geotechni- a. Design analysis. A design analysis con- cal fields and have presented a clearer under- forming to agency standards will be provided standing of the performance of materials and with final plans. This design analysis will include ) structural elements. Therefore, practicing en- seismic design computations for the determi- gineers are able to become familiar with meth- nation of ground motion charateristics, for the ods of dynamic analysis as they are exposed to determination of dynamic characteristics of the new design procedures by means of technical structure, for the stresses in the lateral-force- publications, conferences, and continuing edu- resisting elements and their connections, and cation programs. for the resulting lateral deflections and inters- d. Design philosophy. One way of attempt- tory drifts. The first portion of the Design Anal- ing to reduce the risk of earthquake damage to ysis, called the Basis of Design, will contain the buildings is by imposing a higher design force following specific information: coefficient, such as an I-f actor of 1.5, for essen- (1) A statement on the methodology used tial facilities. This is not always a sufficient or for determining the ground motion criteria, and satisfactory approach to seismic design. In- a description of the response spectra for which creasing the design forces by 50 percent may be the structure will be designed. insignificant if a major earthquake results in (2) A description of the structural system demands several times the design capacity. On selected for resisting lateral forces and a dis- the basis of current knowledge, it appears that cussion of the reasons for its selection. A sym- a two-level (or two-phase) approach to design metrically configured lateral resisting framing will give better insight to postulated behavior system, without vertical irregularities, will be of structures. In this procedure, geotechnical data required. However, if irregular conditions are and probabilistic techniques are used to postu- unavoidable, a statement describing special late the motion for two earthquakes: (1) the analytical procedures to account for the irreg- maximum probable earthquake, which is likely ularities will be submitted for review and ap- to occur one or more times during the life of the proval by the approval authority. building (e.g., an earthquake with a 50-percent (3) A statement regarding compliance with chance of being exceeded in 50 years); and (2) this manual, including a list of the values se- the maximum theoretical earthquake that can lected for damping and maximum inelastic de- occur at the site, but has a low probability of mand ratios for critical structural elements. 1-2 27 February 1986 TM 5-809-lO-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A (4) Any possible assumed future~expansion riods of vibration and equivalent design lateral for which provisions are made. forces and other factors. b. Drawings. Preparation of drawings will (c) Assumptions made for future exten- conform to agency standards for ordinary con- sions or additions. struction, with the following additional specific (3) Site adaption of standard drawings will requirements for seismic construction: include design revisions for the seismic area as (1) Preliminary drawings will contain a required. statement that seismic design will be incorporated in accordance with this manual. The Basis of Design will comply with paragraph a 1-4. References and bibliography. above. Publications that may be required to supple- (2) Construction drawings for seismic areas ment the provisions of this manual are listed in will include the following additional special in- appendix B, References. Publications that may formation: be useful as back-up material and are presented (a) A statement on the seismic ground as suggested reading are included in the bibli- motion criteria including the design peak ground ography. When pertinent to the subject, some accelerations and related response spectra. publications in the bibliography are noted in the (b) A statement on the lateral-force de- text by the bibliography number, in parenthesis. sign criteria including a tabulation of the pe- 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A CHAPTER 2 INTRODUCTION TO SEISMIC ANALYSIS

2-1. Introduction. 2-3. Ground motion caused by This chapter provides an introduction to the basic earthquakes. concepts of dynamic analysis for buildings re- A general introduction to earthquake ground sponding to the ground motions caused by motion is presented in the Basic Design Manual. earthquakes. General guidance is given in the The relationship of a ground motion to the site selection and use of various procedures for the and an introduction to time-history and redesign of structural systems. sponse spectra are presented herein. A detailed methodology for determining site-specific ground 2-2. General. motion characteristics is covered by chapter 3 An earthquake causes vibratory ground mo- of this manual. tions at the base of a structure and the structure a. General. actively responds to these motions. Seismic de- (1) Ground motion is generally strongest in sign involves two distinct steps: (1) determining the vicinity of its source (e.g., a rupturing fault), or estimating the forces that will act on the with the severity of shaking diminishing with structure; and (2) designing the structure to an increase in distance. resist these forces and to keep deflections within (2) The predominant periods of ground mo- prescribed limits. tion vibration generally lengthen as distance in- a. Determination of forces. There are two creases from the source (para 3-6f). general approaches to determining seismic (3) Deep deposits of soft soils tend to pro- forces: (1) an equivalent static force procedure, duce ground surface motions having predomi- such as presented in the Basic Design Manual; nantly long period characteristics. and (2) a dynamic analysis procedure. This man- (4) Deposits of stiff soils or rock result in ual illustrates the dynamic analysis procedure. ground motions having predominantly short pe- Seismic forces are determined from data derived riod characteristics. from the specification of ground motion. These b. Time history. The basic measurement of ground motion data will generally be given in earthquake ground motion is the accelerogram terms of a response spectrum; however, in some record taken by seismometers. When these in- cases the data may be described in terms of a strument records are properly corrected for digitized time history. elimination of recording noise and for base line b. Design of the structure. Structures are adjustment, a primary data base for seismic load generally designed to resist applied forces well specifications is provided. Data banks of past within the elastic capacity of their structural earthquake records from all parts of the world members. This is accomplished either by pre- are readily accessible from earthquake research scribing maximum allowable working stresses centers. A typical seismometer station provides for materials, or by using a strength design con- records of two orthogonal horizontal motions cept with prescribed load factors. However, for and one vertical motion, as illustrated in figure exceptional loading conditions, such as caused 2-1. The corresponding processed accelero- by major earthquakes, structures may be re- grams are intended to be the best representa- quired to resist deformations that exceed the tion of the actual ground acceleration at the elastic capacities of the structural elements. In recording site. For a given component, the time conventional methods of seismic design, it is as- derivative relations between ground displace- sumed that the design criteria will provide ad- ment, x(t); velocity x(t); and acceleration, x(t), equate safety by means of load factors and special allow the presentation of each of these motion details that provide the necessary ductility to histories, as shown in figure 2-2. The maximum resist major earthquake deformations. In the or peak values of displacement (PGD), velocity methods presented in this manual, the design (PGV), and acceleration (PGA) provide the most procedures will give a better insight as to the elementary and popular measures of an earth- performance of a structure when subjected to quake's severity. Duration (or bracketed dura- the exceptional loading conditions of a major tion) of strong motion is also an important earthquake. This method is generally referred measure, but it is not explicitly used in design to as a two-level approach to structural design. criteria at the present time. TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

RECORDED ACCELERATION AT GROU11D LEVEL DURING THE 1971 SAN FERNANDO EARTHQUAKE

Transverse (North)

0.25^- !1 M A

-0.25 , V V. Y .

*0 0.25 Longitudinal (West) 0.2 CU OA R mI .x%' e.~r<-111

-q a)j -0.25

0.25 ) 0 -0.25

* 8 * U M81 Al 81 8& 8

0 3 6 9 12 15 18 21 24 27 30

Time (seconds)

Reprinted from "The San Fernando, Cali- fornia, Earthquake of February 9, 1971," U.S. Covernment Printing Office, 1971. Figure 2-1. Recorded acceleration at ground level for three components of motion.

)

2-2 27 February 1986 TM 5-809-10-1/NAFAC P-355.1/AFM 88-3, Chapter 13, Section A

IMPERIAL VALLEY EARTHOURKE MAY 18. 1940 - 2037 PST IRO01D40.001.0 EL CENTRO SITE IMPERIAL , VALLEY IMRIATION DISTRICT COMP SODE c PEAK VALUES: ACCEL: 341.7 cw(C/C VELOCITY = 33.4 CK/SEc OISPL = 10.9 cm -500

U TSJ V Li0 aJ w Cc "i IC x ki

500 -'0

0- 0 _ K LL. 4J

40 -20

z r

U.)U -J 02 20 I _ __ _ 0 30 MO so TIME - SECONDS

Reprinted from "United States Earthquakes." U.S. Coast and Geodetic Surveys, U.S. Govern- ment Printing Office, 1940. Figure 2-2. Ground accelerationand integratedground velocity and displacement curves. TM 5-809-10-1/NAVFAC P-3S5.1/AFM 88-3, Chapter 13, Section A 27 February 1986 c. Response spectra. For design purposes, it several records can be normalized, averaged, and would be ideal to forecast the acceleration time then scaled according to seismicity to predict history of a future earthquake having a given future ground motion at a given site. The phys- hazard of occurrence. However, the complex ical definition of an acceleration response spec- random nature of an accelerogram makes it nec- trum is shown in figure 2-3. A set of linear elastic essary to employ a more general characteriza- single-degree-of-freedom (SDOF) systems hav- tion of ground motion. Specifically, the most ing a common damping ratio, I, but each having practical representation is the earthquake re- different harmonic periods over the range 0, T1, sponse spectrum. This spectrum is used not only T2, etc. is subjected to a given ground motion to describe the intensity and vibration fre- accelerogram. The entire time history of accel- quency content of accelerograms, but also the eration response is found for each system, and most important advantage is that spectra from the corresponding maximum value, Sa, is plotted

JrJTEM RAspoJAVJX

______GOUIN/ ____PA CCCE(.eATION LINeA urn OF G/VCEN bAMP/NC _~~/iP? WITH AtANGC- OP NA7UIAL 'C.1M~ It7T.. ACCE4ERA7IOm )

ACCELI~eATION dtEJR0 ONJe ~~~~~c e ~l ,MAK.

GAOUN;O ACCEi.eACIGAM 7.

TIME

US Army Corps of Engineers Figure2-3. Description of acceleration response spectrum. 2-4 27 February 1986 TM 5-809-10-1/NAVFAC P-355.I/AFM 88-3, Chapter 13, Section A on the period axis for each system period. The curve provides the maximum response value for curve connecting these Sa values is the accel- any given system period, T. eration response spectrum for the given accelerogram and damping ratio. Actual spectra for 2-4. Site effects. the transverse (north) accelerogram of figure a. Response spectrum shape. Response spec- 2-1 are shown for several damping ratios in fig- tra shapes are determined largely by empirical ure 2-4. A smoothed individual spectrum (fig 2- data. Time history records of past earthquakes 4b), or averages of multiple record spectra, is are used to construct response spectra. As the employed as the seismic load input for the dy- data bank increases, average trends can be ob- namic analysis of structures. Note that the Sa served with respect to the general shape of re-

2.0- SAN FERNANDO EQ 2/9/71 VAN NUYS HOLIDAY INN 1ST FLOOR NORTH

Damping - 0.01, 0.02, 0.05, 0.10

1.2-

I-J .8- -,, = 0.01 Li .0 = 0.02 0 = 0.05 _B = 0.10 A.- 1^ .4 U - 0 .3 .6 .9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 PERIOD, SEC (T) a. RESPONSE SPECTRA: FOUR VALUES OF DAMPING ($)

1 .2 4 B - 0.05 SPECTRUM (from a. above.)

.8 SMOOTH SPECTRUM ,

hExample: For T=0.3 sec. S_=O.7 Q 0 0.3 0.6 0.9 1.2 1.5 1.8 7.1 2.11 2.7 3.0

PERIOD, SEC. (T)

b. SMOOTH RESPONSE SPECTRUM: S - 0;05

US Anny Corps of Engineers Figure 2-4. Response spectra from recorded ground accelerationshown in figure 2-1. 2-5 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 sponse spectra curves. When these data are system is used in textbooks to illustrate prin- catalogued in terms of tectonic region, event in- ciples of dynamics. It represents two kinds of tensity, distance, and site characteristics, spe- real buildings: (1) a single-column structure with cific response spectra shapes can then be a relatively large mass at its top; and (2) a sin- developed that represent the conditions of par- gle-story frame structure with flexible columns ticular sites. Procedures for developing re- and rigid roof system. In the idealized system, sponse spectra are covered in chapter 3, and the mass (M) represents the weight (W) of the illustrative examples are included in appendix D. system divided by the acceleration of gravity (g) b. Soil column. Site soil characteristics can (M = W/g). The pole or columns represent the be used to develop a mathematical model of a stiffness (K) of the system, which is a ratio equal soil column at a building site. For a postulated to a horizontal force (F) applied to the mass bedrock earthquake, analytical procedures can divided by the displacement (8) resulting from be used to calculate the soil column's effect on that force (K = Fi8). If the mass is deflected and the ground motion at the surface or the base of then quickly released, it will freely vibrate at a a structure. These results can be used either to certain frequency, which is called its natural calculate the shape of the response spectrum of freuency of vibration. The period of vibration these particular conditions, or used directly for (T), which is the inverse of the frequency of time history analysis of the structure. vibration, is the time taken for the mass to move c. Foundation design. All inertia forces through one complete cycle (i.e., from one side originating from the masses on the structure to the other and back again (part b of fig 2-5). must be transmitted to and from the lateral- The period is equal to 2irV M/K. In an ideal sys- force-resisting elements, to the base of the tem having no damping (I = 0), the displaced structure, and into the ground. Foundations must system described above would vibrate forever. be designed to provide stability for response due In a real system where there is some damping, to maximum seismic ground motion. It should the amplitude of motion will decrease for each also be noted that the type, size, and depth of a cycle until the structure stops oscillating and foundation system can have an effect on a struc- comes to rest (part c of fig 2-5). The greater the ture's response to seismic motion and that the damping, the sooner the structure comes to rest. actual seismic input is a series of reversing load The amount of damping is defined in terms of a cycles. ratio, or percentage, of critical damping. If the structure has damping equal to 100 percent of 2-5. Dynamic analysis of structures. critical damping (I = 1.0), the displaced struc- Structures that are keyed into the ground and ture will come to rest without crossing the ini- extend vertically some distance above the ground tial point of zero displacement. If oscillating act either as simple or complex oscillators when motion is applied to the base of the system, the subjected to earthquake-caused ground motion. SDOF system will be forced to vibrate. If the Simple oscillators are represented by single-de- oscillating motion at the base is at a period equal, gree-of-freedom (SDOF) systems, and complex or nearly equal, to the period of the SDOF sys- oscillators are represented by multi-degree-of- tem, the motion of the mass will amplify until freedom (MDOF) systems. When a structure's it is substantially greater than the motion at the base is suddenly moved by earthquake ground base. This condition is called resonance. The motion, the upper part of the structure will not lower the value of A, the higher the amplifica- respond instantaneously, but will lag behind be- tion. cause of the structure's inertial resistance and b. Multi-degree-of-freedom systems. Multi- flexibility. This concept is illustrated in the Basic story buildings are analyzed as MDOF systems Design Manual, paragraph 2-4. As time pro- as shown in figure 2-6. They can be represented gresses during an earthquake, the structure's by lumped masses attached at intervals along various natural modes of vibration will be ex- the length of a vertically cantilevered pole (part cited to peak amplitudes of motion as described a of fig 2-6). Each mass can be deflected in one by the response spectrum (para 2-3c). direction or another; for example, all masses a. Single-degree-of-freed6m system. One may simultaneously deflect in the same direc- fundamental system that is investigated by dy- tion (the fundamental mode of vibration), or namic analysis is the simple oscillator or SDOF some masses may go to the left while others are system, as shown in figure 2-5. Represented by going to the right (higher modes of vibration). a single lump of mass on the upper end of a An idealized system, such as shown in part a of vertically cantilevered pole or by a mass sup- figure 2-6, has a number of modes equal to the ported by two columns (part a of fig 2-5), this number of masses. Each mode has its own nat- 2-6 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

z FOR~CE M F : WEIGHT F rl r. MAJJ I--j rmi,10ACc-MEN P O*,K= F II K : JTIPFNE.hff 4 F GP&4V1TY

a. ID~EALIZED JINGLE- LUMMP-MASJ JYJ7GMJ

I 1PJL~kr PERII OF VAIA 4ArI OH: T: 2 Tr .F~w

I -I

/ ~04

b. FREE V/P.RAOTION ( No nAMPI NG) -

VhJ5RATE4 a 0-~'

N 1P.- t

- -

D~AMP'ER c, DAMPED FREAf VIQRA7TON (nAMIsE ATA RATIO 70 CRI7ICAL D4AMPIN& E(QUAL 70 a )

US Army Corps of Engineers Figure2-5. Single-degree-of-freedom system.

2-7 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

4I m7 k 7 *m 6

min mL l

I k

I- - rn-_ -- Multi-Mass Fundamental Second Tiii rd System - Mode Miode Mode

a. Idealized Lumped b. Mode Shapes Mass System

US Army Corps of Engineers

Figure 2-6. Multi-degree-of-freedom system. ural modal period of vibration with a unique mode system. For many buildings, the partici- I/ ) mode shape being formed by a line connecting pation of the higher modes is negligible in re- the deflected masses (part b of fig 2-6). When lation to the participation of the fundamental oscillating motion is applied to the base of the modes of vibration. However, for tall, long-pe- multi-mass system, these masses move. The de- riod, and irregular buildings, the second, third, flected shape is a combination of all the mode and, possibly, higher modes may have a sub- shapes; but modes having periods that are near, stantial effect. The amount of higher mode par- or equal to, predominant periods of the base ticipation depends on both the building's modal motion will be amplified more than the other characteristics and the amplitude-period char- modes. Illustrative examples of MDOF systems acteristics of the response spectrum. Assuming are included in appendix E. that several modes are significant, one must se- c. Multi-mode response to ground mo- lect an appropriate method of combining the re- tion. Each mode of an MDOF system can be sults of the several modes. One method is simply represented by an equivalent SDOF system hav- to add up the effects of each mode (absolute ing a normalized mass (M*) and stiffness (K*) sum). This is an overly conservative approach where the period equals 21 7V'M-7IK (M* and K* because the response spectrum gives the peak are functions of mode shapes, mass, and stiff- response of each mode, and different modes reach ness). This concept, as shown in figure 2-7, pro- their peak amplitudes at different times during vides the computational basis for using site the earthquake. Since the spectrum gives only specific earthquake response spectra based on the maximum values and the time of occurrence SDOF systems for analyzing multi-storied build- is unknown, some approximate method of mode ings. With the period, mode shape, mass distri- combination must be used. The method most bution, and response spectrum, one can compute commonly employed is to combine the modes by the deflected shape, story accelerations, forces, the square-root-of-the-sum-of-the-squares and overturning moments. Using the response (SRSS) of the peak response of each mode (this spectrum method on MDOF systems requires is analogous to a vector sum). This offers a rea- analyzing each predominant mode separately. sonable value between the upper bound as the Results of each individual modal analysis must absolute sum of the modes and the lower bound then be combined in order to analyze the multi- as the maximum value of a single mode. To il- 2-8 27 February 1986 TM 5-809-10-1I/NVFAC P-355.1IAFM 883, Chapter 13, Section A

6 roof I

m7. t -- "- f7 = m 7a7

k7 M4 ---% f6 m6aG kb

m5 I9 -- f5 = m5as F = M*Sa

m4 I ~~~f4 -M~a 4

m3 -'--f 3 m 3a3

k3 K* m12 f2 m2a2

f ml aI

First Mode of a Equivalent Multi-Mass System Single-mass System

M* and K: are normalized values of mass and stiffness that represent the equivalent combined effects of the story masses (M) in(I stiffnesses (K)

US Army Corps of Engineers Figure2-7. Multi-mass system representedby a single-mass system.

2-9 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 lustrate the multi-mode analysis of multi-sto- for modal analysis examples of a 30-story build- ried buildings, two examples are given. Figure ing and a 7-story building. 2-8 shows design response spectra that are used

0.8

0.7 . _ __ __

0.6

0.5 _B=

0.4

2%20

O.1 _...B=19

1.0 2.0 3.0

PERIOD, T(sec)

, ~~~~~SPECTRAL ACCELERATION, Sa~w

i._00.10.48 .50 0.80 1.0 1.25 1.75! 2.0 2.25: 2.5 3.0

2 1 0.64 0.64 0.59 0.37 0.30 0.24 0.201 .171 0.151 0.131 0.121 0.10

5961 % 0.50 0.50 0.48 0.301 0.24 0.192 0.1610-1371 0.12 0.107;0.096 ':0.08 0.50 __ ---. 0.480.24 IJ----- 0.1892j00.9'O0 -- - 1------

7' 0.44 0.44 0.44 0.28 0.22 0.18 0.l5' 0.13 0.11 0.10 0.09 0.07

I . . .0 0.08_..._1... _ --b---- 10% 0.38 0.38 0.38 0.25 0.20 0.16 0A13 0.11. l i .08 0.0661 . .. 27 -7 - 0I2 _ I 0 _08 _ ._.0_

2 0.27 0.27 0.27 0.20 0.16 0.12 0! 000 0-°ioo.081fi0.07 ,0.06 0.05

US Army Corps of Engineers Figure2-8. Design response spectra for examples in figures 2-9 and 2-10. 2-10 27 February 1986 TM 5-809-1O0-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A (1) Thirty-story building. The example in seconds. The periods of the second and third figure 2-9 summarizes the results of a modal modes of vibration are 1.00 seconds and 0.56 sec- analysis of a structural framing system that onds, respectively. From the response spectrum represents one principal axis of a 30-story build- curve in figure 2-8, which represents 5 percent ing. The fundamental period of vibration is 3.0 of critical damping (A = 0.05), it is determined

1ST MODE 2ND MODE 3RD MODE T,=0.56 T1 =3.00 sec T2 =1.00 sec sec 29 ' .29 25 -. 02 21 -. 28 17 13 9 C Groun~d

U- (K) 25 5790 .104 .104 .094 .175 -' - - 25 584t .097 .037 .113 21 5841 .02 7 [-0_ - o - -- 17 58L1 L_' _- .D08h 8( 13 5841 .1321*1!5 036 -;097 .083 _ 9 5841 .020 -. 065 6211 'F, .11_5 Groun c 0 _C_CE E RT4 __g_ (b) MODAL STORY ACCELERATIO~NS (gl!S.)

N: 2C 250 * 601 604 -. E 543 _ __ .. - - 25 215 , 568 7 335 3_ _ 21 180 502 145 * 425 17 /* a 110 * 326 _ 13 I 212 I j -569 484 9 75 V- 40 121 405 57(, - 5 0 Grou~nd 0 (c) MODAL STORY FORCES !1.ip-)

th 29 35 601 604 543 __ 1010 __ 25 35 1169 511 ~~~~1584L 21 35 1677 905 -5 1906 1 17 35* 2)02 ! ;~~~~ 521 T ~ ~ 592225 13 35* 2428 y 4_) J -6~~~~4 5'-2e 2486 t 9 35I 2640 -633 -44 2715 5 40* 2671 -1038 2997 Ground (d) MODAL STORY SHEARS kips)

29 0 0 0 0 25 21035 21140 K 19005 335363 21 61950 4nODS 36890 90084 I8 17 120645 i5640 36715 152461 13 194215 _ 3ID3915 18900 2210771 5 279195 101675 420 297133 5 371595 79520 -1120 3800)0 " Ground 482035 - -- '20160 -___ - -*t3e5_ (e) MODAL STORY OVERTURNING MOMENTS (kip-ft) *Story 29 represents the roof, floors 29 and 28, and one-half of floor 27. Other story designations represent the reference story plus one-and-one-half stories above and below.

US Army Corps of Engineers Figure 2-9. Sample modal analysis of a 30-story building. 2-11 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 that the second mode spectral acceleration higher modes become somewhat insignificant (0.240g) is triple that of the first mode spectral because of the reversal of force directions. The acceleration (0.080g), and that the third mode SRSS curve is essentially equal to the first mode spectral acceleration (0.45g) is over 5 times that curve at the lower stories of the building. of the first mode spectral acceleration. On the (2) Seven-story building. The example in basis of mode shapes and modal participation figure 2-10 summarizes the results of a modal factors (chap 5), modal story displacements, ac- analysis of a structural framing system that celerations, forces, shears, and overturning mo- represents one principal axis of a 7-story build- ments can be determined. For ease of comparison ing. Back-up data for this example are included to the 7-story example (para (2). below), the 30- in appendix E (design example E-1). The pe- story building is compacted to seven lumped riods of vibration are roughly 30 percent of the masses, each representing four stories. Back-up periods of the 30-story building (fig 2-9); pe- data for this example are included in appendix riods of the first, second, and third modes being E (design example E-1). The modal analysis 0.880 seconds, 0.288 seconds, and 0.164 seconds, procedure is covered in chapter 5. respectively. From the 5-percent damped re- (a) Diagram (a) of figure 2-9 shows the sponse spectrum (P = 0.05) of figure 2-8, both modal displacements. Note that the funda- the second and third mode spectral accelera- mental mode (first mode) predominates, while tions (0.500g) are 80 percent greater than the second and third mode displacements are rela- first mode spectral acceleration (0.276g). tively insignificant. The SRSS combination does (3) Comparisons. By comparing figures 2- not differ greatly from the fundamental mode. 9 and 2-10, it can be seen that the influences of (b) Diagram (b) shows story accelera- the second and third modes in relation to the tions. In this form, the second and third modes first mode are larger for the 30-story building do play a significant role in the structure's max- than for the 7-story building. For taller build- imum response. While the shape of an individual ings with longer periods of vibration, the influ- mode is the same for displacements and accel- ences of the higher modes may become larger, erations, accelerations are proportional to dis- and participation of additional modes of vibra- placements divided by the squared value of the tion (e.g., fourth and fifth modes) may become modal period, which accounts for the greater significant. accelerations from the higher modes. The shape d. Response of irregular buildings. When of the SRSS combination of the accelerations is buildings are eccentric or have areas of discon- substantially different from shapes of any of tinuity or other irregularities, the behavioral the individual modes because it accounts for the characteristic are very complex; whereas build- predominance of the various modes at different ings with symmetrical shape, stiffness, and mass story levels. Note that the maximum accelera- distribution and with vertical continuity and tions on stories 5 through 25 do not vary by more uniformity behave in a fairly predictable man- than 10 percent from the mean value, indicating ner. In addition to the single axis of response that the maximum acceleration felt at most floor shown in figures 2-9 and 2-10, the torsional re- levels is fairly constant. However, these maxi- sponse (twisting about a vertical axis) as well mum values would not occur simultaneously or as the interaction or coupling of the two trans- with the same period content. lational directions (longitudinal and transverse (c) Diagram (c) shows story forces whose axis) of response must be considered. For ex- values are obtained by multiplying the story ac- ample, the predominant motion may be skewed celeration by the story mass (or weight). The from the apparent principal axis. This is some- shapes of diagram (c) curves are quite similar what analogous to a Mohr's circle for principal to the shapes of diagram (b) curves because the stresses. Thus, three-dimensional methods of building mass is essentially uniform. analysis are required and each mode shape is (d) Diagram (d) shows story shears, defined in three dimensions by the longitudinal which are a summation of the modal story forces movement, the transverse movement, and the in diagram (c). The higher modes become less angle of rotation. In addition to complicating significant in relation to the first mode because the method of analysis, building irregularities the forces tend to cancel each other due to the complicate the methods used to combine modes. reversal of direction. Except for the top stories, Methods such as SRSS may not be appropriate the SRSS values do not differ substantially from for some three-dimensional methods of dynamic the first mode values. analysis. Procedures for performing three-di-' ) (e) Diagram (e) of figure 2-9 shows the mensional analyses are covered in chapter 5. building overturning moments. Again, the e. Inelastic-nonlinearresponse. In order to 2-12 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

1ST MODE 2ND MODE 3RD MODE T1 =.880 sec T2 =.288 sec T3 =.164 sec SRSS Roo f 7 2.74 .19 1 .04 2.75 6 2.57 -.11 .00 2.57 5 2.30 -.04 2.30 -. 04 4 1.93 -.18I 1.93 3 1.46 -. I8 .00 1.48 2 .96 .02 I .97 - . -~~-.12~ .04 Ground .52 _ .,, (a) MODAL LATERAL DISPLACEMENTS (inches)

l?~~~~~~? Wt (K) Roo f 1410 .360 .234 71 .121 -7o .446 7 1460 .338 .129 -.007,, 1 .362 6 1460 .303 .324 5 1460 .254 -.148 -.112 .315 -.22 5 4 1460 .193 .1 .004- .297 -. 219 .275 1460 .127 3 -. 146 :.20 [) .201 2 1830 .068 Ground 0 (b) MODAL STORY ACCELERATIONS (g's)

Ht Roo f 65.7' 508 330 170 -- 6759 7 57. 0' 494 18B -10-*' A 529 6 48.3' 443 -1 -166 473 5 6' 371 39. -329 , -6 433 .0 4 30.9' 282 I.3 22.2' 185 -7 -319 156 W4oo D -267 219 - 367 Ground 13.5' 125 0 (c) MODAL STORY FORCES (kips)

^h Roof 8.7 508 330 170 , 629 7 160 -6 1139 6 8.7 1002 51 8 8.7 1445 499 1529 5 1846 4 8.7 1816 283 r I -169 2098 -16 2106 3 0 -175 2312 8.7 2283 -365 2 rd-632 200 2498 trrnun,d 13.5 2408 (d) MODAL STORY SHEARS (kips)

Roo f 0 0 0 0 7 4420 -2871 1479 5474 6 13137 -7378 2871 15338 54 25709 -11719 2819 28394 4 ~~41508 -14181 1349 28394 3 59761 -13781 -174 4368L 2 '79623 ______-10605 -339 61330 Ground 211231 I23. -- 20371 112175 (e) MODAL STORY OVERTURNING MOMENTS (kip-ft)

US Arm)y Corps of Engineers Figure 2-10. Sample modal analysis of a 7-story building.

2-13 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 estimate the behavior of a structure that may of motion corresponding to the building's nat- be subjected to a major, damaging-type earth- ural periods of vibration tend to be magnified. quake, it is necessary to investigate its inelastic In other words, a response spectrum of a build- response characteristics and capacity. The gen- ing's floor motion will have predominant peaks eral procedures discussed in paragraphs a at the participating periods of the building. If through d above are on the basis of elastic-lin- elements are rigid and rigidly attached to the ear distortions of the building's structural ele- structure, the maximum accelerations will be ments. When one major structural element the same as the maximum floor accelerations, begins to yield, changes will begin to occur in such as those shown in the SRSS curve of dia- the structure's behavioral characteristics. For gram (b) in figures 2-9 and 2-10. But, if the example, force distribution, periods of vibra- elements are flexible and have periods of vibration, and mode shapes will be altered as parts tion close to any of the predominant building of various elements yield. Dynamic analysis pro- vibration modes, these elements will experience cedures for nonlinear systems can be very com- accelerations substantially greater than the floor plex, requiring step-by-step, time-history-forcing- accelerations. Generally, a time-history analy- functions, and inelastic force-distortion prop- sis is required to determine the peak response erties of all the structural elements and their of flexible or flexibly attached equipment at up- connections. However, approximate methods per levels of a building. A time-history of the have been developed that give rough approxi- ground motion is used to calculate a time-his- mations as to the inelastic response or capacity tory of the floor motion. The floor motion time- of structures. Post-yield analysis procedures are history is then used to construct a floor response discussed in chapter 5 and illustrative examples spectra. This procedure is illustrated in figure are included in appendix E. 2-11. In chapter 6, an approximate method is shown for constructing design floor response 2-6. Nonstructural elements. spectra. Illustrative examples are included in Elements that are housed in the building, as well appendix F. as portions of the building that are not part of b. Elements attached to adjacent floors. the structural system, must also be investigated Elements extending vertically from floor to floor for their response to earthquake motion. These (e.g., full-height partitions, exterior panels, pip- ) elements are generally categorized as architec- ing) will be subjected to two types of dynamic tural, mechanical, or electrical (refer to Basic motion. One type is the response motion de- Design Manual, chaps 9 and 10). scribed in paragraph a above. The other type is a. Elements attached to floors of build- due to the distortion resulting from the inters- ings. These elements (e.g., mechanical equip- tory displacements between two adjacent story ment, free-standing partitions, storage racks, levels. Interstory displacements for each mode suspended fixtures) respond to floor motion in can be obtained by finding the difference be- much the same manner as a building responds tween adjacent modal lateral story displace- to ground motion. However, the floor motion ments (diagram (a) in figs 2-9 and 2-10). may vary substantially from the ground motion. Interstory displacements for a multi-mode sys- The high-frequency components that make the tem can be approximated by combining the modal ground motion complex tend to be filtered out interstory displacements by the SRSS or other at the higher floor levels, while the components methods.

2-14 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Sa Flexibly Mounted FlAor'IRespne Equipment m

Floor Response Floor Response IX Spectrum

__=_~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

WN O.-W WI OIW WIN Al%"% - ~ Ground lotion

US Anny Corps of Engineers Figure 2-11. Response of flexibly-mounted equipment in buildings.

2-15 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A CHAPTER 3 SPECIFICATION OF GROUND MOTION

Section I BASIC STEPS FOR SPECIFICATION OF GROUND MOTION 3-1. Introduction. described in table 3-5 and having locations out- The purpose of this chapter is to describe the side of the limits of paragraph 3-1 b( 1), the ATC methodologies for determining site dependent 3-06 method of section III, paragraph 3-8 of this earthquake ground motions for sites anywhere manual may be used. in the United States. The objective is to develop (3) For sites in the WUS having exceptional design parameters from the available informa- soil conditions conforming to the soil description and seismic ground motion. The principal tion of soil profile S3 as described in table 3-5, method of describing these ground motions will the selection of the corresponding site specific be in the form of acceleration response spectra response spectrum shape will consider and em- for input in the dynamic analysis of a given ploy the recommendations of paragraphs 3-6c(3) structure. or 3-6f(3) as directed by the responsible agency. a. Selected method of description. There are If this WUS site location is outside of the limits several methods of arriving at a description of of paragraph 3-1b(1), then the selected spec- future earthquake loading. These are described trum shape may be scaled by the appropriate briefly along with their advantages and disad- site acceleration coefficient A, given in paragraph vantages in appendix C, paragraph C-3. The 3-8. method employing an attenuated site severity (4) For sites in the EUS having the soil con- factor (such as peak ground acceleration, PGA) ditions conforming to soil profile S3 and outside which is used to scale a normalized site spectral of the limits of paragraph 3-lb(1), the method shape (Dynamic Amplification Factor, DAF) is of paragraph 3-8 may be used. judged to be the most appropriate and practical (5) In all cases where methods other than input for the dynamic analysis of building struc- those of paragraph 3-8 are employed, the re- tures and therefore will be the principal method sults will be compared with those from para- for this manual. However, this empirical method graph 3-8, and any significant differences will may be supplemented by available results from be justified and resolved. All final recommen- the other methods; particularly any findings from dations shall be subject to approval by the re- a site soil column response study, as described sponsible agency. in appendix C, paragraph C-3. c. Scope. The scope of this part of the Man- b. Procedures. The following selection pro- ual includes the description of the essential steps cedures will be followed for the evaluation of and related procedures necessary for the spec- site dependent earthquake ground motions, (see ification of site specific ground motion. These fig 3-1). These procedures are dependent upon are listed in paragraph 3-3 for the Western three conditions: the geotectonic regions of the United States (WUS) and the Eastern United Western United States (WUS) and the Eastern States (EUS), and for the deterministic and United States (EUS) as defined in paragraph 3- probabilistic procedures. 4a, the proximity of seismic sources, and the site d. Current state-of-the-art. It is important soil conditions as described in table 3-S5. to recognize that the field of ground motion (1) For sites located within 20 kilometers specification is in a state of evolution. The gen- from a fault or area source in the WUS, or within eral steps and input variables as outlined in this a tectonic province in the EUS, where the source manual are reasonably well accepted by most of or province has a maximum local magnitude of the researchers and users. However, because of 6.0 or greater, the detailed procedures of para- the very active state of development, it is not graphs 3-3 through 3-7 will be considered and possible to outline a step by step procedure which employed as directed by the responsible agency. will remain the same with time as well as from (2) For sites in either the WUS or EUS hav- region to region. Thus, the steps outlined in this ing normal site soil conditions conforming to manual are to be viewed as guidelines rather the description of soil profile types SI or S2 as than as one universally accepted and recommended procedure. Nothing in this chapter will prevent substantiated alter- e. Format of results. Various methods for native methods or time history procedures if approved by the evaluation of the level of ground motion and the agency command. its time history or frequency content are de- 3-1 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Western United States (WUS)

Source to Site Surface Distance

g _ _~~ II Soil he 20 Kilometers More than Type or less* 20 Kilometers

S1 or Site Specific Hazard ATC 3-06 Method S Analysis (Para 3-8) 2 ~(para 3-3 to 3-7) (aa38

S3 Same as above Site Specific Spectra Development (para 3-6). Site Specific Hazard Analysis not Required.

* If line fault or area source, then source must have maximum Mmax greater than 6.0, otherwise use Column II.

Eastern United States (EUS)

Soil I II Type Within a province All regions having MmaxŽ 6.0 other than in Column I

S or Site Specific Hazard ATC 3-06 Method 1 Analysis (para 3-8) S2 (para 3-3 to 3-7) (

S3 Same as above Same as above

US Army Corps of Engineers Figure 3-1. Selection procedure.

3-2 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A scribed in appendix C, paragraph C-3. Of all these 3-2. Definition of Terms, Glossary, and methods, the empirical method consisting of an Symbols. PGA scaling factor for ground motion severity The methodologies of determining ground mo- at a given risk level, and an effective DAF spec- tion are based on the following disciplines: ge- tral shape, has been selected for the typical con- ology, seismology, dynamics and vibrations, ditions and design objectives of this manual. An probability and statistics. Because of this rather effective response spectrum will be specified for extensive range of subject matter, it is neces- each of the two levels of structural perform- sary to provide both symbols and a glossary of ance. Unless specified by the appropriate agency terms used in this manual along with the related the acceptable risk of exceedance will corre- terminology commonly used in the references spond to: and necessary bibliography. These are given in (1) A fifty percent risk of exceedance in fifty appendix A, Symbols and Notations; and in the years (EQ-I), and Glossary. (2) A ten percent risk of exceedance in one 3-3. General Overview of Seismic Hazard hundred years, (EQ-I1). Analysis and Specification of Ground Table 3-1 shows the relationship between the Motion. exposure time (or economic life of the facility), For engineering design and planning purposes, the probability of exceedance and the return pe- the future earthquake loadings at a site of in- riod. terest must be known. The procedures and steps

Table 3-1. Return period as a function of exposure time and probability of non-exceedance

Exposure Time Years 10 20 30 40 50 100 "Hazard" or Probability of exceeding A

5 195 390 585 780 975 1950 10 95 190 285 390 475 950 20 45 90 135 180 225 449 30 29 57 84 113 140 281 40 20 40 59 79 98 196 50 1 5 29 44 58 72 145 60 1 1 22 33 44 55 110 70 9 17 25 34 42 84 80 7 13 19 25 31 63 90 5 9 14 18 22 44 95 4 7 11 14 18 34 99 3 5 7 9 11 22 99..5 2 4 6 8 10 19

------L_

[IS Ainmy Corps of Liigi rseer±s 3-3 TM 5-809-10-1INAVFAC P-355.1/AFM 88-3, Chapter 13, SectIon A 27 February 1986 for estimating this future loading comes under parameters (such as magnitude, intensity, and the general category of seismic hazard analysis. spectra) to be employed are dependent upon the It should be recognized that there are two dif- type of information available to the analyst and ferent approaches: deterministic and probabi- the needs of the designer. The procedures and listic. Deterministic approaches do not take into the models selected depend on the type, quan- account the uncertainty in the size, the location, tity, and quality of information as well as the and the frequency of seismic events. Probabilis- goal of the analysis. The general procedures for tic approaches incorporate uncertainty in all the evaluating seismic ground motion in the West- above quantities. An overview of the procedures ern United States do not differ greatly from those for deterministic and probabilistic approaches in the Eastern United States. However, since is given in this paragraph. Steps are outlined by the tectonic setting and the available seismic means of flow diagrams and illustrative for- information varies greatly between those two mats. These are shown in figure 3-2 for the two geographic regions, the elements of the proce- main tectonic regions; the Western United States dures are different. A discussion related to se- (WUS) and the Eastern United States (EUS). lection of deterministic or probabilistic a. Algorithm ofBasicStepsofSeismicHazard procedures will be given in paragraph 3-3c. The Analysis. Various earthquake severity param- five basic steps required for the evaluation of a eters at the source and site are described in ap- site specific seismic ground motion are described pendix C, paragraph C-1. The particular below (see fig 3-3). The region-specific flow dia-

Seismic Hazard Analysis Procedure (See Figure 3-3)

I)1

WESTERN UNITED STATES EASTERN UNITED STATES (See Figures 3-4 and 3-5) (See Figures 3-6 and 3-7)

DETERMINISTIC PROBABILISTIC DETERMINISTIC PROBABILISTIC PROCEDURE PROCEDURE PROCEDURE PROCEDURE

US Anmy Corps of Engineers Figure 3-2. General flow diagram selection chart. 3-4 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Sectlon A

IDENTIFICATION AND MODELING OF Step 1 (para 3-4a and 3-4b) SEISMIC SOURCES

DEF1NE SIZE PROBABILISTIC BTAIN PARAMETER SOURCE _ / ~~~~~~~SEISMICITY (para 3-3d) DETERMLNISTIC INFORMATION APPROACH

SELECT LEVEL(S) ESTIMATE LARGEST OF EARTHQUAKE MAGNITUDE MAGNITUDE(s) POSSIBLE FOR Step 11 (para 3-4c ) J ~~~~~~~THESOURCE SELECT MOST CONSERVATIVE RECURRENCE DISTANCE FROM RELATIONSHIP I - SOURCE TO SITE

_. _ _SELECT FORECASTING ATTENUATE ONE OF THE SITE MODEL FOR Step III (para 3-4d ) SEVERITY PARAMETERS THE SOURCE FROM SOURCE TO SITE ,1.~- ATTENUATE THE DEVELOP SPECTRAL SELECTED SITE SHAPE FOR THE SEVERITY PARAMETER Step IV (para 3-5) SITE FROM SOURCE TO SITE. PROBABILISTIC GROUND MOTION INFORMATION F FIXED SEISMIC L DESIGN INPUT CRITERIA FOR THE SITE IDEVELOP EFFECTIVE RESPONSE . . | .~ - - - Step V SPECTRUM FOR GIVEN RISK (para 3-o ) LEVEL AND SITE CONDITION

US Army Corps of Engineers Figure 3-3. General flow chart. 3-5 TM 5-809-1Ol-1NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 grams and illustrations of related procedures formation from experts. The purpose of this step are shown in figures 3-4 and 3-5 for the WUS is to assemble the information required to de- and figures 3-6 and 3-7 for the EUS. Each figure lineate faults and regions within which seismic shows the parallel basic steps as required in the activity can be considered homogeneous. See deterministic and probabilistic procedures. paragraph 3-4b for a detailed discussion and ap- (1) Step I is to identify and model seismic pendix D for examples. sources. The selected type and accuracy of this (2) Step II is to define the size or severity modeling depends on the available geologic, geo- parameter of the seismic event at the source and tectonic, geomorphic, historic, and subjective in- the related recurrence relation. The size will be

DETERMINISTIC PROBABILISTIC

Selection of Earthquake Selection of Earthquake Data Base Data Base

- _F~~~ l Step Irldentify and Model I |Earthquake History and Identify and Mcdel Seismic Sources _ -oGeological Information Seismic Sources I

Determine Largest Earthquake I. Unit Sys Ami I. m- - ¶bL- Incompleteness in Records for Each Source Adjust Data Base Use. Earthquake History and Geological nformation Step II Determine Recurrence Earthquake History and Relationship for each IGeological Informatlon L Select Sround Ile ionio Seismic Source; m 9S max Attenuation Re-ationship J ) T Step 'I:Select Probabilistic Determine FGA at Site Model for Earthquake Occurenc due to Largest event on Each Source and Using I Shortest Distance IStep IV:Select Ground Motion _ Strong Motion Records in Attenuation Relationship Similar Tectonic Setting i

.se Largest PGA

as Design Level Determine Probability of IN IEarthquake Occurence Model I Exceedence of Different and Attenuation Relationship I PCA Levels; Fazard Curve U'se this Largest ?GA to . Scale the Appropriate Site i Response Spectrum Shape Determine PGA Level IType of Facility and Corresponding to Specified I ' AcptableRisk Probability of Exceedence

Step V:Select Appropriate - IRegional Attenuation Effects Response Spectrum Shapet *_ and ~Site _Soil C~onditions I Anchor at PCA Level

11SArmy Corps of Engineers Figure 3-4. Flow diagram for the Western United States. 3-6 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1I/AFM 88-3, Chapter 13, Section A

DETERMINISTIC FROBABILISTIC

Step I

Su:-NCESZ SOURCZANDS IvKCIlvE VISIAJICE

DE7ERY!.NE- YAXIPrJM YAG::'1CED A471 C'~n;t7: EC,. T Step II :-r'!"ACE FO' EAC' 11'.'4''

I.ECU"E.DC

UELRCZ PROBABILISTIC PORECASTIC MO0DEL III (PARA 3-Jid) Step

PGA on F,

Step IV VA on A I

I' K I I

ATIEKUAIOI AlTENUATI O4 (PARA 3-5c)

USE AflTIMIATIW4 1-0 LE-EEhKIN Km'AX!Y.UY -11-A AT SITE USE MAXINUM. n SPECThFWIPF,~ SIiTE

SITE HAZARD CURVE l i~ARA )-4d) S Step V I~~~-

SITt ALSPOr., 5PtCliltM SITE RESPONSE SPECTRUM (P'ARA3-6)

UIS Aru y Caorps of Engineers Figure 3-5. Hazard evaluation of WUS.

3-7 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

DETERMININST IC PROBABILISTIC

Selection of Larthquake Selection of Earthquake |Data Base Data Base T - ~~~___

l Define Tectonic | S-ep I Define Tectonic |Earthquake History anc I Provinces Provinces and Model Tectonic Infcrm2t or ! Seismic Sources _,F _ ___ ~~~~~~~~~~~~~~. I Determine Largest Historical t . Eeent ir each Tectonic Provincej Adjust Data Base Unit System y V.~- -- rl I Incompleteness in Reccrds I |Se'eet Intensity |Azten ua'ion Relationship; Step :I:Determine Recurrence _ Earthq{ ke History anf Relatiorship for each |Tectonic Information I Seismic Source; ,p Imax Determine Site Intensity due to Largest Event in each Psovincee and Using Shortest Distance 'I~ste Ielect ProbabiliSt ic Mollfor Earthuake OccurencJ

Ilse Largest Intetisity as . . r Site Des~gn Intensity |Step IV:Select Intensity Iso Seismal Maps I ) Attenuation Relationship I Corr-late Site Iiesign Intensity i w1 PGth I Cotrelate Attenuated Intensity Intensity and Related I with PCA at Site Ground Motion Data

Use *trt! ILA IC- Scale the Appropriate Site Determine Probability of Earthquake Occurence Model Response Spectrum LEceedence of Different and Attenuation Relations'.Fp M1A Levels; Hlazard Curve _-~ Determine PGA Level IType of Facility andI Ac eris ta l Correspornding to Specified Probability of Exceedence

- Step VaSelect Appropriate Regional Attenuation Effects I Response Spectrum Shape: and Site Soil Conditions Anchor at PGA Level

US Army Corps of Engineers Figure 3-6. Flow diagram for the Eastern United States.

3-8 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

DETERMI NI ST IC PROBABILISTIC

ECTONI C PROVINCE A,

Step I

SJOUCES SOURCEMODEL (PARA 3-'.b.(2))

DETEMbI!E MAXIM'jW I!r*!wSITY ANI. SITE 1S-AW;E PO.-, Step II

FOR A2

I I RECURIENCERELATIONS (PASIA 3-1.c.(I)(fI

SELEC!? PRC~hABIUS?IC Step III POAECAST'ING MODEL ('ARA 3-4id) (Slot Illustrat...)

ICA

KiA Step IV

AYEII'JAI1 IW ATTEHIIUTI UN4 (YAkp 3-5d)

USE AT'kWL'A'J1ONITL;

USEMAXIMUM TO SCALE APP'PMIAIE

SITE HAZARD CURVE IPARA 3-4d) S a 5 / C .(I4~~A i CIJAY) Step V KA a \ S,-(PCA 1)IDAP)

-- ? CITE RESPCAI:L TI J? SITE RESPONSE SPECTRUM (PARA 3-6)

US Army Corps of Engincers

Figure 3-7. Hazardevaluation of EUS.

3-9 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 one of the magnitude scales (ML, mb, MS) or celeration for a given magnitude event on the epicentral intensity I., or seismic moment, Mo. source could be used. The selection of the pa- The most commonly used size or severity param- rameter used for representing the severity and eter at the source is the Richter magnitude ML- the form of its attenuation relation depends on For the deterministic approach, the frequency the region where the analysis is performed and (or number per unit of time) of occurrences of the type of available data. See paragraph 3-5 various magnitude events need not be deter- for a detailed discussion and appendix D for ex- mined, and the assessment of ground motion at amples. a site will be governed only by the maximum (5) Step V is to represent the effects of dis- level of earthquake magnitude. For the proba- tance, local soil conditions, the magnitude of the bilistic approach,the parameters describing the seismic event, and the structural foundation size source seismicity must be obtained. This infor- and mass on the frequency content of the ground mation usually is in the form of a "recurrence motion. This is represented by the shape (DAF) a relationship," and an upper magnitude or in- of the effective response spectrum for the site tensity cut-off. The recurrence relationship pro- and its formulation is described in paragraphs vides information on magnitude or intensity and 3X6 and 3-7. The final specified spectrum is of the corresponding rate of occurrence or exceed- course scaled down by the forecasted site se- ence of that magnitude anywhere on the source verity. See paragraph 3-8g for examples. under consideration. The upper magnitude cu- b. Use of Results. This available informa- toff consists of the largest (maximum) possible tion on ground motion is utilized for design and/ event that the source can generate. The method or analysis of structures. Chapter 4 shows this of obtaining the above information depends on utilization for prescribed structural perform- the type of region and the data base available ance and selected risk levels. for the region. See appendix C, paragraph C-i c. Selection of Method. The deterministic for background, paragraph 3-4c for a detailed procedures as outlined in the flow diagrams are discussion and appendix D for examples. used exclusively for those important structures (3) Step III is to project the recurrence in- where the consequences of failure are cata- formation from regional information and past strophic; such as nuclear power plants, liquified data into forecasts concerning future occur- natural gas facilities, and dams. These proce- rence. This step is needed in the probabilistic dures tend to compound conservatism (cer- ) approach only. The forecasting model depends tainty of occurrence, largest magnitude and on the type and reliability of the data base. The closest distance from epicenter to the site) and most commonly used forecasting model is the will generally result in extremely large design Homogeneous Poisson probability model. Ho- requirements. For most structures, these highly mogeneous implies a memory-less occurrence of conservative design values cannot be justified events in time and location. When this homo- economically for use. This disadvantage of ex- geneity in time does not appear applicable, Semi- treme conservatism has actually resulted in the Markov and Markov chain models are used (see adoption of probabilistic procedures even for Patwardhen et al. (Biblio 50), Vagliente (Biblio some critical facilities. Deterministic proce- 68), Nishioka and Shah, (Biblio 45). These models dures, therefore, will not be discussed further allow inclusion of memory or time since last event in this manual. and are more involved and require substantially d The STASHA program. The purpose of this more information than the Poisson model. A manual is to provide the user with an over-all simple extension of the Homogeneous Poisson understanding of the procedures, assumptions, model, known as the Non-homogeneous Poisson and computational methods of ground motion model, may be adapted to incorporate time- hazard analysis. However, it is most important dependent information such as the rate of stress to recognize that any actual site hazard evalu- build-up and the time since last event, see Savy ation would require the use of the computer for and Shah (Biblio 52). Another model, usually a development of the various empirical relations uniform probability function, may be employed and the multiple calculations required for prob- to represent the random location of event oc- abilistic accuracy, and prediction uncertainties. currence on the source. See paragraph 3-4d for In order to perform these calculations in an or- a detailed discussion and appendix D for ex- derly manner for each step of the hazard anal- amples. ysis, the STASHA Program has been developed (4) Step IV involves the attenuation of the by the John A. Blume Earthquake Engineering severity parameter from its location on the source Center at Stanford University. Both the user's to the site. Either intensity or peak ground ac- manual and computer program tapes for 3-10 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A STASHA are available at the Corps of Engi- tained in the STASHA user's manual (Stanford neers Office. In the text of this manual, the University, Technical Report No. 36). A descrip- STASHA Program will be referenced whenever tion of STASHA and examples are given in ap- there is a need for extensive computational ef- pendix D. fort or for the representative examples con- Section 11. PROCEDURE FOR SITE SPECIFIC GROUND MOTION 3-4. Determination of Source Seismicity. However, since the future event could occur Each of the probabilistic hazard analysis pro- anywhere over the tectonic province and, there- cedures as presented in paragraph 3-3, and in fore, could be very near the site, the attenuation figures 3-4 to 3-7 is described in this paragraph distances (R) can therefore be short. Also, even and in the following paragraphs 3-5 to 3-8. though there are considerable variations in seis- a. Geotectonic and seismotectonic environ- mic severity patterns in the (EUS), these are ment. In the United States, two general re- not as well defined as in the (WUS). There is a gions are defined which are dependent upon the general smoothing effect over each entire tec- available geologic, geotectonic, geomorphic, his- tonic province and the boundaries between torical, and subjective expert information. It will provinces are often controversial. Also, the rel- be shown that each of the steps for seismic haz- atively low rate of seismic activity in the East ard analysis are region dependent. These re- makes the recurrence estimation over small areas gions are the Western United States (WUS) and very difficult. Further, because most Eastern the Central and Eastern United States (EUS). events have occurred in "pre-instrument" times, The boundary between these regions can be de- their source severity data are in terms of the fined by the eastern boundary of the Rocky more subjective value of intensity rather than Mountains, (Biblio 5). magnitude. Finally, the almost complete lack of (1) Regional Approaches. Due to the in- strong motion recordings makes the direct em- herent difference in the geologic structure in pirical development of attenuation relation- the two regions, two major approaches are used ships in terms of acceleration or velocity in defining seismic sources and assessing future impossible. However, both historical reports and seismic activity. In the Western United States seismological studies indicate significantly lower (WUS) and in many other parts of the world, rates of attenuation in the EUS. A summary of earthquakes occur on faults that extend to the regional differences is given in figure 3-8. surface of the earth. However, in intraplate re- b. Source modelling. Step I in seismic hazard gions, such as the Eastern United States (EUS), analysis is to identify and model seismic sources. this is not necessarily true, and it is difficult to This step depends on the following information recognize and delineate active faults. The two (see figs 3-9 and 3-12): major approaches are (see Biblio 17): -Type and amount of historic seismic oc- -Active Fault Approach currence data base. -Tectonic Province Approach -Geologic, geotectonic, and geomorphic data (2) Procedurefor each approach. The two base. regional approaches require different procedures for seismic hazard evaluation. In the ac- -Subjective opinions of experts concerning tive fault approach, seismic sources are relatively the seismicity of the region. well defined along plate boundaries or faults and, The process of source modelling provides two hence, the concentration of seismic events and essential portions of information for site hazard the resulting level of seismicity per unit length analysis: of the source or unit area of the source is relatively high. Also, because of the definite loca- -First, the configuration of the source and tion of the source, the source-to-site attenuation its size establishes the number and loca- distances (R) for the seismic severity parame- tion of seismic events for the evaluation ters are reasonably well defined. In the tectonic of source seismicity in paragraph 3-4c. province approach, the seismicity is diffused over a large area because no specific faults are iden- -Second, the configuration and location of tified. Each identified source area is assumed to sources relative to the site determines the have homogeneous (uniform) seismicity, and, attenuation distances (R) for ground mo- therefore, the seismicity per unit area is small. tion severity in paragraph 3-5. 3-11 TM 5-809-10-1INAVFAC P-355.1/AFM 88-3, Chapter 13, Sectlon A 27 February 1986 WESTERN UNITED STATES _WJS9

- Well defined sources

- Significant amounts of data in the fonn of historical repoits.

accelerograms, and geological creep measurements.

- Attenuation data in the form of records at different distance

and soil conditions.

- Relatively high occurence rates.

- High attenuation of ground motion severity

mainly within 100 kilometers.

EASTERN UNITED STATES (EUS) ) - Vague description of source provinces. I' - Some historical reports, and very few strong motion records.

- Relatively low occurence rates.

- Low attenuation of ground motion severity

with significant values at 200 to 300 kilometers.

US Army Corps of Engineers Figure 3-8. Regional differences.

It should be mentioned that currently, the USGS for source identification in each region are de- researchers are attempting to define seismic scribed as follows: source zones for five interior regions of the (1) Source modelling in the Western United United States, preparatory to the construction States. In this region (see fig 3-9), seismic of new national probabilistic ground motion sources are identified and modelled in the fol- seismic hazard maps. The five regions are the lowing ways: Great Basin, the Northern and Southern Rocky (a) Point source. This source charac- Mountains, the Central Interior and the North terizes a small region where repeated past Eastern United States (see Biblio 67). Since this earthquakes have occurred. However, no geo- work is not yet complete, this manual will de- logically identifiable fault exists. Typically, the velop procedures based on the two regions, the size of the region is small compared to the dis- WUS and the EUS. The particular approaches tance from this source to the site. Occasionally, 3-12 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Sectlon A

OBTAIN EPICENTRAL MAP OF REGION FROM DATA BASE, COE UP TO 1980 AND NOAA AFTER DEC. 1980

OBTAIN FAULT MAP OF REGION FROM USCS, STATE AND/OR NRC

INDEPENDENT ASSESSMENT OF THE POSSIBLE PRESENCE OF UNMAPPED FAULTS

MO)DEA, KNUIWN FAULTS BY LINEAR D1PI'lNG PLANE SOURCES TO MArCH TIIE EPICENTRAL AND FAULT MAPS

ASSIGN LTHE SOURCE, AND POINT SOURCE AS APPROPRIATE __Z11______.

ASSIGN AREA SOURCE IF EPICENTERS DO NOT MATCH THE KNOWN FAULTS AND THEN AFTER CONSIDERING GEOLOGY

ASSIGN BACKGROUND SEISMIC SOURCE FOR ALL UNASSIGNED EVENTS (AREA SOURCE)

US Army Corps of Engineers Figure 3-9. Flow chart for step I source identificationand modelling for the WUS.

3-13 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 volcanic sources can be identified as point planes and line sources are used: (Biblio 41), sources. and (Biblio 70). An example to demonstrate as (b) Line sources. Fault traces are taken to how sources are modelled is given in appendix as lines at a certain fixed depth below the ground D. surface. In California, this depth is usually be- (2) Source modellingin the Eastern United tween 5 to 35 kilometers. This "active fault" States. In the Eastern United States, the tec- modelling approach is used wherever the tectonic province approach is used (see fig 3-12). tonic structure is more or less evident at the There are various reasons for adopting such an surface. approach; the most important being that the (c) Area sources. This source model is degree of fault and seismic activity in the East- used when the occurrence of earthquakes in a ern United States is low, resulting in very little region cannot be correlated with known faults geologic and historic evidence. Also, in large areas or the geologic structure of the region. There of the Eastern United States, there is a scarcity are also cases where the number of small faults, of geologically recent deposits that would re- or a source of clustered activity, may be consid- cord evidence of recent fault activity. In addi- ered together as an area source. tion, the heavy vegetation covers the faults and prevents their detection. Finally, the recent de- (d) Dippingplane. This source model is velopments of evaluating fault activity in the used when one geologic plate thrusts under an- (WUS) have not been applied in the east due to other plate so as to create a distributed source excessive cost and time involvement; except in of earthquakes. This feature is called a Benioff a few regions such as New Madrid where fault- Zone, and can be modelled by means of dipping ing evidence has been substantiated (Biblio 71). planes upon which earthquakes have variable epicentral depths. Geological conditions such as (a) Area source configuration. One of this occur in Alaska and in Central America. the key features of tectonic province approach is to delineate these provinces as area sources (e) Background area source. In gen- that have a uniform potential to generate earth- eral, events that occur somewhat randomly quakes. Within that area, the future earthquake throughout the region and that cannot be as- activity should be homogeneous. Due to lack of sociated to any fault or source are treated as sufficient historical and geological evidence, background seismicity. They are considered to there is no unique and generally consistent way be part of a large area source with uniformly of delineating these area sources. Two examples low seismicity that extends over the area not on area source configurations for the Eastern covered by the other sources. The earthquake United States are shown in figures 3-13 and 3- location, if not included within one of the pre- 14. viously defined sources, is then in the background zone to account for the possible (b) Using subjective input as furnished occurrence of the random or "floating" earth- by interviews from ten experts, Mortgat (Biblio quake. The effect of the background zone is gen- 63 and 64), has developed homogeneous area erally small since the contribution of the other sources as shown in figure 3-15. With respect to sources are governing the hazard. In some par- this method of using expert opinion, it is well ticular cases however, where the hazard is low, to recognize that experts form their objective the background contribution may be non neg- biases from the particular data and other geo- ligible. logic and seismologic evidence that they may have seen. Since most of the experts work with a sim- (f) Western source conditions. The point, ilar data and information base, the variability line, and area source models are shown in figure in their individual source configuration is due 3-10, and the dipping plane model in figure 3- to their personal biases. Barstow et al (Biblio 11. In source modelling, historical records and 5) have studied statistical techniques to provide the knowledge of geotectonic features of the a methodology for the production of working region play an important role. Due to the high tectonic province and tectonic structure maps seismic activity in the Western United States, for the Eastern and Central United States, iden- and the relatively good geological evidence of tifying areas of uniform seismic hazard. faults, surface rupture, and other tectonic features, line sources are used most extensively. c. Source seismicity. Step II in seismic haz- Area sources are common in the Pacific North- ard analysis is to evaluate the seismicity of each ' west. In regions such as Alaska, both dipping of the modelled source (see fig 3-16). Evalua-

3-14 27 February 1986 TM 5.-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Fault Length L1 IL II_I Line Source

~Site R2 -1 '

I-, Ri N-1 \ ~~~~~~~~~I

\ R3

Line Source \ 6 Point Source

US Army Corps of Engineers

Figure 3-10. Point, line and area sources.

3-15 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 L'w

Ruptured Zone

Latitude distance

Deep Boundary

Dipping A Shallo Planes SiSt te- .0/Boundary

Longitude distance

Ground

US Army Corps of Engineers

Figure 3-11. Dipping plane source.

3-16 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

OBTAIN EPICENTRAL MAP OF REGION FROM DATA BASE

HQ-USACE* UP TO 1980 AND NOAA** AFTER DECEMBER 1980 i IDENTIFY THE TECTONIC PROVINCES AND THE RESULTING AREA SOURCES, INCLUDE FAULT MAP IF AVAILABLE FROM USGS, STATE AND/OR NRC. OBTAIN EXPERT

OPINION ON SOURCE LOCATIONS

ASSIGN BACKGROUND SEISMICITY

FOR EVENTS THAT

CANNOT BE ASSIGNED A SPECIFIC AREA SOURCE

* DAEN-ECE-D Washington, D.C. 20314

** NOAA/NGSDC/TGB 325 Broadway, mail code D-623 Boulder, CO 80303 NOTE: If at a future date, specific faults are identified, then they can be modeled by means of line or dipping plane sources.

US Army Corps of Engineers

Figure 3-12. Flow chart for step I source identification and modelling for the EUS.

3-17 TM 5-809-10-1/NAVFAC P-355.1I/AFM 88-3, Chapter 13, Section A 27 February 1986

I I I

)

RE-printed from "Effects of Uncertainty in Seismicity on Estimates of Seismic Hazard for the East of the United States," McGuire, R. K., Bulletin of the Seismological Society of America, Vol. 67, No. 3, 1977, with permission from the Seismological Society of America.

Figure 3-13. Seismic sources after Algermisson and Perkins (1976).

3-18 13, Section A 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter

~~~ -

Reprinted from "Effects of Uncertainty in Seismicity on Estimates of Seismic Hazard for the East of the United States," McGuire, R. K., Bulletin of the Seismological Society of America, Vol. 67, No. 3, 1977, with permission from the Seismological Society of America. Figure 314. Seismic sources after Hadley and Devne (1974).

Ki'

3-19 . . ,r. ILLINOIS INDIAVIM: _ 1/I t~r~vua /? i I iO

MIS&WAI H~~~~~~~~~~~~~~VIAGINIA ~~UT .

. @X~~~/ it- '" ";W /g n

A7-~~~~~~~~~~~~~~~~~-

L. . , y k: UA "'..# KZ5f~ p I "' L A'\ &WAAS _ _ Io T.__t " ,&&,.,.& .. g \ ( 3

0 J ~ ~ ~~~~ ~~~~~~~~~~~~~~~~ Le

Reprinted from "Seismic Hazard Mnalysis- a Solicitation of Expert Opinion," Nuclear a Regulatory Commission, Tera Corporation, NURFG/CR-1582, Vol. 3, 1980. Figure 3-15. Seismic source after Tera (1981). Z 0. K C~~~~~~~~~~~~~~~~~~~O 27 February 1986 TM 5-809-1 0-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

FOR A GIVEN SOURCE AND CORRESPONDING HISTORICAL PROVIDE INPUT FROM EVEtITS, PLOT MAGNITUDE EXPERT OPINION INCLUDING GEOLOGICAL OR INTENSITY VS I FREQUENCY OF INPUT OCCURRENCE I

I - I

SELECT AN ANALYTICAL FROM GEOLOGICAL EXPERT FORM, COMMlONLY THE LOG-LINEAR FORM FOR THE RECURRENCE OPINION, ASSIGN RELAT!ONSHIP AND FIT IT I TO THE ABOVE MAXIM4UM MAGNITUDE INFORMAT ION

OBTAIN NORMALIZED

~ECURRENCE RELATIONSHIP

FOR THE SOURCE I REPEAT THE ABOVE

STEPS FOR ALL SOURCES

OF INTEREST

US Army Corps of Engineers Figure 3-16. Flow chart for step If source seismicity and recurrence relationshipfor WUS and EUS.

3-21 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 tion of seismicity involves the following com- The main problem with this approach is that it ponents: reduces the size of the useful sample and mean- ingful statistical averages of large earthquakes -Collection and processing of occurrence cannot be obtained because of their infrequent ) data and formulation of the recurrence occurrences (Biblio 6). An alternative is to cor- relationship. rect for incomplete reporting by a random sim- -Determination of the size of the maximum ulation of missing data (see STASHA). The earthquake a given source is capable of Gutenberg-Richter relationship is given by generating. equation (3-1). (1) Collection of data and formulation of In N(m) = a + f3m (eq 3-1) the recurrencerelationship. The data base for where seismic events on a given source is often incom- In = Natural log to the base e plete, nonhomogeneous in time, and lacking in refinement. The appropriate processing of this N(m) = Average Number of events occurrence information is very important be- greater than or equal to the cause the reliability of results of the hazard magnitude m. analysis are strongly dependent on the consist- a, 1 = constants. ency and the completeness of the input data base. The magnitude-frequency or recurrence rela- Very often, this relationship is used in a slightly tionship is formulated from the number of different format where logarithm to the base 10 earthquakes that a source has generated and is used instead of to the base e. their respective magnitudes. The most common logioN(m) = a + bm (eq 3-2) method of determining this relationship is from historic data. Occasionally, other information One would convert the equation from base e to sources, such as geological evidence and slip rate base 10 by means of the following simple con- of the fault, are used to supplement this histor- version: ical data base. Statistical regression analysis is a = 0.43429a (eq 3-3) commonly used to obtain the best line fit with the "least squared" error. Expert subjective b = 0.43429P (eq 3-4) ) opinion can also be incorporated in order to sup- Such magnitude-frequency relationships are plement the historical data base. The most com- called "recurrence relationships" in the litera- monly used magnitude-frequency relationship ture and a general example is shown in figure is the one suggested by Gutenberg and Richter 3-17. After the recurrence relationship is ob- (Biblio 26). In this relationship, the source se- tained, the following normalization process can verity parameter could be either magnitude or be performed. epicentral intensity. The type of parameter and (a) Normalization to unit length and the constants of the magnitude-frequency re- time. Let T be the time-period over which the lationship vary from one region to the other. recurrence data has been obtained. If the source Data adjustment is usually necessary before us- is a line source, let L be the length of this source. ing the data to determine the parameters of the Then, N(m) = average number of events equal magnitude-frequency relationship. It has been to or greater than magnitude m during the time observed that the completeness of earthquake period T and on source length L for the line records varies with time. In the past, due to low source. population density and lack of interest in earthquake activity, only large events were recorded. Let With increased instrumental coverage, inter- N0(mW = N(m) mediate and lesser earthquakes have been re- N'() - LT corded with more frequency, producing an apparent increase in seismic activity with time then which biases the statistics from uncorrected ln(N'(m)) = In N(m) - InN(m) -ln(LT) catalogs of data. In recognition of this time bias, LT the evaluation of the degree of completeness of ln(N'(m)) = a + 1 m - In(LT) the available earthquake record is an important =a - In(LT) + 1 m step in the analysis of data. One possibility is to confine analysis to sections of the record that or are complete for the earthquakes of interest. ln(N'(m)) = a' + 1 m (eq 3-5) 3-22 27 February 1986 TM 5-809-1-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A where or N'(m) average number of events equal ln(N'(m)) = a' + ( m, to or greater than magnitude m with a' = a - ln(AT) per unit time and unit of source (eq 3-6) length Where N'(m) and a' are now normalized with a' = a - ln(LT) respect to the source area A. Note that the value of a does not change when (c) Sampling uncertainty. For a given the recurrence relationship is normalized. This magnitude m, the fitted line gives the average step of normalizing the recurrence relationship value of N(m) or N'(m), and this average or is usually done by the seismic hazard analysis expected rate value is required for the proba- computer program. The purpose of presenting bilistic forecasting model in paragraph 3-4d. this step here is to indicate that in the normal- However, there is considerable scatter of the ization, it is assumed that for a given source, the actual recorded number of events. To take this number of events equal to or greater than a scatter into account, a probability distribution given magnitude is homogeneous in time and function is generally assumed for the number space. Thus, the mean rate of occurrence does of events equal to or greater than a given m. not change with time or along the given source. Further, the fitted recurrence line, because of More will be discussed on this topic when the limited data base and the largely subjective eval- probabilistic-forecasting models are presented. uation of the maximum magnitude, has a sam- (b) Normalization to unit area and pling error. This sampling error is an indicator time. If the area source with area A was con- of the difference between the sample fitted line sidered instead of the line source, the relation- from the limited data source and the true line ship would have a simlar format: that would be obtained from a very large data source, figure 3-17. The STASHA, (Stanford N'(m) N(m)T University, Technical Report No. 36) program gives a probabilistic representation for this ln(N'(m)) = a - ln(AT) + p m sampling uncertainty in the N(m) value.

lnN (m)

L \ Fitted 'line -lnN (m) = a + Sm

.. Ic bound for sampling \-. X. error of fitted line

Data IN

US Army Corps of Engineers Figure 3-17. Linear Recurrence Relationship. 3-23 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 (d) Non-linear relations. Other forms of the recurrence constant for most of the WUS recurrence relationships have been used by re- sources lies between about 1.1 to approximately searchers. Dalal (Biblio 21) has used Gaussian 2.5. Figure 3-19 shows the recurrence relation- and log-Normal probability distribution models. ship for the northern section of the San Andreas Mortgat et al (Biblio 42) have used a bilinear Fault in California. It should be mentioned here relationship as shown in figure 3-18. Here, two that one large fault such as the San Andreas lines are fitted to the data. The point where the may be broken down into two or more homo- two lines meet is usually determined subjec- geneous segmental sources and the recurrence tively from the geologic considerations concern- relationship may be determined for each of these ing capabilities or rates of large magnitudes on segmental sources. This use of homogeneous the source. Cornell and Merz (Biblio 39) have segments is quite common in California where used a quadratic form for their recurrence re- there is evidence of varying degrees of seismic- lationship. Recently, Dong et al. (Biblio 23) have ity on the large sources. The source severity pa- applied the maximum entropy concept to obtain rameter employed in developing these recurrence minimally biased recurrence relationships. (See relationships in the WUS is usually the Richter app D for some examples). magnitude (which can be considered to be the (e) Recurrence relationship for sources same as the local magnitude ML)- In appendix in the Western United States. The "active fault" C, paragraph C-1, these variations magnitude approach is usually employed in this region. scales are defined. Therefore, based on the fault locations and the (f) Recurrence relationshipsfor sources modelling of these faults as line sources, past in Eastern United States. The tectonic prov- seismic events are assigned according to their ince approach is used for modelling sources in relative proximity to the different sources. This the eastern United States. Therefore, all the process of event assignment is usually per- sources are area sources, and these usually cover formed by expert judgement with recognition rather large regions. With respect to the source that epicentral locations are subject to error and severity parameter, most of the historical data that events are more likely to occur on the known in the East is compiled in the form of the Mod- fault rather than on the adjacent area. The ified Mercalli Intensity Scale. However, there are STASHA program has a procedure for event as- cases where the most recent data is in local Mag- ) signment. It has been found that the value of nitude (ML) or body wave magnitude (mb).

lnN(m)

nN(m) = a1 + 8

reak Point

7- 1 nN(m) = a2 + BI

Maximum Possible Magnitude for the Source (l m maM Imax

US Army Corps of Engineers

Figure 3-18. Bilinear Recurrence Relationship. 3-24 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

1000.0

'100.0010~~~~~~E k \

lnN(H) 8.59 1.18M

10.0 _ N

3 < s s~~~~~~~~~~~~~~~~~~~~~~~1 z N.,~~~~~~~~~

¢1.0 _ \ \ s N? _

3.00 4.00 S.00 6.00 7.00 8.00

Richter Magnitude (M)

US Army Corps of Engineers

Figure 3-19. Recurrence relation for North San Andreas TM 5-809-10-1/NAYFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 Therefore, in order to make all the data con- the term "maximum credible" event. Such a term sistent, one approach consists in converting the should be discouraged from use. Instead, use of magnitude into an epicentral Modified Mercalli a term such as the "maximum earthquake size' Intensity (MMI). should be encouraged. The size of the maximum'n" ) Let 1o be the epicentral MMI earthquake is used in source seismicity determination in two ways: M be the Richter magnitude. -Deterministic use of the maximum earth- In paragraph C-1, appendix C, the relationships quake in the design process (see figures between these two parameters for the Eastern 3-4 and 3-6). United States are given. -Probabilistic use of the maximum earth- Also, Nuttli (Biblio 46) has developed a rela- quake, in the recurrence relationship. Here, tionship between the body wave magnitude mb the value of this earthquake size provides and the epicentral intensity I., the upper cut off magnitude in linear recurrence relationship, or it could be an mb = 1.75 + 0.50Io (eq 3-7) asymptote in the non-linear recurrence Using relationships such as these, the occur- relationship, see figure 3-18. rence data in the form of the source intensity 1. can be obtai- ±d. The Gutenberg-Richter re- The estimate of the size of the maximum earthquake for a given source is based on the follow- currence formal ',r intensity is then written in the following form: ing factors: 1-Geologic evaluation of the regional tec- ln[N(I )] = aj + 03iI0 0 (eq 3-8) tonic framework. Where atcand pi are regression constants. Ye- gian (Biblio 71) and TERA (Biblio 63,64) have 2-Historical seismicity of the source and given values of pi, for the EUS. A shortcoming the surrounding region. of using epicentral intensity (I.) as a parameter 3-Geologic history of displacement (from is that I, unlike magnitude, is not a direct meas- trenching investigations). ure of a source severity. By definition, intensity ) is a number corresponding to particular ob- 4-Relationship between earthquake mag-__ served effects and these are often influenced by nitude and fault rupture length. both the site condition and the prevailing local 5-Relationship between earthquake mag- types of construction. In order to overcome this nitude and amount of fault displace- shortcoming, an alternative approach involves ment. the estimation of magnitude of the historical events (before instrument records) in terms of Out of the five factors mentioned above, the tec- their estimated epicentral intensity, felt area, tonic province approach in the EUS would per- and fall-off intensity. This requires a large mit the use of only the first three. When the amount of background research effort. How- active fault approach is employed in the WUS, ever, most large events in the EUS have been then all of the five factors will be used for such assigned a magnitude based on this method by an evaluation. Whether one decides to use a spe- different researchers (Nuttli, et al. (Biblio 47) ). cific maximum earthquake value or a probabi- Smaller events of less importance in the anal- listic distribution representation of the maximum ysis can be converted to magnitude using one of earthquake value, the STASHA program can the relationships in appendix C-1, or equation handle both forms of this input information. 3-7. In the formulation of the recurrence rela- (a) Determination of the Size of the Max- tion in the EUS, it is usually assumed (because imum Earthquake-Western United States. In this of lack of data) that the same pi value applies region, seismic sources are usually line sources throughout very large regions and that local (active fault approach). For such sources the variations apply only to the level of seismicity maximum earthquake size is usually based on (parameter al). The range of values for the pa- the fault rupture length or the maximum amount rameter PI' is from 0.80 to 0.92. of displacement that may be associated with the (2) Determination of the maximum earth- causative fault. Not only the historical data base quake. One of the most controversial and im- is used, but also geological data from trenching, portant variables of interest in representing or other geomorphological studies; Sieh, (Biblio "- ) source seismicity is that of the size of the max- 60) can be employed. Recently, (Aki, (Biblio 1); imum earthquake. Past literature has employed Kanamori and Geller, (Biblio 24); Molnar, (Bib- 3-26 27 February 1986 TM 5-809-10-1/tNAVFAC P-355.1/AFM 88-3, Chapter 13, Section A lio 40)) seismic moment has been related to the sponding event can be considered as an upper fault rupture area, along with the fault shear bound. This last approach should include all modulus and average slip. Relating the maxi- available information such as local or regional mum seismic moment Mo.max to moment mag- strain release or stress field data (See para nitude Mm gives the value of the largest moment 3-4c(3)). magnitude. It is useful to note that Mm is equal (3) Use of Seismic Moment to Represent to ML for ML values between 5 and 7. Empirical Source Seismicity. One of the more recent de- relationships between M, fault rupture length velopments in seismic hazard analysis is to use L and fault displacement D are developed from seismic moment (M,) to describe source seis- world wide data (Bonilla and Buchanan, (Biblio micity. Seismologists have introduced a "phys- 11); Slemmons, (Biblio 61)). Paragraph C-4, ap- ical" parameter called seismic moment M, to pendix C gives these relationships. The tables describe size of an earthquake. This develop- and relationships presented in paragraph C-4 ment is relatively new and its practical imple- should not be used exclusively but together with mentation for seismic hazard analysis has not historical and other geologic evidence. The his- been achieved. Paragraph C-4, appendix C, in- torical record of earthquakes in a given region troduces the users of this manual to this new may be one of the few indicators of the potential concept. for future earthquakes. However, extreme cau- d. ProbabilisticForecastingModels. Step III tion must be exercised when extrapolated fore- is to forecast source severity of future earth- casts are made. The time period of records in quakes on each of the identified sources (see fig the United States is relatively short and there- 3-20), once the sources of seismic activity have fore statistical prediction should always be com- been identified (para 3-4b) and the seismicity pared or modified by expert judgment concerning of the identified sources has been determined seismicity. In paragraph C-4, table C-11 shows (para 3-4c). These forecasting models are not the slip rate activity of some of the faults of the based on extrapolation of past data, but are based Western United States, and figure C-10 shows on stochastic models. These models from 'the fault slip versus time. This type of information probability theory field of stochastic processes can also be incorporated probabilistically in as- may however employ data for the evaluation of sessing fault activity and in estimating the size their parameters. The type of stochastic fore- of maximum earthquake events. This will be dis- casting model selected depends on the accept- cussed further in the forecasting paragraph, able type and level of assumptions about the 3-4d. seismic occurrence on each of the sources. The (b) Determination of the Size of Maxi- most widely used model is called the homoge- mum Earthquake-Eastern United States. In this neous Poisson Model. Typical examples of this region, seismic sources are modelled by the tec- approach are given in the following references: tonic province approach. The most commonly Cornell (Biblio 18), Cornell and Van Marcke used method of determining the size of the max- (Biblio 19), Stepp (Biblio 62), Algermissen (Bib- imum earthquake is through historical records. ho 3), McGuire (Biblio 37), Shah et al. (Biblio Very little information (if any) is available on 58), Wiggins (Biblio 69), Der Kiureghian and the fault rupture or fault displacement and hence Ang (Biblio 22), Liu and Fagel (Biblio 34), Kir- these two parameters cannot be related to the emidjian and Shah (Biblio 32). This is normally size. To overcome the problem of limited histor- called a memoryless process because of the as- ical data in estimating the maximum earth- sumption that the probability of occurrence or quake size, the opinions of experts should be nonoccurrence of an earthquake in any given obtained. Two principal methods are used to de- year and for a given source does not depend on termine the maximum earthquake size. The first the time interval since the last occurrence. For one consists of using the size of the largest his- most practical cases where the future time ho- torical event subjectively incremented by a safety rizon is of the order of fifty to one hundred years, factor such as half a magnitude or one intensity this is a reasonable assumption and is suitable unit. The other consists in using the earthquake for the purposes of this manual. A non-homo- size corresponding to a 1000 to 5000 year return geneus Poisson model has also been used to ac- period from the recurrence relationship. Al- count for the dependence of the mean rate of though this last method is somewhat ad hoc it occurrence on time. Savy and Shah 1981, (Biblio is felt that, in the present geologic framework, 52) have shown the use of this model. In order the near future will be similar to the past and to account for the lack of sufficient historic oc- that the 1000 to 5000 year choice represents a currence data and also to take into account geo- low enough probability such that the corre- logical data (such as slip rate, size of past rupture 3-27 TM 809-10IM"NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

FROM NORMALIZED RECURRENCE RELATIONSIP,

OBTAIN MEAN RATE OF OCCURRENCE FOR

MAGNITUDE OR INTENSITY OF INTEREST

SELECT STOCHASTIC FORECASTING MODEL COMPATIBLE WITH THE GEOLOGICAL AND SEISMOLOGICAL INFORMATION

o Homogeneous Poisson Model (widely used) o Non Homogeneous Poisson Model o Bayesian models

MODIFY THE MEAN RATE OF OCCURRENCE IF. GEOLOGICAL INFORMATION AND/OR EXPERT) SUBJECTIVE OPINION-CAN SIGNIFICANTLY CHANCE THE STATISTICAL ESTIMATE OF THE RATE OF OCCURENCE e i

OBTAIN PROBABILITY OF OCCURRENCE OF DIFFERENT MAGNITUDES OR INTENSITIES FOR FUTURE TIME PERIOD T AND FOR TOTAL SOURCE DIMENSIONS

I X -T~~~~~~~ REPEAT PREVIOUS STEPS FOR ALL THE SOURCES

US Army Corps of Engineers Figure3-20. Flow chart for step III seismic forecasting model.

' _ /)

3-28 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A length and the amount of fault displacement per and event), Bayesian models have been developed. These models assume a Poisson occurrence model x is the mean rate of occurrence. along with a Bernoulli model for the size of each If one defines the return period (TR) as the time occurrence. The STASHA program describes this interval during which the expected number of type of model; see appendix D for an example. occurrences is one, then this much used engi- (1) When the occurrence of a future event neering parameter in risk analysis is obtained is independent of the past occurrences, then the as follows: the expected number of events for homogeneous Poisson model is a reasonable the Poisson process of equation 3-9 is given by model. The Poisson model of occurrence can be written as E(N(t)lk) = Xt (eq 3-11) where E(N(t)l) = Expected number of events t ( t)n (eq PN(nt) = e 3-9) for future time t given X. where PN(n,t) =Probability of having n events If equation 3-11 is equated to one, we get the in a future time period t definition of return period. n =number of events KTR= 1 1 and hence TR-= (eq 3-12) X = mean rate of events per unit of time (years) TB is therefore the average time interval be- (2) If Xis independent of time, then the pro- tween events, and is also the reciprocal of the cess is called homogeneous. If Xvaries with time, annual risk of occurrence. The value of Xis usu- the process is called non-homogeneous. ally obtained from the recurrence relationship (3) For earthquake events to follow the ho- developed in paragraph 3-4c. Let N'(m) = a' + mogeneous poisson model, the following as- p m be the average number or rate of events sumptions must be valid: equal to or greater than magnitude m per unit of time and per unit of source dimension. Then, -Earthquakes are spatially independent; using the Poisson occurrence model, the prob- -Earthquakes are temporarily indepen- ability of n events equal to or greater than mag- dent; nitude m in future time t for source of length L (or area A) is given by -The probability that two seismic events exp(-N'(m)Lt )n (N'(zn)Lt)" will take place at the same place and at P(n,m,t) = the same instant of time approaches zero. (eq 3-13) The first assumption implies that occurrence or Thus, nonoccurrence of a seismic event at one site or location or source does not affect the occur- P(O,m,t) = exp(-N'(m)Lt) (eq 3-14) rence or nonoccurrence of another seismic event or probability of at least one event above mag- at some other location or source. The second nitude m for a source of length L in future time assumption implies that the seismic events do t is given by not have memory in time. The third assumption implies that for a small time interval dt, no more 1 - P(O,m,t) = 1 - exp(-N'(m)Lt) than one seismic event can occur. This assump- (eq 3-15) tion is considered to be realistic and fits the Equation 3-15 provides the most elementary physical phenomenon reasonably well. hazard statement for the occurrence of a given (4) It can be shown that if the arrival of magnitude (or greater) on a given source. The earthquake events follow the Poisson process, probability of exceeding a given level of site in- then the random description of the time interval tensity (such as PGA) needs consideration of between two events follows exponential distri- the location of the event (epicenter or rupture bution. Thus, length) on the source and also the consideration f(t) = ke"' t ¢ 0 (eq 3-10) of all sources affecting the site. This is treated in the next paragraph 3-5. = 0, Otherwise f(t) is the probability distribution function for the interarrival time t between events, 3-29 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 3-5 Selection of the attenuation relation ponent of interest and the distance from the for the determination of seismic source. These types of developments are avail- severity at a site. able for body waves (See Savy, (Biblio 53)). ) Step IV of the seismic hazard analysis deals with However, the most commonly used methods for the methods of evaluating the severity of ground ground motion estimation in engineering and motion at the site where the structure is located, for seismic hazard and risk analysis are the ones given the information developed in the previous based on empirical relationships. In this man- three steps. ual, a short description of these empirical tech- a. Attenuation of ground motion. When a niques will be presented. For a detailed study rupture along a fault plane occurs, vibratory see Idriss (Biblio 30) or the OASES study by ground motions are generated. These motions Woodward-Clyde Consultants (Biblio 70). It is travel out from the source as body and surface commonly accepted by seismologists and geo- waves (See fig C-2). As these waves travel far- physicists that the type, the amount, and the ther out from the source, they are attenuated. geometry of the rupture surface influences the The type and amount of attenuation depends on amplitude and frequency of motion near the many factors, the most important of which are source. Other factors influencing the near-source listed below: motion characteristics are the velocity of rupture, the stress drop, the physical properties of -Size or source severity of the event on the the fault plane material, and the pattern of non- source uniformity of rupture on the rupture surface. -Type of fault mechanism The larger the rupture surface, the greater the ground motion. However, there are definite up- -Transmission path of the seismic waves per limits for both the rupture size and the re- from source to the site sulting motion. The wave patterns generated at -Vibration or wave frequency of interest the source travel out in all directions in the form of the seismic ground motion of complex wave forms. The regions through which these wave forms travel from source to -Distance from the source to the site site constitute the "transmission path." It has -Local site soil response effect been observed that the transmission path influences the attenuation of wave forms in both the frequency and amplitude domains. The decaying In estimating the type and severity of ground of amplitude with distance is usually referred motion that would exist at a site due to some to as the "attenuation." In the frequency do- future seismic event, the analyst should incor- main, higher frequency components in the wave porate the above parameters in his model. The form get filtered out as the distance from the current state-of-the-art methods for estimating source to site increases. In this paragraph, only the ground motion can be classified into two the amplitude attenuation will be discussed. groups. Paragraph 3-6 considers the aspects of fre- -Methods based on wave propagation the- quency attenuation and its influence on the re- ories through elastic and non-elastic sponse spectrum shape. media with appropriate damping charac- b. Empirical attenuation relations. Various teristics. empirical relationships are available in the literature to describe the relationship between the -Empirical methods based on past data. size of the event, the distance from the source In the first method, various researchers in re- and the site ground motion parameter of inter- cent years have developed models to study dis- est (see fig 3-21). In working with these rela- placement (or some other ground motion tionships, the question of distance from the parameter) wave forms as a function of the type source to the site arises. The most "realistic" of event and the distance from the source. In distance to be selected could be either the epi- particular, the models for estimating the sur- central distance, hypocentral distance, distance face wave patterns have been quite good and fit from the site to the energy release center, or the the data well (See Boore, (Biblio 12); Frazier, distance from site to the closest rupture loca- (Biblio 4); McCann, (Biblio 35)). There are some tion on the fault. Earlier relationships have used other models which look at the attenuation of epicentral distance; however, with the availa- Fourier spectra with distance. Such models take bility of more data in recent years, it has becomeK ' / into account the damping characteristics of the evident that this distance is not the most rele- transmission media, the wave frequency com- vant. Some studies have used hypocentral dis- 3-30 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

WLI S EUS REGION OF INTEREST

USE PGA AS SITE USUALLY INTENSITY SEVERITY PARAMETER DATA IS USED FOR ATTENUATION EQUATION - ___ __- I CONVERT ATTENUATED SELECT TRANS. PATH INTENSITY FOR THE SITE TO DESIRED GROUND 1- MOTION PARAMETER SELECT THE APPROPRIATE I ATTENUATION RELATIONSHIP DISTANCE WEIGHTING IF DESIRED I _F MAGNITUDE WEIGHTING IF DESIRED INCORPORATE UNCERTAINTY INFORMATION -~~~~I- I SOIL EFFECT, IF INFOR- MATION IS AVAILABLE

I V USE 50 PERCENTILE VALUE INCORPORATE OF PGA FOR SITE L UNCERTAINTY INFORMATION SEVERITY SCALING

USE 50 PERCENTILE VALUE

OF PGA FOR SITE SEVERITY SCALING

US Army Corps of Engineers Figure 3-21. Step IV, attenuation of ground motion from source to site.

tance. The recent relationships use the concept some of the distance definitions used in the of significant distance. This is the shortest dis- literature. tance to the ruptured source. Figure 3-22 shows 3-31 TM 5-809-10--1/NAVFAC P-355.1/AFM 88-3, Chapter 13, SectIon A 27 February 1986 Rf

RC - Distance to energy center Be - Epicentral distance R- Distance to causative fault Rat - Hypocentral distance m- Map distance to energy center as- Significant distance

Reprinted from "Offshore Alaska Seismic Exposure Study (OASES)." 1978, with permission from Woodward-Clyde Con- sultants. Figure 3-22. Attenuation distances.

(1) Recent studies have indicated (OASES, the Western United States. For most earth- Biblio (70) that the transmission path B is very quakes in California and Hawaii, transmission important. Thus, for shallow earthquakes path A should be assumed. Also, there are im- (transmission path A in fig 3-23) there is one portant differences in rates of attenuation for attenuation relationship; whereas for deeper the WUS and EUS regions. These will be dis- earthquakes, (transmission path B in fig 3-23) cussed in the paragraphs for these regions. there is a separate attenuation relationship. This (2) Many empirical attenuation relation-' transmission path dependence has been ob- ships are available in the literature. They all served in data collected in Alaska, Japan and in have their shortcomings in both accuracy and 3-32 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

W-J W

U 'C

3 10 30 100 300 1000 DISTANCE EKMI

Reprinted from "Offshore Alaska Seismic Exposure Study (OASES)," 1978, with permission from Woodward-Clyde Con- sultants.

Figure 3-23. OASES attenuation. applicability for a given site. The scatter of data -OASES Model (Biblio 70) with respect to the estimated relationships is Figure 3-24 shows the first two of these rela- considerable. Hence, this scatter should be prop- tionships. The third relationship is given in erly accounted for in the use of the attenuation figure 3-23. relationships. See appendix D for an example. c. Attenuation of ground motion in the West- (1) The mathematical relationship used for ern United States. The abundance of strong modeling the attenuation of peak acceleration motion records in the WUS makes empirical with distance is expressed by Campbell (Biblio 14) by the regression analysis the ideal tool to predict equation: ground motion. A number of assumptions can PGA = aexp(bM)(R + C(M))-dexp(-rR) have a significant impact on the results of such (eq 3-16) regression analyses. The most important ones where PGA are the attenuation mathematical forms, the is the mean of the peak acceleration scaled from the regression techniques (linear, non-linear, horizontal component of the ac- weighted vs. non-weighted), the data base se- celerogram in g units. lection criteria, the definition of magnitude, at- M is the magnitude (M = ML for mag- tenuation, and site soil condition. Three of the nitude less than 6.0) most recent attenuation models developed for (M = Ms for mag- the WUS are given below: nitude greater than -Campbell Model (Biblio 14) 6.0) -Joyner and Boore Model (Biblio 31) 3-33 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 I

zCP 2 0 ti W-J V C) I 0 N -J 0I- w 0B Ld

.01 I 10 100 DISTANCE (kn)

Reprinted from "Near-Source Attenuation of Peak Horizontal Acceleration," Campbell, K. W., and "Peak Horizontal Acceleration and Velocity from Strong Motion Records," Joyn.er, W. B. and Boore, D. M., Bulletin of the Seismological Society of America, Vol. 7I, No. 6, 1981, with permission from the Seismological Society of America. Figure 3-24. Attenuation Relations.

r is the absorption coefficient which af- PGA = 0.22 exp(0.734M)(R + 0.567exp 089 fects the rate of attenuation. (0.345M)Y) 1 exp ( - rR) (eq 3-17) R is the closest distance in kilometers to where the value of r for the WUS is given by the surface projection of the rupture r = 0.0423 - 0.00911M + 0.000573m2 (eq 3-18) zone. The 84th percentile value is obtained by multi- a, b, and d are regression constants. C(M) is a plying equation 3-17 by 1.49. This step assumes function which models possible nonlinear mag- that the natural logarithm of PGA has a stand- nitude and distance scaling effects in the near ard error of 0.40. field that may be supported by the data. Ac- cording to Campbell, The Joyner and Boore relationships (1981) are as follows: C(M) 0.567 exp(0.345M) logA = - 1.02 + 0.249M, - logR1 Substituting this into equation 3-16 along with - 0.00255R, + 0.26P - (eq 3-19) the values for a, b, and d gives the following equation for the median value of peak acceler- where R, = (d2 + 7.3)2 (5.0 < Mo S 7.7) ation: (eq 3-20) 3-34 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A A is the peak horizontal acceleration in g tion model for the EUS is a difficult task for units several reasons. First, there is not much strong motion data available from EUS earthquakes. M. is the moment magnitude. Second, it is generally agreed that one cannot d is the closest distance to the surface pro- directly use a ground motion model developed jection of the fault rupture in kilome- for the Western United States (WUS) because ters. data from a number of sources, e.g., Nuttli (Bib- Ho 48), Chung and Bernreuter (Biblio 15) that P is zero for 50 percentile value and one the attenuation of seismic energy in the EUS is for the 84 percentile value. much different (more gradual) than in the WUS. (2) The OASES (Biblio 70) relationship has Four approaches appear applicable to develop the following mathematical format: an EUS ground motion model. Given the limited amount of intensity data available for the EUS, PGA = biexp(b M)(R + C)b (eq 3-21) 2 3 three of the approaches use intensity as an in- where PGA is the peak horizontal acceleration termediary variable to compare the ground mo- in cm/sec2 . tion between WUS and EUS: bl, b2, and b3 are regression constants Let Is = site intensity R is the closest distance to fault rupture IC = epicentral intensity in kilometers. C is a constant dependent on magnitude R =distance from source to the site M, but independent of transmission M = magnitude path. C = 0.864exp(0.463M.) (eq 3-22) F() and g() functional forms GM =ground motion parameter, such For different transmission paths and soil con- as peak acceleration or peak ditions, values of regression constants b1, b2 and velocity b3 along with the standard deviation of In ( PGA) are given in table 3-2. Use of any one of the Distance Weighting three attenuation relationships should give rea- Is = f (I., R) (EUS Data) sonable results. d. Attenuation of ground motion in the East- Log GM = g(I,,R) and in some cases ern United States. Developing a ground mo- G(ISMLR) (WUS D

Table 3-2. OASES attenuation constants for median PGA values.

Standard Range Deviation of Mag- bI b3 of log nitudes (PGA) Mc_

(Shallow siti 191 0.823 -1.56 0.568 4 to 7.5

Focus ______Events) rock Eve )site 157 1.04 -1.90 0.579 4 to 7.5

Path B (Deep Focus stiff 284 0.587 -1.05 0.70 5 to 8.5 or Subduc- site tion Zone rock 276 0.68 -1.20 0.70 4 to 8.5 Events) site 27 068 1 120 0704t 8. I

Reprinted from "Offshore Alaska Seismic Exposure Study (OASES)," 197S, with permission from Woodward-Clvdc Consultants. 3-35 TM 5-809-10-1/NAVFAC P-355.1IAFM 88-3, Chapter 13, Section A 27 February 1986 Magnitude weighting the future. (EUS Data) (1) Empirical models using an intensity Is = f(I.,R) attenuation data base. The first three ap Log GM = g(l,,M) (WUS Data) proaches require a relation giving the atten-._./ uation of intensity as a function of distance. It No weighting would be ideal to have a number of earthquakes I. = f(I.,R) (EUS Data) with a range of epicentral intensity (IJ) and many (WUS Data) reports of site intensity (Is) for each earth- Log GM = g(15) quake. Then it would be possible to obtain the The fourth method uses a theoretical approach required relation of the form through a simple such as Nuttli's (Biblio 48) model. It combines regression analysis: theoretical modeling with measured regional Q values (damping value of the transmission me- (Is - IW)= C1 + C2R + C3InR (eq 3-23) dium), assumes the near-source ground motion However, no such data set exists in a usable in the EUS is the same as in the WUS, and scales form. Considerable data does exist, but it is in only by magnitude. If it is kept in mind that the the form of isoseismals for given earthquakes. elements of ground motion models are a com- Isoseismals have a number of drawbacks, in- bination of source travel path and local site ef- cluding the fact that they are generally subjec- fects, it can be seen that all four approaches tively determined. Of even greater significance make a common assumption. This is that the set is the fact that isoseismals represent the aver- of WUS earthquakes, making up the strong age distance at which a given intensity was felt, ground motion data set, adequately represents rather than average intensity at a given dis- future earthquakes in the EUS in terms of such tance. Six earthquakes, that have been studied parameters as dynamic stress drop, static stress in enough detail to develop sufficient data for drop, seismic moment, and focal mechanism. determining the required coefficients in equa- Validity of this common assumption can be ver- tion 3-23 by regression analysis, are listed be- ified only as more information is generated in low. Maximum Analysis Name Date Intensity Source Southern Illinois 11-9-1968 Vll G.A. Bollinger ~ (Biblio 9) Cornwall-Massena 9-4-1944 V1l R.J. Holt (Biblio 9) Ossippee 12-20-1940 VlI R.J. Holt (Biblio 9) Giles County 5-31-1897 VII-VIll G.A. Bollinger (Biblio 9) Charleston 8-31-1886 X G.A. Bollinger (Biblio 9) New Madrid 1811-1812 XI-XII 0.Nuttli (Biblio 9) (2) Stronggroundmotiondata base. This to be correlated with spectral amplitude as well data base allows correlation of site intensity with as PGA, the data sets are more limited. The most such information as peak ground acceleration common one consists of the California Institute (PGA), velocity (PGV), distance from recording of Technology (CIT) data tapes, such as those site to the epicenter and/or nearest approach of of Trifunac and Brady or McGuire and Barn- the fault rupture plane, earthquake magnitude, hard. These sets are then used to obtain rela- and information about site geology (See para- tions of the form: graph C-1, appendix C-1). A number of such data bases have been developed, e.g., Murphy In GM = Cl + C21, + C3 In R (eq 3-24a' and O'Brien (Biblio 43), Trifunac and Brady (Biblio 66), McGuire and Barnhard (Biblio 38), or Boore et al., (Biblio 13). If the site intensity is In GM = C1 + C21. + C3M (eq 3-24b) 3-36 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A or Sa of interest. Several models are plotted for PGA in figure 3-25. Based on the methods sug- In GM = Cl + C I1 (eq 3-24c) 2 gested in this section, any one of the following and four attenuation relationships can be used.

In GM = C, + C2M + C3 In R + C4S 1. Gupta and Nuttli model (1976). (Biblio (eq 3-24d) 25). where 2. Bollinger model (1977). (Biblio 8). 3. Ossippee model (1977). (Biblio 64) GM = Ground motion parameter (PGA, PGV, 4. Model developed by Tera Corporation. or spectrum S, at a given period) (b) The Tera Model is based on the first Is = Site intensity three models mentioned above. This model has R = distance measure (epicentral, closest the following format: approach, etc.) log PGA = 0.74 + 1.12 mb - 0.733 In R - M = generally local magnitude 0.0007R (for R > 20 kilometers.) S = Site type parameter (for soil S = 0; for rock S = 1) = -1.47 + 1.12 mb The parameters C. are determined by regression (for R s 20 kilometers.) analysis using an appropriate data set. The val- PGA is in cm/sec2 ues of I., R, and site type for some records differ Mb is the body wave magnitude = significantly between data sets. Thus some (0.98ML - 0.29) choices are involved. R is the epicentral distance in Kms. (3) Site Correction Factor. The ideal way to include a generic correction factor for rock e. Uncertainty associated with ground mo- sites is to perform the required regression anal- tion model applied in the east. One weakness ysis using only the rock subset of the data in of the approach applied in the EUS has to do place of equation (3-23) one could use: with apportioning an attenuation model into submodels. The uncertainty contained in each Is - 1o = C + C R + C In R + C4S 1 2 3 of the submodels increases the uncertainty in (eq 3-25) the final prediction (Cornell, et al., (Biblio 20). where S = site type (S = 0 for soil and S = 1 Although at the present time, there does not for rock), and in place of equations 3-24a, b, c, appear to be any rational alternative to this. one could include a site type in the relation be- This added uncertainty significantly influences tween ground motion, site intensity, and dis- the seismic hazard results. Improved estimates tance or magnitude. Unfortunately, the intensity could be obtained through additional work on attenuation data does not include the site type this topic. When an attenuation model is derived and the intensity assigned is not generally at a directly from recorded ground motion, the sta- site where an accelerograph would be located, tistical uncertainty usually corresponds to a one but rather it is determined from isoseismals or standard deviation confidence level of 1.6-2.0 nearby reports of intensity. This reduces the times the mean. When the uncertainty in mean applicability of the above approach. predictions of intermediate parameters (such (a) Another method consists of intro- as intensity) is rigorously included, this multi- ducing the variation between soil and rock sites plicative factor becomes 2.0-2.9 (Cornell, et al., at the level of equations (3-24) and the general (Biblio 20). A hazard analysis, which results in ground motion model for the EUS is the com- a one standard deviation confidence level equal bination of equation (3-23), the appropriate form to 2 or 3 times the mean predicted value of site of equations (3-24) and the inclusion of the term, severity is being dominated by this multiplica- C4S (S = 0 for soil sites arid S = 1 for rock sites) tive factor. It should be recognized that a large where C4 is obtained from WUS data, (In(GM = part of the uncertainty is due to the use of data C4S + C1 + C2ML + C31nR). The resulting ground representing all possible earthquake types and motion is of the form: all possible travel paths. The necessity for this is to acquire a sufficient statistical sample size ln GM = Cl + C2I0 + C3R + C4ln R for averages and empirical prediction equa- (eq 3-26) tions. However, in most cases the seismic hazard where GM is PGA, PGV or any spectral ordinate at a particular site is largely determined by a

3-37 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

)

lu.^ 1X0 * 1000 Epicentral disunce ikm)

"Seismic Hazard Analysis-Solicitation of Expert Opinion," Nuclear Regulatory Commission, reprinted from NUREG/CR-1582, Vol. 3, 1980.

Figure 3-25. Comparison of ground motion models for Mb = 5.5.

particular type of earthquake (e.g., magnitude the random uncertainty associated with predic- range, depth, focal mechanism, etc.), with a par- tion of median PGA levels in the EUS should be ticular path. It is believed that a detailed con- substantially different than in the WUS for given sideration of this specific local knowledge would parameters. Therefore uncertainty measures significantly reduce the attenuation model un- similar to those values obtained in the WUS from certainty. Also, as stated in the next paragraph, direct regression on strong motion data are rec- the median forecasted value of PGA is used for ommended for use in the EUS. scaling the response spectrum shape. The high f. Site severity for scaling the response spec- uncertainty in actual PGA values does not enter trum shape. For the purpose of scaling the ap- into this scaling procedure; only the statistical propriate site response spectrum shape (DAF) sampling uncertainty of predicted median PGA as described in the next paragraph 3-6, it is rec- as it estimates the true (infinite sample size me- ommended that the median or 50 percentile value dian value) median is of concern. Aside from the of PGA be used in the attenuation equation. The use of sub-models (such as conversion of I to mean value shall be used if the median is not M), there is no a priori reason to believe that given by the attenuation equation. For a given 3-38 27 February 1986 TM 5-809-10-1 /NAVFAC P-355.1 /AFM 88-3, Chapter 13, Section A convoluted seismic hazard or return period of 'probability of exceeding a given level of site in- severity at the site, it is judged that the median tensity (such as PGA) involves the convolution value is sufficiently conservative for spectral of the probabilities of all the possible combi- scaling purposes. Note that PGA data used for nations of source intensities (M or I) and at- empirical attenuation relations is the PGA from tenuation distances R that can produce or exceed the principal component of the recorded time the given level of PGA. Figure 3-26 provides a history. Further conservatism due to the spec- simplified illustration of the typical condition tral enveloping property of the specified DAF for a line source and an area source. shape is discussed in paragraph 3-7. (1) On the line source the set of all possible g. Computation of total hazard at the combinations of rupture length location, its cor- site. The process of computing the hazard or responding attenuation distance RHand mag-

iRupture length due to M having random location Line Source on source

jRI

Site having given level of PGA

Area element having random location on source M occurs in this element.

Area Source US Army Corps of Engineers Figure 3-26. Descriptionof sets of M and R required for a given PGA. 3-39 TM 5-809-10-1 /NAVFAC P-355. I/AFM 88-3, Chapter 13, Section A 27 February 1986 nitude Mi are able to produce or exceed the given -Analytical Soil-Column Response PGA at the site. Similarly the set of the M; and area element location Rj produces the PGA at (see para C-3, app C for an overview of all meth- the site from the area source. ods). The results of any or all of these methods (2) The total probability of exceeding the may be combined to define the appropriate spec- PGA is the probability of the union of the oc- tra for structural design and analysis; this is currences of all the sets of Mi and Ri combina- usually done in a rather subjective manner to best represent the quality of information from tions on the line source, and Mj and Rj combinations on the area source. The convolu- each method, (See SEAOC Pamphlet, (Biblio tion operation required for this total probability 55)). However, before proceeding to the descrip- for a selected range of given PGA values can be tion of these methods and the formation of the very lengthy and is best performed by a com- site specific spectra, it is useful to review the puter program such as STASHA (Stanford Uni- major factors that govern the shape and size of versity Technical Report, No. 36). A simple the response spectrum. example of this type of calculation is given in a. Spectral shape factors. It is generally rec- paragraph 3-7c. ognized that the frequency content and corresponding response spectrum shape is governed (3) Finally, a sensitivity analysis involving the probable upper and lower bound values of by the following source and site factors. the parameters of the hazard analysis may be -Characteristics of Soil Deposits Underly- performed. For example, when large uncertain- ing the Site ties exist due to sparse data and (or) judge- -Magnitude of Seismic Event producing the mentally assigned values in source locations R, Site Ground Motion recurrence parameters a, I, Mmax, and different but applicable attenuation relations, then sep- -The Source Fault Rupture Characteristics arate runs of PGA evaluations may be performed using probable upper and lower bounds -The Source-to-Site Travel Path Charac- for each individual parameter. The results of teristics of Distance and Wave Attenua- this analysis are useful to identify the impor- tion Properties tant factors that significantly effect the calcu- The second and third factors are recognized sub- lated PGA, such that perhaps more information jects of research, but are not generally incor- ) can be obtained to better evaluate these factors porated in site spectra with the exception that of parameters. Also, the resulting probable records for spectral averaging purposes may be' bounds on a PGA for a given return period pro- grouped according to magnitude levels. The first vide a numerical description of the quality or "soil type" factor is well established and used in. stability of the hazard analysis and can assist in most site specific ground motion studies. The the final assignment of the design spectral scal- fourth "travel path" factor is also an estab- ing value for the PGA. lished procedure for both distant sites in all regions, and for the representation of the low 3-6. Site specific response spectra, step V. attenuation rates in the Eastern United States. The exact prediction of future ground motions Detailed discussions and procedures for deter- (such as the accelerogram x(t)) at a site is not mination of spectra are given in appendix C, par- possible. Therefore, forecasted response spec- agraphs C-2 and C-3. tra representative of this motion offer the most b. Statistical averages of normalized re- effective method of specifying the future. Hav- sponse spectra. In this first empirical method, ing the value of site severity from step IV of the the shape of the spectrum is determined by a seismic hazard analysis, this value provides the statistical analysis (evaluation of averages and basis for scaling the response spectrum shape standard deviations) of past earthquake strong resulting from step V, treated in this paragraph, motion accelerograms; as classified according to and summarized in figure 3-27. site conditions, distance from the source and In practice, the response spectrum shape may size of the event. All the response spectra for a be obtained by three rather common tech- common set of conditions are normalized by the niques; two of which are empirical, and one ana- recorded PGA, see figure 3-28. lytical method: The mean and standard deviations of the normalized spectra (referred to as the Dynamic -Averages of Normalized Spectra Amplification Factor or DAF) are then calcu- -Attenuation of Spectral Ordinates lated. This statistical summary is used to fore-

3-40 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

GIVEN FORECASTED MEDIAN PGA FOR EQ-I AND EQ-II (para 3-le) DETERMINE FORECASTED RESPONSE SPECTRA 1 4'I AVERAGES OF ATTENUATION OF ANALYTICAL SOIL- NORMALIZED SPECTRAL ORDINATES COLUMN RESPONSE SPECTRA HAVING FOR APPROPRIATE FOR APPROPRIATE COMMON SITE SOIL TRAVEL PATH, TIME HISTORIES CONDITION MAGNITUDE, AND ON BED ROCK (para 3-6b) SITE SOIL CONDITION AND SOIL COLUMN (para 3-6c) MODEL (para 3-6d)

ATC 3-06 SHAPE AS SPECIFIED IN PARA 3-8 ] -I ____

COMPARE AND JUSTIFY FINAL SPECTRAL SHAPE USING INFORMATION FROM A.LL AVAILABLE METHODS (appendix C, para C-4)

SCALE FINAL SPECTRAL SHAPE ACCORDING TO EQ-I AND EQ-II LEVELS OF PGA AND DAMPING VALUES (para 3-7 and 3-8)

US Anny Corp~s of Eiigineers

Figure 3-27. Step V, site specific response spectra.

3-41 TM 5-809-1 0-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

,Sa DAF 1 a(t)1

B DAMPING

tV,06 v , t T T

Sa 2 DAF2

t T T DAF Sa n a(t) n I n )

'04-00 -I!, A A AA . . t - V V \1 V , T T n iMDAF X DAF. MDAF = 1 1 (For all values of T) n

n 2 E (DAF - I MDAF) Variance (DAY) I (For al 1 (n-i) values of T) T

US Army Corps of Engineers Figure 3-28. Statisticalaveraging of normalized spectra.

3-42 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A cast the spectral shape of future events according information is not complete. See appendix C, to the particular site conditions. The method, paragraph C-3. even though widely used for practical applica- e. Site specific earthquakespectra. The pro- tions, has some shortcomings. The procedure of cedures of paragraphs 3-6b, c, and d, have all or normalizing according to PGA creates a large in part lead to generalized versions of earth- coefficient of variation (standard deviation di- quake spectra. Some of the important recom- vided by average), particularly in the long pe- mendations resulting from these procedures are riod region. However, since no better means of given here and in the next paragraphs on shape normalization is yet available, this technique has effects. These include the methods of: provided the primary source of design earthquake spectral shapes. See Seed et al. (Biblio -Newmark-Hall, (Biblio 44) 56), Kiremedjian and Shah (Biblio 33) and ATC -Seed et al, (Biblio 56) 3-06 (National Bureau of Standards, Special Publication 510). -Kiremidjian and Shah, (Biblio 33) c. Attenuation of spectral ordinates. The -ATC 3-06 second empirical approach of forming a site (1) Newmark-Hall Method of Constructing spectrum is by the use of attenuation equations Elastic Response Spectrum. This is an empirical for spectral ordinates at specific period values method of constructing an elastic spectrum. It for a set of records and then statistically ana- employs the following normalized values for lyzing these attenuated ordinates. This again ground motion: provides a mean and standard deviation description of the site spectrum such that an upper Acceleration 1g confidence limit can be given in terms of one or Velocity 48 in/sec. more standard deviations. This method has the advantage of avoiding a normalization method Displacement 36" with its inherent creation of large spectral var- Thus, for a peak ground acceleration of interest, iability. This advantage is offset, however, by as forecasted for the site, construct the ground the need for the use of spectral attenuation re- motion parameters on the tripartite plot. As an lations that have large prediction error. Also, example, let the PGA value be 0.35g. For this the development of these relations requires a case, ground motion values are: sufficient set of records applicable for a common seismic region; the method is therefore limited Acceleration A = 0.35g to these regions (see app C, para C-3d). This (Og x 0.35) method, however, may find increased applica- Velocity V = 16.8 in/sec. bility in the Eastern United States (see Nuttli: (48 in/sec x 0.35) Biblio 47), not because of the availability of data for that region, but because the method can in- Displacement D = 12.6" corporate expert opinion and theories for wave (36" x 0.35) transmission peculiar to the region and its pos- Draw this ground motion spectrum on the tri- tulated sources of seismicity. The most current partite paper. (fig 3-29). application of this technique is given by NUREG/ (a) The second step is to construct an CR-1582, Vol. 3 and 4, (Biblio 63, 64). "elastic" response spectrum. To construct this d. Analytical soil column response. The third spectrum, a table of amplification factors, based or analytical method of obtaining a spectral shape on the study of past spectra, is available. See is based on a site specific study of the strong table 3-3 from (Biblio 44). motion accelerogram. If the acceleration time These amplification factors are functions of history at the bedrock level for a given site can damping ratios, and the described confidence be formulated, then using the overlying soil lay- level. As an example, consider a 5 percent damp- ers as a filter, the response on the surface can ing ratio, and the median level. be determined. Thus, the transfer function of (b) The lines of constant acceleration, ve- the soil layer and the motion at the bedrock level locity, and displacement representing the elastic determines the time history and corresponding response spectrum are given by the correspond- spectral shape at the surface. The problem with ing ground motion values times the appropriate this method is that a time history at the bedrock factors from the table. level has to be formulated. This may not be an easy task for a region where the seismotectonic S.= (.35g)(2.12) = 0.74g

3-43 TM 5-809-10-1/NAVFAC P-355.1I/AFM 88-3, Chapter 13, Section A 27 February 1986

)

FREQUENCY - Hz 300.0 30.0 IC0 0I litIlEI I I .,, I I I r L , ...... - 100.0 -______

10.0

L- U 0

z 0 1.0 a. a W )

a- 4 a 0S a

P in 0.1

0.01 0.ol 0.1 I 0 FuRIOD-SEC Reprinted from "Earthquake Spectra and Persig,." Newmark, N. M. and Ilal), W. J., EERI Monograph Series, 1982, with permission from the niarthqtaakr Engineering Research Institute. Figure 3-29. Newmark-Hall Spectrum.

3-44 27 February 1986 TM 5-.809-1O0-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A Table 3-3. Spectrum amplification factors for horizontal elastic response.

Damping, One Sigma (S4.1o) Median (50%) 9eCritical A V D A V D

0.5 5.10 3.84 3.04 3.68 2.59 2.01 1 4.38 3.38 2.73 3.21 2.31 1.82 2 3.66 2.92 2.42 2.74 2.03 1.63 3 3.24 2.64 2.24 2.46 1.86 1.52 5 2.71 2.30 2.01 2.12 1.65 1.39 7 2.36 2.08 1.85 1.89 - 1.51 1.29 10 1.99 1.84 1.69 1.64 1.37 1.20 20 1.26 1.37 1.38 1.17 1.08 1.01

Reprinted from "Earthquake Spectra and Design," Newmark, N. M. and Hall, W. J., EERI Honograph Series, 1982, with permission from the Earthquake Engineering Research Institute.

S, = (16.8 in/sec) (1.65) = 27.7 in/sec response spectrum. This total risk must involve Sd= (12.6')(1.39) = 17.5 in. the convolution of probability functions for both the forecasted PGA scaling factor and the DAF (c) These constant levels are plotted on spectral shape. See Kiremidjian and Shah (Bib- the tri-partite paper, and along with recom- lio 33) for examples. A more simplified reliabil- mended connecting lines as given in (Biblio 44), ity calculation is given in paragraph 3-7. the complete spectrum is defined. This New- (4) The ATC 3-06 method uses much of mark/Hall method provides a direct procedure methods (1) and (2) as background justifica- of forming a spectrum, and also has the advan- tion. It, however, goes further to provide sim- tage of constructing inelastic yield force and de- plified DAF shapes for not only the soil types formation spectra in terms of structural ductility but also the tectonic region. Because of this sim- factors (see Biblio 44). Also the site soil con- ple, yet representative quality, it is recom- ditions can be represented by either the known mended that these ATC 3-06 shapes be used for forecasted peak ground velocity or prescribed the appropriate site conditions and tectonic re- relations between peak ground acceleration, ve- gion. Therefore, unless there are special site locity, and displacement. However, since the conditions, close active sources, or high risk f a- representation and description of site soil con- cilities, these shapes as scaled by the forecasted ditions are not as detailed as in the following site severity values can provide the input spec- methods, the use of this Newmark/Hall method tra for design and analysis. The complete ATC is not recommended except for general compar- 3-06 method for site severity and response spec- ison with other methods. tra is given in paragraph 3-8. In order to rep- (2) SeedetaL. This method provides mean resent the particular regional attenuation effects DAF, and mean plus one standard deviation that are indicated when the A, value exceeds the shapes for different categories of site condi- Aa value on the contour maps* given in para- tions, see figures 3-30 and 3-31. These DAF graph 3-8, the spectral shape should be found shapes may be scaled to the forecasted PGA value using the respective contour map values of A, having a given risk value at the site. and A., then this shape should be scaled by the (3) Kiremidjian and Shah. This method is ratio of the forecasted PGA to the contour map similar to method (2), and a definite listing of value of A.. The PGA value corresponds to the the data base and the site soil conditions is pro- hazard level or return period of EQ-I or EQ-Il. vided. Also, in addition to mean and mean plus f. Factors affecting response spectral one standard deviation shapes, probability func- shapes. As mentioned in paragraph 3-6a there tions are given for the random DAF values as are several important conditions or factors that they are scattered about the mean value. This can alter the shape or frequency content of the probability information is most useful for cal- response spectrum. culating the total risk of exceeding a specified 3-45 TM 5-809-1O0-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

0 E a E a

0 0.5 ID L5 2.0 25 3.0 Period - seconds

Reprinted from "Site-Dependent Spectra for Earthquake Resistant Design," Seed, It.B. et al, Report No. EERC 74-12, University of California at Berkeley, 1974.

Figure3-30. Average acceleration spectra for different site conditions.

(1) Type and duration of fault rup- source to the site increases. In other words, the ture. Generally the type and duration of the predominant period of motion increases with fault rupture affects the frequency content of distance and size of the seismic event. The en- the seismic wave. Various seismological papers gineering implication of this observation is ob- are available which describe the theoretical for- vious. Taller structures are affected more by large mulation of the above mentioned dependence. distant earthquakes than are the shorter (or (Haskell, (Biblio 28, 29); Savage, (Biblio 51)). stiffer) structures at the same location. According to these models, the seismic wave (3) Local site soil conditions. The effects characteristic in the time and frequency domain of local site soil conditions on the frequency con- is a function of the radiation pattern (source tent can be very significant. The response of a and propagating geometry), seismic moment given layered soil media to a seismic bedrock (size of the event or energy release level) and motion depends heavily on the transfer function the source mechanism. of the soil. Thus, stiffer soils transfer higher (2) Size of event in terms of magnitude or frequency components whereas softer soils seismic moment and distance from source to transfer lower frequency components. Exten- site. Based on the recorded ground motion sive studies of the available strong motion ac- characteristics, many empirical relationships are celerograms by many researchers have shown available to show the dependence of the re- that the shape of the Response Spectrum changes sponse spectrum shape on the size of an event, with the site condition. There are usually three the distance from the source to the site and the classifications of soils: soft alluvium deposits predominant period (or frequency) of the mo- (soil class 0), intermediate stiff soils (soil class tion. Figures 3-32 and 3-33 show such empirical 1) and firm soils or rocks (soil class 2). These results. It can be seen from these figures that classifications could be made on the basis of shear the higher frequency components are filtered wave velocities. As a guide to such a possible out from seismic waves as the distance from the 3-46 27 February 1986 TM 5-809-10-1 /NAVFAC P-355.1 /AFM 88-3, Chapter 13, Section A

C 0 C

0I'l 4.1

U C

E X0 EI WI aU I

Period - seconds

Reprinted from "Site-Dependent Spectra for Earthquake Resistant Design." Seed, H. B. et al, Report No. EERC 74-12, University of California at Berkeley, 1974. Figure 3-31. 64 Percentile acceleration spectra for different site conditions.

3-47 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 )

1.4

1.2

1.0 A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

i0.8

J0.6 AA

04 LEGEND ) _;_ 0 0 ~ ~~~~~~~~~~.0SO(SmWUtmY PD 0 Auaf.tu Pod 02 A COOMbnwat

0 150 200 300 350 400 450 500 Uo DO 00 Epicantr Difv4c-km

Reprinted from "Characteristics of Rock Motions During Earthquakes," Seed, R. B. et al, Report EERC 68-5, University of California at Berkeley, 1968. Figure 3-32. Predominantperiods for motions in rock-earthquakemagnitude = 7.

3-48 27 February 1986 TM 5-809-10-1/lNAVFAC P-355. IAFM 88-3, Chapter 13, Section A

5.2

M.?

0.6 M.6~~~~~~~~~~~~~~~~~..

10 40 8M10- 20 20 .5326 ICA_.AA._.

N~ow fromn CousWir F&A -kem

0 25 50 75 BOO 125 ISO 175 200 2wz Distonceforom Cavwivev Podt-fmies

Reprinted from "Characteristics of Rock Motions During Earthquakes," Seed, H. B. et al. Report EERC 68-5, University of California at Berkeley, 1968. Figure 3-33. Predominantperiods for maximum accelerationsin rock.

3-49 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 classification, the following procedure is rec- soils of class 2. Under very special conditions, ommended (Vs is the shear wave velocity): (such as in Mexico City, where the city is on an old lake bed), the spectral peak could occur at Firm Site: Vs - 450 meters/sec. a period as long as 1.5 to 2.5 seconds. Intermediate Stiff: 250 - Vs < 450 meters/ (4) Regional geology. This is a most im- sec. portant effect, not only for the Western United States where there is a reasonable amount of Soft Alluvium Deposits: Vs < 250 metersl strong motion records, but for the Eastern sec. United States where data is sparse and predic- Also, for the purpose of this manual, these soil tions of future ground motion must be based classes 0,1,2 may be considered to correspond to upon geological features. The future develop- the soil types SI, S2, S3 respectively, as described ments in ground motion prediction will depend in table 3-5. Figures 3-34, 3-35 and 3-36 taken strongly upon inferred behavior of possible from Kiremidjian and Shah, (Biblio 33), show earthquake source mechanisms, and the corre- the effect of the soil conditions on the frequency sponding propagation of effects in the general content of ground motion. It can be seen from geological structure. One of the most prominent these figures that for soil class 0, the spectral characteristics of Eastern United States seis- peak occurs at higher period than for stiffer micity is the exceptional transmission of peak

mean + one standard deviation 3.' I.' 0 u *~ -- Kiremidj ian and Shah ) 0

-4 'a. '44

.-4

U 1.0 C,

0. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Period T in sec.

Reprinted from "Probabilistic Site- Dependent Response Spectra," Kiremidjian, A. i. and Shah, H. C., Journal of the Structural Division, Proceedings of the ASCE, %ol. 10D, No. STI, January 198o, with permission from the American Society of C:ivil Engineers.

Figure3-34. Comparison of DAF from Kiremidjian and Shah to Seed et al, soil class - 0, damping = 5%. 3-50

Fu 27 FebruarY 1986 TM 5"09-1 -1NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

V q4 I I 1.' 11 Kjiremidjian and Shah 03 . I"~ I ……- -- Seed et al C. ~I, to

mean + one standard deviation

U -4

(0 sUI~

mean

0. 0.5 0.0 1.0 1.5 2.0 2.5 3.0 Period T in sec.

Reprinted from "Probabilistic Site- Dpeendent Response Spectra, K;rnfiifiaIt A. S. and Shah. it. C., Journal of the Structural Division, Proceedings of the ASCE. Vol. 106. No. ST1. January 1980, wit permiSsion from the American SocietY of

Civil Engineers. Co present study to DAF from Seed e Figure 3-3. Comnparisonof DAF from rsn td oDFfo ede l olcas 1 apn %

3-51 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

-I)

4.0

In I! I

J-% I -Kiremidjian and Shah II I -- … Seed et al 0 mean + one standard deviation

CU rU 0 6.14 . C4 mean U 1.0 V-4 M ) CU .

0.1 1.0 2 Period T in sec.

Reprinted from "Probabilistic Site- Dependent Response Spectra. Kiremidjian, A. S. and Shah, H. C., Journal of the Structural Division, Proceedings of the ASCE, Vol. 106. No. STI, January 1980, with permission from the American Society of Civil Engineers.

Figure 3-36. Comparison of DAF from present study to DAF from Seed et a], soil.dcass = 2, damping = 5%.

3-52 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A velocity effects (low attenuation). A repres applicable to the site and how the resulting DAF tation of this velocity propagation effect is gi shape may coincide with the dynamic frequency by the ATC 3-06 Spectra for the appropri characteristics of the structure. seismic areas of the Eastern United States. I g. Formulation of effective response spec- will be shown in paragraph 3-8. All shape fac tra. For the cases where the ATC3-06 method effects are summarized in figure 3-37. When of paragraph 3-8 is to be supplemented or re- lecting a design earthquake spectrum, the placed by special site information (para 3-3 to gineer will consider which of these factors 3-6, and perhaps a site response analysis such

Large Magnitude

T DAF

Region

Distance

Soil

Ub Army Corps of Engineers Figure 3-37. Factors effecting spectral shape. 3-53 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 as SHAKE (Biblio 54), then the mean (or me- for the exceedence of structural performance dian) spectral shape (DAF) will be used. The criteria (elastic design level or functional level) specified site spectrum will be mean (or median) the corresponding site severity parameter (PGA) PGA times mean (or median) DAF. The mean is derived from the following measures of seis- ) DAF values for site soil conditions are given by micity and attenuation: Seed, (Biblio 56) and Kirimedjian and Shah, (Biblio 33) and these may be supplemented by -Site to source distance (R), for the one or the results from a site response analysis. For more sources capable of producing the PGA example, if one or more spectra are available at the site. from a site response analysis, and or if any ac- -Magnitude or source-intensity (M or I.) tual recorded event spectra are judged to be ap- necessary to produce PGA at the site. propriate for the site, then these spectra will be -The appropriate attenuation relation for normalized to the mean (or median) PGA value the geotectonic region and site conditions, and averaged with the empirical mean PGA X DAF shape. The averaging should be based on and the relation of PGA to site-intensity. a weighted judgement of the relative quality and -The probability model and combinatorial applicability of the available spectral informa- procedures required for the evaluation of tion, see paragraph C-3f, appendix C. the PGA corresponding to a given return h. Effective response spectra. In paragraph period TR- 3-8e, there is a discussion of the concept of an effective response spectrum where high fre- The resulting forecasted PGA is subject to the quency (short period) response peaks are re- uncertainties in the above listed measures. It duced to represent the absorption or filtering can be represented as an estimated mean (or effect of the actual building size on the short median) value of PGA. This forecasted mean spikes of ground acceleration input. For the case PGA is scattered about the true mean PGA (cor- of the mean PGA times mean DAF specified in responding to a given return period) with an paragraph 3-6g, it is assumed that this mean estimated (sampling error) coefficient of vari- spectrum is the effective response spectrum; the ation Vp equal to about 10 to 20 percent. mean DAF represents both a smoothed or re- (2) The envelope quality of a statistical duced peak shape in the short period range and DAF. The primary source of spectral shape or ) an average conservative envelope of near and DAF information is by the statistical averages far event ground motion response in the longer of records from common general categories of period range. It therefore provides for the same distance (R), magnitude (M), and soil condi- effects as discussed in paragraph 3-S8e. tions (S). However, in order to have a sufficient sample size, there is rather wide variation in the individual record conditions (R, M, S) within 3-7 Interpretation and summary. any general category. This individuality causes The various concepts and methods of specifying a large contribution to the coefficient of varia- ground motion have been presented. This par- tion VDAF of the DAF; but in terms of forecast- agraph provides discussions of the uncertainty ing future ground motion, it has the following in forecasted values; and the relation of selected useful interpretation. Referring to figure 3-38, levels of ground motion to design criteria. the possible single events at a site can have (for a. Recognition of uncertainty in forecasted example) either condition "A" or "B"; corre- values. Each step in the specification of site sponding to large magnitude and near source ground motion involves uncertainties due to ("A") or moderate magnitude and far source empirical relations fitted to limited data; vary- ("B"). The average envelope curve would there- ing assignment of values to general measures fore be exceeded only in the case where the ac- of magnitude, intensity, and source-to-site dis- tual event conditions are not enveloped by this tance; and varying expert opinions. These in- upper curve. Thus, in this example, for periods dividual uncertainties have been discussed in the less than T1, the envelope is much more con- appropriate paragraphs dealing with each pa- servative if conditions "B" were to occur. The rameter necessary for the ground motion fore- chance that this curve will be exceeded by the cast. It is intended to assemble these uncertainty actual future event DAF is the chance of having measures so as to describe the total reliability both conditions "A" and structural period less of a specified site ground motion. than T.. This would be the product of the two (1) Site severity (PGA). Given the accept- probabilities of (condition "A") and of (period ) able hazard in terms of the return period (TR) T v TI), and would be small. As a rough, but 3-54 27 February 1986 TM 5-809-10-1 /NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A DAF

Condition "A"

Condition "B"

_ _- DAF Envelope

1.og'\ I

I %' I T1 T

UIS Ann. Corps of Engineers

Figure 3-38. Envelope quality of the DAF shape. reasonable value, it is assumed that the com- describe the design DAF in terms of a central bined envelope shape would be approximately value and coefficient of variation. It is estimated equivalent to a 90 percent confidence interval that the design DAF represents at least a 90 for a single event spectrum. Therefore, in order percent upper confidence limit on the true DAF to best represent the fact that the envelope curve that could occur at the site; or in terms of prob- and its simplified design DAF version is an en- ability, the probability that a future event DAF velope of many possible future event conditions, would exceed the design DAF is about 10 per- the design DAF in the next paragraph (3) is cent. assumed to be equivalent to 90 percent confi- b. Reliability of specified ground motion. dence limit. The classical hazard analysis (STASHA) pro- (3) Smoothed or simplified design DAF. vides a central PGA value for a given return The mean or median value DAF results directly period or risk of exceedance. Due to prediction from the statistical average of the normalized error, the true PGA for the given return period (DAF) values from the site-representative has a 50 percent chance of exceeding this central earthquake records. The common range of coef- PGA. ficients of variation is 0.3 to 0.5. However, when (1) Then, with the recognition that the DAF the mean or median DAF values are smoothed shape is a conservative envelope of DAF's from and simplified to provide a design DAF (see ATC near and far events, and assigning a very rough 3-06), the final shape represents an envelope for judgemental probability of 10 percent that the any of the possible spectral shapes that could DAF of any single event would exceed the en- occur at the site. Because of this necessity for velope shape, the reliability of the effective de- the simplified envelope in order to provide a sign spectrum (PGA)(Design DAF) is given by, practical input (without steep peaks and val- leys) for dynamic analyses, it is not possible to 1 - (0.5)(0.10) = 0.95 or 95% 3-55 TM 5-809-1 0-1I/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 While this reliability measure is based on very of site PGA during a given exposure time t, and subjective measures of uncertainty, it provides where PGA is the forecasted mean or median a reasonable description of the actual condi- value from the hazard analysis. This central tions. In summary, given an accepted return pe- forecasted PGA value is the measure of ground--o' ) riod for the forecasted ground motion, there is motion severity and is used (in step V) as the only a 5 percent chance that the design spectrum spectral scaling factor for the site response would be exceeded. The STASHA program of- spectrum fers a more rigorous and complete method of establishing the reliability by means of its Baye- Sa = PGA x DAF, sian Hazard Analysis option, see appendix D. where the DAF is a reliable envelope shape for (2) The effects or consequences of uncer- all of the spectral shapes that could be produced tainties and variabilities in specified ground mo- by the events capable of generating the PGA at tion values for a site are best evaluated after the site. Because there may be more than one the consideration of the total structural design source and (or) more than one possible earth- process in chapter 4. When the forces and de- quake event at different locations on a source, formations in the structural model have been it is not possible to calculate directly the value evaluated for the specified ground motion, then of a PGA having a specified hazard or probability judgements can be made concerning the effect of exceedence. Several values of hazard P[PGA of seismic input variations on the performance > PGAA] must be evaluated for given incre- of the final design. For example, if critical mem- mented values of PGAj, and then a hazard curve bers have high levels of inelastic demand, and is constructed through the plot of the hazard if reasonable variations in input can increase versus PGAj points; a hazard curve is shown in this demand beyond the failure threshold, then figure 3-39. With this curve it is possible to de- the designer should strengthen or modify this terinine the site PGA value corresponding to a part of the structure. specified hazard value for a given exposure time: c. Site specific hazard curves. Hazard is defor example, the PGAI for EQ-I having a 50 per- fined as the probability of exceeding a given level cent chance of exceedence in 50 years. ) ~P(PGA> PGA )- Hazard

100% - - - _ . _

PGA

50%X - - - - -

0 I Mp'GA PGA I

US Army Corps of Engineers Figure 3-3. Hazard curve for site PGA with exposure time of 50 years. 3-56 27 February 1986 TM 5-809-1 0-1 /NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A In appendix D, a simplified example I shows the 2 and 3, of appendix D show the more detailed individual steps necessary to calculate one of procedures using the STASHA computer pro- the incremental hazard curve points PGAj = 0.20g gram as required for the practical evaluation of for a 50 year exposure time. The other examples, the hazard at a given site. Section IlIl. THE ATC3-06 METHOD 3-8 The ATC3-06 method. site location the contour maps, figures 3-40 to This method as documented in ATC3-06 (Na- 3-43 provide the basis for evaluating the site tional Bureau of Standards, Special Publication severity or scaling factors for EQ-1 and EQ-22. 510) and as prescribed in this paragraph will be These figures provide contour values Aa and A, used according to the guidelines in figure 3-1. having a 10 percent probability of exceedence in The resulting design spectra are to be consid- 50 years. Definitions of Aa and A, are given in ered as the minimum seismic loading criteria. figure 3-44. Figure 3-45 gives curves that con- Where there are exceptional site conditions such vert the contour values to the Aa or A, values as close source proximity, or highly responsive corresponding to the probabilities of exceed- soil columns, or if the configuration or use of ence for EQ-I (50% in 50 years) and EQ-I1 (10% the structure is very different or special, then in 100 years). The value for EQ-I is found where the hazard analysis methods in paragraphs 3.1 the contour level curve intersects the 50% prob- to 3.7 are to be used to supplement these mini- ability line for 50 years. The value for EQ-I1 is mum criteria. Any changes from these criteria found where the contour level curve intersects are subject to approval by the reviewing agency. the 10% probability line for 100 years. a. Determinationof site severity. For a given

010/0/(y. 0 L11:

_405~~~~~~40.

100

010

006 0,,

morE: THE NUMBERS ON THE CONTOURS ARE VALUES OF EPA IN UN ITS OF ACCELERATION OF GRAVITV.A/

Reprinted from "Tentative Provisions for the Development of Seismic Regulations for Buildings ATC 3-06,' National Bureau of Standards, Special Publication 510, 1978. Figure 3-40. Contour map for effective peak acceleration. 3-57 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

ALASKA

7>9 ' PUERTO RICO HAWAII

Reprinted from "Tentative Provisions for the Development of Seismic Regulations for Buildings ATC 3-06," National Bureau of Standards, Special Publication S10, 1978. Figure 3-41. Contour map for effective peak acceleration.

3-58 C. ~~~~~~~~~~~~~~(

"'4

0 GokLW:

0~~~~~~~~~~'

0 0~~~

NOTE: CONTOURS SNOW VALU E OF AV

Reprinted from "Tentative Provisions for the Development of Seismic Regulations for a Buildings ATC 3-06,"1 National Bureau of Standards, Special Publication 510, 1978 .

Figure 3X2. Contour map for effective peak velocity-related accelerationcoeffient. TM 5-809-10-1/NAYFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

)

ALASKA

PUERTO RICO

Reprinted from "Tentative Provisions for the Development of Seismic Regulations for buildings ATC 3-06," National Bureau of Standards, Special Publication 510, 1978. Figure 3-43. Contour map for effective peak velocity-related acceleration coefficient. N-A

3-60 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

10 [

P 0

-j

k-) EPA =s 0~ U) 0.1 EPV =S

0.1 0.5 1 5 10 50 PERIOD (SECONDS)

Map values of A = EPA in g's Map values of A = EPV/30 in g'sand EPV is in inches/sec. Av is the velocity related acceleration value.

Reprinted from "Tentative Provisions for the Development of Seismic Regulations for Buildings ATC 3-06," National Bureau of Standards, Special Publication 510, 1978. Figure 3-44. Schematic representationshowing how effective peak acceleration and effective peak velocity are obtained from a response spectrum.

3-61 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

50 100 years years

0.1 l . -m0.7 % (0.005%) I

'I 50% ,EQ-I NO11_ 0.01 61% (37%)

D - C 90% (81%) Si) 0.001! I \ \ 1 19595% /. (90%) ,EQ-IIEQ-11

-.1 V0 98%f%nal (96%)(967.) z z 99% (98%) 4 0.00 If I I I -- 99.5% (99%) )

'I \ I

0.00001 _ __, _ 99.95% (99.0%) 0.01 0.02 0.05 0.1 0.2 Q5 1.0 a orAv ing's

Note: axis on right provides probabilities of non-exceedence in exposure times of 50 years and 100 years.

Reprinted from "Tentative? Provisions for the lkefrelopuent of Seismic Regulations for buildings Ale 3-0b5, National :Iureau of SaI.dlallb. Special Publication 510. 1978. Figure 3-45. Annual risk of exceeding various effective peak accelerationsfor locations on the indicated contours of A. and A. in figures 340 to 3-43.

3-62 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A (1) Table 3-4 gives a summary of the re- ATC3-06, the stated probability values are as- sulting A. and A, values for each corresponding sumed here to be also applicable to the A, val- map contour values. These Aa and A, values are ues, such that both Aa and A, can be converted to be used to scale the response spectrum shape to the EQ-I and EQ-I1 probability values, at all DAF as per equations 3-27 to 3-30 in paragraph locations in the United States. This assumption 3-8c. is considered valid because any A, value is de- (2) Note in figure 3-45, that any 100 year rived from the A. value at a given map location probability of non-exceedence can be obtained and therefore has the same probability value as by the square of the corresponding 50 year prob- the Aa. ability; the occurrence of two successive 50 year b. Determination of site soil type. The site periods of non-exceedence. soil profile type will be determined and identified (3) Also, even though figure 3-45 was orig- as Si, S2, or S3 according to the definitions given inally meant to be used for EPA = A. values in in table 3-5.

Table 3-4. Map contour and ground motion levels.

ATC 3-06 Design Ground Motion Level Aa or AV Map Contour and Probability of Exceedance*

Level Aa or AV EQ-I EQ-II

in units of g (50% in 50 years) (10% in 10.0 years) (figs 3-40 to 3-43)

0.05 0.02 0.06 0.10 0.04 0.12 0.20 0.08 0.25 0.40 0.20 0.45

* For use in equations 3-27 to 3-30

US Army Corps of Engineerb 3-63 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Table 3-5. Site soil profile types.

SOIL PROFILE TYPE SI is a profile with:

1. Rock of any characteristic, either shale-like or crystalline

in nature. Such material may be characterized by a shear

wave velocity greater than 2,500 feet per second, or

2. Stiff soil conditions where the soil depth is less than 200

feet and the soil types overlying rock are stable deposits

of sands, gravels, or stiff clays.

SOIL PROFILE TYPE S2 is a profile with deep cohesionless or stiff

clay conditions, including sites where the soil depth exceed 200

feet and the soil types overlying rock are stable deposits of sands,

gravels, or stiff clays.

SOIL PROFILE TYPE S is a profile with soft-to-medium-stiff 3 clays and sands, characterized by 30 feet or more of soft-to-medium-stiff

clays with or without intervening layers of sand or other cohesionless

soils.

In locations where the soil properties are not known in suffi-

cient detail to determine the soil profile type or where the profile

does not fit any of the three types, Soil Profile S2 shall be used.

Reprinted from "Tentative Provisions for the Development of Seismic Regulations for Buildings ATC 3-06," National Bureau of Standards, Special Publication SIO, 1978.

'S ')

3-64 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A c. Determinationof the design respcrnse spec- equation 3-27 differs in form from that of the tra. With the known values of Aa aiid A, for base shear equation EQ-I1 and the site soil type (SI, S2, o r S3), the 5 percent damped, EQ-I1 acceleration response V = 12A S. spectrum is given by the following e4quations; note that these equations specify con:stant lev- given in the ATC 3-06 document. The 1.2 value els of spectral acceleration S., spectra 1 velocity is a round-off of the 1.22 value in equation S., and spectral displacement Sd, withijn the pre- 3-27, the T" exponent value allows the base shear scribed ranges of structural period T (refer to equation to represent multi-mode response ef- the spectrum relations given in fig 3- 44 and in fects. The base shear equation is for the equiv- para C-2b of appendix C). alent static force method at a single period value For T S 4 seconds: and needs this empirical method of allowing for the combination of response from all modes. S,1 22 AS gs, (eq 3-27) (1) The 5 percent damped EQ-I Spectrum ( eq ~ is equal to the EQ-Il spectrum multiplied by the (constant S, = 75AS, inJ ratio of the EQ-I to the EQ-Il values given in sec) table 3-4. Linear interpolation may be used for but always less or equal to values between those given in this table. (eq3-28) (2) The flat plateau for S. as given by equa- Sa = 2.5Aa g's (constant S. in g's.) (eq 3-28) tion 3-28 or equation 3-29 provides a conserv- and ative (high) representation of response for the higher (higher than first mode) modes of struc- Sa = 2.OAa g's when Si = 1.5 and A. ¢ 0 30 tural response where the modal periods are less (eq 3-29) than 0.2 or 0.3 seconds. However, this conserv- For T > 4 seconds: ative response measure may be excessive for a Soil Profile Type S3. Referring back to figure Sa = =4.88-AvSi g's (constant Sd (eq 3_30) 3-30 of paragraph 3-6, the corresponding soft to medium clay and sand site condition has a 150 v~i inches) mean spectral shape that rises from the zero period value to the plateau at about 0.3 seconds. Values for Si are given in table 3-6. These equa- Higher modes can have periods below this value tions for Sa are equivalent to the conistant ac- and therefore would have S. values lower than celeration, velocity, and displaceme nt levels the flat plateau. Following the recommended re- shown on the general tripartite, logarilthm scale lation given in the commentary of chapter 5 in graph in figure 3-46. A specific example!is shown the ATC3-06 (National Bureau of Standards, for Aa = A, = 0.40 in figure 3-47. DZote that Special Publication 510); for the case of Soil

Table 3-6. Soil profile coefficient. Soil Profile Type

S1 S2 S3

S. = 1.0 1.2 1.5 1.

Reprinted from "Tentative Provisions for the Development of Seismic Regulations for Buildings ATC 3-06." National Bureau of Standards, Special Publication 510, 1978. 3-65 TM 5-809-10-1NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 S (in/sec)

S, a 1.0, 1.2, 1.5) 75 A S. Sa(&) / V I (inches)

(150/.M) AVSi

/ l a - 5 percent I I

T 4.0 seconds

US Army Corps of Engineers

Figure 3-46. Tripartite representationof EQ-IL

Profile Type S3, and for modes higher than the Biblio 44). first mode, the Sa values may be determined from e. Representation of the effective response a straight line extending from the Aa value at spectrum. In regions of strong seismicity, and ) zero period to the plateau at period equal to 0.3 for site locations near to sources, the response seconds. spectra from the single possible events (pro- d Considerationof structuraldamping ratio. ducing the same site PGA) can either have a All of the design spectra given in paragraph high frequency peak shape for near events, or 3-4c are for structural damping equal to 5 per- have a more constant shape at lower frequen- cent of critical damping. These spectra may be cies for a distant large event, see figure 3-48. converted to other damping ratios by use of the The ATC3-06, spectral shape provides a reliable factors given in table 3-7. Linear interpolation envelope of the spectra from both near and far may be used to provide factors for intermediate events. Further, the horizontal plateau of (2.5A, damping values. The factors in this table are < 2 .5Aa) provides the effective structural re- based upon empirical relations given by New- sponse spectrum: the high frequency peak re- mark and Hall, (Biblio 44). The median spectral sponse values, usually present in near-source shape given in this Biblio (44) is sufficiently close records and spectra would be filtered out by the to the shape in this paragraph, so that the damp- structure size, mass, and foundation configu- ing relations are applicable. The table 3-7 fac- ration, and actual structure response is repre- tors represent rounded-off average of the sented by the plateau level in this high frequency Newmark values for the constant acceleration range. Note that the PGA at the site is the same plateau and the constant velocity (1IT) range for each (near and distant) event. For example, of the spectral shape. Since the specified spectra a PGA = 0.60g may correspond to the ATC3-06 in this paragraph are formed by various simpli- map contour value of Aa = 0.40g. It is important fied factors such as the (2.5Aa) effective pla- to recognize that the EPA = A. = 0.40g = 2/3 teau, and the soil type coefficients (S,, S2, SA), (PGA = 0.60g) applies to the effective spectrum the rounded-off average damping factors in plateau in the high frequency range; the re- table 3-7 are judged to be consistent with mainder of the spectral envelope corresponds to these other factors. If more accurate values are the site severity as represented by the fore- desired, then the Newmark and Hall relations casted central PGA value. may be used for the median spectral shape, 3-66 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

FtEQUEINCT - Hz )00.0 10O 10 01 1 . I I I 11 I I I I I I III1 II . I I 11 100.0-

0, eb 'CO I

u ,C-

a 10.0 i o.e4 .10ll 'I

; t 1.0

aI 'I a

S 0 a ¢"I-4

wk 0.1 aL

100

PIRIOD-SIC

US Arm% Corps of Engineers

Figure 3-47. EQ-l spectra for A. = A, = 0.40, and j3 = 5%.

3-67 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 Table 3-7. Damping adjustment factors.

8 Percent MuLti 1ying Factor for the 5 Percent Spectrum

2 1.25

5 1.00

7 0.90

10 0.80

15 0.70

20 0.60

US Anny Corps of Engineers

High Frequency Peak Response

)

PGA

Period T

US Army Corps of Engineers ) Figure 3-48. Effective spectral envelope. 3-68 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A f. Representationof regionalattenuation dif- plitude of moderate frequency ground motion ferences. The ATC3-06 contour maps provide components, or a low attenuation of these com- A. and A, values, and the spectral plateau rule ponents which is characteristic of the wave requiring 2.5 Av - 2.5 Aa is a simple yet effective propagation in the EUS and in some regions of method of representing the low attenuation rate the WUS outside of California. of ground motion in some areas of the EUS and WUS, see figure 3-49. When the map gives A, 2 g. Examples using the ATC3-06 method. A., then the plateau value of 2.5A. extends fur- (1) Site location. Las Vegas, Nevada. Soil ther on the period scale and gives a spectral shape type S2; S = 1.2 from table 3-6. having larger values in the moderate frequency (a) Find Map Contour Values: range. This represents a preservation of the am- figure 3-40, A. = 0.10

S a 02.5A where A > A a a V

2.5 A wh ere A < A a a v

T T Perfod T v a

T V a

US ArMY Corps of Engineers

Figure 3-49. Regional shape difference. 3-69 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 figure 3-42, A, = 0.15 (a) Find map contour values: (b) Obtain Special Scaling Factors from figure 3-46, Aa = 0.40 Table 3-4: figure 3-48, A, = 0.40

Using Interpolation, (b) Obtain Special Scaling Factors from '' table 3-4. EQ-I, Aa = 0.04, A, = 0.06 EQ-I1, A. = 0.12, A, = 0.18 EQ-I, A. 0.20, A, = 0.20 (c) The specified Structural System EQ-II, A. = 0.45, A, = 0.45 Damping Values are given as 5 percent for EQ- (c) The specified structural system damp- I and 10 percent for EQ-I1. Table 3-7 provides ing values are given as 5 percent for EQ-I and Damping Adjustment Factors of 1.00 for j3 = 5 7 percent for EQ-II. Table 3-7 provides Factors percent and 0.80 for f = 10 percent. Using these of 1.00 for 1 = 5 percent and 0.90 for 1 = 7 damping factors, the Acceleration Response percent. Using these factors with equations (3- Spectra are given by equations (3-27) and (3- 27) and (3-29) for T S 4 seconds. 28) for T G 4 seconds. EQ-I EQ-I Sa = (1.22/T)AvS, X Damping Adjustment S. = (1.22/T)AvSi X Damping Adjustment Factor Factor, = (1.22)(0.20)(1.5)(1.00)IT = (1.22)(0.06)(1.2)(1.00)/T = (0.366/T) g, = (0.0878/T)g, but always less or equal to but always less or equal to S. = 2.OA. X Damping Adjustment Factor S. = 2.5Aa X Damping Adjustment Factor = 2.0(0.20)(1.00) = 2.5(0.04)(1.00) = 0.40g = 0.1Og EQ-I EQ-I Sa = (1.22)(.45)(1.5)(0.90)/T Sa = (1.22)(0.18)(1.2)(0.80)/T = (0.741/T)g = (0.211/T)g but always less or equal to, but always less or equal to S. = (2.0) (0.45) (.90) S.= 2.5(0.12) (0.80) = 0.81g = 0.24g (3) These EQ-I and EQ-I1 Spectra are shown These EQ-I and EQ-II Spectra are shown in fig- in figure 3-51. Note that the higher mode tran- ure 3-50. sition spectrum shape is shown for each spec- (2) Site location. Emeryville, California. trum in the zero to 0.3 second period range. Soil Type S3; Si = 1.5 from table 3-6.

3-70 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

LS in g's

0.24 EQ-II,B =10 percent

< A EQ-I , =5 percent 0.1 0.11

-T seconds 0 1.0 2.0 3.0 4.0

US Army Corps of Engineers

Figure 3-50. Las Vegas, Nevada site spectra for soil type S2 .

S in g's

0.81

EQ-I ,I =7 percent

0.45 I'll > EQ-I 3 =5 percent 0.40 I

0.20

T seconds 0 1.0 2.0 3.0 4 .

US Army Corps of Engiveers

Figure 3-51. Emeryville, Californiasite spectra for soil tvpe S3 . 3-71 27 February 1986 TM 5-809-1O--1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A CHAPTER 4 CRITERIA FOR STRUCTURAL ANALYSIS

4-1. Introduction. the determination of the foundation design cri- This chapter prescribes the dynamic analysis teria, special recognition will be given to the dy- criteria for the development of a seismic-resist- namic nature of the forces, the expected ground ant structural concept, the determination of the motions, and the design basis for strength and seismic forces to be applied to the structure, and ductility of the structure. the design and analysis of structural members (2) Structures will be designed for dead, live, and connections. The criteria and design stand- snow, and wind and/or seismic forces as given ards for the dynamic analysis approach herein, in the applicable agency manuals and in this for the seismic design of buildings, will be used manual. Every building or structure and every only when directed or approved in lieu of the portion thereof will be designed and constructed lateral static forces procedure of the Basic De- to resist the stresses and distortions produced sign Manual. The procedures to determine ef- by the dynamic seismic analysis procedure in fective response spectra for selected risk levels combination with dead and live loads as speci- and site conditions are developed in chapter 3 fied in this chapter. Where prescribed wind loads (e.g., fig 3-3). This chapter provides the struc- govern the design of some or all structural ele- tural performance requirements for the se- ments, the design analysis will be prepared for lected risk levels in accordance with paragraph both the wind and seismic criteria and the struc- 3-3b. tural elements will be sized for the most severe a. Essential facilities. Criteria set forth in loading condition. this chapter have been developed primarily for (3) Stresses and deformations will be cal- the design of essential facilities, as classified in culated as the effect of the dynamic analysis paragraph i-id, that are assigned an I-factor being applied horizontally and coming from any equal to 1.5 in the Basic Design Manual. horizontal direction. The effects of vertical ac- b. High-risk structures. Criteria set forth in celerations will also be considered in the design this chapter may be applicable to the design of of horizontal cantilever and horizontal pre- high-risk buildings, as classified in paragraph 1- stressed components. Id, that are assigned an I-factor equal to 1.25 in (4) Materials and details will conform to the Basic Design Manual. the seismic provisions, applicable guide specifi- c. All others. Applicable portions of criteria cations, and criteria herein, including the seis- set forth in this chapter may be used as a means mic reinforcing details in the Basic Design for considering the dynamic characteristics of Manual. The provisions of this chapter apply to irregular structures or framing systems to com- the structure as a unit and also to all parts ply with the Basic Design Manual, paragraph 3- thereof, including the structural frame or walls, 3(E)3, and as a means for establishing the lat- floor and roof systems, anchorages and supports eral design forces and distributions by dynamic for architectural elements and mechanical and analyses to comply with the Basic Design Man- electrical equipment, and other elements. ual, paragraph 3-3(I). b. Definitions. Definitions listed in the Basic Design Manual, paragraph 3-3(B), will apply to 4-2. General requirements. this manual. Additional definitions are listed in a. General. Design and construction will the glossary. conform to the provisions of the Basic Design c. Symbols and notations. Symbols and no- Manual if not superseded by or in conflict with tations listed in the Basic Design Manual, par- the requirements of this manual. agraph 3-3(C), will apply to this manual. (1) The structural system or type of con- Additional symbols and notations are listed in struction will admit to a rational analysis in ac- appendix A, Symbols and Notations. cordance with established principles of mechanics d Dynamic analysis procedure for buildings. and dynamics. A continuous load path, or paths, (1) Essential buildings. Essential build- with adequate strength and stiffness, will be ings will be designed to resist two levels of provided to transfer all forces from the point of earthquake motion. The first level of motion is application to the final point of resistance. The designated EQ-I and the second and larger am- foundation will be designed to accommodate the plitude of motion is designated EQ-I1 The lat- forces developed or the movements imparted to eral-force-resisting structural systems of these the building by the design ground motions. In facilities will be designed to resist EQ-I by elas- TM 5-809-10-1 INAYFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 tic behavior as prescribed in paragraph 4-3. The 70 percent of EQ-I responses), unless otherwise facilities will be evaluated for their ability to directed. The lateral-force-resisting structural resist EQ-II by post-elastic behavior with duc- systems of these facilities will be designed to tility limitations as prescribed in paragraph 4- resist the modified EQ-I as prescribed in para- 4. Guidelines for these dynamic analysis proce- graph 4-3. In general, this procedure will be used dures are described in chapter 5. only for those buildings that may be highly un- (2) High-risk buildings. Subject to the di- usual or irregular in the distribution of mass or rection of the approval authority, high-risk stiffness or in the configuration of the framing. buildings will be designed by either of the two e. Lateralforceson structuralcomponents and following procedures: nonstructuralelements of structures. (a) Two-level approach. Using two lev- (1) Essential buildings. All components or els of ground motion in accordance with the pro- systems that must remain intact or functional cedure described in paragraph (1) above, except during and after a major earthquake shall be that the forces resulting from the EQ-I spectral designed with consideration of the dynamic response may be reduced by 15 percent (i.e., use characteristics of both the components or sys- 85 percent of EQ-I responses), unless otherwise tems and the structure in which they occur. The directed. The lateral-force-resisting structural accelerations and interstory drifts that are cal- systems of these facilities will be designed to culated from the dynamic analysis of the struc- resist the modified EQ-I as prescribed in para- ture will be used, where applicable, to design graph 4-3. components, systems, and their anchorages. For (b) Single-level design. Using the pro- the design criteria for nonstructural elements, cedures described in paragraphs (3) (a) or (3) (b) refer to chapter 6. below using an importance factor (I) equal to (2) High-risk and other buildings. All 1.25. components or systems essential to life safety, (3) All other buildings. Buildings that are which must remain intact during and after a not classified as essential or high-risk facilities major earthquake, will be designed in accord- will be designed in accordance with one of the ance with the Basic Design Manual or the de- following three procedures: sign criteria for nonstructural elements in (a) Basic Design Manual criteria with chapter 6. modified seismic force distribution. Determine f. Dynamic analysis procedures for struc- ) the distribution of seismic forces in accordance tures other than buildings. For design criteria with the modal analysis procedure of paragraph for structures other than buildings, refer to 4-3 with an appropriate response spectrum for chapter 7. EQ-I. Normalize the resulting forces such that the net total seismic shear at the base of the 4-3. Elastic design provisions. building is not less than the total lateral force, The structure will be designed to resist the forces V, determined from the requirements of the Basic caused by design earthquake EQ-I that has a Design Manual, paragraph 3-3(D), formula 3- 50-percent probability of being exceeded in 50 1 (i.e., V = ZIKCSW). Complete the design in years, or as otherwise specified by approval au- accordance with the provisions of the Basic De- thority (see para 1-ic), in accordance with the sign Manual. criteria prescribed in this paragraph. (b) Single-level design with minimum a. Method of analysis. The total lateral de- story shear requirements. Design the structure sign force representing earthquake effects and to resist EQ-I as prescribed in paragraph 4-3. its distributions will be determined by a re- However, the net story shears at each story will sponse spectrum modal analysis. This require- be at least 50 percent greater than the story ment does not prohibit the use of a properly shears determined from the minimum earth- substantiated time history response analysis quake forces of the Basic Design Manual, par- procedure. agraph 3-3(D). For clarification of this b. Design response spectrum. The response requirement, refer to paragraph 5-3d(2). In this spectrum.representing EQ-1I will be determined procedure, the structure need not be evaluated from the methodology prescribed in chapter 3, for EQ-IL. section II or III, as applicable. The damping value (c) Two-level approach. Using two lev- will be determined from table 4-1. The require- els of ground motion in accordance with the pro- ment is that the structure will resist these forces cedure described in paragraph (1) above, except by elastic, or nearly elastic, behavior. Nearly that the forces resulting from the EQ-I spectral elastic behavior is defined in paragraph e below. response may be reduced by 30 percent (i.e., use 4-2 27 February 1986 TM 5-809-10-1 /NAVFAC P.355.1 /AFM 88-3, Chapter 13, Section A Table 4-1. Damping values for structural systems.

Structural System Elastic-Linear Post Yield

Structural Steel 70 17% Reinforced Concrete 12%0 Masonry Shear Walls 7%

Wood 10 o

Dual Systems (1) (2)

1. Use the value of the primary, or more rigid, system. If both

systems are participating significantly, a weighted value, pro-

portionate to the relative participation of each system, may be

used.

2. The value for the system with the higher damping value may be

used.

US Army Corps of Engineers

c. Modal analysis methods. For a building (a) Mathematical model. The building that is regular and essentially symmetrical in will be modeled as a system of masses lumped size, shape, and configuration, a two-dimen- at each floor level, each mass having one degree sional model (a vertical plane with vertical and of freedom, that of lateral displacement in the horizontal movement within the plane) will gen- direction under consideration. The computed erally be sufficient for the modal analysis of the masses will be in conformance with the weights structure in each of its two horizontal compo- prescribed in the Basic Design Manual, para- nents of motion. When a structure is unavoid- graph 3-3(D)5. The stiffness of the lateral-force- ably not symmetrical in plan (refer to para resisting system will be determined by estab- l-3a(2) for requirements), has unavoidable dis- lished methods in accordance with the guide- continuities in the vertical or horizontal planes lines in paragraph 5-4b of this manual. (refer to para l-3a(2) for requirements), has (b) Mode shapes and periods of vibra- large length-to-width ratios, has flexible hori- tion. The analysis will include, for each major zontal diaphragms, or has other irregularities, axis, all significant modes of vibration with a a three-dimensional model will be required for minimum of three modes for buildings with 6 or the modal analysis. more stories. The relative significance of higher (1) Two-dimensional (2-D) models. The modes will be determined by the values of modal modal analysis procedure for two-dimensional participation factors and modal spectral accel- models is outlined in paragraphs (a) through erations (see para 5-4c(2) for additional dis- (i) below. Variations of this procedure may be cussion). The natural periods and mode shapes acceptable with proper justification and ap- will be computed by established methods of proval. Additional guidelines are included in structural mechanics and in conformance with paragraph 5-4 and design examples are illus- the mathematical model described in paragraph trated in appendix F. (a), above. 4-3 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 (c) Modal story participation fac- (f) Modal base shear. The total lateral tor. The story modal participation factor will force corresponding to mode m is calculated be calculated for each mode using the equation using the equation 4-4: 4-1: Vm = amSamW (eq 4-4) I where: PFxm = (eq 4-1) Vm = Total lateral force for mode m. W = Total dead load of the building and applicable portions of other loads (Basic where: Design Manual, para 3-3(D)5)). PFxm = Modal participation factor at level x for (g) Modal shears and moments. Story mode m. shears and overturning moments for the build- wjIg = Mass assigned to level i. ing and shears and flexural moments for the structural elements will be computed for each 4*im = Amplitude of mode m at level i. mode separately, by linear analysis, in conformance with the story forces determined in equa- 4xm = Amplitude of mode m at level x. tion 4-3. n = Level n. (h) Modal deflections and drifts. Modal lateral story displacements will be calculated It should be noted that some references define using the equation 4-5: the "modal participation factor" as the quantity 2 within the brackets in equation 4-1 above. Also, Bxm = PFxmSdm = PF.rSarn(T./2it) g (eq 4-5) in some references, 4 is normalized to 1.0 at the where: uppermost mass level and other references will &xm = Lateral displacement at level x for normalize the value of X(w/g)42. (d) Modal base shear participationfac- mode m. tor. The effective modal weight (or modal base Sdm = Spectral displacement for mode m cal- shear participation factor) will be calculated for culated from the response spectrum for each mode using the equation 4-2: EQ-I.

4 Tm = Modal period of vibration. / n WI im )2 The modal interstory drift in a story, Axm, will am n Wi n (eq 4-2) be computed as the difference of the displace- s g 5 wi2 ments, 8,, at the top and bottom of the story i-I i-I g 4im under consideration (i.e., Axm = B, + I)m - bxm). (i) Combinations of modal values. The where: combined effects of the individual modal actions am = Modal base shear participatii on factor (shears, moments, axial forces, etc.) and defor- for mode m. (am = Cbm/Sam 'Athere Cbhi mations (lateral story displacements, interstory is the modal base shear coefficient and drifts, etc.) for the structure and the members Sam is the modal spectral accelleration). will be obtained by taking the square-root-of- (e) Modal story lateral forces. The lat- the-sum-of-the-squares (SRSS) of the values of using the all significant modes. These total values are sub- eral forces for mode m are calculated ject to modification by other provisions of this equation 4-3: chapter (e.g., torsional, orthogonal, see para Fxm = PFxmSamwx (eq 4-3) 4-3e). (2) Three-dimensional (3-D) models. When where: a 3-D analysis of a building is used or is re- F = Story lateral force at level x for mode quired, some modification to the procedure out- m. lined for 2-D models (paragraphs (1) (a) through wX = Weight at or assigned to leve1 x. (1) (i) above) will be necessary. These modifi- Sam = Spectral acceleration for modle m from cations will be most significant for structures the design response spectrum Iprescribed with large eccentricities, for structures that do in paragraph 4-3b (as a rattio of the not have orthogonal axis of symmetry, and for acceleration of structures where the forces are applied from a gravity, g). direction that is not parallel to one of the major 4-4 27 February 1986 TM 5-809-1O0-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A axes of the building. Supplementary require- to conform to the base shear prescribed by the ments to those for 2-D models are listed below. Basic Design Manual. In no case will the total Guideline procedures are included in paragraph lateral force at the base of the structure be less 5-4. than 3 percent of the total dead load of the build- (a) At each floor level, there will be three ing, W, in zones of high seismicity and 2 percent degrees of freedom. The primary displacement in other areas. Zones of high seismicity include will generally occur in the component parallel seismic zones 3 and 4 of the Basic Design Manual to the direction under consideration. There will and areas where the effective peak accelera- also be a displacement component normal to the tions are greater than 0.20 in figures 3-40 and direction under consideration and rotation about 3-41. the vertical axis of the building. When the floor e. Structural component load effects. All diaphragm is not rigid, the horizontal flexibility building components will be provided with will be considered. strengths sufficient to resist the combined ef- (b) A minimum of nine modes will be re- fects of the seismic forces prescribed herein and quired in order to include three horizontal modes applicable gravity loads. The requirements of in each of the principal directions and three tor- paragraph 4-2d state that the structure will re- sional modes. The possible coupling effects of sist the seismic forces by elastic behavior. How- the various components of motion will also be ever, in some cases, nearly elastic behavior is investigated. applicable. (c) Modal story participation factors in (1) Nearlyelasticbehavior. Nearly elastic equation 4-1 will be adjusted for 3-D effects (re- behavior is interpreted as allowing some struc- fer to para 5-4d(2) for clarification). tural elements to slightly exceed specified yield (d) Modal base shear participation fac- stresses on the condition that the elastic-linear tors in equation 4-2 will be adjusted for 3-D ef- behavior of the overall structure is not sub- fects (refer to para 5-4d(2) for clarification). stantially altered. For a structure that has a (e) Modal story lateral forces will have multiplicity of structural elements that form the three components: primary forces in the direc- lateral-force-resisting system, the yielding of a tion under consideration, forces normal to the small number of elements will generally not ef- direction under consideration, and a torque due fect the overall elastic behavior of the structure to rotational motion. if the excess load can be redistributed to other (f) Modal base shears will have three structural elements that have not exceeded their components consistent with (e) above. yield strengths. In lieu of a substantiated ana- (g) Modal shears and moments will be de- lytical procedure, this condition will be consid- termined from three components consistent with ered satisfied by allowing the following (e) and (I) above. percentages of exceedance to the elastic capac- (h) Modal displacements and drifts will ity requirements of paragraph 4-3f (based on a vary within the horizontal plane of each floor linear analysis). level as well as along the vertical axis. (a) Ductile framing systems. Ductile (i) The total forces and deformations for framing systems are defined as those systems the structure and the members will be obtained conforming to Basic Design Manual classifica- by an approved method to account for a rational tions for K = 0.67 or 0.80. For these systems, a combination of the modal values. limited number of the lateral-force-resisting d. Minimum lateralforces. The story shears structural elements in the direction of the force and story overturning moments determined from may exceed the flexural elastic capacity require- the elastic design modal analysis will be comments of paragraph 4-3f by a value of up to 25 pared to the lateral static shears and overturn- percent (e.g., the load combinations of para- ing moments prescribed by the Basic Design graph (2) below will be equal to or less than 1.25 Manual. If the values obtained from the modal times the elastic capacity (EC). The number of analysis are less than the values prescribed by horizontal flexural elements having flexural ov- the Basic Design Manual (including adjust- erstresses is limited to 20 percent of the hori- ments for load factors and stress require- zontal seismic-resisting elements in the direction ments), a reevaluation of the site specification of the force on any story. The number of vertical of ground motion and of the dynamic structural elements having flexural overstresses is limited model will be made and a statement justifying to 10 percent of the vertical seismic elements on the lower story forces will be provided in the any story. design analysis. In lieu of a justifying state- (b) Other framing systems. Framing ment, the forces will be proportioned upwards systems conforming to Basic Design Manual 4-5 TM 5-809-1 0-1 /NAVFAC P-355.1 /AFM 88-3, Chapter 13, Section A 27 February 1986 classifications for K = 1.0 may have a limited cases a more severe condition may occur when number of the lateral-force-resisting structural the force is applied at a horizontal direction not elements in the direction of the force that ex- parallel to the main axes. For some elements of ceed the flexural elastic capacity requirements a building, the effects of concurrent motion about of paragraph 4-3f by 10 percent (e.g., the load both principal axes should be investigated. Re- combinations of paragraph (2) below will be fer to Basic Design Manual, paragraph 4-4c(1), equal to or less than 1.10 times the elastic ca- for additional considerations. pacity (EC). The number of horizontal elements (5) Horizontal distribution of forces and having flexural overstresses at any story is lim- torsionalmoments. Forces will be distributed ited to 20 percent and the number of vertical in proportion to the relative rigidities (Basic De- elements having flexural overstresses at any sign Manual, para 3-3(E)4) and a minimum tor- story is limited to 10 percent. sional eccentricity of 5 percent will be applied (c) Box systems. Lateral-force-resist- (Basic Design Manual, para 3-3(E)5). Guide- ing systems that have the Basic Design Manual lines and alternative procedures are discussed classifications with K greater than 1.0 may not in paragraph 5-4 of this manual. exceed the elastic capacity requirements of par- (6) Overturning. Structures will be de- agraph 4-3f. signed to resist the overturning effects in ac- (2) Design load combinations. The struc- cordance with Basic Design Manual, paragraph ture will have the elastic capacity (EC) to resist 3-3(F). Guidelines and alternative procedures the effects of the design load combinations shown are discussed in paragraph 5-4 of this manual. in equations 4-6 and 4-7 (refer to para 5-4e(1) (7) Lateral displacements and drift lim- for clarification): its. Structures will be designed to limit the lateral displacements and interstory drifts EC > 1.2D + L.OL + L.OE (eq 4-6) calculated in accordance with paragraph 4-3c to EC ¢ 0.8D + L.OE (eq 4-7) the following values: (a) Drift. Lateral deflections, or drift, where: of a story relative to its adjacent stories will not EC = Elastic capacity required to resist the exceed 0.005 times the story height for essential loads or their effects facilities.For high-risk and other buildings, this limit is 0.007. ) D = Dead load (b) Building separations. All portions of L = Live Load structures will be designed and constructed to act as an integral unit in resisting horizontal E = Earthquake forces unless separated structurally by a dis- (3) Vertical accelerations. The vertical tance sufficient to avoid contact under deflec- component of earthquake motion (i.e., up and tions from the prescribed seismic action. down motion) will be considered in the design f. Elastic capacity criteria. The criteria for of horizontal cantilever and horizontal pre- the elastic capacity (EC) provisions herein are stressed elements. For horizontal cantilever ele- based on yield strength capacities of the struc- ments, these effects will be satisfied by design- tural components. Thus, the provisions for the ing for a net upward force of 0.2D as an additional material strengths prescribed in the Basic De- load case. For other horizontal elements em- effects will be sat- sign Manual and other applicable agency man- ploying prestressing, these uals will be upgraded to a yield strength criteria isfied by substituting equation 4-8 for equation for seismic forces in combination with applica- 4-7. ble gravity loads. EC - 0.5D + L.OE (eq 4-8) (1) Reinforced concrete design. The criteria used to design reinforced concrete will be due to where D represents the member forces the ACI Building Code (ACI 318 without app A) the vertical dead weight and E represents those as modified in the Basic Design Manual. due to the horizontal earthquake forces (refer (2) Structural steel design. In lieu of a to para 5-4e(1) for clarification). These provi- strength design criteria for structural steel, sions parallel those of the Basic Design Manual, paragraph 4-4c(2) (a). working stresses specified in agency manuals for (4) Orthogonal effects. In general, the ordinary or nonseismic construction may be in- horizontal design earthquake forces are applied creased by 70 percent (e.g., nonconcurrently in the direction of each of the Fa fbx 'b 1. main axes of the structure. However, in some I Fb, Fby 1.7).

4-6 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A (3) Reinforced masonry design. In lieu of bers will have a strength reduction factor of a strength design criteria for reinforced ma- 4) = 0.75. This reduction fctor will be applied sonry, working stresses specified in agency man- to the yield strength of the connection material. uals for ordinary or nonseismic construction may be increased by 70 percent (e.g., f, < 1.7Fa). 4-4. Post-yield analysis provisions. (4) Wood design. In lieu of a strength cri- The structure conforming to the design criteria teria for wood construction, working stresses of paragraph 4-3 will be analyzed to resist the specified in agency manuals for ordinary or forces caused by design earthquake EQ-I1 in ac- nonseismic construction may be increased by 100 cordance with the criteria prescribed in this percent (e.g., f (calculated) _ 2.0 f (allowable)). paragraph. (5) Connections. All connections that do a. Method of analysis. The total lateral de- not develop the strength of the connecting mem- sign forces and/or deformations representing

homent-Curvature ftlationship In Elastc Model Moment

Koment-Curvature Relation for Inelastic Response

'I V~ V [e ity

K >r 7

Inelastic Demand Ratio - maximum computed moment in elastic model - 1) elastic moment capacity '_iI u- Arm, Corps of Engineers

Figure 4-1. Definition of inelastic demand ratios for fiexural members. 4-7 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 earthquake effects and their distribution will be below). Either of the two acceptable procedures determined by a response spectrum modal anal- may be used; however, these requirements do ysis procedure. Two acceptable procedures are not prohibit the use of other properly substan- presented: Method 1, an elastic analysis proce- tiated inelastic response spectrum methods or dure that evaluates overstresses of individual inelastic time-history procedures. elements (para c below); and Method 2, an ap- b. Design response spectrum. The response proximate inelastic analysis procedure (para d spectrum representing EQ-II will be determined DUCTILITY CHECK OF STEEL COLUMNS

1. At a braced location:

H H x + MY -p H PCX hPcy

2. Stability between braced points:

Cmx Mx + ' uc 1 ucx ucy

where:

Po ", and M - axial load and moments from first order elastic analysis

[I pcx - 1.18 HPX - (P/Py)J )

Mpcy - 1.19 M [i - (p/py)2J

ucx Mux I - (P/PcrJ] 11 - (P/P e] M ucy Py [1.0 (PpPlasttcara iti (p/Pey)]

= pl1as ti c moment capac i ties

M ux - p 11 .07 - X ] Px

pe , Py - Euler buckling loads for x and y axes

P AFa (P/Pcr - 0.5) cr W 1.7

taxi C - 0.6 -0.4 (H/M2) t 0o4

tI - allowable ductility (inelastic demand ratio)

US Army Corps of Engineers Figure 4-2. Ductility check of steel columns. 4-8 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

DUCTILITY CHECK FOR CONCRETE COLUMNS

Compression:

x 1-B + .Y ' # M 8 M ux uy

H X < A H 8 M uy ux

Tension:

Mx 1-B + M a T - mx u

Mx M 8 M T my mx u

T < 0.5 T u

where:

M ,M and T = Moments and net axial ternsioiv fromi ei-tic x y ~~analysis5

M and M = Uniaxial ultimate nymient capacitieis floll ux uy interaction diagrams

mx and M Uniaxial ultimate moment capacities in the mxmy absence of axial load

Tu = Ultimate tensile capacity of vertical reinforcement EA F = s y

B = Coefficient from PCA Advanced Engineering Bulletin No. 20

= Allowable ductility (inelastic demand ratio)

US Amy Corps of Engineers Fiture 4-3. Ductility cheek for concrete columns. 4-9 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 from the methodology prescribed in chapter 3 (c) Hinging of columns at a single story for the earthquake ground motion that has a 10 level that will cause a mechanism. percent probability of being exceeded in 100 years (d) Discontinuity in vertical elements that or as otherwise specified by approval authority can cause instability or fracture. (see para 1-ic). The damping values will be de- (e) Unusual distributions of inelastic determined from table 4-1. mand ratios. c. Method 1. Elastic analysis procedure. The (6) Engineering judgment is required for structure that was designed in accordance with the structural evaluation of the post-yield anal- the criteria prescribed in the elastic design pro- ysis. If the review of the inelastic demand ratios visions of paragraph 4-3 will be reanalyzed to satisfies the requirements of paragraph (5) determine its capacity to perform to the de- above, it may be assumed that the inelastic drift mands of the larger earthquake represented by is adequately approximated by the elastic anal- EQ-I1. An elastic analysis procedure that eval- ysis. Limits for inelastic deformation are gov- uates overstresses of individual elements is out- erned by paragraph 4-4e. Guidelines are provided lined below. Guidelines for this procedure are in paragraph 5-5. presented in chapter 5, paragraph 5-5. Design d Method 2: Capacity spectrum method. A examples are illustrated in appendix E. step-by-step approach is used to approximate the (1) Perform a modal analysis of the struc- inelastic capacity of the structure. This capacity ture (para 4-3c) using the appropriate EQ-I1 is compared by means of a graphical procedure response spectrum. The stiffness of the lateral- to the demands of the EQ-II response spectrum. force-resisting system and the computed pe- Guidelines for this procedure are presented in riods and mode shapes will be established in ac- paragraph 5-5. Design examples are presented cordance with the guidelines in paragraph 5-5. in appendix E. A general outline of the proce- (2) Calculate the forces on all of the struc- dure follows: tural elements. Load combinations are pre- (1) By use of a modal analysis, determine sented in paragraph d below. These forces will the level of excitation that causes first major be defined as the demand forces and denoted yielding of the structure (see paragraph e below with subscript D (e.g., MD, VD, FD). for load combinations). (3) Calculate the yield or plastic capacities (2) Revise the stiffness or resistance char- ) of all the structural elements in the same force acteristics of all structural elements that are units used in paragraph (2) above. These forces within 10 percent of their yield capacities to rep- will be defined as the capacity forces and de- resent a plastic hinge. noted with the subscript C (e.g., MC, Vc, Fc). (3) Apply additional lateral forces to the (4) Calculate the ratio of the demand forces structure, by means of a modal analysis, until to the capacity forces of all the structural ele- an additional group of structural elements ments. These ratios will be defined as the in- reaches their yield capacities. elastic demand ratios. A graphical illustration (4) Repeat the above until the combined re- for flexural members is shown in figure 4-1. A sults reach an ultimate limit (e.g., a mechanism, method determining the inelasticdemandratios instability, or excessive distortions) (see para e for steel and reinforced concrete columns, by below for evaluation criteria). means of ductility ratios, is shown in figures 4- (5) Convert the results into a capacity curve 2 and 4-3. The equations in these figures were based on the periods and spectral accelerations adapted from the general interaction equations for the fundamental mode of vibration. for steel and concrete. (6) Graphically compare the demand of the (5) Review the inelasticdemand ratiosfor EQ-I1 response spectrum to the capacity of the uniformity, symmetry, mechanisms, and rela- structure.. tive values. Compare value to limits set forth in (7) Approximate the lateral deformations table 4-2. If any of the following conditions ex- and compare to the drift limits of paragraph e ist, the structure must be analyzed in accord- below. ance with Method 2 (para d below) or the e. Evaluation criteria. The structure will be deficiencies must be corrected by a redesign of evaluated for its ability to resist the combined the critical elements. effects of the seismic forces prescribed herein (a) Exceeding the inelastic demand ra- and the applicable gravity loads within the pre- tios of table 4-2. scribed lateral distortion limits. (b) Unsymmetrical yielding, on a hori- (1) Load combinations. The demands on zontal plane, that will decrease the torsional re- the structure will be equal to the combined ef- sistance. fects of the dead (D), live (L), and seismic (E) 4-10 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A Table 4-2. Inelastic demand ratios.

Building System Element Essential High Risk Others

Steel DMRSF Beams 2.0 2.5 3.0 Columns* 1.25 1.5 1.75 Braced Frames Beams 1.5 1.75 2.0 Columns* 1.25 1.5 1.75 Diag. Braces* 1.25 1.5 1.5 K-Braces*** 1.0 1.25 1.25 Connections 1.0 J.25 1_25

Concrete DMRSF | Beams 2.0 2.5 3.(} I Columns* .1.25 1.5 1.75 Concrete Walls Shear 1.25 1.5 1.75 Flexure 2.0 2.5 3.o

Masonry Walls Shear 1.1 1.25 1.5 Flexure 1.5 1.75 2.o - t ~______--1.75. ,_ Wood Trusses 1.5 l . 75 I.-0 Columns* 1.25 1 .5 I . 7S Shear Walls 2.0 2.5(0 3}.0} Connections 1.25 I .5() 2 . (1 (other than nails)

*In no case will axial loads exceed the elastic buckling capacity.

**Full panel diagonal braces with equal number acting in tension and compression for applied lateral loads.

***K-bracing and other concentric bracing systems that depend on-compressioi. diagonal to provide vertical reaction for tension diagonal.

uS Army Corps of Engineers loads shown in equations 4-9 and 4-10: that the effects of pounding will not cause loss Demand = D + L* + E (eq 4-9) of function, instability of the affected portion Demand = D + E (eq 4-10) of the structure, or hazard to life-safety. For example, if all the floors of adjacent buildings where the live load (L*) is equal to a realistic are in vertical alignment with each other, then estimate of the actual live load. The value of Lo the pounding associated with the extreme con- may be as low as 25 percent of the design live ditions of EQ-I1 might cause only some minor load (L). local damage to the material in contact. How- (2) Lateral displacements and drift limits. ever, if the floor of one building was in align- (a) Drifts. Interstory drifts will not ex- ment with mid-height of columns in the adjacent ceed 0.010 times the story height for essential building, pounding could cause column insta- faciities. For high-risk buildings and all other bility due to buckling and P-delta effects. If some buildings, the limit is 0.015. contact is acceptable for EQ-Il, the minimum (b) Building separations. Under the separation between buildings will be governed conditions of these requirements, some contact by the requirements for EQ-I as prescribed in between buildings is acceptable if it can be shown paragraph 4-3e(7) (b). If contact is to be avoided 4-11 TM S-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 for EQ-II, the minimum separation between bined with the gravity forces (P) will be buildings will be governed by the combined max- investigated. imum displacements of the adjacent buildings (3) Structural materials and details. due to the seismic actions of EQ-I1. The maxi- Structural elements and connections will con- mum story displacements, at respective loca- form to the requirements of the Basic Design tions, may be combined by the square-root-of- Manual and will be evaluated for their ability the-sum-of-the-squares to determine the mini- to sustain the implied ductility demands of the mum separation. post-yield analysis procedures. (c) P-delta effects. The secondary effects of the lateral displacements (delta) com-

)

4-12 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A CHAPTER 5 STRUCTURAL DESIGN PROCEDURE

5-1. Introduction. tions of severe earthquakes is not directly This chapter describes general procedures for proportional to the equivalent design seismic the design and analysis of buildings to resist the forces or to the amplitudes of the peak ground earthquake lateral forces specified in chapter 4, accelerations of earthquakes. The design Criteria for Structural Analysis. Guidelines are strength of a structure is governed by a com- provided for a dynamic analysis approach to bination of lateral-force criteria (e.g., wind and seismic design of buildings. Guidelines for con- earthquake) and gravity load criteria (e.g., dead ventional static force procedures are provided and live loads). Some of the excess capacity built in the Basic Design Manual, chapter 4. into the gravity load design will be available to resist lateral forces. In addition, if the structure 5-2. Preliminary design considerations. has ductility and/or redundancy, it will respond a. Design response spectra. Before proceed- to excessive lateral forces in an inelastic man- ing with the design of a building by means of a ner thay may result in demands that are less dynamic analysis approach, geotechnical data severe than the demands applied to a fully elas- will be required to determine the design ground tic structure. This can be explained by the de- motion and foundation design criteria. The crease in stiffness due to inelastic action, which methodology for specifying the ground motion lengthens the effective period of vibration, and and site-specific response spectra for a partic- by the increase in energy absorption and the ular site is prescribed in chapter 3, Specification reduction in response amplification due to in- of Ground Motion. Unless otherwise specified by elastic action. These effects are represented by approval authority (para 1-ic), the following a longer structural period together with a larger criteria will apply: value for effective damping. These relationships (1) EQ-I response spectrum. The re- are illustrated in figures 5-1, 5-2, and 5-3. sponse spectrum representing EQ-I has a 50- d. Foundationcapacities to resistdemands of percent probability of being exceeded in 50 years. earthquakes. The geotechnical and/or soils (2) EQ-II response spectrum. The re- foundation consultant will establish criteria sponse spectrum representing EQ-I1 has a 10 based on ultimate capacities of the soils to resist percent probability of being exceeded in 100 years. the effects of short-term seismic loading con- (3) Damping. Damping values will be as ditions in combination with the long-term grav- indicated in table 4-1. ity loading. For load combinations with EQ-I, b. Selection of structural system. The pos- the soil capacities must be sufficient to provide sibility of structural damage and collapse can resistance essentially within the elastic limits be minimized by effective structural planning. of the soil. A factor of safety of 2 on the ultimate For general guidelines to the selection of the capacity is recommended. For load combina- structural system, refer to the Basic Design tions with EQ-II, the soil capacity must be suf- Manual, paragraph 2-8. The objectives of effec- ficient to prevent sudden failure of the soil. Some tive structural planning are to maintain sym- minor differential movement due to soil defor- metry, minimize building torsion, provide direct mation is acceptable under the conditions of vertical paths for lateral forces, and to provide EQ-II. proper foundations. A continuous load path, or paths, with adequate strength and stiffness that 5-3. General design procedures. will transfer all forces from the point of appli- The scope of this chapter covers design proce- cation to the final point of resistance must be dures for three general classifications of struc- provided. The foundations must be designed to tures: essential facilities; high-risk; and all other accommodate the forces developed or the mo- buildings. A general flow chart is shown in table ments imparted to the building by the design 5-1. Outlines of the general procedures for each ground motions. Additional discussions on tech- of the three classifications are presented in ta- niques of seismic design, path of forces, and de- bles 5-la, 5-lb, and 5-ic, respectively. sign of foundations are covered by the Basic a. Initial trial design. In many cases, a build- Design Manual, paragraphs 2-9, 4-4d, and 4-8. ing designed in accordance with the static force c. Capacities of buildings to resist demands procedure of the Basic Design Manual will sat- of earthquakes. The ability of structures to re- isfy the requirements of the dynamic analysis sist the excessive accelerations and deforma- procedure of this manual with little or no mod- 5-1 TM 5-809-10-1/NAVFAC P-355.1 /AFM 88-3, Chapter 13, Section A 27 February 1986

Crmvitv/Seismle-Load Relsatonshlps. Because ot the relationshipe between gravity losds (dead load L) a live load CLL)) Ad lateral forces (Ielamic loads), the stresses in the structural elements are not dirctly proportional to the seismic forces. For eample, If the lateral forces are tripled. the combined stresses In the structuril elementU will not neermurily triple beesuae the dead load and live load stresses will rtmain essentially eonstnt. To Illustrate thesc relatIonshlps, sample caleulations, whieh sisume a boom with negative bending moments at the Pzpports of -100 k-tt, are zhown below:

1. Neptive seismic bendirg moments at vA of beam.

a. Design Bending Moments DL * LL v -100 lk-ft Selmle a - so 1-r, Total Design Moment i-W5i

b. Triple Seismic Forces DL . LL a -10D k-ft 1eismie a -150 k-ft Total Beam Bending Moment * 2-15 6 U e. Ratio of Triple Seismic Forces to Design For"s (b I * 250 a 10 1.17 c -3.00

2. Positive seismic bending moments at end of beam. a. Design Bending Moments (consider DL moment only): 0.3 DL a 0.9 (-70) a -GI k-ft Seismic * 50 k-ft Net Moment (no load reversal) a -13 k-Jt

b. Triple Seismic Pos 0.9 DL a - 13 k-ft Seismic * 150 k-ft Net Moment (Reverses to a* 7 rit positive bending moment) e. Ratio of Triple Seismic Forces to Design Foreem Case e: No positive bending moment Cas be 17 k-ft positive bending moment Ot7* O * m (infinity) 3. Axial forces on a column. aL Design Axial Fores 0.3 DL ) Seismic Axial Force Therefore, no tension In column b. Triple Seismic Forem. 0.9 DL c Seismic Arial Force Therefore, there Is tension in column c. Ratio of Triple Seismic Forces to Design Forces, SImIL to Sample 2, Is equal to Wntinty.

Reprinted from "An Investigation of the Correlation Between Earthquake Ground Motion and Building Performance," ATC-1o, U.S. Geological survey, 1982.

Figure 5-1. Gravity/seismicload relationships.

5-2 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Dynamic Structural Characteritlics. Becou"e of the rolationrhipc hetwPi vnemic characteristics of structures and the dynamicr prooertips of xeietni' ground motion, the effective forces applied to the structure are not dirprck- proportional to the peak ground acceleration of the earthqumkp. ThN- peindt of vibration of a building, as well as the effective *apmiring of the qtruetiir, 4 will varv with the amplitude of motion. For exinaplo. a h illdinig will ru.qp.fr1'it a certain period and damping value for a moderate earthquake in an OlN-Oi' manner. For an earthquake two times larger (e.g.. rtesr--nse "etrn with twi- the spectral accelerationsl, some structural elementr mav ex'eed their el-1lir limits, the period of vibration will be slightly longer and the dainiFIg will increase; thus, the spectral acceleration for the larger earthquake will be le- than twice the value of the moderate earthquake. These rlpltionsbipc are Illustrated in sample response spectra shown in Figure 1 and are Nummeriz-1 below: 1. The sample building responds elastically at Point A ISI 0.8 g), for earthquake E-Q-1 at 5SI damping (Peak ground acceleration, AG, Is 0.3 EL). 2. If the building remained elastic for AG equal 0.6 E. the building would respond at Point B (Sa = 1.6 E) for earthquake E-Q-2. But the building does not remain elastic because some structural elements yield.

3. The fundamental building period shifts from 0.5 seconds to en effective value of 0.7 seconds due to stiffness degradation. Due to inelastic response and energy absorption, the effective damping Increases from 5% to 10%. Thus, the sample building has a peak response at Point C (Ss = 1.1) for earthquake E-Q-2. 4. Therefore, the peak response of the building is 40% greater (1.1 E vs. 0.8 E) for an earthquake ground acceleration twice as large (0.6 E vs. 0.3 g). Structures with degrading stiffnesses are extremely sensitive to the time factor In earthquake behavior. Reduction In stiffness occurs in reinforced concrete when cracks, which open during an inelastic loading cycle, do not close on the reverse cycle due to elongation of the tension steel. This reduces the effective cross section and the corresponding stiffness. As a result, the fundamental period of vibration will tend to lengthen and the damping will tend to increase, which will increase dissipation of the seismic input. If the period elongation and the damping increase can reduce the seismic input at a faster rate than the reduction in stiffness, the structure will survive. It will simplv readjust itself so that It is oscillating in an elastic manner about a new equilibriurr position having a reduced stiffness and an increased damping. If geometrical effects of the vertical axial loads also contribute to the reduction in lateral stiffness, however, the stiffness may reduce faster than the seismic input. Ir this case, structural failure may result. In either case, the duration of strong ground shaking is the critical factor.

Reprinted from "An Investigation of the Correlation Between Earthquake Ground Motion and Building Performance," ATC-10, U.S. Geological Survey, 1982.

Figure 5-2. Dynamic structuralcharacteristics. TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Sample response spectra for figure 5-2

%SI EQ-II, 59 damped, AG = 0.60 %a U EQ-II, 10% damped, AG = 0.60

94 EQ-I, 5% damped, AG = 0.30 '41

'a8 0. ,5 'a .)

0 0 0.5 1.0 1.5 2.0 Period, T (see)

Reprinted from "An Investigation of the Correlation Between Earthquake Ground Motion and Building Performance," ATC-10, U.S. Geological Survey, 1982.

Figure 5-3. Nonproportionalrelationship between peak ground accelerationand spectral acceleration.

5-4 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A Table 51. Seismic design procedures.

Irregular Buildings (8DM para 3-3(E)3

I * 1.5 1I 1.25

1 Minimum

Minimum

Aon

EQ-I Elastic Response Basic Design _ Manual Pro- (pares 4-3 and cedure Modified 5-4) b) (pares 4-2d(3)(a) and 5-3d(l))

"Option" requires approval of cognizant agency (see para 1-lb))

Note: All paragraph references are to this document unless indicated as "BDM for Basic Design Manual U.S. Army Corps of Engineers

5-5 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Table 5-la. Seismic design of essential facilities.

Requirements Procedure

Classification of building 4-la General requirements 4-2a Dynamic nalysis procedure 4-2d (1) 5-3b,

EQ- I Select response spectrum 4-3b Select structural system 4-2a(J) F5-2hi Initial trial design 5- 3aI Modal analysis 4-3c 5-4 a, ,b, c d Minimum lateral forces 4-3d 5-4 1 Drift limits 4-3c(7) 5-41f Load combinations 4-3e(2),(3) 5-4e(I) Structural components 4-3e(l),4-3f S-4 e Orthogonal, torsion, overturning 4-3e(4),(5),(6) 5-4h, i Foundations 4-2a(l) 5-2d ,5-41i Nonstructural 4-2e,6-2 6-3, 5- 4 g

EQ-Il Select response spectrum 4-4b 3-6,3-8,5-2a(2) Analysis procedures: Method 1 4-4c 5-5a Method 2 4-4d Load combinations 4-4e(l) S-5a(3) Drift limitations and P-6 effects 4-4e(2) S-4f,5-5b(2) (h), S-5c,S-5d Structural components 4-4e(3) S-Sa(4) ,5-5b(2) Foundations 4-2a(l) S-2d

US Army Corps of Engineers

5-6 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Table 5-lb. Seismic design of high-risk buildings. Requirements Procedure

Classification of building 4-lb General requirements 4-2a Dynamic analysis procedure 4-2d (2) S-3

Two Level Approach 4-2d(2) (a)

Same as essential facilities (Table 5-la) except the following:

EQ-I Response spectrur 85% of EQ-I, 4-2d(2) (a) Drift limits Increase 40%, 4-3e(7)

EQ-II Drift limits Increase 50%, 4-4e(2) Inelastic demand ratio High-risk column of table 4-2

Single Level Design

Same as Basic Design Manual Procedure with modified seismic force distribution and Single level design for EQ-I with minimum story shear requirements for other buildings (Table 5-lc). Minimum lateral forces governed by Basic Design Manual will be 25% higher because the I-coefficient equals 1.25.

US Army Corps of Engineers

5-7 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Table 5-ic. Seismic design for other buildings. Requirements Pro:edure

Classification of building 4-ic General requirements 4-2a Dynamic analysis procedure 4-2d(3)

Basic Design Manual Procedure with modified seismic force distribution General 4-2d(3)(a) 5-3d Response spectrum EQ-I 4-3b Select structural system Basic Design Manual Initial design Basic Design Manual Modal analysis 4-3c 5-3d(l) Minimum lateral force Basic Design Manual Normalize modal analysis 4-2d(3)(a) 5-3d(l) Final design Basic Design Manual

Single level design for EQ-I with minimum story shear requirements General 4-2d(3)(b) 5-3d(2) Response spectrum EQ-I 4-3b Select structural system Basic Design Manual Initial trial design Basic Design Manual 5-3a Modal analysis 4-3c Minimum lateral force 4-2d(3)(b) 5-3d(2) Drift limits 4-3e(7) Load combinations 4-3e(2) (3) 9 Structural components 4-3e(l),4-3f Orthogonal, torsion, overturning 4-3e(4) , (5) (6) Foundations 4-2a(l) 5-2d,5-4h

Two level approach General 4-2d(.1) (c) ; -.')d (33 )

Same as essential facilities except for the following:

EQ- I Response spectrum 709j of F+-1 4-2d(3) 5- 3d (3) (~i) Drift limits Increased 40' 4-3c(7) S-3 (LI) (3) (b)

EQ-II Response spectrum 4-4b - 2 a(2) Drift limits Increased 50% 5-4f,5-r!li(2) (hi) 4-4e(2) 5-5c,5-5d Inelastic demand ratio Table 4-2 5.-Sa(4)

US Arm) Corps of Engineers

5-8 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A ifications. The primary purpose of the proce- (1) Code comparison concept. dures of this manual is to provide a more rational (a) Compare the EQ-I design spectrum approach to the fulfillment of the intent of the with the curve representing the static base shear Basic Design Manual. The initial selection of trial coefficients ZICS. For example, the EQ-I spec- structural member sizes can be made in a man- trum may be similar to the 5-percent curve in ner similar to that of conventional static design figure 2-8. The ZICS curve may be similar to the procedures, as outlined in the Basic Design T. = 1.0 curve in Basic Design Manual figure Manual. Following is a suggested procedure for 4-3, with the C x S values multiplied by 1.5 to the initial design. An alternate procedure is out- account for Z = 1.0 and I = 1.5. An example of lined in paragraph (2) below. these two curves is shown in figure 5-4.

,,,- Assume peak extends to ,/ T = 0 for 1st mode

Use for higher modes only

0.5 I,- EQ-I, 5% damped design response spectrum from Figure 2-8

0.14 I S = 6 a 0.3 g I I I 0.3 T = 0.7 sec-,

C-1 LA

0 t 0.2

0.1 Base coefficients ZICS for Z =1.0, I = 1.5, and T = 1.0 sec (from Basic Design Manual, Fig. 4-3 and Table 4-3)

0 0 1.0 2.0 3.0

T (PERIOD), sec

US Army' Corps of Engineers

Figure5-4. Sample EQ-I spectrum and ZICS curve. 5-9 -

TM 5-809-10-1 /NAVFAC P-355.1 /AFM 88-3, Chapter 13, Section A 27 February 1986 (b) Estimate the period of the funda- ing, criteria established for other buildings at mental mode of vibration of the structure by or near the site, and the decision of the approval methods described in the Basic Design Manual. authority. For example, the building may be part For example, the period of a 7-story frame struc- of a large hospital complex that has essential ~- / ture may be estimated at O.IN = 0.7 seconds, as facilities as well as high-risk buildings. The de- illustrated in figure 5-4. signer will have site ground motion specification (c) Compare value of S. of EQ-I with ZICS data available and will have had to develop dy- for the estimated building period. namic two-level approach procedures for the es- 1. If Sa is roughly 2 times ZICS or less, sential facilities. Therefore, the premium for the static design procedure will probably result designing the high-risk building in accordance in a reasonable initial design. The factor of 2 is with the two-level approach may be insignifi- based on a combination of load factors, partic- cant. In another example, the building may have ipation factors, and underestimation of the unavoidable irregularities that generate con- building period. cern about the ability of the structure to sat- 2. If Sa is substantially greater than 2 isfactorily sustain a major earthquake without times ZICS (e.g., 3 to 4 times), the initial static serious damage. Thus, a two-level approach may design should be based on a porportionately be justifiable. In a third case, the building may higher value of ZICS. be the only building at a site where ground mo- (2) An alternate procedure is to estimate a tion specification data are not available and yield level base shear coefficient directly from where no other special conditions exist that the EQ-I spectrum. would justify the additional effort of a two-level (a) Estimate the fundamental period of approach. Therefore, a single-level design pro- vibration. cedure is adequate. (b) Determine the value of Sa from the (1) Two-level approach. The procedure is EQ-I response spectrum. the same as used for essential structures with (c) Estimate the fundamental base shear the following exceptions: participation factor, a (para 4-3c(1) (d)), from (a) The EQ-I response spectrum is re- the following: duced by 15 percent (para 4-2d(2)(a)). The ef- 5 stories: a = 0.80 fect of this reduction is that the structure will ) 4 stories: a = 0.83 remain elastic for ground motion less than that 3 stories: a = 0.86 specified by EQ-I or, conversely, that some dam- 2 stories: a = 0.90 age will be accepted for the EQ-I ground motion. 1 story: a = 1.00 (b) The drift limits for EQ-I (0.007) and (d) Estimate the base shear coefficient by EQ-[I (0.015) are less severe (paras4-3e(7) and multiplying Sa by a. 4-4e(2)). (e) Use the base shear coefficient to es- (c) The limits on inelastic demand ratios timate lateral forces on the building in the same are less severe (table 4-2). manner used in the static design procedure. Use (2) Single-level design. The procedures are these forces initially to size the structural mem- the same as used for all other buildings in par- bers; however, the capacities will be on the basis agraphs 4-2d(3) (a) and (b) with the exception of yield strength in lieu of allowable stresses. that the minimum values will be calculated on (f) If S. is not significantly greater than the basis of I = 1.25. The procedures are de- ZICS (e.g., 50 percent greater), refer to para- scribed in paragraphs d(l) and d(2) below. graphs 4-3d and 54j for minimum lateral force d. Dynamic analysis procedure for all other requirements. buildings. Three alternative procedures are b. Dynamic analysis procedure for critical and prescribed in paragraph 4-2d(3): Basic Design essential buildings. Critical and essential fa- Manual criteria with modified seismic force dis- cilities will be designed to resist two levels of tribution; single-level design with minimum story earthquake motion as prescribed in paragraph shear requirements; and two-level approach. The 4-2d(l). The procedure is described in para- choice will depend on the data available and on graphs 5-4 and 5.-. particular requirements of the facility. Para- c. Dynamic analysis procedure for high-risk graphs 4-2d(3) (a) and (b) are both single-level buildings. High-risk buildings will be designed design procedures. These procedures will gen- in accordance with either a two-level approach erally be sufficient for most buildings. Para- or a single-level design, as prescribed in paragraph 4-2d(3) (c) is a two-level approach. This graph 4-2d(2). The choice will generally depend procedure may be required by the approval au- on the seismic severity of the site, type of build- thority-for buildings that have unavoidable highly 5-10 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1IAFM 88-3, Chapter 13, Section A irregular configurations or other unusual con- ues will be used for the design of elements of ditions. structures. (1) Basic Design Manual criteria with mod- (g) Use the interstory drifts to determine ified seismic force distribution (para 4-2d(3) (a)) . conformance with the Basic Design Manual drift This procedure uses the modal analysis method provisions. to determine the distribution of lateral forces (2) Single-level design with minimum story along the height of the structure in liew of the shear requirements. This procedure provides for distribution determined from Basic Design a single-level modal analysis of the structure to Manual equations 3-6 and 3-7. For buildings with withstand the actions of EQ-I in conformance large differences in lateral resistance or stiff- with paragraph 4-3. However, a lower limit equal ness between adjacent stories, the differences to 1.5 times the Basic Design Manual is specified. between the two methods can be significant. The The 1.5 value is used to account for the differ- modal analysis procedure requires a response ences between working stress or load factor cri- spectrum. The EQ-I response spectrum is pre- teria used in the Basic Design Manual and the scribed. However, if data are not available for yield strength criteria used for EQ-1. This pro- EQ-I, a standardized shape for a response spec- cedure can result in significantly larger forces trum may be substituted (e.g., an ATC 3-06 spec- than the procedure described in paragraph (1) trum). The amplitude of the peak ground above, if the site specific earthquake, EQ-I, so acceleration is not significant because the re- indicates. In some cases, the analysis for EQ-I sults are later normalized to equal the base shear may result in lower force levels than those ob- determined in the Basic Design Manual. There- tained from paragraph (1) above. However, the fore, this procedure has the advantage of not lower limit of 1.5 times the Basic Design Manual requiring site specific earthquake data. A sum- will generally keep the capacity of the resulting mary of the procedure follows: structure from being less than that of the struc- (a) Determine the story shears, story ture designed in accordance with paragraph (1) overturning moments, story accelerations, story above. A summary of the procedure follows: displacements, and interstory drifts by means (a) Complete the modal analysis pre- of a response spectrum modal analysis in ac- scribed in paragraph 4-3 for EQ-I. List all the cordance with paragraph 4-3. This includes the combined modal story shears. total lateral force at the base, VT = \/;Z: If (b) Determine all the story shears as pre- data to develop the EQ-I response spectrum are scribed in the Basic Design Manual. not available, the equations in paragraph 3-8c (c) If any story shear determined in par- may be used to determine values for S.. Any agraph (a) is not at least 1.5 times the corre- single value may be used for A. and A, (e.g., Aa sponding story shear listed in paragraph (b), = A, = 0.20), because the base shear normali- increase all values determined by modal analysis zation process prescribed in paragraph (d) be- proportionately to satisfy this requirement. For low will equalize the results. The soil profile example, the modal analysis gives a third-story coefficient, Si, will be determined from table shear equal to 14 kips, and the Basic Design 3-6 in conformance with the decriptions in table Manual method gives a third-story shear equal 3-5. to 10 kips. The ratio is 1.4, which is less than 1.5. (b) Determine the total lateral force, Therefore, multiply all values in the modal anal- V = ZIKCSW, in accordance with the Basic De- ysis by 1.07 (1.5 - 1.4 = 1.07). sign Manual. (d) Use the revised values to complete the (c) Calculate the ratio, Rv, of the Basic design of the building in accordance with the Design Manual base shear to the modal analysis provision of this manual to resist EQ-I. The base shear: structure need not be evaluated for EQ-IL. (3) Two-level approach. This procedure is Rv = ZIKCSW/VlV. (eq 5-1i) the same as that used for essential facilities (ex- (d) Multiply all the values in paragraph ceptions in paras (a), (b), and (c), below) and (a), above, by Rv. is substantially more complex than the proce- (e) Use the resulting story shears and dures in paragraphs (1) and (2) above, it will overturning moments to design the building in only be used under special conditions, as di- accordance with the provisions of the Basic De- rected by the approval authority, such as for sign Manual: highly irregular or unusual buildings. The dis- (f) Use the story accelerations to com- cussion in paragraph 5-3c on the use of the two- pare with the coefficients ZICp of Basic Design level approach for high-risk buildings also ap- Manual equation 3-8. The larger of the two val- plies. The procedure for the two-level approach S-11 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 is described in paragraphs 5-4 and 5-5. Excep- program will generally be more efficient and will tions are listed below: generally give more accurate results, the single- (a) The EQ-I response spectrum is re- mode analysis can be done by hand calculations. duced by 30 percent (para 4-2d(3) (c)). The ef- (a) Estimate the fundamental period of fect of this reduction is similar to that indicated vibration (e.g., Basic Design Manual, equations above for high-risk facilities (para 5-3c( 1) (a)). 3-3A or 3-3B), assume a straightline mode shape (b) The drift limits for EQ-I (0.007) and and calculate or estimate the story weight. EQ-I1 (0.015) are less severe (para 4-3e(7) and (b) Calculate the modal participation 4-4e(2)). factors PF. and a. Approximate the spectral ac- (c) The limits on inelastic demand ratios celeration, S., for the estimated period using the are less severe (table 4-2). EQ-I response spectrum. (c) Calculate the story forces, F. (refer 5-4. Designing for EQ-I. to appendix E, design example E-1, for the pro- The structure will be designed to resist the forces cedure). of EQ-I within the elastic range of the capacity (d) Calculate the deflected shape of the of the lateral-force-resisting system. An initial structure. This can be done by hand calculations trial design is developed in accordance with par- (though somewhat difficult and time-consum- agraph 5-3a. The initial design is then checked ing) or with the aid of a computer program. for conformance to the criteria by means of a (e) Use the calculated deflected shape as modal analysis for the EQ-I response spectrum. a new estimate for the mode shape and repeat a. Modal analysis procedure. Periods, mode paragraphs (b) and (c) above. shapes, and participation factors are required, (f) If the story forces of paragraph (e) in conjunction with the design response spec- compare favorably with the original values of trum, to perform a dynamic analysis. The ac- paragraph (c) (e.g., within about 10 percent), curacy of these factors and the degree of assume the deflected shape of paragraph (d) to sophistication required in the analysis is de- be acceptable. If not, repeat paragraph (d) to pendent on the size and complexity of the build- calculate the deflected shape for the revised story- ing. forces. (1) Single-story building. Unless the (g) Calculate the period of vibration building is unusual or irregular in plan, the modal using the Basic Design Manual equation 3-3. A ). analysis procedure essentially becomes equiva- quicker method is by means of the following lent to a static design procedure. equation, using the forces and displacements (a) The period of vibration will generally calculated above: be in the range of 0.1 to 0.2 seconds, thus placing it at the peak of the response spectrum for a T = 2r N/8nw./Fng (eq 5-2) maximum value of Sa. Note that the peak of the response spectrum is assumed to extend back where 8, wn, and F, are the displacement, weight, to T = 0 for the fundamental mode as noted in and force at the roof. This equation can be de- figure 5-4. In general, even a very rigid structure rived from equations 4-3 and 4-5. with a short natural period of vibration will re- (h) If the period of vibration calculated spond at a slightly longer period due to soil- in paragraph (g) above is substantially differ- structure interaction. ent than the value assumed in paragraph (a) (b) For a single-story building, the base above, repeat paragraph (b) and adjust the forces shear participation factor will be equal to unity and displacements in proportion to the new value (e.g., a = 1.0). Therefore, the base shear coef- for S.. ficient will be equal to the spectral acceleration, (3) Moderate-risebuildingsfrom 5 to about Sa. 15 stories. For buildings over 5 stories, some (c) The total lateral force on the build- of the effects of higher modes of vibration may ing, for each direction of motion, will be equal be significant. In lieu of a detailed analysis, the to the spectral acceleration times the weight of dynamic characteristics can be approximated. the building (V = Sa x W) in accordance with Table 5-2 shows the general modal relationships equation 4-4. for a fairly uniform 7-story reinforced concrete (2) Low-rise buildings up to about 5 sto- frame building. For a 14-story building, a modal ries. Unless the building is unusual or irreg- analysis could be approximated as follows: ular in elevation or plan, the modal analysis can (a) Estimate the fundamental period of ) generally be limited to the fundamental mode vibration (e.g., Basic Design Manual, equations of vibration. Although the use of a computer 3-3A or 3-3B). 5-12 27 February 1986 TM 5-809-10-1/NAYFAC P-355.1/AFM 88-3, Chapter 13, Section A (b) Approximate periods for the second E-1. The results for the 7-story building are through fifth modes of vibration using the ra- summarized in table 5-3 and are illustrated tios shown in table 5-2 (e.g., second mode period graphically in figure 2-10. equals 0.327 time the fundamental mode pe- (g) Calculate the deflected shape of the riod). building separately for each mode of vibration. (c) Approximate the mode shapes by This will generally require the use of a com- using the shapes shown in table 5-2 and inter- puter. Compare the deflected shapes to the mode polating for the taller structure (e.g., for the shapes approximated in paragraph (c), above. second mode, assume 1.00 for the roof and 0.550 (Note: some computer programs will perform for the 13th story. Estimate the 14th story at paragraphs (a) through (g), above, directly.) If 0.775). the shapes are similar, continue with the anal- (d) The participation factors can be taken ysis. If there are significant differences in mode directly from table 5-2 or new values can be cal- shapes, a modification of paragraphs (d) through culated from the mode shape by using equations (g), above, may be required. 4-1 and 4-2. (h) Calculate the periods of vibration (e) Determine the spectral accelerations, using the Basic Design Manual equation 3-3. An S., for each modal period from the response alternate method is to use equations 4-3 and spectrum. 4-5 and solve for T. for each mode at several (f) Calculate story forces for each of the story levels as follows: modes as shown in appendix E, design example T. = 2,r Vliiw ./F,,g (eq 5-3) Table 5-2. Generalmodal relationships.

Mode 1 2 3 4 5 l Period (seconds) 0.880 0.288 0.164 0.106 0.073

! Ratio of Period to !1st Mode Period 1.000 0.327 0.186 0.121 0.083

Participation Factor 12 at Roof 1.31 _ _-0.47 0.24 -_.__ 0.05

Base Shear I 0.828 Participation 0.120 0.038 0.010 0.0c)O i .9 9 1 i I I

.1: I Roo f I .000 1.000 I.000 I .000 I .O(. 1) I 1 Mode 7 0.938 0.550 -0.059 -0.8tr2 -1.7J 141, I Shape 6 0.839 -0.056 -0.904 -1 .08) (. 1' h i at 5 0.703 -0.631 -0.971 0.526 I.6,711 i Story 4 0.535 -0.961 -0.034 1.259 l-I.0f %PI Levels 3 0.351 -0.933 0.883 -I1.1i %Q I (normalized) 2 0.188 -0.625 0.990 -1.1 5" I.3 I 0 S i 0 0 0 0 0

II I f ______- .

US Army Corps of Engineers

5-13 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 Table 5-3. Seven-story building-transversedirection-summary of modal analysis.

Story Forces (kps) Shears (kips) OTH (k-ft)

Vt Levelkips I 2 3 SRSS 1 2 3 SRSS l 2 3 SRSS

Roof 1410 508 -330 170 629 503 -330 170 629 0 0 0 0 7 1160 494 -188 -10 525 1002 -518 160 1139 4420 -287! 1, .79 5474 6 1460 443 19 -166 173 1445 -499 -6 1529 13137 -7378 2871 15338 5 1460 371 216 -163 159 1B16 -283 -169 1846* 25709 -11719 2819 28394 X 1460 282 329 -6 433 2098 46 -175 2106 41508 -1I.181 1349 43884 3 1460 185 319 156 400 2283 365 -19 2312 59761 -13781 -174 61330 2 1830 125 267 219 367 2408 632 200 2498 79623 -10605 -339 80327 Groun 0 0 0 0 112131 -2073 2361 112175

Story Acceleration_ D is lacent (ft) Inters tory XDriftuft)| 1 2 3 SRSS 1 2 3 SRSS I 2 3 SRSS Aa/hs{

Roof .360 -. 234 .121 .X*6 .228 -.016 .003 .229 _014 .007 .003 .016 .0018 7 .338 -. 129 -.007 .362 .214 -.009 .000 .211 .022 .010 .003 .021. .0028 6 .303 .013 -.114 .324 .192 .001 -.003 .192 .031 .009 .000 .032 .0037 5 .254 .148 -. 112 .315 .161 .010 -.003 .16i .039 .005 .003 .039 .0045 1 .193 .225 -.004 .297 .122 .015 .000 .123 .042 .000 .002 .042 .0048 3 .127 .219 .107 .275 .080 .015 .002 .081 .037 .005 .001 .037 .0043 2 .068 .1X6 .120 .201 .043 .010 .003 .044 .043 .010 .003 .044 .0033 Ground 0 0 0 0 0 0 0 0 9 US Army Corps of Engineers

If the mode shapes are reasonably accurate, the (4) High-rise buildings. As buildings get calculated value of Tm will be the same at each taller, the higher modes of vibration become more story. significant, relative to the fundamental modes (i) If the calculated periods of vibration (refer to para 2-5c and figures 2-9 and 2-10 for are substantially different than the values as- examples). These buildings generally require the sumed in paragraphs (a) and (b), above, repeat use of computer programs that can calculate the paragraph (e) and adjust the modal forces and dynamic characteristics (e.g., periods, mode displacements in proportion to the new values shapes, and participation factors), as well as the of S.. member stresses and story displacements. (j) Compare the responses of the higher (5) Irregular buildings. Buildings that modes of vibration to the actions of the fun- have vertical discontinuities, that are irregular damental modes (e.g., refer to fig 2-10 and de- in plan, that have large horizontal eccentricities sign example E-1). This includes story shears, (center of mass not coincident with center of story accelerations (i.e., story force divided by rigidity), or have other irregularities will gen- story weight), story overturning moments, and erally require the aid of computer programs to interstory displacements. If all the higher mode determine the dynamic characteristics, member responses are small relative to the fundamental stresses, and story displacements. When hori- mode, they can generally be omitted from the zontal eccentricities exist, the analysis must be analysis. If in no case the square-root-of-the- in three dimensions to account for the twisting sum-of-the-squares (SRSS) of all the modes is deformations and the lateral deformations nor- less than 10 percent greater than the funda- mal to the direction of the seismic forces. Refer mental mode, it can be assumed that the higher to paragraph 5-4d, below, for use of three-di- modes are negligible in the overall design. mensional computer programs. 5-14 27 February 1986 TM 5-809-10-1 /NAVFAC P-355. 1/AFM 88-3, Chapter 13, Section A b. Mathematical modeling of structuralcom- (4)The effects of structural elements that ponents. The results of a lateral-force analysis are not included in the lateral-force-resisting can be very sensitive to the assumptions made system. This may include flat-slab and column for the stiffness of the structural elements when systems and structural steel frames with stand- constructing a mathematical model of the struc- ard connections. The effects of these elements ture. As the stiffness is overestimated, the pe- on the stiffness of a building with shear walls riod of vibration shortens and the displacements or braced frames may properly be ignored, but reduce. However, a shorter period may possibly they may have a significant effect on the stiff- attract higher forces. When the stiffness is ness of a building with a moment frame lateral- underestimated, periods lengthen, lateral dis- force-resisting system. In the latter case, the placements increase, and lateral forces may be moment frames will be designed to resist 100% reduced. When the relative rigidities of various of the lateral forces, but the modeled stiffness lateral-force-resisting elements are not accu- of the frames will be adjusted to reflect the ad- rately utilized, there can be a great amount of ditional stiffness of the above elements, includ- uncertainty in the torsional characteristics of ing any torsional effects due to asymmetry in the structure. The effects of nonstructural ele- the location of elements. ments, as well as structural elements not part (5)The effects of relatively rigid nonstruc- of the lateral-force-resistant system, can have a tural elements, such as masonary partitions, will significant effect on the response of the overall be evaluated. If the stiffness of these elements structure to earthquake ground motion. There- is significant as compared to the stiffness of the fore, it is important to account for possible in- assumed lateral-force-resisting system, the ele- accuracies in the mathematical model. When ments will be designed and reinforced as shear there are uncertainties, an attempt should be walls or will be isolated from the structural sys- made to envelope the possibilities to assure good tem by means of expansion joints at the sides performance of the structure in case of an and top of the element. earthquake. The stiffness characteristics may (6)Evaluate the effects of assumptions for vary with amplitude of lateral motion, thus the modeling shear walls of various cross-sections. model used for a code design level analysis may For example, the relative stiffnesses of an L- vary from the model that represents the yield shaped wall and a wall that consists of a single level capacity or the ultimate post-yield capac- plane. Also, the relative stiffness of a shear wall ity. For an elastic analysis, the following factors system and a moment frame system. should be considered: c. Two-dimensional computer programs. (1) Gross concrete section properties are The designer must be familiar with all of the considered appropriate for modeling the stiff- features and limitations of computer programs ness of reinforced concrete members. used for the design and analysis of buildings. A (2) The effects of column widths and beam two-dimensional computer program essentially depths on the rigidity of frames should be eval- places all the lateral-force-resisting structural uated. This is particularly important for con- frames and shear walls within a single vertical crete frames or for steel frames with relatively plane and analyzes for lateral motion within that deep members and short spans or low story vertical plane. In a sense, each of the lateral- heights. force-resisting column lines of the building are (3)The effects of the floor slab system act- linked end-to-end. The two-dimensional analy- ing compositely with the frame beams or gir- sis does not allow for any rotation about a ver- ders. Although the composite action may have tical axis of the building (i.e., ignores horizontal an insignificant effect in resisting negative mo- torsion) and does not allow lateral sidesway ments, it provides a significant contribution to normal to the direction of the applied force. The the effective beam moment of inertia for posi- two-dimensional computer programs are appli- tive moments and increases the stiffness of the cable to buildings that are generally symmetr- beams acting as members of a rigid frame. In ical in plan and are not subject to torsional most cases, the beams will be modeled as pris- deformation. matic members and engineering judgement will (1) Features and limitations. There are a be required to determine an effective portion of variety of two-dimensional computer programs, the floor system to be modeled compositely with each having certain features and limitations, the beams. This composite action is used in the such as the following: model of calculate the dynamic characteristics, (a) Dynamic characteristics. Some com- but should be reevaluated for member design to puter programs will calculate member forces and resist negative moments. lateral deformations, but do not calculate the 5-15 TM S-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 periods or mode shapes of the structure. These of locations should always be made to assure programs can be used for low- to moderate-rise that static equilibrium is maintained. These buildings where only the fundamental mode of checks are made not only to confirm the validitx vibration is required. The fundamental period of the computer program, but they also alert the,,__,/ and mode shape can be calculated and the ef- designer to possible irregularities or to the pos- ) fects of higher modes can be approximated by sibility of data input errors. procedures outlined in paragraph 5-4a. How- (4) Accidential torsion. The two-dimen- ever, computer programs are available that will sional computer analyses do not account for tor- calculate periods and mode shapes for all the sional motion due to horizontal eccentricities. modes of vibration. However, the effects of horizontal eccentricities (b) Axial, shear, and flexural deforma- or the requirement for accidential torsion can tions. Some computer programs are limited on be approximated by hand calculations in con- the degrees of element deformations. Beams are junction with the results obtained from the generally considered as flexural elements. Some computer analysis. The horizontal torsional mo- computer programs also account for shear de- ment can be calculated from the product of the formation. Shear and flexural deformations are story shear and the assumed eccentricity. The generally accounted for in column elements, but torsional moment can then be distributed to the not all programs account for axial deformation. lateral-force-resisting elements in proportion to Axial column deformation can be significant in the product of their relative rigidities and dis- high-rise buildings however, caution must be used tances from the center of rotation (Kd) divided when applied to gravity loads because of the se- by the torsional moment of inertia (XKd 2 ). The quence of construction. Shear walls are gener- forces obtained from the computer can then be ally analyzed for shear and flexural deformations. proportioned upward to account for the addi- (2) Number of modes and use of partici- tional forces due to torsion. The minimum tor- pation factors. In general, the first three modes sional eccentricity that is to be applied to a of vibration in each horizontal direction of a structure is equal to 5 percent of the maximum building are sufficient for the model analysis. building dimension (Basic Design Manual, para For tall buildings or for buildings with vertical 3-3(E)4). A rational alternative to this require- irregularities, a greater number of modes may ment is to calculate accidental torsions by usinr have to be analyzed. A review of the partici- eccentricities that result by moving the centei~,' ) pation factors for the first three modes will give of mass of each story 5 percent of the maximum a good indication if more are required. The sum building dimension to either side of its calcu- of the participation factors (PFxm) for all the lated position (Basic Design Manual, para 5- modes at a particular story (x), as calculated 2d(4)). An example is included in design. ex- from equation 4-1, equals unity. Also, the sum ample E-2. of all the modal base shear participation fac- (5) Flexible horizontal diaphragms. Two- tors, (a), as defined in equation 4-2 will equal dimensional computer programs assume that the unity. Therefore, if the sum of the participation diaphragms are infinitely rigid. In some build- factors for the first three modes is within 10 ings, the horizontal diaphragms may exhibit some percent of unity, it can generally be assumed flexibility relative to the vertical lateral-force- that all the major modes have been included. resisting elements. For very flexible dia- For an example, refer to table 5-2. The sum of phragms, the forces should be distributed to the the participation factors at the roof for three vertical lateral-force-resisting elements by means modes equals 1.08 (i.e., 1.31 - 0.47 + 0.24) and of tributary areas. When a limited amount of the sum of the base shear participation factors flexibility is anticipated, the forces on the less is equal to 0.986 (i.e., 0.828 + 0.120 + 0.038). rigid elements of the rigid diaphragm model Both 1.08 and 0.986 are within 10 percent of the should be increased to account for possible ad- value of 1.0. ditional forces due to tributary area distribu- (3) Check static equilibrium. Some com- tion. Some judgment decisions are required. puter programs present the results for each in- When there is difficulty in determining the proper dividual mode and others only present the results distribution of forces, a three-dimensional anal- in modal combinations. Once the modes have ysis that accounts for diaphragm flexibility may been combined, it is not possible to check the be required. statics for the overall building or for localized d. Three-dimensional computer program, areas, such as at a beam-column joint. There- Three-dimensional computer programs becomet._ fore, static checks must be made prior to making much more complex than the two-dimensional .) the modal combination. Spotchecks at a variety programs, and more care must be taken to fully 5-16 27 February 1986 TM 5809-10-1/NAVFAC P-355.1/AFM 88X3, Chapter 13, Section A understand their features and limitations. Three- program being used in relation to the building dimensional programs can account for rotation being analyzed. about a vertical axis and horizontal movement (2) Modes and participationfactors. in any direction. Some programs, usually those (a) Mode identification. In three-di- using finite element procedures, can allow for mensional analyses, it is sometimes difficult to flexibility in the horizontal diaphragm. The con- identify the characteristics of the various modes tents of paragraph c, above, in general also ap- of vibration. For a regular building, the first three ply to three-dimensional programs. Additional modes will generally include the fundamental comments, which apply to three-dimensional modes that represent primary motion in the programs, follow: translational transverse direction of the build- (1) Featuresand limitations. There are a ing, the translational longitudinal direction of variety of three-dimensional computer pro- the building, and the rotational torsional action grams, each having certain features and limi- of the building. The first nine modes listed in tations, such as the following: the order of decreasing lengths of period will (a) Three-dimensional compatibililty. generally include the first three modes of each Some three-dimensional computer programs of those directional motions. However, for un- were developed as extensions of two-dimen- usual buildings, the sequence of the modes may sional programs. The three-dimensional fea- be highly irregular. For example, a building with tures are determined by combining the very low torsional rigidity will have torsional components of two-dimensional analyses. In modes with long periods of vibration, thus the some cases, where a structural element is part translational modes may not be identified until of both a transverse and longitudinal lateral- after several torsional modes are calculated. force-resisting system, compatibility of common Another example is in buildings with flexible actions from both directions of force is not diaphragms. If the diaphragms are more flexible maintained (e.g., axial forces and vertical de- than the overall structure, the modes for each formations in a column common to two inter- of the flexible diaphragms will be calculated be- secting systems are not truly compatible). fore the primary building modes are identified. (b) Horizontal eccentricities. Addi- Each of these examples would indicate that the tional care must be taken in preparing the data building may have some undesirable character- for three-dimensional computer programs. Tor- istics or that there may be an error in the mod- sional characteristics of a building are sensitive eling of the building. Modes can be identified by to the size and location of the story weights and plotting the mode shapes in three-dimensional the rigidity properties of lateral-force-resisting representations. elements on the horizontal story plane. In some (b) Participation factors. The concept computer programs, mass moments of inertia of participation factors also becomes more dif- are required. In other programs, the masses are ficult to interpret in three-dimensional anal- distributed on the horizontal planes. Assump- yses; therefore, the guidelines given in paragraph tions used in modeling a variety of shear walls 5-4c(2) to identify the number of modes re- and frames can be critical in the evaluation of quired for analysis may not be applicable for torsional properties and horizontal eccentrici- buildings with unusual three-dimensional char- ties; therefore, methods to envelope the uncer- acteristics. For each direction of applied earth- tainties as discussed in paragraph 5-4b should quake forces there will be a major component be investigated. in the direction of motion, a translational com- . (c) Modal combinations. Because the ponent normal to the direction of applied forces, computer programs allow for three-degrees-of- and a rotational component. The participation freedom (longitudinal, transverse, and rota- factors, based on the mode shapes (4) in the tional), combining the modes in three-dimen- direction of applied motion will not add up to sional analysis becomes substantially more 1.0, as occurs in the two-dimensional programs, complex than combining modes for two-dimen- because of the contribution of the other com- sional analysis. In some cases, the use of the ponents of motion. If the base shear partici- SRSS can give erroneous results, especially when pation factors (ac) do not add up to within 90 the loads are applied in a direction not parallel percent of unity, then all of the values of the to the major axes. Therefore, other procedures modal analysis will be increased proportionately for combining the modes are required. The de- to satisfy the 90-percent requirement. signer must be aware of the procedures and pit- e. Stresses and load combinations. The loads falls that may be inherent in the computer on the structural elements resulting from the

5-17 TM 5-809-10-1/NAYFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 modal analysis procedure for EQ-I must be com- f. Displacements and drifts. Lateral story bined with the gravity loading to determine if displacements for each mode of vibration are the structure has remained essentially elastic. calculated from equation 4-5, and examples are (1) Load combinations. The seismic loads given in appendix E, design example E-1. Max- due to the actions of EQ-I will be combined with imum story displacement by the SRSS method. gravity loads in accordance with equations 4-6 CAUTION: the maximum interstory drifts can- and 4-7. Equation 4-6 is used when the gravity not be obtained from the maximum story dis- loads are in the same sense as the seismic loads placements. The interstory drifts must first be (e.g., both sets of loads result in compression in obtained for each individual mode. The inter- a column or negative bending moments in a story drifts for each mode may then be combined beam). Equation 4-7 is generally used when there by the SRSS method to obtain the maximum is a potential for load reversal (e.g., tension in interstory drifts. It is these maximum interstory column due to seismic loading may be greater drifts that will satisfy the limitations of para- than compression due to minimum dead load, or graph 4-3e(7) (a). The maximum story displace- the positive bending moment due to seismic ments are required for the criteria for building loading is greater than the negative bending separations in paragraph 4-3e(7) (b). In three- moment due to minimum dead load). The 1.2 and dimensional analyses, should there be an ap- 0.8 coefficients for the dead load are established preciable amount of rotation of the horizontal to represent possible vertical seismic accelera- diaphragms, the displacements and the inter- tions as well as some uncertainties in the actual story drifts at the outer limits of each floor level dead weight of the structure. Equation 4-8 is a will be determined. If the portion of displace- special case for use on horizontal prestressed ments due to rotation begins to approach the components that are especially sensitive to up- portion of the displacements due to translation ward vertical accelerations. (e.g., if the displacement at the outer edge of (2) Elastic capacity ratio. The elastic ca- the building is greater than 1.5 times the dis- pacities of the structural elements are com- placement at or about the center of rotation);. puted in accordance with the provisions of an evaluation of the potential for torsional insta- paragraph 4-3f. The elastic capacities of the bility will be investigated as outlined in para-- structural elements will generally be equal to or graph i below. greater than the load combinations determined g. Accelerations. Story accelerations for each. in paragraph (1) above. Some exceptions are mode of vibration are calculated from equation permitted in accordance with paragraph 4-3e( 1). 4-. The story acceleration is equal to the story. The elastic capacity ratio is a term used to de- lateral force (F.m divided by the story weight termine if there is any reserve elastic capacity (wa). Maximum story accelerations may be ob-- remaining beyond the demands of EQ-I. It is tained by the SRSS method. Floor accelerations calculated from equations 4-6 and 4-7 as fol- are used to establish criteria for the design of lows: elements attached to the floors of the building, as prescribed in chapter 6. In three-dimensional Elastic capacity ratio = (EC - 1.2D - 1.0L) analyses, should there be an appreciable amount -1.OE (eq 54) of rotation of the horizontal diaphragms, the or 6 = (EC+0.8D) * 1.OE accelerations at points of interest at various locations on each floor level will be determined. (eq 5-5) Modal accelerations at these locations can be whichever is less. Note that the elastic capacity calculated from the modal displacements deter- is reduced by gravity loads when they are in the mined in paragraph f above by equation 5-6, same sense as seismic loads per equation 5-4 which is derived from equations 4-3 and 4-5: and the elastic capacity is increased by minimum 2 a.. = F,./w. = B.. (27r/T) - g dead loads when they are in the opposite sense (eq 5-6) of seismic loads per equation 5-5. The elastic h. Overturning. The structure, that portion capacity ratio of the overall structure is equal above the foundation interfacing with the sup- to the lowest value for any group of major struc- porting soil medium, will be designed to resist tural elements. It is used to define when first the overturning effects of the seismic loading. major yielding occurs and to establish peak floor In some portions of the structure, the resulting accelerations and response spectrum for non- forces may cause uplift at the foundation inter- structural elements in paragraph 6-4. For its face, thus creating an apparent overturning use in the EQ-I analysis, refer to paragraph instability condition. However, structures de- 5-Sb. signed for force levels substantially less than 5-18 .27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A those experienced during actual earthquakes the EQ-I forces and the static force criteria of have not exhibited this behavior. Although the the Basic Design Manual. If the EQ-I forces state-of-the-art of earthquake engineering has should be less than the adjusted Basic Design not been able to establish a consistent recom- Manual forces, justification is required. This re- mendation for evaluating this condition, it is quirement is made to reduce the risk of error generally acceptable that buildings can be sub- or misinterpretation of the seismic design pro- jected to rocking on their bases, that the re- cedures of this manual and applies to all build- sulting displacements do not approach an ing classifications. In lieu of a justification incipient overturning condition, and that the statement, the EQ-I forces may be increased by maximum displacement is limited by the short a value that results in net story shears at least time interval between load reversals. When the 50 percent greater than the story shears deter- design engineer determines that uplift condi- mined from the minimum earthquake forces tions exist, two basic choices exist: (1) tie down prescribed in the Basic Design Manual. The pro- the foundation to prevent uplift; or (2) do not cedure is outlined in paragraph 5-3d(2)(a) provide any additional restraint on the potential through (c). The absolute lower limits of 3 per- uplift. The decision requires some judgment of cent and 2 percent apply to buildings with very the engineer. If the foundation is tied down, the long periods (e.g., T greater than 3 seconds). resulting forces on the structure will generally be increased in the event of a large earthquake 5-5. Designing for EQ-l. because of the added rigidity of the overall The structure will be analyzed to determine its structural system. If uplift is allowed to occur, ability to resist the forces and deformations the resulting seismic forces may actually be re- caused by design earthquake EQ-I1. At this point duced because of increased energy absorption in the design, the initial design has been devel- and the nonlinearity of the base rocking; how- oped as outlined in paragraph 5-3a, and the ever, the redistribution of loads to other por- structure modified, if necessary, to be able to tions of the foundation may cause some distress withstand the forces of EQ-I elastically, as out- in the structure or at the foundation. When uplift lined in paragraph 5-4. Two procedures are pre- is allowed to occur, the designer will provide jus- sented for post-yield analysis provisions in tification for the assumed redistribution of loads paragraph 4-4 as acceptable methods for eval- and for the adequacy of the structure and foun- uating the capacity of the structure to resist the dation. actions of EQ-I1. i. Horizontal torsional moments. Torsional- a. Method I: Elastic analysis procedure. resisting elements, as part of the lateral-force- This is an elastic analysis procedure that is es- resisting system, should preferably be located sentially the same as the procedure outlined in at or near the periphery of the building to max- paragraph 5-4 for EQ-I. The exceptions are imize torsional rigidity. When this cannot be ac- noted. complished or when there are large horizontal (1) Modal analysis procedure. The proce- eccentricities, the structure must be analyzed dure is the same as outlined in paragraph 5-4a. for potential torsional instability. The spectral accelerations will generally be (1) Compare the forces due to transla- larger; however, there will be a higher percent- tional motion to the forces due to torsional mo- age of damping and the periods of vibration may tion for all lateral-force-resisting components. be slightly longer. If the torsional portion is a substantial amount (2) Mathematical modeling of structural of the total design force (e.g., one-third of the components. The comments of paragraph 5-4b total), then torsional stability will be evaluated. generally apply; however, some modification to (2) Review the mathematical modeling as- the modeling assumptions may be made. sumptions and calculations to evaluate the va- (a) Allowances may be made to account lidity of the modeling techniques. Determine if for the reduced section properties of cracked or uncertainties in assumptions would increase or partially cracked concrete. decrease the torsional characteristics. (b) Allowances may be made for flexibil- (3) Investigate the consequences of the ity at beam-column joints. worst-case conditions. (c) Unless the floor slab system is inte- (4) Evaluate the feasibility of revising the grated into the design of the beams and girders, lateral-force-resisting system to minimize the composite action need not be considered. effects of horizontal torsional moments. (d) The effects of nonseismic frames j. Minimum lateral forces requirements. should be reevaluated in regards to the larger Paragraph 4-3d requires a comparative study of deformations resulting from EQ-II. These ef- 5- 19 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 fects would usually be ignored in the mathe- tion of the inelastic demand ratios that exceed matical model unless they provide redundancy a value of 1.0. Conditions to be evaluated are for the overall lateral-force-resisting system. listed in paragraphs 4-4c(5) (b), (c), and (e) and (e) The effects of nonstructural ele- are discussed in paragraphs (d), (e), and (f), ments is not included in the mathematical model below. to calculate periods, displacements, and member (d) Unsymmetrical yielding on a horizon- forces. However, the possible detrimental ef- tal plane. This provision is used to check for the fects of rigid nonstructural elements must be possibility of torsional instability, as discussed considered in the overall evaluation of the struc- in paragraph 5-4i. For example, if all the in- ture. elastic demand ratios on the north side of the (f) The modification of modeling as- structure were greater than 1.0, and all the ra- sumptions can result in the lengthening of pe- tios on the south side were less than 1.0, a po- riods of vibration by 25 percent to 50 percent. tential for torsional instability exists. Yielding (3) Stresses and load combinations. The of the north side will reduce the stiffness of that loads on the structural elements resulting from side of the building relative to the south side, the modal analysis procedure for EQ-II must thus the center of rigidity moves to the south. also be combined with the gravity loading. How- If this condition increases the horizontal eccen- ever, the load factors on dead and live loads have tricity of the building, torsional moments in- been revised in accordance with equations 4-9 crease geometrically and the potential for and 4-10. Only the actual dead load need be con- collapse is present. sidered, and the design live load may be reduced (e) Hinging of columns at a single story. to a value that is consistent with actual live loads This provision is used to check for the possibility that are likely to be in place at the time of a of an unstable soft story. For example, if in- severe earthquake. This reduced gravity loading elastic demand ratios were equal for about 1.5 is justified on the basis of the probability that at the tops and bottoms of 80 percent of the it is unlikely that both maximum live loads and columns for the first story of a multistory build- maximum earthquakes will occur at the same ing and inelastic demand ratios for columns at time. every other story were less than 1.0, the poten- (4) Inelastic demand ratios. The Method tial for instability at the first story exists. Be- 1 evaluation procedure is based on the assump- cause the columns are yielding only at the first tion that EQ-II will result in a number of lat- story, all the inelastic energy will have to be eral-force-resisting elements being stressed absorbed at that level. This subjects the first beyond their elastic limit yield capacities. story to the possibility of excessive interstory (a) The calculated forces on the struc- displacements. tural elements are obtained from an elastic (f) Unusual distributions of inelastic de- analysis. Therefore, these are the force demand ratios. This is a more general case of par- mands of EQ-II if the structure had remained agraphs (d) and (e), above. This provision is elastic. used to check the efficiency of the overall lat- (b) The capacities are defined as the eral-force-resisting system. If a limited number strength of the element at the point of yielding. of structural elements have large inelastic de- (c) The ratio of the demand to the ca- mand ratiosand the remainder of the elements pacity (i.e., the inelasticdemand ratio) is an in- have ratios less than 1.0, it might be prudent to dication of the ductility that may be required consider some structural modifications to re- for the structural element to withstand the forces duce the potentially high demands on a small of EQ-II. As the first elements of the overall number of structural elements. structure begin to yield (i.e., inelastic demand b. Method 2: Capacityspectrum method. This ratio exceeds 1.0), forces will be redistributed is an approximate inelastic analysis procedure. to other elements of the lateral-force-resisting The ability of the structure to resist the forces system. The limiting values of inelasticdemand and deformations caused by EQ-II is deter- ratios for structural elements prescribed in ta- mined by a graphical method. The procedure re- ble 4-2 have been established as acceptable lim- quires the construction of two curves. One curve its for a structural system that has a reasonable represents the capacityof the structure to resist amount of redundacy and is not subjected to lateral forces and the other curve represents the premature vertical or torsional instability or to demand of the ground shaking. The capacity

a premature mechanism at a single story level. curve is developed from a force (F or V) versus . Possible weak links in the overall structural sys- displacement (8) relationship of the overall tem are detected by investigating the distribu- structure. Modal analyses are used to determine 5-20 27 February 1986 TM 5-809-10-l/NAYFAC P-355.1/AFM 88-3, Chapter 13, Section A levels of excitation to yield structural elements. two response spectra representing EQ-I1. The The capacity is defined by the forces and dis- 5-percent damped demand curve is used for the placements of the fundamental mode. The force- elastic capacity (T < 0.80 sec) and the 10-percent displacement curve can be converted into a spec- damped demand curve is used for the ultimate tral acceleration (S.) versus period (T) curve capacity (T < 1.4 sec). A transition curve is drawn (i.e., a capacity spectrum) by means of equa- between T = 0.80 sec and T = 1.4 sec. Following tions 4-3,4-4, and 4-5. The demand of the ground are guidelines for constructing the capacity curve shaking is represented by an EQ-II response using a step-by-step method and approximating spectrum curve. This curve is a composite of the the lateral displacements and drifts. two damping values (elastic-linear and post- (1) General procedures for constructing the yield) determined from table 4-1. The capacity capacity curve. The capacity curve is a simplified curve and the demand curve are plotted on the global representation of the building capacity. same graph; their intersection is considered to As localized yielding occurs (e.g., bending at the be the reconciliation between demand and ca- end of a girder), the overall (or global) char- pacity. A sample building, six stories and a 66- acteristics of the building are modified. If the foot height, is used for illustration. Figure 5-5 localized yielding is at a critical structural ele- shows the force-displacement capacity curve for ment, the global characteristics may change sig- the sample building. It plots the base shears (V) nificantly. Conversely, if the localized yielding is and roof displacements (80). In table 5-4, the V at a redundant location, the change to the global and B. values are converted to spectral accel- characteristics may be insignificant. For single- erations (S.) and periods (T) using equations story buildings and low-rise buildings up to about 4-4 and 4-5 with the participation factors (PFn 5 stories, the modal analysis procedure for con- and at) for the fundamental mode of vibration. structing the capacity curve can generally be The capacity curve is plotted on figure 5-6 with limited to the fundamental mode of vibration.

3000

2000

L~J U., 1000

0 0 5 10 DISPLACEMENT AT ROOF, 6n (inches)

US Army Corps of Engineers Figure 5-5. Force-displacementcapacity curve. TM 5-809-1O-1INAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Table 5-4. Conversion of V and b, to S. and T.

Point V 6N V/W PFN a Sa Sd T (kips) (in) (g) (in) (sec)

A 2200 2.3 0.22 1.30 0.78 0.280 1.77 0.80

B 2600 3.1 0.26 1.28 0.80 0.325 2.42 0.87

C 2800 4.1 0.28 1.28 0.80 0.350 3.20 0.97

D 3000 .8.7 0.30 1.26 0.83 0.361 6.90 1.40

V/W: V = Base Shear, W = Weight = 10,000 Kips

6 = Lateral roof displacement due to V N~~~~~~~~ PFN = (E+ ( zm ),,modal roof participation factor (eq. 4-1) 2 2 a=(rm) 2/(Am)('m 2), effective modal weight (eq. 4-2)

S = Spectral acceleration = V/w . a (eq. 4-4)

Sd = Spectral displacement = 6N *.PFN (eq. 4-5)

T = 2 Sd/(S a)(g), fundamental period of vibration (eq. 4-5)

ZrO = Summation of story mass times mode shape factor from the roof to the base of the building

US Army Corps of Engineers

5-22 27 February 1986 TM 5-809-10-1/NAVFAC P-355.I/AFM 88-3, Chapter 13, Section A 1.0

0.9

0.8

0.7

Cn 0.6

0) .W 0.5

U 0.4

U 0.3 0n. 0.2

0.1

0 0 0.5 1.0 1.5 2.0 2.5

Period, T (sec.) US Army Corps of Engineers Figure 5-6. Capacityspectrum method.

For taller buildings, effects of higher modes of pacity curve. The following procedure can be set- vibration may become significant, thus a multi- up in tabular form: mode analysis may be required. The results from (a) Determine the elastic capacity (EC) the EQ-I design can be used to determine the for each structural element (e.g., negative and effects of the higher modes and the necessity of positive moment capacities at each end of each using them in the EQ-I1 analysis., The capacity girder, interation diagrams at + = 1.0 for each curve is developed by a step-by-step procedure, column, and shear and moment capacities of using superposition, where the structure is lat- shear walls at various key locations). These ca- erally distorted to a limiting value, frozen in that pacities are defined as the strength of the ele- 4 position, local yielding elements are relaxed, and ment at the point of yielding and should be the structure is laterally distorted to a new value. available from the EQ-I DESIGN. The procedure is repeated until an ultimate limit (b) Determine the net capacity available is reached. The capacity curve is constructed by for earthquake loading in each element using means of superposition of straight lines. The the EQ-I1 load combination criteria of equa- period and stiffness characteristics are deter- tions 4-9 and 4-10, paragraph 4-4e(1). For ex- mined from the secant modulus drawn from the ample, equation 57 for negative moments and origin to the various points on the force-dis- equation 5-8 for positive moments at ends of placement curve. girders. Note that the net earthquake capacity (2) Single-mode capacity curve. If it is de- is reduced by gravity loads when they are in the termined that only the fundamental mode is re- same sense as seismic loads per equation 5-7 quired (i.e., higher modes are insignificant), the and the net earthquake capacity is increased by shape of the ground motion response spectrum dead loads when in the opposite sense per equa- is not required for the construction of the cation 5-8. TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 Net earthquake = EC-D -0.25L (eq 5-7) duced EI's used in the yielding mathematical capacity model. Ductility demands for flexure should not exceed 2 times the Inelastic Demand Ratios of Net earthquake = EC + D (eq 5-8) table 4-2, and for all other conditions they should capacity not exceed the values shown in table 4-2. In- (c) Divide the net earthquake capacities terstory displacements are determined by su- for each element by the corresponding earth- perposition of the lateral story displacements quake loads determined in the EQ-I design. This of the sequential models. For the sample six- gives local elastic capacity ratios for each ele- story building, the ultimate global capacity of ment. The lowest ratio, or group of ratios with the structure is represented by point D at V = a 10-percent variation, establishes the global. 3000 kips and {in = 8.7 inches in table 5-4 and elastic capacity ratio for the structure as de- figure 5-5. scribed in paragraph 5-4e(2), adjusted for (h) Deterine lateral displacements and EQ-I1 load factors. drift demands. The capacity curve is converted (d) Establish the point of initial major to Sa anlT coordinates and superimposed on yielding, the first point on the capacity curve, by the EQ-II response spectrum curve. If the curves multiplying the EQ-I design base shear and lat- do not intersect, irreparable damage or collapse eral roof displacement by the global elastic ca- of the structure is anticipated for EQ-I1. If the pacity ratio for the structure. This point is curves do cross, the intersection can be used to represented as point A by V = 2200 kips and B.i approximate the response of the structure to = 2.3 inches for the sample six-story building EQ-II. For the sample six-story building, data characterized in table 5-4 and figure 5-5. from table 5-4 are shown in figure 5-6. The in- (e) Determine the first post-yield seg- tersection of the capacity and demand curves is ment of the capacity curve. The structure is es- about S. = 0.35g and T = 10.0 seconds. The lat- sentially frozen at the point of initial major eral story displacements at this intersection are yielding. The balance of net capacity in each ele- calculated from equation 4-5. ment still available for additional earthquake loading is tabulated. Elements that are at or Bn = PFnSa (T/27r) 2 g near (e.g., within 10 percent) their yield capac- = 1.28 x 0.35 (l/27r) 2 386 = 4.38 inches ities are modeled as plastic hinges (e.g., beam .J ) elements might have their moments of inertia The roof displacement equals about 4.4 inches reduced to 5 percent of their elastic values). Lat- for a six-story building, 66 feet high. Maximum eral forces proportional to the fundamental mode interstory displacements can be obtained from shape are applied to the revised mathematical a composite deflected shape estimated from the model. For the sample six-story building, the base sequential incremental analysis done above, or shear of the applied forces was 1000 kips. The by proportioning the interstory drifts by the ra- resulting forces on the elements were compared tio of the EQ-II displacements to the EQ-I dis- to the balance of net earthquake capacities and placements. For the sample building, the average lateral displacements were calculated. It was de- interstory drift is 0.73 inches. The maximum in- termined that 40 percent of the applied loads terstory drift, which is at the second story, equals will form a new group of yielding elements. A 1.1 inch or 0.0083 times the story height. Thus, second point on the capacity curve was deter- it satisfies the requirements of drift (i.e., less mined at V = 2600 kips and B.i= 3.1 inches (2200 than 0.010) as prescribed in paragraph 4- kips at point A plus 40 percent of 1000 kips and 4e(2) (a). 2.3 inches at point A plus 40 percent of 2.0 inches), (i) The results of this procedure give an represented by point B in table 5-4 and figure estimate of the inelastic response of a building 5-5. to a severe earthquake. In general, it will result (f) Determine sequential post-yield seg- in lower force levels and larger displacements ments on the capacity curve by repeating the than the results of Method 1 in paragraph 5-5a. procedure in (e) above (e.g., points C and D in Neither procedure is necessarily more accurate table 5-4 and figure 5-5 using revised mode than the other; however, an evaluation of both shapes and mathematical models). procedures should give the designer enough in- (g) The procedure is repeated until a fail- sight to determine the weak links of the struc- ure mechanism, instability, or excessive defor- tural system, evaluate the potential for mations occur. Rotational ductility demands can instability, and suggest needs for possible struc- be approximated by using MWEI diagrams of the tural modifications. yielding girders, taking into account the re- (3) Multi-mode capacity curve. If it is de- 5-24 27 February 1986 TM 5-809-1.-1 /NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A termined that the higher modes are significant, exceptions noted in (e) above. a multi-mode analysis is required. The shape of (g) Same as paragraph (2) (g), except that the ground motion response spectrum is re- the interstory displacements determined by su- quired for the construction of the capacity curve. perposition of fundamental modes represented In general, the shapes of the EQ-I and EQ-I1 in the capacity curve must be increased propor- response spectra are similar; therefore, the tionally to represent the multi-mode analysis. EQ-I response spectrum is usually used because For example, the interstory drifts between the of data available from the EQ-I analysis. The sixth and seventh stories in table 5-3 are 0.024 procedure for constructing the multi-mode ca- feet for the multi-mode analysis and 0:022 feet pacity curve is the same as the procedure for the for the fundamental mode. Therefore, inter- single-mode capacity curve, paragraph (2) above, story displacements determined by superposi- with the following exceptions: tions of the sequential fundamental modes will (a) Same as paragraph (2) (a). be increased by a factor of 0.024/0.022 equals (b) Same as paragraph (2) (b). 1.09. Between the third and fourth floors, the (c) Same as paragraph (2) (c), except that values are the same and no correction is re- the corresponding earthquake loads deter- quired. mined in the EQ-I design are determined by a (h) Same as paragraph (2) (h) except that multi-mode analysis. the lateral displacements that represent the first (d) Same as paragraph (2) (d), except that mode component must be increased proportion- only the fundamental mode component of the ally to also represent the multi-mode compo- EQ-I design base shear and lateral roof dis- nents. For example, in table 5-3 roof displacement are multiplied by the global elastic placements will be increased by a factor of capacity ratio. For example, assume the data in 0.229/0.228= 1.004. table 5-3 represents the initial major yielding (i) Same as paragraph (2) (i). for the seven-story building. The multi-mode base (4) Variations of the procedures outlined shear is 2498 kips, but the fundamental mode above for constructing a capacity curve are ac- component is 2408 kips. The multi-mode roof ceptable with justification. displacement is 0.229 feet and the fundamental c. Displacements and drifts.. Lateral dis- mode roof displacement is 0.228 feet. Although placements and drift limits are prescribed in 2498 kips represents the forces used to deter- paragraph 4-4e(2). Methods of calculating the mine the initial major yielding in the building, displacements are described in paragraphs 5-5a the values of 2408 kips and 0.228 feet represent and 5-5b. In general, the results of Method 2 the "point A" used in the capacity spectrum (i.e., will give larger displacements than the results such as table 5-4 and fig 5-5). of Method 1; however, the reverse can occur in (e) Same as paragraph (2) (e), except that some cases. If the differences of the two meth- the lateral forces are applied by means of a multi- ods will effect the outcome of the design of the mode response spectrum analysis (e.g., use EQ- structure, a reevaluation of the procedures or I response spectrum). If the EQ-I response spec- assumptions will be made to justify an accept- trum, with a peak ground acceleration of 0.10g able solution. A secondary effect of lateral dis- is applied to the revised mathematical model and placements, when combined with gravity loads, it is determined that 40 percent of the resulting is the possibility of P-delta instability. Guide- multi-mode forces will form a new group of lines are given in paragraph 5-5d. yielding elements, the second segment of the ca- d. P-delta effects. The P-delta effects in a pacity curve is determined by using 40 percent given story are due to the eccentricity of the of the fundamental mode component of base gravity loads above the story. If the story drift shear and lateral roof displacement. This is the due to the lateral forces are delta, the bending same as finding the spectral acceleration for the moments in the story would be augmented by first mode period on a response spectrum that an amount equal to delta times the gravity load has a peak ground acceleration of 0.04g (i.e., 40 above the story. The ratio of the P-delta moment percent of 0.lOg). First-mode spectral acceler- to the lateral-force story moment can be des- ation and period can be converted to base shear ignated as a stability coefficient, 0. If the sta- and roof displacement by the formulas shown bility coefficient is less than 0.10 for every story, in table 5-4. As in paragraph (d) above, the forces then the P-delta effects can be considered insig- in the elements are determined by the multi- nificant. If, however, the stability coefficient, 0, mode analysis, but the capacity spectrum is rep- exceeds 0.10 for any story, then the P-delta ef- resented by the fundamental mode component. fects for the whole building must be determined (f) Same as paragraph (2) (f) with the by a rational analysis. 5-25 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A CHAPTER 6 NONSTRUCTURAL ELEMENTS

6-1. Introduction. b. Maximum floor acceleration. The maxi- This chapter prescribes the criteria for non- mum floor accelerations will be determined from structural elements that must remain intact or the modal analysis methods prescribed in chap- functional after a major seismic disturbance. The ter 4. Modal story accelerations will be deter- provisions of this chapter include the determi- mined using the equation 6-1: nation of the seismic forces to be applied to the elements, the determination of the deforma- axm = PFxmSam (eq 6-1) tions that the elements will withstand, and the where: criteria for the design of architectural, mechanical, and electrical elements to resist the pre- axm = modal story acceleration at level scribed forces and deformations. The criteria and x for mode m. design standards of this chapter provide a dy- PF,. = modal participation factor as namic analysis approach to the seismic design determined by equation 4-1. of nonstructural elements and their anchorages that may be used in lieu of, or as supplements Sam = spectral acceleration for mode m. to, the provisions of chapters 9 and 10 of the Equation 6-1 is derived from equation 4-3, where Basic Design Manual. a.. = Fxm/wx. (1) For 2D analyses, the maximum floor ac- 6-2. General requirements. celeration will be determined from the SRSS The elements and their anchorages will be de- combination. signed to resist the forces and deformations caused by the motion of the building in which (ax)max = (eq 6-2) they are placed, as prescribed in paragraph 4- (2) For 3D analyses, the maximum floor ac- 2e. The effects of the nonstructural elements on celeration will be determined by an approved the performance of the structure must also be method to account for a rational combination considered. of the modal values. When torsional motion is a. Under the conditions of EQ-I, the elements significant, relative to translational motion, will be designed to resist the applied forces and variations of modal accelerations within the deformations without exceeding yield stresses. plane of the floor level will be considered. Guide- b. Under the conditions of EQIl, the ele- line procedures are included in paragraph 5-4. ments will be analyzed for their ability to with- c. Design floor response spectrum. A pro- stand the applied forces and deformations, such cedure for approximating a design floor re- that: (1) they will not collapse or endanger life sponse spectrum is outlined herein. This safety when subjected to the provisions of par- procedure uses the peak modal accelerations de- agraph 6-4; and (2) they will remain functional, termined from equation 6-1, the modal periods if required, in accordance with the provisions of of vibration of the structure in accordance with paragraph 6-7. the provisions of chapter 4, and the magnification factor (M.F.) curve shown in figure 6-1 (re- 6-3. EQ-I provisions. produced from Basic Design Manual fig 10-2). The elements in or on the structure will be de- For each floor of the structure, the following signed to resist the forces and deformations procedure is used: caused by the response of the structure to EQ- (1) For each significant modal period of vi- I, in accordance with criteria presented in this bration (Tm) and from the dynamic responses paragraph. of the structure, calculate the story accelera- a. Method of analysis. The total design force tions, ax, using equation 6-1 for the story where representing earthquake effects will be deter- the equipment is supported (see table 6-2 for mined from the maximum floor (or roof) accel- an example at the roof level). erations of the building and from a design floor (2) Establish a coordinate system with Sfa (or roof) response spectrum based on 2 percent (floor spectral acceleration), the ordinate, and damping for the elements. This requirement does T. (period of the equipment or architectural ap- not prohibit the use of properly substantiated pendage), the abscissa. Develop the floor re- time history response analysis procedures. sponse spectrum as follows:

6-1 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 0.8 1.2 8

2 1.0 0 0 0.5 1.0 1.5 2.0 2.5 3.0 Ta

US Army Corps of Engineers Figure 6-1. Design MF. versus period ratio. (a) For each modal period, Tm, develop a e. Design requirements. plot of Ta versus Sfa from the standardized mag- (1) Rigid and rigidly mounted equipment or nification curve in figure 6-1 using the following appendages (e.g., Ta < 0.05 sec) will be designed relationships: to resist the forces due to the maximum floor acceleration in accordance with the equation Ta/Tm = Ta/T (eq 6-3) 6-5: ) Sf. = axm (M.F.) (eq 6-4) Fp (ax)maxWp (eq 6-5) Table 6-1 illustrates the tabulation of the pertinent data required for such a plot for an ex- where (ax)max is determined from paragraph 6- 3b and W, is the effective weight of the equip- ample where Tm = 2.0 sec and axm = 0.12g. (b) Draw a horizontal line intersecting the ment or appendage. (2) The flexible or flexibly mounted equip- ordinate at Sfa = (ax)max, where (ax)max is the ment or appendages that can be represented as maximum floor acceleration from paragraph 6- SDOF systems will be designed to resist the forces 3b. This line establishes the lower limit for Sfa. (c) The floor response spectrum is de- due to the appropriate floor spectral accelera- fined by the envelope of the curves of paragraph tion in accordance with equation 6-6: (a) above and the lower limit established by par- Fp= SfaxWp (eq 6-6) agraph (b). An example of the procedure is illustrated by figure 6-2 from the data in tables where Sf. is the design spectral acceleration, 6-1 and 6-2. The example is for the roof of an Sfa, at floor x as defined in paragraph 6-3c for assumed building. At other story levels of this period T. of the equipment or architectural ap- building, the corresponding Sfa values will be pendage. proportional to the modal accelerations at those (3) Multi-mode systems will be designed by levels. a modal analysis procedure similar to the pro- d. Maximum interstory drifts. The maxi- cedure used for buildings in chapter 4, except mum lateral relative displacement between ad- that the floor response spectrum of paragraph jacent stories caused by EQ-I will be determined 6-3c will be used in lieu of ground motion re- from the combined modal interstory drifts in sponse spectrum. accordance with chapter 4. Design example E-1 (4) Nonstructural elements that are rigidly shows a method of determining attached to two parts of the building that can the interstory move relative to each other will be designed to drifts for each mode and the combined SRSS take the resulting deformations determined in values are shown in table 5-3. paragraph 6-3d.

6-2 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Table 6-1. Example of a response amplification curve for the building's fundamental mode of vibration.

Example:

Given: First mode period of vibration of building, Tm = 2.00 sec. Maximum floor acceleration for first mode, axm - 0.12 g. Find: Sfa values for response amplification curve for the first mode of building vibration.

Procedure: Ta/T and M.F. values are from figure 6-1. Ta is obtained from equation 6-3. Sfa is obtained from equation 6-4.

Tm = 2.0, am = 0.12

_ Or ______. __ _ _ ._ ____ Ta /T 0 0.5 0.8 1.2 2.0 3.0 fig. 6-1 m.F. 1.0 1.0 7.5 _7.5 1.0 1.0 fig. 6-1 Ta 0 1.0 I .6 2.4 4.0 6.0 eq. 6-3 .. . _ 1I Sfa 0.12 0.12 0.90 . 0.90 0.12 0.12 eq. 6-4 I.. .- _ .. Ta ' Tm (Ta/T) - 2.0 (Ta/T) Sfa - axm (M.F.) - 0.12 (M.F.)

US Army Corps of Engineers

6-3 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Table 6-2. Data for the floor (roof) response spectrum example of figure S-2. ExaMple of Figure 6-2.

Mode I Mode 2 Mode 3 SRSS

Tm (building), sec 2.00 0.61 0.36

Sam' 9 0.089 0.29 0.38

PFxM (x = roof) 1.30 0.45 0.22

axm 9 0.12 0.13 0.08 0.19

S (MF = 7.5) 0.90 0.98 o.60 f a ______9

Tm from building analysis (chapter 4)

Sam from response spectrum for building period Tm

PFm from building analysis (eq.4-1)

axM = PFXmSam is model story acceleration at level x for mode m (eq.6-1)

Sfa = ax (M.F.) for maximum values at M.F. = 7.5 (eq.6-4). See Table 6-1 for other values on the amplification curve for mode I

US Army Corps of Engineers

6-4 'IN

, ___ __ Peak Response Amplifications £ for 2nd and 3rd Modes (Table 6-2)

Response Amplification Curve for the Building '\ \ U U U Fundamental Mode of \ 0 0 a) 0X \ Vibration (Table 6-1)

1.5 \ O 7 % C J O 2.0 0 -0.98 w 0~~~~~~~~~~~~~~~~~~~~~~~~~~~*

0 C~~~~~~~~~~ ~~z 0 M -~0.60 I

0.5 .

US CorpsAnny o' Engin * * 0.08-~~~~~~~~~~~~~~~~~~~~~~~~~~~~-

Fe i g u Sr R S S 1 9s t

MODE~ 2 ~ ~ ~ ~ ~ OD 30

USArmy Corps of En;ineerS Figure 6-.Sample roof response spectrum. TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 6-4. EQ-il provisions. (1) Condition 1. If the elastic capacity of The elements in or on the structure will be ana- the structure significantly exceeds the demands lyzed for their performance to the forces and of EQ-I, the amplitudes of the floor response distortions caused by response of the structure spectrum calculated in accordance with para- to earthquake motions that exceed the demands graph 6-3c will be multiplied by the elastic ca- of EQ-I, up to and including the demands of EQ- pacity ratio, as defined in paragraph 6-4b( 1). II, in accordance with the criteria prescribed in (2) Condition 2. The magnification fac- this paragraph. tors associated with post-yield response of the a. Method of analysis. The total design force structure will tend to be less than those asso- representing earthquake effects will be deter- ciated with linear-elastic response of the struc- mined from the maximum floor (or roof) accel- ture. Thus, the procedure outlined in paragraph erations of the building and from design floor 6-3c is modified by use of the magnification fac- (or roof) response spectra in the same manner tor curve shown in figure 6-3. as presented in paragraph 6-3, except as modi- d. Maximum interstory drifts. The maxi- fied below. mum lateral relative displacement between ad- b. Maximum floor acceleration. The maxi- jacent stories caused by EQ-II will be determined mum floor accelerations will be determined as from the combined modal interstory drifts in prescribed in paragraph 6-3b for two condi- accordance with chapter 4. tions: (1) the maximum elastic capacity of the e. Design requirements. The requirements structure; and (2) the post-yield response of the prescribed in paragraph 6-3e will apply, except structure caused by EQ-I1 criteria. The condi- that references to paragraphs 6-3b, c, and d will tion that results in the largest accelerations will be changed to paragraphs 6-4b, c, and d. govern the design of the nonstructural elements. If the elastic capacity of the structure 6-5. Architectural elements. exceeds the demands of EQ-II, the elastic re- Architectural elements must: (1) safely resist sponse to EQ-II will govern the design. horizontal forces equal to the design accelera- (1) Condition 1. If the elastic capacity of tions times their own weight; and (2) be capable the structure is approximately equal to the de- of conforming (accommodating) to the lateral mands of EQ-I, Condition I is automatically sat- deflections that they will be subjected to during ,) isfied by the provisions of paragraph 6-3. lateral deformation of the building in which they However, if the elastic capacity of the structure are located. The design of architectural ele- significantly exceeds the demands of EQ-I, max- ments will conform to the provisions of this imum story accelerations greater than those de- chapter and the applicable portions of the Basic termined from an inelastic analysis (Condition Design Manual, chapter 9. Architectural ele- 2) can result. The maximum floor accelerations ments that are part of essential systems will determined from the elastic capacity of the also conform to the provisions of paragraph structure are equal to the values obtained from 6-7. the provisions of paragraph 6-3b multiplied by the ratio of the elasticcapacity of the structure to the demands of EQ-I. This ratio is designated 6-6. Mechanical and electrical elements. as the elastic capacityratio (not to be confused a. General. The anchorage and support of with the inelastic demand ratio), and is deter- mechanical and electrical equipment will be de- mined from the provisions included in para- signed in accordance with the provisions of this graph 4-3. Guidelines are provided in paragraph chapter and the applicable portions of the Basic 5-4e(2). Design Manual, chapter 10. (2) Condition 2. The maximum floor ac- b. Equipment certification. Manufacturers celerations for the post-yield response caused of essential mechanical and electrical equip- by EQ-II will be determined from the combined ment will provide certification, based on exper- modal story accelerations conforming to the imental or approved analysis, that the equipment provisions of paragraph 4-4. will not sustain damage that may impair its c. Design floor response spectrum. The pro- function if it is subjected to the postulated mo- cedure outlined in paragraph 6-3c will be mod- tion. ified to determine the floor response spectra for c. Essential systems. Mechanical and elec- two conditions: (1) the maximum elastic capac- trical equipment that is part of essential sys- ity of the structure; and (2) the post-yield re- tems will conform to the provisions of this sponse of structure caused by EQ-II criteria. chapter, paragraph 6-7.

6-6 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1 /AFM 88-3, Chapter 13, Section A r- Light dashed line ; representsc desji;n i M.F. in Fiqgure 6-1 0.7 1. 5 8

L. 4

1 . () 0 0 0.5 .1.0 1.5 2.0 2.5 3.0 Ta T

US Army Corps of Engineers Figure 6-3. Post-yield M.F. curve.

6-7. Essential systems. exit corridors and all approaches to exits must Critical facilities are by definition those facili- be designed with extreme care. Door frames must ties that must provide needed services following be rigid enough to withstand imposed lateral a major disaster such as an earthquake. This forces and be detailed to allow wall movement. implies that not only must the structure survive Stairs must also be given special attention so a major seismic disturbance, but also that es- that they will not fail due to lateral loads or sential nonstructural systems include all ele- structural deformations (Basic Design Manual, ments that are needed for the performance of chap 4, para 4-7d). Any glass used within exit- emergency services or that may, by their failure, ways shall be tempered and its frame shall be cause bodily injury or impair the performance designed to allow deformations (Basic Design of services. These systems are outlined in table Manual, chap 9, para 9-4e). Nonessential ele- 6-3. ments, such as display cases, should not be lo- a. Fire protection. The fire protection sys- cated in or near exitways where they may hinder tem, including both fire-fighting equipment and egress. means of egress, is an important nonstructural b. Protection against hazardous materials. system, since post-earthquake fires often cause Hazardous materials pose a threat to post- more damage and injury than the earthquake earthquake operational capability of the facility itself. as well as human safety. (1) Special attention must be given to the (1) The types and quantities of hazardous protection of fire-fighting equipment. The sprin- materials present should be identified in the pre- kler system piping shall be braced in accordance liminary design phase. with NFPA No. 13 (Basic Design Manual, chap (2) All distribution and storage systems for 10, para 10-7a), and fire pumps shall be gov- such materials shall be designed with extreme erned by NFPA No. 20. Mounting brackets for care. Fuel lines, bottles of laboratory chemicals, hung and free-standing fire extinguishers shall lead storage safes for radioactive materials, liq- be designed to prevent release of the extin- uid oxygen storage tanks, and similar con- guisher caused by horizontal or vertical earth- tainers must be braced and protected from quake motions. damage cause by movement or failure of adja- (2) Exitways must not become blocked after cent elements. Seismic-activated shut-off valves an earthquake. Walls, ceilings, and lighting in shall be used at appropriate locations on supply 6-7 ~~~~~~. 9..r rt N>Fnttig-E;.,

<^>i ~~~~ -

--_ -;,S Table 6-3. Essentialnonstructural systems.

FIRE PROTECTION . COMMUNICATIONS Sprinkle ,rand Standpipe Systems Alarms Air Handling Units, Blowers, Risers * Mains, and Branch Telephone and Fans ILines Radio Cooling Towers Valves and Sprinklers PA System Furnaces Z Support Hangers, Bracing and Paging System Chimneys Clamp s Intercom System Miscellaneous Fire Pumps Nurses' Call Vacuum Pump and Piping Water Tanks Refrigeration and Medical Extingui shers TRANSPORT Compressors 'U Exits Elevators/Dumbwaiters Kitchen Equipment Stairs Cabs Laundry Equipment Doors Rails Maintenance and Repair uin Corrid ors Counterweights Supplies KATERIALS GenaMotors Cleaning Supplies. HAZARDOUS MATERIALS ~~~Generators ...... A Storage Tanks, Bottles, Controls ARCHITECTURAL 3 Cylind ers, and Pipes Exterior Walls, Panels,and Contai ning: MECHANICAL Glazing Natura 1 Gas Water System Interior Partitions and Facing °2 Tanks Materials N2 0 Heaters Ceilings Anesth,etic Gases Pump S Light Fixtures .a Chemic als Risers, Mains, and Branch Horizontal and Vertical Pro- 'U Radioaictive Materials Lines jections Fuels Valves Ornamentation Sanitary System Storage Units EMERGENCY IPOWER Soil Stacks and Branch Essential or Potentially Substatiion Lines Hazardous Furnishings Transfi rner Vent Stacks and Branch Computer Floors ControlIs Lines Switch gear Storm Leaders (ifcon- ESSENTIAL SUPPORT. Engine-GI Seerator nected to sanitary) (to be defined for each type of facility) > Engine t~~~~~t .. y &'~s*n-4-U .Af a.C . Fuel Tank and Piping HVAC Systems Coolin g System Boilers OTHERS Exhauslt System Pipes, Ducts and Hangers Elements in Proximity of Batterie!&and Racks Converters Critical Equipment Switchboiirds and Panelboards Heat Exchangers Expensive Equipment )trollers Motor Coi and Control Compressors Computer Equipment *In Centers Condensers Chillers Cr a

US Army Corps of Engineers 04 ( ( 27 February 1986 TM 5-809-10-1/NAVFAC P-355.I/AFM 88-3, Chapter 13, Section A lines for natural gas and other hazardous ma- shall be braced. terials. (6) An on-site fuel supply sufficient for the c. Emergency power and circuits. An emer- maximum estimated emergency period shall be gency system consisting of separate emergency provided. The fuel storage tank should be lo- circuits and an alternate on-site power source cated underground and properly anchored. Flex shall be provided. loops should be used in fuel lines between the (1) For health care facilities, this system tank and building and at the connection to the shall be governed by the provisions of NFPA generator. Malleable fittings and valves should No. 76-A and TM 5-838-2. For all other critical also be used. facilities, the provisions of NFPA No. 70, Article (7) Conductors should cross earthquake or 700, and this section shall apply. The require- expansion joints only at lower levels and with ments for the bracing of elements of the me- adequate provision for differential movement. chanical system, given in paragraph 6-7f, shall Separate grounds for branch circuits crossing also apply to elements of the emergency power these joints should be provided. system. d. Communications. The post-earthquake (2) Emergency circuits shall consist of sep- communication requirements of a facility must arate circuits serving lighting and equipment be defined during the preliminary design phase. that is essential for life-safety and the perform- (1) An internal communication system that ance of post-earthquake operations. The extent can operate independently of the telephone sys- of this system shall be determined for each fa- tem and normal power supply may be required. cility during the preliminary design phase. In An external communication system capable of general, it will include: contact with community and state emergency -Illumination of means of egress. services as well as mobile units (such as police -Alarm and alerting devices. cars or ambulances) shall be provided. -Emergency communications systems. (2) Emergency communication equipment -Illumination of generator set location. must be located in a nonvulnerable portion of -Task illumination for essential services. the facility, preferably the lower levels, and must -Essential equipment. be designed and mounted to resist seismic mo- -At least one elevator, plus ventilation, tion. communications, and lighting for all other e. Transport. All elevators, shafts, and ac- elevators. cessories shall be designed to resist the lateral- (3) The emergency circuits shall be served force requirements. At least one elevator, plus by the normal power source of the electrical sys- the ventilation, communication, and lighting for tem and, upon failure of the normal source, by all elevators, shall be connected to the emer- at least one alternate source. The main feeders gency power system. for the emergency circuits shall be physically (1) For traction elevators (Basic Design separated from normal wiring to prevent their Manual, fig 10-3, chap 10, para 10-10), insure simultaneous destruction. that counterweights cannot become derailed by (4) The normal power source preferably strengthening their guide rails using additional should consist of two separate full-capacity ser- or stronger rail brackets and installing safety vices, connected in such a manner that one will shoes on the counterweight assembly. Guide rails automatically pick up the load upon loss of the for cars are normally designed for large lateral other. Upon failure of both sources, the load forces, but it may be necessary to install spacers shall be transferred to the alternate power between back-to-back rails at midpoints be- source. No power source shall have a capacity tween spreader beams. Use of loose traveling less than that required by the emergency circuit cables in hoistways should be avoided if possi- system. Automatic transfer devices shall be lo- ble, or sheave guards should be used to contain cated in protected places and adequately an- the cables. Motor generators, motor drives, and chored. traction machines shall meet the criteria given (5) The principal alternate power source for mechanical systems in paragraph 6-7f. shall be a generator set driven by an acceptable (2) Hydraulic elevator equipment should be prime mover located on the premises, preferably properly secured and splash-proof oil tanks at ground level. If possible, a generator with an should be used. integral radiator cooling system should be used. (3) All elevator door frames must accom- If an auxiliary cooling system is necessary, the modate predicted interstory movement to pre- cooling tower or remote radiator should be in- vent jamming. Selector and controller panels and stalled at grade level. All equipment and piping their components must be adaquately secured. 6-9 TM 5-809-10-1 /NAVFAC P-355.1 /AFM 88-3, Chapter 13, Section A 27 February 1986 Heat-sensitive call and floor buttons shall not overturning, and inhibit resonance. be used. (5) Equipment without vibratoryisolation. f. Mechanical. The seismic design of me- All equipment shall be bolted or rigidly attached chanical systems requires attention not only to by other means to the floor slab or supporting ) the various system components, but also to their structural member. Suspended equipment shall interfaces and linkages, since failure most often be adequately braced against movement in all occurrs at these points during an earthquake. directions or mounted tightly against a struc- Safe and easy access to all components shall be tural member. provided to facilitate maintenance and repair of (6) Piping. Pipes with an inside diameter the mechanical systems. A program of periodic of 21/2 inches or larger, as well as all fuel gas testing and inspection must also be established. pipes, acid waste pipes, and pipes within boiler (1) Water system. Two independent con- and equipment rooms, must be braced (Basic nections to the exterior water supply are re- Design Manual, chap 10, para 10-7). Maximum quired (Basic Design Manual, chap 12, paras 12- spacing for transverse bracing is 40 feet on cen- Sb and 12-Cc). Water testing equipment for ter, and for longitudinal bracing is 80 feet on monitoring the normal water supply and standby center. Transverse bracing for one pipe section chlorination equipment for disinfection of the may also act as longitudinal bracing for a per- water may also be necessary. A separate water pendicular pipe section if the brace is within 24 storage facility containing a water supply ade- inches of the connecting elbow or tee. Branch quate for the post-earthquake emergency pe- lines may not be considered bracing for the main riod shall be provided. The water distribution line. Each vertical riser shall be supported at a system within the facility shall be designed to point or points above its center of gravity. Also, conserve the emergency supply through the use laternal guides should be provided at the top of shutoff valves for branches to nonessential and bottom of the riser and at intermediate fixtures. points not to exceed 40 feet on center. Care must (2) Sanitary system. For high-occupancy be taken in routing piping. Piping should cross facilities such as hospitals, an emergency sew- building seismic or expansion joints only in the age-holding facility shall provide for temporary lower levels of the facility. Flexible joints and retention of sewage discharged during a period damage control valves must be provided where ) of four days. Sewer and vent lines must be pro- pipes pass through such joints, where rigidly '> tected from damage to structural deformation supported pipes connect to equipment on resil- or movement of adjacent elements. ient mountings, and where pipes enter and exit (3) Heating, ventilation, and aircondition- the facility. Piping shall be designed to prevent ing (HVAC) systems. Critical heating, venti- damage from movement of the structural sys- lation, and air conditioning requirements will tem. Pipes within a partition should be anchored vary according to the facility and location. Means to the same structural member as the partition. of closing off nonessential portions of the HVAC A rigid piping system should not be fastened to systems shall be provided and special attention dissimilar structural elements or building parts, shall be given to design of the portions that must since their responses to earthquake motion may remain functional following an earthquake. All differ. Appropriately located zone or damage HVAC equipment, piping, and ducts shall be de- control valves are required for unbraced pipes signed and braced according to the require- to limit system outages in case of failure. Malle- ments of this section. able rather than cast-iron fittings and valves shall (4) Equipment with vibration isolation. be specified. Pipe sleeves large enough to allow Much of the damage to mechanical systems that anticipated differential movement shall be pro- occurs during earthquakes is incurred by equip- vided where pipes pass through floors or walls. ment with vibration isolation, such as helical A 6-inch lateral clearance is required between springs, air cushions, rubber-in-shear mounts, unbraced piping and adjacent piping, ducts, or fiber-in-shear mounts. All vibration isolation hangers, and other elements. systems shall be capable of resisting the same (7) Ducts. Lateral bracing must be pro- horizontal force per inch of travel that is re- vided for all ducts with a perimeter greater than sisted the same horizontal force per inch of travel 120 inches and for all ducts in boiler and equip- that is resisted vertically. The systems shall be ment rooms. Maximum allowable spacing for attached to both the floor slab or supporting transverse bracing is 30 feet on center. Trans- structural member and the supported equip- verse bracing shall also be installed at each turn ) ment. Restraining devices shall be provided to in the duct and at the end of a duct run. Lon- limit all horizontal and vertical motion, prevent gitudinal bracing shall occur at 60 feet, maxi- 6-10 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A mum spacing. Transverse bracing for a duct Damage can be prevented by anchoring each section may also act as longitudinal bracing for partition along one edge to a single structural a duct section perpendicular to it, if the bracing member and allowing movement at the other is installed within 4 feet of the intersection of edges. Brittle facing materials, such as ceramic the ducts and if the bracing is sized for the larger tile or glazing masonry, suffer extensive damage duct. No bracing is required if attachment is during earthquakes and should be used only when made from the top of the duct directly to the necessary. supporting structural member; if the distance (3) Ceilings. Flexible ceiling systems, such between the top of the duct and the member is as exposed tee bar, concealed spline, or lumi- 12 inches or less; and if a 6-inch laternal clear- nous systems, shall not be used unless the fol- ance is provided between adjacent piping, ducts, lowing provisions are made (Basic Design hangers, or other elements. Walls, including Manual, chap 9, para 9-4a). They shall be braced nonbearing gupsum board partitions, may be at regular intervals against lateral and vertical considered transverse bracing for ducts that pass motion, cross runners shall be securely fastened through them. Ducts may be grouped in a la- to main runners with locking clips or wire ties, ternal bracing frame if the frame is sized and the ceiling shall be isolated from walls and par- designed for the total group. Diffusers, regis- titions by a soffit or edge angle wide enough to ters, and grilles shall be positively attached to allow movement, and hangers shall be provided the ductwork. If ducts are flexible, positive con- at the perimeter so that the wall does not sup- nections must also be made to the ceiling, wall, port the ceiling. Gypsum board and lath and or floor system. plaster ceilings are more rigid and, therefore, (8) Site utilities. All on-site utility lines tend to be more earthquake-resistant. However, shall be designed to minimize disruption by bracing shall be provided at regular intervals earthquakes (Basic Design Manual, chap 12). against vertical movement and at the perimeter Natural gas lines shall be equipped with earth- against lateral movement. Gypsum board ceil- quake-sensitive automatic shut-off valves in ad- ings shall be reinforced at nail points with steel dition to manual shut-off valves. Dual supply nailing strips. Allowance shall be made at ceil- systems shall be separated as much as possible ing openings for movement of diffusers, sprin- to limit the chance of simultaneous disruption klers, and other equipment connected to rigid of both supplies. mechanical systems. g. Architectural. Architectural systems, par- (4) Light fixtures. No light fixture shall ticularly walls, ceilings, and floors, shall be be installed without positive attachment to the detailed to maintain the integrity of building supporting element by means of bolts or locking seismic or expansion joints. If these elements devices (Basic Design Manual, chap 10, para are continued without break over the joints, they 10-6). Fixture accessories, such as louvers, dif- may act to tie the building sections together, fusers, and lenses, shall also have lock or screw thus changing the response to seismic motion. attachments. Recessed and lay-in fixtures shall (1) Exterior wall systems. Allowance of in- be supported by and secured to the main run- terstory drift is extremely important in detail- ners of the ceiling support system, not furring ing exterior wall systems, including glazing. The cross runners or nailing bars. Where the posi- calculated story drifts or 1/2-inch, whichever is tions of the main runners do not coincide with greater, shall be used in design. Special atten- the lighting configuration, auxiliary support tion must also be given to the method of an- members of equal strength shall be provided. choring exterior wall panels (Basic Design Secondary supports consisting of two wires, each Manual, chap 9, para 94b). Care should be taken capable of supporting four times the fixture to prevent corrosion from reducing the strength weight, shall be placed at the diagonal corners of the connections. Stone panels with metal an- of each fixture and attached to the structural chors are particularly susceptible to damage system. Pendant fixture should not be used, since during earthquakes and are not recommended they are highly susceptible to damage from for use on buildings with predicted interstory earthquakes and can also inflict considerable drift greater than L/300, where L is the height damage on ceilings because of their large re- between floors in the same units as the inter- sponse motions. If high ceilings necessitate the story drift. use of a lower lighting system, a supporting grid (2) Interior particions and facing mate- designed and braced according to ceiling re- rials. Interior walls and partitions that are not quirements should be used. shear walls be designed to allow for interstory (5) Horizontal and vertical projections. drift (Basic Design Manual, chap 9, para 9-4a). All balconies, overhangs, parapets, and other 6-11 TM 5-809-10-l/NAYFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 projecting elements shall be braced against lat- systems shall be adequately braced. eral and vertical movement. Special attention h. Essential support. For each facility, the must be given to elements that might be af- equipment essential to the performance of post- fected by deflection of the cantilevers. earthquake services shall be identified during (6) Storage units. Overturning or sliding the early stages of design. Guidance for medical storage units can cause personal injury in ad- systems in health care facilities is given in TM dition to disorder. Units shall be anchored and 5-838-2. In general, the following should be done braced to resist lateral and uplifting forces. Par- to insure that an element should survive an allel rows of racks, shelves, or file cabinets should earthquake in operable condition: have rigid bracing across the tops of the units -Check the adequacy of the element to re- to stabilize the entire configuration. File draw- sist its inertial force. ers and cabinets shall have latches that will pre- -Brace it in a manner convenient for daily vent their opening and subsequent spilling of use. contents during the earthquake. Shelves shall -Insure that it will not be damaged by be provided with face bars to prevent spilling of structural deformation or the failure or contents. movement of adjacent elements. (7) Computer floors. Computer floors shall i. Others. Throughout the design process, be adequately braced and drop-in panels de- care should be taken to identify elements that tailed to preven* displacement during an earth- merit special seismic considerations. Such ele- quake. ments may be unusually expensive equipment, (8) Essential or potentially hazardousfur- computer equipment, or elements in close prox- nishings. Furnishings that are essential for imity or critical equipment. The general guide- post-earthquake operation or that might pose a lines given for essential support equipment shall serious hazard either to persons or to essential also apply to these elements.

)

6-12 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A CHAPTER 7 STRUCTURES OTHER THAN BUILDINGS

7-1. Introduction. prescribed degree of redundancy can be dem- This chapter prescribes the seismic design cri- onstrated. This is justified on the basis that these teria for structures other than buildings that structures generally do not have the multiplicity must remain intact or functional after a major of structural and nonstructural resisting ele- seismic disturbance. This includes structures, ments characteristic of most buildings. Excep- independent of buildings, that are located on tions: redundancy can be assumed for ductile the ground. The criteria and design standards structures for the following: of this chapter provide a dynamic analysis ap- (1) When the structure consists of two col- proach to the seismic design of structures other umn lines of lateral-force-resistance in each than buildings that is used in lieu of the lateral principal horizontal direction of motion and there static force procedure of the Basic Design Man- are a minimum of four vertical elements in each ual, chapter 11. column line designated to resist the horizontal forces, flexural strength requirements may be 7-2. General requirements. exceeded by a value up to 15 percent. Structures other than buildings will be designed (2) When the structure consists of four col- in accordance with the general requirements and umn lines with a minimum of four vertical ele- the design and analysis provisions of chapter 4 ments each to resist horizontal forces in each of this manual, with the exceptions noted in this direction, or where there are two column lines chapter. with a minimum of eight vertical elements each a. Damping. Damping values for structures to resist horizontal forces in each direction, flex- other than buildings will be lower than the val- ural strength requirements may be exceeded by ues allowed for buildings of similar lateral-force- a value up to 25 percent. resisting systems. Thus, damping values of table 4-1 will be modified, as shown in table 7-1. The 7-3. Elevated tanks and other Inverted lower damping will result in larger lateral forces pendulum structures. and distortions. This is justified because of the Structures that represent inverted pendulums, general lack of partitions and other nonstruc- such as an elevated tank supported by a tower tural elements that contribute to the energy- structure that is light in weight relative to the absorbing characteristics of buildings. Where it tank and contents, will use the lower damping can be demonstrated that these energy-absorb- values of paragraph 7-2a and will not be per- ing characteristics are present, the higher mitted the exception of paragraph 7-2b. The damping values may be used. value for W will include the effective weight of b. Structural component load effects. For the contents. The accidental torsion will be com- structures other than buildings, the percent- puted as for buildings. The structure will be ana- ages of exceedance to strength requirements of lyzed for earthquake forces in any horizontal paragraph 4-3e(1) are not permitted unless a direction. Table 7-1. Damping values for structures other than buildings.

Buildings Structures Other Than Buildings 0.03 0.015

0.05 0.02

0.07 0.05

0.10 0.07

US Anmy Corps of Engineers 7-1 TM 5-809-1O-1INAVFAC P-355.1/AFM 88-, Chapter 13, Sectlon A 2 eray18 a. Elevated tanks on cross-braced columns. eration on the design response spectrum unless The provisions of the Basic Design Manual, par- a lower value can be substantiated by a properly agraph 11-3b, generally apply. calculated period of vibration for the tank struc- b. Hydrodynamic effects. The provisions of ture. ) the Basic Design Manual, paragraph 11-3b gen- b. Hydrodynamic effects. For tanks where erally apply. The procedure for analyzing a two- the liquid is not rigidly contained, the hydro- degree-of-freedom system, taking into account dynamic effects of the sloshing liquid may be the effects of the sloshing liquid, may require a considered. The rigid body forces will be deter- parameter study representing various levels of mined from the peak spectral acceleration on liquid containment. The response characteris- the design response spectrum, and the sloshing tics will vary with the percentages of liquid in liquid forces will be determined by the spectral the elevated tank. Thus, the critical condition acceleration consistent with the sloshing period may not always occur with a full tank. For ex- (Basic Design Manual formula 11-4, para 11- ample, the analysis might consider the condition 3a(2) (b)) . of the tank three-fourths full, one-half full, and one-fourth full. 7-5. Horizontal tanks (on ground). c. Elevated tanks, pedestal-type. Pedestal- The provisions of the Basic Design Manual, par- type elevated tanks will not be permitted in zones agraph 11-5, generally apply. Response spectra of high seismicity (i.e., Basic Design Manual may be substituted for base shear coefficients seismic zones 3 and 4). where applicable. 7-4. VertIcal tanks (on ground). 7-6. Retaining watts. The design criteria for vertical storage tanks on The provisions of the Basic Design Manual, par- the ground will follow the general procedures agraph 11-6, generally apply. Response spectra prescribed in the Basic Design manual, para- may be substituted for base shear coefficients graph 11-4, except that response spectra will be where applicable. substituted for coefficients ZIKCS. a. Rigidly contained liquid. For tanks in 7-7. BurIed structures. which the liquid is rigidly contained (i.e., slosh- The provisions of the Basic Design Manual, par- ) ing prevented), for tanks holding highly viscous agraph 11-7, generally apply. Response spectra - materials, and for pressure tanks, the design may be substituted for base shear coefficients forces will be based on the peak spectral accel- where applicable.

7-2 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A APPENDIX A SYMBOLS AND NOTATIONS

A-1. Symbols and notations t = time in seconds Symbols and notations are divided into two sec-

A-2 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A APPENDIX B REFERENCES

Government Publications. Department of the Army. TM 5-809-10 Seismic Design for Buildings TM 5-838-2 Army Health Facility Design Department of the Air Force. AFM 88-3, Chapter 13 Seismic Design for Buildings Department of the Navy. NAVFAC P-355 Seismic Design for Buildings NAVFAC P-355.1 Seismic Evaluation of Supports for Existing Electrical-Mechanical Equipment and Utilities National Bureau of Standards (NBS). National Technical Information Service, 5285 Port Royal Road, Springfield, VA, 22161 or Superintendent of Documents, U.S. Government Printing Office, Washington, DC, 20402 Special Publication 510 (514 pages), Tentative Provisions for the Development of Seismic Reg- ulations for Buildings (ATC-3-06), 1978 Nongovernment Publications. National Fire Protection Association, Inc. (NFPA) Batterymarch Park, Quincy, MA, 02269 NFPA No. 13, Sprinkler Systems NFPA No. 20, Centrifugal Fire Pumps NFPA No. 76-A NFPA P. 70, Article 700 Stanford University, The John A. Blume Earthquake Engineering Center, Stanford, CA, 94305 Technical Report No. 36, Computer Programs for Seismic Hazard Analysis-A User Manual (STASHA), G. A. Guidi, 1979 American Concrete Institute (ACI), Box 19150, Redford Station, Detroit MI, 48219 ACI 318-77, Building Code Requirements for Reinforced Concrete Portland Cement Association (PCA), Old Orchard Road, Skokie, IL, 60076 Advanced Engineering Bulletin No. 20, Biaxial and Uniaxial Capacity of Rectangular Columns, 1967

B-1 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A APPENDIX C GROUND MOTION BACKGROUND DATA

C-i. Earthquake Source and Earthquake of the ratio of the maximum amplitude on a Size Definition. seismogram written by a Wood-Anderson seis- The actual release of earthquake energy along mometer at a distance of 100 kms (62 miles) the fault plane in the crust of the earth is a very from the epicenter and the standard amplitude complex phenomenon. All the physical proc- of one thousandth of a millimeter. Tables were esses that occur just before, during and after a constructed empirically to reduce from any given seismic event are still not completely under- distance to 100 kms. Since the scale is logarith- stood, and considerable research is going on to mic, an increase of one step on the magnitude better describe this phenomenon. However for scale increases the amplitude scale by a factor engineering purposes, the above complex phe- of 10. (See fig. C-3). nomenon is idealized, and figure C-1 gives the c. Other magnitude measures. In recent resulting simplified model representation of the years, different types of instruments are used earthquake source. to obtain similar magnitude values which are a. Earthquake location. Epicenter and Hy- referred to as local magnitude, ML. The body pocenter are the two terms most commonly used wave magnitude mb and the surface wave mag- to describe the source location of an event. Even nitude Ms are also used. In most studies, the though most of the seismic energy is released local amplitude scale ML is taken as a Richter as the fault ruptures and that a substantial vol- magnitude. This assumption does introduce some ume of the earth's crust (along the fault plane) errors in magnitude assignments. The local is involved, it is generally assumed that there magnitude scale ML can be related to the body exists a discrete point where the rupture initi- wave magnitude mb and the surface wave mag- ates. This point where the initial rupture of the nitude MS by the following empirical relation- rocks within the earth's crust begins is called ships: the hypocenter. The point directly above the hy- 34 pocenter on the earth's crust is called the epi- ML = 1. mb - 1.71 (eq C-1) center. In recent times (since the beginning of ML = 2.2Oms - 3.80]'2 + 2.97 (eq C-2) seismographs), the location of the hypocenter and hence the epicenter is made by means of Surface-wave magnitude M. is usually based on instruments. Before the advent of the instru- the amplitude of 20 second waves recorded at ments, the epicenter was located by means of distances of thousands of kilometers. The rea- finding the region of intense shaking. It is quite son for preferring local magnitude is that for often that the field epicenter (region of intense large earthquakes the surface-wave magnitude shaking) and the instrumentally located epicen- may increase as the physical size of the source ter do not coincide. See figure 3-22. region increases without a corresponding in- b. Earthquake size. Various empirical rela- crease in the amplitude of ground motion in the tionships are available to relate the size of the period range affecting normal structures. This event with the rupture length and fault slip. The is well illustrated by the Kern County earth- fault rupture length is the length of the fault quake of 1952 which had a surface wave mag- that actually breaks on the surface of the earth. nitude of 7.7 and a local magnitude of 7.2 and The fault slip is the relative displacement of the by the San Francisco earthquake of 1906 with a two plates with respect to each other at the fault surface-wave magnitude of 8.25 and a local mag- plane. Figure C-2 shows different types of fault nitude of 7.2 or less. It is generally believed that slips. Again, empirical relationships are avail- the local magnitude scale saturates in the range able to relate earthquake size with slip length. of 7 to 7.5. The largest measured value to date To define the size of an earthquake, Charles is 7.2. Richter developed a Richter Magnitude scale. This d Seismicmoment. As more is known about scale is intended to be a rating given to an earth- the earthquake source mechanism and about the quake event, independent of the location of ob- size of earthquake events, it is becoming in- servation. The size was determined by means of creasingly clear that the existing magnitude a standard Wood-Anderson seismometer, with scales are extremely inadequate to describe the natural period of 0.8 seconds. Richter defined overall size or the energy content of earthquake the Magnitude as the logarithm to the base ten events. To overcome this deficiency, seismolo-

C-1 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 North' Fault Trace

Strike / /

Epie erFal

[ /g~~Angle X

Hypocenter

Direction of Wave Travel r Surface Waves _ z ~~~Ground Surface t

For P-zipWae -- R-WavPte o Particl Particle Motion jPWave ~~~ricle Direction of

\ot Motion/~ ~ ~ ~ ~~ c n of

Hypocenter

US Army Corps of Engineers Figure C-1. Earthquake source model

C-2 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Seicil A

a. STRIKE-SLIP FAULT b. NORMAL-SLIP FAULT (LEFT-SLIP FAULT) AB - dip-slip= slip AC - throw or vertical component AB-strike-stipEslip eC heave or horiz. extension

c. REVERSE-SLIP (THRUST) FAULT d. LEFT-OBLIQUE-SLIP FAULT 4. AB - reverse-slip - slip .1") *. AC = throw or vertical component AB= oblique-slip = slip BC = heave'= horiz. shortening AC = dip-slip component AE - strike-slip component AD v throw = vertical component DC a heave = horiz. extension

US Army Corps of Engineers Figure C-2. Types of fault slips.

_11 -

TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

AMPLITUDE A P SI 23 mm

A^"

100 6- 5 C -5- - 20 200- - I0 4- 5 100 10 - 2 60 _ I 40 ) 4 2- - 0.5 0.2 20- - 2 2~~~~~~ 3 0.1 0-5 - 2-0 O DISTANCE S-P MAGNITUDE b IPL)TUDE km sec mm *D A SO DItTLxE zARTHQvAxr MACNITUDI YE CONHECT 0. THE CHMAT

A. THE MAXMllN MPLITUDE RECOR.DI BY A STANDARD SEISMOKETER, AID 5. TUE DISTANCE SEISXOIITETU FRO#ITHE EPICENTER OF THE EARTHQUAKE (Ol DITIERZECe IN ARRIVAL TIMES Of F AND S WAVES) nI C. A STRAICIT LINE. D. READ THE IXlCHTUD1, ON CENTER SCALE.

Reprinted from "Elementary Seismology,' C. F. Richter. 1958, with permission from W. H. Freeman and Company.

Figure C-3. The Richter Scale.

C-4 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A gists have introduced a new "physical" param- the ruptured zone. Comparative values of the eter called seismic moment, M., to describe the surface wave magnitudes and seismic moments size of an earthquake. This parameter is related of some famous earthquakes are given in table to the size of the fault rupture area, the average C-1. slip on the fault and the property in shear of

Table CGe. Magnitude and seismic moment. Earthquake M M S 0 1960 Chili Earthquake 8.3 to 8.5 2. 5 x .1030 dyne-cms 1964 Alaska Earthquake 8.3 to 8.4 7.5 x 1029 dyne-cms 1976 Tangshan Earthquake 7.8 to 8.0 1.0 x o027 dyne-cms 1906 San Francisco Earthquake 8.2 to 8.3 1.0 x 1028 dyne-cms 1971 San Fernando Earthquake 6.4 1.0 x 1029 dyne-cms

US Army Corps of Engineers

In order to relate this new size parameter with become more common. Table C-4 shows the ap- the existing magnitude scales, a moment mag- proximate relationship between the MM scale nitude (Mm) is introduced. In the ML range of and the RF scale. It is important to note that all 5.5 to 7.0, Mm corresponds to ML. Mm is related of the above scales are subjectively assigned by to seismic moment M. by the following empirical investigators after observing and reviewing the relationship. earthquake effects in a given region. The assignment of proper intensity value therefore re- Mm = ilogM, - 10.7 (eq C-3) quires a careful analysis of the affected region. M. is defined as: Unless the guidelines for assigning intensities are properly and correctly followed, there could Mo=GAS (eqC,4) be an error in the assigned value. where f. Relations for magnitude and intensity. G = average shear modulus over the rupture Empirical relationships are available in the lit- zone erature to relate the magnitude of an earthquake and the epicentral intensity. The following A = fault rupture area show such relationships. S = average slip on the fault during the Gutenberg and Richter (1956) (Biblio 87), earthquake ML = 1 + 1il (eq C-5) e. Intensitymeasures. Another means of de- Krinitzky and Chang (1975) (Biblio 92), scribing the size of an earthquake at a given location is the intensity scale. The two intensity ML = 2.1 + 110 (eq C-6) scales used in the United States are? Chinnery and Rogers (1973) for Northeast- -The Rossi-Forel Scale (RF Scale) ern United States (Biblio 85) -The Modified Mercalli Scale (MM Scale) ML = 1.2 + 0.6I, (eq C-7) Where the Modified Mercalli Scale is the most where ML = Richter Magnitude or local mag- common. A simplified version of this scale is given nitude in Table C-2. Table C-3 gives the Rossi-Forel scale. The russian scale is very similar to the I = Modified Mercalli Intensity in the epi- MM scale. The RF scale which was developed in central area the late 19th century was used in this century All such relationships, including those derived until 1930. Since then, use of the MM scale has for specific sites where specific data are avail- C-5 TM 5-809-10-1NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Table C-2. The Modified Mercalli intensity scale. Mercalli's (1902) Improved 1nternsity scale served as the basis for the scale advanced by Wood and Nuemann (1931). known as the modified Mercalli scale and commonly abbreviated MM. The modified version Is described below with some improvements by Richter (1958). To eliminate many verbal repetitions In the original scale, the following convention has been adopted. Each effect is named at the level of intensity at which it first appears frequently and characteristically. Each effect may be found less strongly or more often at the next higher grade. A few effects are named at two successive levels to indicate a more gradual increase. Masonry A, B. C, D. To avoid ambiguity of language, the qualfty of masonry, brick, or otherwise is specified by the following lettering (which has no connection with the conventional Class A, B. C construction). Masonry A. Good workmanship, mortar, and design; reinforced, especially laterally, and bound together by using steel, concrete, etc.; designed to resist lateral forces. Masonry B. Good workmanship and mortar; reinforced, but not designed in detail to resist lateral forces. Masonry C. Ordinary workmanship and mortar; no extreme weaknesses like failing to tie in at corners, but neither reinforced nor designed against horizontal forces. Masonry 0. Weak materials, such as adobe; poor mortar; Tow standards of workmanship; weak horizontally. Modified Mercalli Intensitv Scale of 1931 (abriqed and Rewritten dv C. F. Richt-e-7). I. Not felt. Marginal and long-period of large earthquakes. 11. Felt by persons at rest, on upper floors, or faborably placed. Ill. Felt indoors. Hanging objects swing. Vibra- tion like passing of light trucks. Duration estimated. May not be recognized as an earthquake. IV. Hanging objects swing. Vibration like passing of heavy trucks or sensation of a jolt like a heavy ball striking the walls. Standing motor cars rock. Windows, dishes, doors rattle. Glasses clink. Crockery clashes. In the upper range of 4, wooden walls and frames crack. V. Felt outdoors; direction estimated. S'eepers wakened. Liquids disturbed, some spilled. Small unstable objects displaced or upset. Doors swing, close, open. Shutters, pictures move. Pendulum clocks stop, start, change rate.

Reprinted from "Elementary Seismology," C. F. Richter, 1958, with permission from W. H. Freeman and Company.

C-6 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Table C-2. The Modified Merca li intensity scale-continued. VI. Felt by all. Many frightened and run outdoors. Persons walk unsteadily. Windows, dishes, Olassware broken. Knickknacks, books, and so on, off shelves. Pictures off walls. Furnittere moved or overturned. Weak plaster and masonry IIcracked. Small bells ring (church, School). Trees, bushes shaken visibly or heard to rustle. VII. Difficult to stand. Noticed by drivers of motor cars. Hanging objects quiver. Furniture broken. Damage to masonry D including cracks. Weak chimneys broken at roof line. Fall of plaster, loose bricks, stones, tiles, cornices, unbraced parapets, and architectural ornaments. Some cracks in masonry C. Waves on ponds. water turbid with mud. Small slides and caving in along sand or gravel banks. Large bells ring. Concrete irrigation ditches damaged.

VIII. Steering of motor cars affected. Damage to masonry C; partial collapse. Some damage to masonry B; none to masonry A. Fall of stucco and some masonry walls. Twisting, fall of chimneys, factory stacks, monuments, towers, elevated tanks. Frame houses moved on foundations if not bolted down; loose panel walls thrown out. Decayed piling broken off. Branches broken from trees. Changes in flow or temperature of springs and wells. Cracks in wet ground and on steep slopes. IX. General panic. Masonry D destroyed; masonry C heavily damaged, sometimes with complete collapse; masonry B seriously damaged. General damage to foundations. Frames racked. Conspicuous cracks in ground. In alluviated areas, sand and mud ejected, earthquake fountains, sand craters.

X. Most masonry and frame structures destroyed with their foundations. Some well-built wooden structures and bridges destroyed. Serious damage to dame, dikes, embankments. Large landslides. Water thrown on bansk of canals, rivers, lakes, etc. Sand and mud shifted horizontally on beaches and flat land. Rails bent slightly.

XI. Rails bent greatly. Underground pipelines completely out of service. XII. Damage nearly total. Large rock masses displaced. Lines of sight.

Reprinted from "Elementary Seismology, C. F. Richter, 1956swith permission from W. H. Freeman and Company.

C-7 TM 5-809-10-1 /NAVFAC P-355. 1/AFM 88-3, Chapter 13, Section A 27 February 1986

Table C-3. The Rossi-Forel scale. The most commonly used form of the Rossi-Forel (R.F.) scale reads as follows: I. Microsiesmic shock. Recorded by a single seismograph or by seismographs of the same model, but not by several seismographs of different kinds: the shock felt by an experienced observer. II. Extremely feeble shock. Recorded by several seismographs of different kinds; felt by a small number of persons at rest. III. Very feeble shock. Felt by several persons at rest; strong enough for the direction or duration to be appreciable. IV. Feeble shock. Felt by persons in motion; disturbance of movable objects, doors,' windows, cracking of ceilings. V. Shock of moderate intensity. Felt generally by everyone; disturbance of furnature, beds, etc., ringing of some bells. VI. Fairly strong shock. general awakening of those asleep; general ) ringing of bells; oscillation of chandeliers; stopping of clocks; visible agitation of trees and shrubs; some startled persons leaving their dwellings.

VII. Strong shock. Overthrow of movable objects; fall of plister; ringing of church bells; general panic, without damage to buildings. VIII. Very strong shock. Fall of chimneys; cracks in the walls and buildings.

IX. Extremely strong shock. Partial or total destruction of some buildings. X. Shock of extreme intensity. Great disaster; ruins; disturbance of the strata, fissures in the ground, rock falls from mountains.

Reprinted from "Elementary Seismology," C. F. Richter, 1958, with permission from W. H. Freeman and Company. L'w

C-8 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A Table C-. The relation between Modified Mercalli intensity (MM) and Rossi-Forel intensity (RF).

MM RF

II I-II

III 1III

IV IV-V V V-VI

V I VI-VI1

VII VII I VIII VIII+ to IX-

IX IX+

X-XII X

Reprinted from "Elementary Seismology," C. F. Richter, 1958, with permission from W. H. Freeman and Company.

able, are extremely approximate and the scatter acceleration time history to account for instru- of data about the predicted lines is large. Note ment bias and base line correction, the resulting that much of the scatter is due to the necessity corrected acceleration record can be used by en- of empirically converting site intensity data to gineers. This corrected acceleration record can the equivalent 10 value at the epicentral area; yield ground velocity and ground displacement so as to normalize the site distance attenuation by appropriate integrations, see figures 2-1, and effects. Figure C-4 (taken from Krinitzky and 2-2 in paragraph 2-3b. Chang, Biblio 91) shows the above relationships h. Relations for recorded ground motion and along with the data behavior. intensity. To relate the instrumentally re- g. Recording instruments for ground mo- corded parameters such as acceleration, velocity tion. With the introduction of modern strong and displacement with intensity parameters, motion instruments, the size of the ground mo- empirical equations have been developed by var- tion at a given location is often expressed by ious researchers. It should be cautioned again means of the instrumentally recorded ground that such relationships are obtained from widely motion parameter. The most commonly used in- scattered and sparse data and should only be struments for engineering purposes are the used with recognition of their inherently large strong motion accelerographs. These instru- prediction error. From studies related to earth- ments record the acceleration time history of quake damage estimation and earthquake in- ground motion at a site. Figure 2-1 of paragraph surance, it has been observed that the Modified 2-3b shows a typical accelerogram recorded by Mercalli intensity scale is the easiest and most such an instrument. By proper analysis of this convenient with which to work. Most of the C-9 -

TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

,0X

LEGEND

* MC EVIL.LY. RAMIN, AND CASAI o CorFMAN AND VON HAKE

3V 3E s lr :1= xt: x Xan MM INTENSITY

Reprinted from "Specifying Peak Motioas for Design Earthquakes." Krinitzski, E. L. and Chang, F. K., Report No. 4 in the ) series, State-of-the-Art for Assessing Earthquake Hazards in the United States, U.S. Army Engineers Waterways Experiment Station, Misc. Paper S-73-1, 1975. Figure C-4. Relation between earthquake magnitude and intensity.

available damage statistics are related to the Gutenberg and Richter (1942) log A = - 0.5 + 0.331 MM intensity at a site. However, for the rela- (Biblio 88) (eq C-8) tively recent instrumentally recorded data, the Hershberger (1956) log A = - 0.9 + 0.43I information on ground motion is usually in the (Biblio 89) (eq C-9) form of a peak ground motion parameter such Ambrasey (1974) log A= -0.16+0.36I (Biblio 84) (eq C-10) as the PGA, and many empirical relationships Trifunac and Brady (1975) log A = 0.014 + 0.31 are available in the literature to relate the MM (Biblio 103) (eq C-il) intensity with the PGA. Peak ground acceleration is an instrumentally recorded continuous variable whereas Modified Mercalli intensity is All the above relationships are log-linear in for- a subjectively assigned discrete integer variable. mat. Recent work by McCann and Shah (Biblio Thus, it should be expected that there will be a 100) has shown that the assumption of a log- range or increment of continuous PGA values linear relationship between PGA and MMI may corresponding to a given intensity level. In the not be a reasonable one. Figure C-5 shows the past, a number of researchers have developed following suggested relationship with two other PGA-MMI relationships. In each of the rela- relationships from above: tionships given below, I is Modified Mercalli in- McCann and Shah (1979) log A = -0.024I2 + tensity and A is peak ground acceleration in cm/ (Biblio 100) 0.5951-0.68 sece. (eq C-12) C-1 0 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

1.001

0.80.

0.60. Anbraseys

0. 40 ( Suggst.ed Relationship

! 0.20 W

-CI. Gutenberg and Richter

' 0.10 I 0.08

. 0.06

0.04

0.02

IV V VI VII VIII IX X XI Xi

Modified Mercalli Intensity

US Army Corps of Engineers Figure C-5. McCann and Shah relationship.

In this relationship, it is assumed that a range tics of the structure. This paragraph provides of peak ground acceleration values are associ- the definitions and discussions of the response ated with each intensity level. Figure C-6 shows spectrum representation of this inter-relation- the PGA-MMI relation and the interval associ- ship between ground motion input and struc- ated with each intensity. Table C-5 lists this range tural response. of PGA values associated with each MMI level. a. Single degree-of-freedom system response. Figure C-7 shows the system and the C-2. Response Spectrum Representation definition for seismic input and response. of Seismic Ground Motion at Site. (1) Response to General Input x(t). For Seismic ground motion may be roughly char- any given ground acceleration X(t), the relative acterized as a set of time-varying harmonic vi- displacement response is brations having a fairly broad range of U(t) = - 1 t (re (-) frequencies. Structures subjected to this input (eq C-13) motion tend to amplify the harmonics near their sin1rD(t-T)JdT own natural frequencies and filter or attenuate the others. The resulting structural response and for the case of zero damping this equation therefore, depends upon the frequency content simplifies to of the harmonics in the ground motion and their u(t) = - I f(.r)sin[w(t-.r)JdT (eq C-14) relation to the dynamic frequency characteris- C-aI TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

1 .00I I N 0.Do X- 1 '11Z 0.60 _

0.40

?CA Interval U 0.20j

Va,

0.10.

U .4 0.0a

0.06, N. N N'. 0.Q4

0.02

V VI VII Vill IX X Xi XlI

ModifIed Kercalli Intensity

US Army Corps of Engineers Figure C-6 The PGA-MMJ relationshipshown with the intervals assocated with each intensity.

zI)

C-12 27 February 1986 TM 5-809-10-1/NAYFAC P-355.1/AFM 883, Chapter 13, Section A

Table C-5. Relationship between MMI and PGA.

HMI PGA(in g unit)

V 0.03< A ' 0.08

VI 0.08' A' 0.15

VII 0.15' A< 0.25

VIII 0.25< A< 0.45

IX 0.45< A< 0.60

X 0.60' A< 0.80

XI 0.80< A< 0.90

XII A> 0.90

Reprinted from "Elementary Seismology," C. F. Richter, 1958, with permission from W. H. Freeman and Company.

C-1 3 TM 5-809-10-1/NAYFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

| / | C = K = Stiffness / S~~~amping/

x(t)|

System Properties

= j KM= undamped natural frequency

0 = 2 = fraction of critical damping

wD = wU 2 - damped natural frequency

Ground Motion

x(t) = displacement

x(t) = d = velocity

'x(t) = 2= acceleration dt

US Army corps of Engineers Figure -7. Single degree of freedom system.

C-14 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1 /AFM 88-3, Chapter 13, Section A Relative velocities and accelerations are given most useful in the explanation of how predom- by the time derivatives u(t) and d(t) respec- inant harmonics in ground motion, due to spe- tively. tWD is damped natural frequency. cial soil conditions, can p'i. vlify the ordinates of (2) Response to Sinusoidal Input. If the the response spectrum. ground acceleration i(t) were to be a single unit b. Response spectra. For a given ground ac- amplitude sinusoid at frequency 0 celeration x(t) such as shown in figure 2-4, and I(t) = sinflt then the corresponding response given damping, the absolute maximum values is given by u(t) = [H(wj)]sin [fit + + found from the complete time history solution of equation C-13 provide the response spectrum where + is a phase angle and values at the system frequency woor period T= 2w . A response spectrum is traditionally HM [ dd(lIflz)2+4SU,)2]v2 (eq C-15) presented as a curve connecting the maximum response values for a continuous range of fre- is the system frequency response function which values, such as shown in fig- the response ac- quency or period either amplifies or attenuates ures 2-4 of paragraph 2-3c. cording to the frequency fbw ratio, and the damping ratio I, see figure G-8. This function is The different response spectra are defined as:

US Army Corps of Engineers Fiure C-8. Maximum dynamic load factor for sinusoidalload. C-15 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 SD = u(t) maxRelative Displacement ification of the acceptable risk of exceeding the Response Spectrum structural performance levels such as the dam- SV = ti(t) max =Relative Velocity age threshold, functionality level, and condem- SV~ ~ RsoneSecrmnation threshold, in order to'establish the corresponding level of ground motion severity. SA = 9(t) max= u(t) + x(t) max a. Selected representative ground motion. = Absolute Acceleration Response Given the structure site, its soil column condi- Spectrum tions, and the geological description of the ef- Then using th close approximationofa)=)Dfor fective earthquake sources and their corre- A0.1, the more commonly employed versions sponding travel paths to the site: a set of time for engineering purposes are: histories (commonly three to five) is selected so as to have reasonably similar soil columns, source Sv = w (SD) = Pseudovelocity Spectrum and travel path characteristics, distances, and (eq C-16) magnitudes with these conditions at the site. 2 . The magnitude is selected according to the per- (e C-19t formance and reliability criteria for the struc- (eq '-19) ture. Both actual records and artificially For the common structural damping values, and generated time histories are both used for the the earthquake type of input motion, there is selected set. essential equality for the real and pseudo- (1) This method has the advantages of pro- values, viding a definite set of structural response time SvaF SV (eq C-18) histories or response spectra. These results may Sv SV be (eqaveraged 18) to provide a single description of S. ~ SA (eq C-19) forecasted structure performance. The set of re- Of course, for long period structures, the veloc- sponse spectra may be averaged (arithmetically ity equality breaks down since Sv approaches or graphically) to provide the most represent- zero, while SV approaches PGV. This is because ative response spectrum ordinates in the par-, zeroawhile dsplapproahesapGV.This ise beause ticular period range of the structural system. displacementrelativedisplacement value, andapproaches there therelis small gioundmotion uaineatosndpcrl(DFsheswhThis method does not require the use of atten- of the mass. The relationships between SD, Sv and spectral (DAF) shapes With A) and S. can be justified by the following physical their high variances of prediction error. behavior of the vibrating system. At maximum (2) The disadvantages are that it is often-- relative displacement SD, velocity is zero, and difficult to find the representative records that maximumspring force equawould correspond to the particular site condi-- tia forcex tion; and the end results are based on an av- tia force, erage representation of a very small sample. k(SD) = m S. Much depends upon how sincerely the engineer giving Sv = k/m(SD) =) 2(SD) (eq C-20) believes that the selected small sample can actually forecast the future ground motion. Fur- their computation from reas s are given ther description and discussion is given in (Biblio in (Biblios 7,3,12). An example of a typical accelerogram spectrum is shown in figure 2-4. Also b. Analyticalsite-soilcolumn response. This because of the relations S. = w Sv = 2gd, it is method uses a somewhat similar method to that Decase r t e rahon w.= X v= d, I ISof the selected method in C-a. The main dif- possible to represent spectra on tri-partite log f the selected timeGhistorie must paper, see figure 3-29 in paragraph 3-6e(l). ference IS that the selected time histories must paper, sbe representative of bed rock motion. For a given magnitude, a set of rock site accelerograms is C3. Methods of forecasting earthquake selected (or scaled) so as to best represent the ground motion. forecasted duration, amplitude and spectrum The following methods of ground motion spec- shape of the site bed-rock motion. Then with the ification are employed by engineers for the seis- data from the site soil boring investigations, a mic resistant design of structures ranging from dynamic model of the site soil column is for- nuclear facilities to ordinary buildings. Herein mulated. This model is subjected to the set of the term "ground motion" is used in its general bed rock motions and the resulting set of site sense to include both, the time history and re- surface time histories is obtained. These histo- sponse spectrum representations of earthquake ries or their averaged (and smoothed) spectra effects. Also, all methods require an initial spec- are used for the structural input. The principal C-1 6 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A advantage of this method is that it provides the prediction error (50 to 100%) about the central best analytical representation of the effects of or median predicted value. the site soil column on the surface response. The (2) The PGA at the site is represenative of disadvantages are inherent in the selected spec- accelerogram peak records. This "instrumen- ification of the limited set of bed rock time his- tal" value is converted (by judgement) to an tories, and in the accuracy of the analytical model effective EPA value, which when used to scale of the site soil column. The uncertainties due to the spectral (DAF) shape should produce a re- a small data set to represent the future forecast liable structural response spectrum. With the are also present as in the method C-3a. (Biblios "properly" formulated analytical model of the 93,98,99) give detailed discussions on this method. structure, this spectrum "should" provide a re- In the assignment of a particular weight, as will liable estimate of the actual structural defor- be discussed in paragraph C-3f, of preference mations that would result from the event or any for the spectral shape as provided by a site soil- one of the events included in the seismic hazard column response analysis, the following items analysis (with stated risk of exceedance such as should be considered and assessed for validity 10% in one-hundred years). This method is based and applicability: on the statistical principle that the best predic- (1) The time histories and scaling factor for tion of the future is the average behavior of bed-rock earthquake motion. Are the histories many past records. Despite the disadvantages inclusive of duration and frequency content rep- listed below, it is a common practical way to resentative of the various possible sources and forecasting and specifying ground motion. Its travel paths? Has the scaling factor (for PGA) results may be modified by the results of the been evaluated by a hazard analysis similar in other methods given herein. The disadvantages quality to that used for surface ground motion? are: (2) Soil-Column Model: Have adequate (a) The high prediction error in the at- boring investigations and related tests been made tenuation equations for PGA. to reasonably establish the dynamic model prop- (b) The high variability of the spectral erties. Is there adequate geological information shape DAF as obtained from the average of nor- to supplement the boring data? Is the model ap- malized spectra having roughly similar soil con- propriate for the site. ditions. The method of normalizing the spectra (3) Have a sufficient number of bed-rock to a common unity value of PGA contributes time histories been used to establish a reason- much to the high variability of the DAF shape. ably reliable statistical average and measure of d. Empirical forecasts of spectral ordinates. dispersion of surface motion spectra. This method is a refinement of paragraph C-3c, c. Empirical forecasts from representative where the response spectrum value S. or S, at records. This method involves two basic steps: a given period (rather than the zero period PGA given the risk of exceedance, forecast a spectral value) is attenuated from source to site. The scaling factor (PGA or EPA) corresponding to advantage is that the site spectrum is obtained this risk; then apply this scaling factor to a re- directly in terms of: the source-to-site distance, sponse spectrum shape (DAF) representative of the travel path geology, the event magnitude the general site soil column condition. The first and the site soil conditions. It is not necessary step may be either "deterministic" such that the to employ the highly variable empirical DAF most severe magnitude event occurs on the spectral shape as needed by the method in C-3c. source at the epicentral location nearest to the The disadvantage is that the attenuation rela- site: or may be probabilistic such that the union tions for the spectrum ordinates are much more or combination of the probabilities of all the subject to prediction error than these relations effective event magnitudes, sources, and epicen- for PGA. The available data for near-source tral locations is considered in the seismic hazard spectra and corresponding spectra at various site of the specified ground motion description (PGA) distances is from only a few recent events (such x (DAF). For a given magnitude of event M at as 1971 San Fernando and 1980 Imperial Val- a given source to site distance R, this method ley). The data is therefore both sparse and very consists of: sensitive to the geological conditions of the re- (1) Attenuation of the spectral scaling pa- gion where the records were obtained. rameter (such as PGA) to the site. These atten- e. Mathematical or theoretical modeling of the uation relations are derived from past data and seismic event. This method models the source vary according to the data used and the statis- fracture size and sequence of rupture impulses. tical model and fitting procedure (usually These impulses are then propagated by wave regression analysis). There is usually a large mechanics through a model of the source to site C-1 7 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 path. This allows inclusion of all that is both ect, the individual results should be reviewed for theoretically and empirically known about source consistency and resolution of significant differ- mechanics and site response (included are di- ences. Of course any knowledge available from rectivity and magnitude effects). Disadvan- results of the other methods can contribute to tages are lack of data and knowledge concerning this consistency and resolution process for the the faulting mechanism and the travel path ge- final ground motion specification. In actual ology. practice, when there are two or more sources of f Summary. For any actual site hazard study spectral shapes, the smoothing and averaging requiring specified ground motion description, process is done by judgement rather than by any the most popular methods are those in C-3b and formal statistical method, see figure C-9. C-3c. When both are used for a particular proj-

C-18 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Sa Empirical Mean Spectrum for Site Seismicity and Soil Class ( Judgemental Weight - 50% )

_ T

Analytical Results From Three or More Site Soil Column Response

Spectra ( Judgemental Weight - 50% )

Smoothed Average

-Final Weighted Judgement Shape

Analytical Average

US Amy Corps of Engineers

Figure C-9. Judgemental averagingof empirical and analytical site spectra.

C-19 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 C-4. Emperical relations for seismicity displacement, and earthquake magnitude, Bib- and fault activity. Ho (101) and degree of fault activity in terms of The following tables and figure are given to pro- slip rate, Biblio (100). vide supplementary information concerning empirical relationships between fault length, fault

Table C-B Magnitude-displacementrelation.

Equations of Beat Straight-Line Fit for Magnitude

Versus Log Displacement: H * a 4 b Log D

Stead rd CorrelatcJ,, Fault No. a b Deviation Coefficient

North Ajerics 21 6. tk5 0.995 0.595 O.BO0 Best of vorld 51 6.821 1.120 0.51,9 C.463 Yorldvide 75 6.150 1.297 0. 561 0.791 A normal-slip 20 6.827 1.05O 0. lsig 0.777 B reverse-slip 11 7.002 0.986 o. 469 0.71.

C normal-oblique-slip 8 6.750 I .260 OI.395 0.(I 2 D reverse-oblique-slip 6 6.917 -0.150 O.tJ -0. 063 strike-slip 30 6.717 1.214 0.639 0.811 A+ C 28 6.757 1.226 0. "31 0.774 B+ D 17 6.846 1.023 0.506 0.674 C* D * E 44 6.705 1.206 0.586 o.794. C *D 14 6.692 1.165 0. 451 o.568 B E 1h 6.767 1.200 o.606 0.811 I1-1/ A* C + E 58 6.737 1.221 0.549 0.806 B* D t E 47 6.742 1.188 0.597 0.795

Reprinted from "Fault and Earthquake Magnitude," Slemons, D. B., State-of- the-Art for Assessing Earthquake Hazards in the United States, Report No. 6, Miscellaneous Paper S-73-1, U.S. Army Engineer Waterways Experiment Station, 1977.

C-20 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Table C-7 Displacement-faultlength relation.

Equations of Best straight-Line Ft. for Lor Displacement Versus Lor lSenth: Los D - a . b Log L

Standsrd Correlation Fault No. a b Deviation Coefficient

North America 26 -4 720 1.036 0.632 0.737 Rest of vorld h8 -1 654 0.h1. 0.320 0.589 Vorldvide 71 -3.185 071.7 0.515 o.645 A normal-slip 20 -1a.375 1.01oh o 567 0.620 .B reverse-slip 9 -2.123 0.568 0.226 0.832 C normal-oblique-slip 8 -0.107 0.128 0.279 0.183 D reverse-oblique-slip 6 1.2142 -0.220 0.154 -0._81 E strike-slip 31 -3.571 0.805 0.541 0.703 A + C 28 -2.898 0.705 0.351 0.685 F + D 15 -1.665 0.h62 0.276 0.700 C + D + E 1i5 -2.921 0.684 0.516 0.624 C + D 11' 0.033 0.081 o 265 0.130 B + E hO -3.1.69 0.797 0.506 0.722 6 A + C + E 59 -3.239 ,0 75 0.171 0.680 B + D + E 1.6 -3.119 0.728 0.501 0.682

Reprinted from "Fault and Earthquake Magnitude," Slemmons, D. B., State-of- the-Art for Assessing Earthquake Hazards in the United States, Report No. 6. Miscellaneous Paper S-73-1, U.S. Army Engineer Waterways Experiment Station, 1977.

C-21 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Table C-8. Magnitude-fault length relation.

Fquatior.s ot Best Strhixht-Line Fit for Magnitude VersuN Los Fault LenRth: 2H n * b Lop L

Standard Correlation No. a b Deviation CoeffJcient

Nortb America 26 -0.146 1.504 o.628 0.815 Rest of vorld 49 2.971 0.920 0.500 0.680 Worldwide 75 1.606 1.182 o.603 0.724 A normal-sltp 18 1.845 1.251 0.521 0.575 B reverse-slip 9 4.145 0.717 0.167 0.932 C normal-oblique-slip 10 3.117 0.913 0.457 0.604 D reverse-oblique-slip 7 4.398 0.568 0.340 0.522 E strike-slip 31 0.597 1.351 C.AY4 0.775 A+ C 28 2.042 1.121 0.490 o.666 ) B* D 16 3.355 0.847 0.320 0.833 C * + E 48 1.149 1.262 o.6S,0 0.737 C+ D 17 2.992 0.918 0.q37 o.652 B+ E 40 1.042 1.277 0.664 0.773 A+ C + E 59 1.204 1.260 0.6Jq 0.724 B+ D + E 47 1.357 1.217 0.638 0.758

Reprinted from "Fault and Earthquake Magnitude," Slommons, D. B., State-of- the-Art for Assessing Earthquake Hazards in the United States, Report No. 6, Miscellaneous Paper S-73-1, U.S. Army Engineer Waterways Experiment Station, 1977.

C-22 27 February 1986 TM 5-809-1O-1NAVFAC P-355.1/AFM 88-3, Chapt;r '3, Set -3n A

Table C-9. Magnitude-length times displacement relation.

Xauations of Best Straight-Line Oit for Kagnitude Versus Log Length Times Displacement: K ae b LOg LD

Standard Correlation Fault No. a b Deviation Coefficient North America 24 3.510 0.701 0.503 0.889 Rest of world *6 4.158 o.610 o.161 0.731 Worldvide 70 3.710 o.68o 0.489 0.828 A norsal-alip 18 &.551 0.530 0.121 0.750 B reverse-slip 9 5.310 0.123 0.213 o.886 C normal-oblique-slip 8 3.281 0.785 0.325 0.793 D re'vrse-oblique-slip 6 3.706 0.678 0.353 0.550 Z strike-slip 29 3.220 0-T59 0.567 0.859 A C 26 3.691 0.707 0.388 0.792 + D 15 4..78 0.550 0.327 0.e34 C +D t Z 13 3.238 o.766 0.510 0.850 C *D 11. 3.168 0;802 0.340 0.78h B +Z 38 3.424 0.728 0.536 0.8"9 A C C E 55 3.393 0.7Tb5 0.503 0.837 B +D * Z Isi 3.641 0.726 0.515 0.853

Reprinted from "Fault and Earthquake Magnitude," Slammons, D. B., State-of- the-Art for Assessing Earthquake Hazards in the United States, Report No. 6. Miscellaneous Paper S-73-1, U.S. Army Engineer Waterways Experiment Station, 1977.

C-23 TM 5-809-10-lINAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 w

Table G-10. Magnitude-length times squared displacement relation.

quntions oftSest Straight-Line Fit for Nawnitude Versus Lns 2 lenxth limes Szuare of Displacement: X . a * b Lor LD

Standard Correlation rauat No. A b Deviation Coeffticent

North America 26 *.808 0. 420 0.526 0.o78 Pest ot vorld 116 I.967 0.412T 0.473 0.719 Vorldvide T0 *.865 0.427 0.496 0.823 A normal-sli, 18 5. 568 0.29" 0.427 0.712 3 reverse-slip 9 5.865 0.289 0.242 0.850' C normal-oblique-alip 8 1.103 0.573 0.309 0.815 D reverse-obliqu*-slip 6 *.290 0.522 0.373 0. .68 1 strike-slip 29 1.191 0. 480 0.574 0.855 A. C 26 4.752 0.159 0.381 0.796 ) E + D 15 5.162 0.382 0.350 0.808 C + D * E 43 .4173 0.489 0.513 0.818 C * D 11 3.985 0.590 0.340 0.785 38 *.597 o.468 0.535 0.859 A * C + E 55 1.582 0. 4T7 o.L99 0.840 E * D + E tk1 *.587 0. .69 0.516 0.852

Reprinted froa "Fault and Earthquake Magnitude," Sleumons, D. B., State-of- the-Art for Assessing Earthquake Hazards in the United States, Report No. 6, Miscellaneous Paper S-73-1, U.S. Army Engineer Waterways Experiment Station, 1977.

C-24 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A Table C-ll. Degree of fault activity.

MAX SLIP SLIP RATE CALCULATED CUMULATIVE SLIP IMI nIECtURRFNrF

. FAULT . IE VENT ICM/Y EARI INTERVAL I'VRS.? 10K yto 35K yrs jIlOK VrISI r IME TERSI 1 4 4---4 I--I 4 Fain..eathe.r Ak. t.e No 2030 b6Ow 29000 10 170

Sone Andrew.* Co. 3.7 370 1295 3700 116500 t0 270

Heyward: Ca. 60 210 600 3000 2 300

Coyote Creek. Ca. .3 30 105 300 1600 1.5 600

Rhimne Graben, Get. .023 2.3 5.5 23 116 2000

Orraben. Get. .005 .5 1.76 6 26 .3 6000

OewIw" Hill. Ca. .0006 .09 .21 .60 3 .24 30000

Rawhide Flat Wmt. Co. £0025 .02t A.7 .26 1.26 08 32000

Negc Jack Point. Ca. .00007 .007 .026 A7 .35 .02 29000

.1 1. I

US Army Corps of Engineers

- E~~~~~~~~-

ILl D~~A24

I0 U<

I-

TIME

US Army Corps of Engineers

Figure C-10. Relative degree of fault activity. C-25 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A APPENDIX D DESIGN EXAMPLES-GROUND MOTION

D-1. Purpose and Objectives. been converted to equivalent magnitude values The purpose of this appendix is to provide M, and the more recent events have directly examples of the assumptions, procedures, and measured magnitudes. Based on the fault length, calculations required for each step of the prob- along with its depth and slip activity, a maxi- abilistic hazard analysis for site specific ground mum magnitude of M = 7.5 is assigned for this motion. Example 1 is a simplified version that source. Area source 2 has a period of t2 = 300 shows hand calculations for all steps; it is in- years of reported history. All events except the tended to provide a direct understanding of how last one are in terms of MMI intensity I0, and each successive value is obtained. Examples 2 the last event has a measured magnitude. The and 3 represent the more detailed, actual types MMI values are converted to equivalent local of hazard analyses necessitating the use of a magnitude values by use of the Gutenberg- computer program. Example 2 covers steps I and Richter equation C-5 given in appendix C. The II and detail; and example 3 provides additional geological structure within source 2 is judged examples of steps I and II and then shows steps to be capable of a maximum magnitude of M = III and IV leading to the description of hazard 6.5. The recurrence relation for source 1 is de- as the complementary cumulative distribution veloped by linear regression analysis as follows. function or hazard curve for site PGA. The eight recorded events are ranked according to descending magnitude values such that the D-2. Introduction for Simplified Example 1. number N of events having magnitudes equal The purpose of this example is to show a simple, to greater than a given ranked magnitude is the by-hand set of calculations for each of the steps ranked order number. These data are shown in I through IV for a site hazard analysis. A point figure D-2 along with the corresponding loga- is to be determined on the hazard curve (fig 3- rithm values In N. A plot of In N versus M in 39), for P (PGA < PGAJI with PGAj = 0.20g, for figure D-3 shows that a single straight line can an exposure time of t = 50 years. Then assuming represent the source 1. recurrence relation that the complete hazard curve has been determined from a set of similarly calculated values In N = as + j31M of PGAj, a selected response spectrum shape is Letting y = In N, and x = M, the linear regres- scaled to illustrate step V, and provide an EQ-I sion analysis calculations for the least-squared- site specific spectrum. error line a. Step L Identification and Modeling of, Seismic Sources (para 3-4b). The building site y = al + pIx is located in a region containing two distinct are shown in figure D-2, along with the nor- sources of seismicity; a line source 1, and an malization required to give area source 2. Source 1 has been identified by the surface trace and subsurface geological In Ni = ai + A3M = 1.29 - 1.32M structure of a strike-slip fault along with a his- for a one kilometer, one year basis. A similar tory of earthquake reports and. records associ- processing of the source 2 data provided the re- ated with this fault. Source 2 is a general area currence relation within which a history of earthquake reports have occured; there may be faults with this area, In N2 = 5.81 - 0.95M however there is no surface evidence of their for the 300 year time period and the 400 square location. Figure D-1 shows the line and area kilometer area. Normalization then gave models of sources 1 and 2, the estimated epicentral locations of past earthquakes along with In N'2 = cQ'2 + 0 2 M = -5.89 - 0.95M the listings of historical records of earthquakes for a one square kilometer, one year basis. assigned to each source. c. Step III. Probabilistic Forecasting Model b. Step I. Evaluation of source seismicity and (para 34d). The Poisson occurrence model is recurrence relations (para 3-4c). As shown in assumed to forecast the probabilities of mag- figure D-1, the line source 1 has a period of t1 nitude levels for both sources 1 and 2. Referring = 150 years of reported seismic events and rec- to equation 3-14 of paragraph 3-4d; given a ords along its assigned length LI = 30 kilome- length increment AL and the future time period ters. The older reports in terms of intensity have t for source 1, the probability of no events greater D-1 TM 5-809-10-1INAVFAC P-355.1IAFM 88-3, Chapter 13, Section A 27 February 1986

SITE 0

6.1

.6.2

LINE SOURCE 1. AREA SOURCE 2. Length=30 km Area=400 sq km 150 Years of Record 300 Years of Record Date M Date Io IVM* 1830 6.5 1682 VII 5.7 1852 6.1 1765 VI 5.0 1871 6.6 1812 VI 5.0 1890 6.2 1920 VII 5.7 1911 5.9 1982 V 4.3 1920 6.3 * M=1.0+(2/3)IO (eq C-5) 1946 7.4 1980 5.7

US Army Corps of Engineers Figure O1I. Source models and recordsfor sources I and 2.

D-2 27 February 1986 TM 5-809-1O-1JNAVFAC P-355.1/AFM 88-3, Chapter 13, Sectlon A

LI/"e 5aURC-' 1, L = 3O km 7- = 50 qf cQ '-.s A-imo-j 7. S

/V. V Al (Z -:F.) I C%- get I (tf -- g ) - -t t I z 0 7.4- -". 33 1.04 l./Z -1,4 / C.C -o0. 6# 0. Z 0.07 -0. /5

3 A./c 46,5 -0.23 0./4 0.03 -0.04

4 /99 C.3 0.04 -0.04 0 0 5 /h./ -0.14 0.0a -0.04 0. fi C. .79 C./ ,oC7 -0.z4 0.oc -0.1/

7 /.95 50? -0,4# 0.19 - 0.Z7 0. &5Z a 2.08 S'.7 -0.C4 0.4/ -0.,4 I~ ~ ~ 4 _ E- /0.4/ 5a.7 .2: /.?O - Z, S'O - /.D.0/ =_ 0 /. 33., Z.L8 .&3 a E - xE= - -z5-o. = - / sex - ~/.90

Morma/,z-d' o . /k /, 3 3-3)C. 3 O) =.70

eA/, d 1/3, I . 70 - /, 3 Z MV

a~it &f 3 -5S) 2 coo I =,C< -7-

C<~4- = h -1 X~arorn 7. 5'

US Army Corps of Engineers

Figure D-2. Recurrence relation calculationsfor source 1.

D43 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

2.00

\S Regression Line

lnN1 (m)=9.70-1. 32m

1.00

0.00 .

-1.00 ' 5.0 6.0 7.0 7.5=Mmax

US Army Corps of Engineers

Figure D-3. Recurrence data plot for source 2

D-4 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A than M, = m is these equations is that which can produce the attenuated value of PGA = 0.20g at the building P [Ml - m) =P(o,m,t) =exp [-N'1 (m) AL ti site when the earthquake event occurs at the where N', (m) = at', + A1m. center of the increments AL and AA of sources I and 2 respectively. In order to determine these Similarly given an area increment &A and t for magnitudes it is necessary to divide the sources source 2, into elements, measure the element-to-site dis- P [M2 < m]=P(o,m,t) =exp [-N'2 (m) LA tQ tance R, and then use the attenuation relation in Step IV. Figure D-4 shows the element mod- where N'2 (m) = aC'2 + Num eling of the sources. The value of magnitude m to be employed in Site

LINE SOURCE 1. AREA SOURCE 2. L=30 km A=400 sq km n=3 Elements n=4 Elements AL=10 km 6A=100 sq km Transmission Path A Transmission Path B For the given PGA.=O.20g ,the OASES attenuation curves in figure 3-23 provide the magnitudes m. for each of 1 the measured element to site distances Ri. SOURCE 1. SOURCE 2.

i Ri km m i i Rikm mi 1 15 6.5 1 22 5.0 2 18 6.7 2 28 5.3 3 24 7.2 3 32 5.7

US Army Corps of Engineers 4 37 6.1

Figure D-4. Source location and element properties. D-5 TM 5-809-10--/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 d Step IV Selection of the Attenuation Re- on the other source, the total probability at the lation (para 3-5). The OASES relationship given site is by equation 3-21 and as shown in figure 3-23 P[PGA--0.20g] = P [PGAi-0.20g] P[PGA%-0.20g] has been judged to be appropriate for the source Source 1 Source 2 depth, travel path, and site soil characteristics. and hazard P[PGA>0.20g] is 1-P [PGAs0.20g]. With the measured source element-to-site distances R given in figure D-4, and the given ob- The complete set of calculations is shown in jective PGA = 0.20g = 196cm per second squared, figure D-5. the corresponding magnitude values can be found f. Construction of the site hazard curve. The by interpolation between the curves of figure 3- calculations as performed for PGAj = 0.20g, are 23. The results are tabulated in figure D-4. repeated to evaluate P IPGA > PGAJ] for suc- e. Combination of element and source prob- cessive incremented values of PGAj such as abilities. With the magnitudes m necessary to (0.10g, 0.15g, 0.25g, and 0.30g). The site hazard produce PGA = 0.20g at the site, the normalized curve is drawn through the plot of the calcu- recurrence relations are used to evaluate the lated hazard values verses their respective PGAj corresponding rate values of N'1 (m) and N'2 (m) values, as shown in figure D-6. for use in the Poisson probability equations; Since this curve is for the exposure time of t = these rates are tabulated in figure D-5. 50 years which corresponds to the exposure time The total hazard P [PGA> 0.20g] is calculated for EQ-I, the spectral scaling value PGA, for this by I - P [PGA - 0.20g], where.P [PGA 6; 0.20g] level of ground motion can be taken directly from is the total probability of no exceedence of 0.20g the curve at the 50 percent hazard value. The at the site. This total probability is the proba- curve gives PGA i = 0.23g. bility of the intersection or mutual occurence of g. Step V Site Specific Response Spectrum the occurences of (M imn) at all of the elements for EQ-I. The soil conditions correspond to ALi and AAi of sources 1 and 2 respectively. In those for the soil class 1 as defined in paragraph order to evaluate this intersection probability, 3M6f(3). It is therefore judged that the Kire- an independent point source model is assumed midjian and Shah mean DAF shape in figure for elements ALi and AA. Accordingly, for the 3-35, for the soil class = 1, damping = 5% is given level of PGA =0.20g and the future time appropriate for the site. Having the scaling PGA1 ) t = 50 years, the elements AL, and AAi are con- = 0.23g, the EQ-I acceleration response spec- sidered as point sources with seismicity rate N', trum S,, is found by multiplying the selected (mi) AL t and N'2 (Mi)AA t respectively. Here DAF shape by 0.23g. This Sa. is shown in figure for each element the mi is the magnitude level D-6. It should also be mentioned that the ATC necessary to produce 0.20g at the site. Having 3-06 response spectrum shape (para 3-8) for the normalized rates NYA(m) and N'2 (mJ)from the soil type S2, as scaled by the PGAI = 0.23g, the recurrence relations, the individual element would have been suitable for this site. probabilities of no magnitudes mi capable of exceeding 0.20g at the site are: D-3. Introduction for Computer Examples 2 and 3. P [MI - ml] = exp [-N', (m4AL t] It is assumed that computer programs for seis- for elements AL, on source 1 and mic hazard analysis such as the Stanford Seis- mic Hazard Analysis = STASHA, are available P [M2 - Mi] = exp [-N'2 (mI) AA t for use. A complete flow chart describing the for elements AA, on source 2. Since each point seismic hazard methodology is presented. This source is assumed to be independent of the oc- will be followed by numerical examples describ- curences of events on the other point sources, ing the separate stages of the model. It is im- the intersection probability P [PGA G 0.20g] for portant to note that computer programs must each source 1 and 2 is found by the product of be available to conduct the probabilistic hazard the individual element probabilities for each analysis as outlined in paragraphs 3-3 through source: P [PGA < 0.20g] due to source 1 is the 3-5. Figure D-7 shows the general flow chart for product of all of the (i = 1, 2, 3) element prob- seismic hazard analysis. Figure D-8 shows fur- abilities exp [-N'1 (mi) AL t] and equals (be- ther subtasks within each of the three stages cause exponents are added), exp [ -MN', (mi) outlined in figure D-7. In most of the available AL t]. Similarly P[PGA 6 0.20g] due to source computer programs, the plotting programs are 2 is exp [-IN'2 (Mi) AA t]. Finally since each usually system dependent. In the examples, it -I) source is independent of events that may occur will be assumed that stage I, the raw data, has

D-6 27 February 1986 TM 5-809-1O-l/NAVFAC P-355.1I/AFM 88-3, Chapter 13, Section A

S~~c-RcE/. 6LLwikrr1 i$--= , O0Y -ec - S

E/em~. NI(^) /O ,L- AN( 1) J1L NY(" XA L.t 9 U -q 4 / .5 -7.Z9 Le.6 2 0.341

.3 7.-2.. - 0. / 2.7 71 _ _ _1 _ _ _ _

7- -AL-f.= 0'.74-0 PEjPaA~jo.zoj3 o'ue *o 5.ource/, ex pf-. N,&mAI~ / eyp 1-0.74o]=04•77

.5ougcogZ. 4AA= /to sel /#4 t=5a Ye4s-

____ mi lmi•(em) Nz(v)XIOr Al' >A l

/ ~~is"0 -/0a(;4 Z. aI0 /. 2. 5.3 -/ 3 /,79 0.090 3 5~~.7 -/1.3/ /Z I7-.c ~./ -(/.~ 0 0.8 5 0 .04 3 a J.~ ~ 0. 1 Pb[ AP ( ~ z o~ J du e e-c s u c e 2

- e p [ - N t[,'3~ ~ a . A 'i =A '4 6 .73 1

P[P&A!!o0210 7 due -A bo1lh svcwr-ccs =(o.#.L77)(O'.734) = ,4l Pa ~ =PtsCA >.'. Z4e0 7 =/ .34-vi = e'. ~ 5/

US Army Corps of Engineers

Figure D-5. Probabilitycalculations for event combinations giving the hazard P [PGA> 0.20gJ.

D-7 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Sectlon A 27 February 1986

100.0%

values,not calculated

65.1% 50.0%I.

0 0. 23g=PGAI

SITE HAZARD CURVE

)

SaI in g's

0.50g

5% Damping

0.23g

"T risec. 0 1.0 2.0 SITE RESPONSE SPECTRUM

US Army Corps of Engineers

FigureD-6. Site hazard curve and scaled site spectrum for El Q2-I

D48 27 February 1986 TM 5-809-1-1 /NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A already been treated and that the seismic sources STDV(LNNM) = Standard deviation of of stage II have been identified; these corre- (LNNM). spond to step I of the hazard analysis. The next CONF. VALUE = Value of t-student's section will give an example of how one deter- distribution for the fitted mines the recurrence relationship for the iden- line. tified seismic sources; step II of the hazard analysis. UPCNF = Value of upper confidence interval for a given RM. D-4. Example 2. Figure D-9 shows a listing of earthquakes for DNCNF = Value of lower confidence a region between 1850 and 1967. There were 18 interval for a given RM. events with magnitudes between 3 and 5.5. The Figure D-11 shows the fitted recurrence line to- data base is for a 125 year time period. The for- gether with the data points and the confidence mat in which the data is read is given in section interval. Note that the regression line is ex- 6.3 of STASHA. A log-linear recurrence rela- tended beyond the last data point in order to tionship of the form needs to be fitted to these intercept the cutoff magnitude line. In the above data (Step II). The analyst does not wish to nor- example, the RMBK, the breakpoint for the malize with respect to the source length (or area) Richter magnitude was defined as zero; (See fig or the time period over which the data was avail- D-10). This indicates that only one single line able; (See para 3-4 for normalization). A mag- was used to relate In N(m) to m. Close exami- nitude increment of 0.2 is used to compute the nation of figure D-11 shows that the regression cumulative histogram. It is assumed in this ex- line does not fit well to the data. For example, ample that a single log-linear line will suffice to for the magnitude range between 4 and 5, the describe the source seismicity. An upper cut- fitted line underestimates the cumulative num- off magnitude of 6.5 (which is obtained from ber of occurrences, and beyound the 5.0 mag- geological considerations) is given for the source; nitude the fitted line overestimates the (see para 3-3). Figure D-10 shows the output cumulative number of occurrences. Thus, it seems of the computer program which gives the re- reasonable to try a bi-linear fit with RMBK at currence relationship. The following nomencla- 4.2. Figure D-12 shows the new output format ture is used in figure D-10. and figure D-13 shows the bilinear fit. The resulting recurrence lines provide the mean num- NBRC = Number of earthquake ber or rate of events equal to or above Richter records used in the analysis. magnitude m. This rate is used in the Poisson AREA = Area or length of the model (para 3-4) to estimate the probability of seismic source under future activity for a given source (Step III). consideration. (In this example, it is shown as zero D-5. Example 3. since normalization of a is In this example, the seismic hazard at a site in not needed) terms of probabilistic peak ground acceleration RMBK = Breakoff magnitude will be obtained. Figure D-14 shows a seismic region with two line sources and one area source. X-Mean = Mean of the independent Occurrence data for each of the sources are variable (Richter magnitude given in figure D-15. The seismic sources in this case) were modelled after correlating past events to Y-Mean = Mean of the dependent major fault systems and the tectonic features variable (number of identified within the region (Step I). The future earthquakes, log-scale) seismic exposure (PGA) for "CITY2" (see fig D- 14) for a time period of 50 years is equired. For XVAR = Variance of independent this purpose, the following assumptions are variable. made: YVAR = Variance of dependent a. Past earthquake events (as recorded for variable. the region) have been classified as shallow % th hypocenters between 0 and 15km. COVARXY = Covariance for X and Y. b. The average depth of the three seismic VAR(LNNM) = Variance of the log to the sources has been set equal to 10 km (0.087 de- base e of the cumulative grees for the particular geographic location). number of occurrences. D-9 TM 5-809-1O-1INAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 c The length in degrees of the two line sources g. Coordinatesfor sources and site. are, respectively: Line X-coordinate of origin = 30.500 Line Source 1 = 0.871° Source 1: (longitude) Y-coordinate of origin.= 31.970 Line Source 2 = 0.764° (latitude) These lengths have been obtained in the follow- X-coordinate or end = 30.92° ing manner: I (longitude) Y-coordinate or end = 32.62° (latitude) End (4,y°) Line X-coordinate of origin = 30.510 Source 2: (longitude) Line Source Y-coordinate of origin = 31.750 (latitude) Origin (x,y°) L = V(_xv,.-_x'4.5+(y.-y.) X-coordinate of end = 31.30° (longitude) d The radius (in degrees) of the area source Y-coordinate of end = 31.00° is (latitude) Area X-coordinate of center = 32.39° R = 0.749° Source 1: (longitude) and is defined as the distance from the centroid Y-coordinate of center = 31.078° of the epicenters associated to the source to the (latitude) most distant epicenter in the source. Site X-coordinate = 32.00° e. From regression analysis the following (City2): (longitude) recurrence coefficients have been obtained h. The input data format is given in section (Step II). 7-2 of STASHA. Figure D-16 shows the listing Line Source 1 (bi-linear recurrence relation- of the output program ACC.LINE.AREA ship) (STASHA, 1979). The output contains the input ALPHA1 = 2.58, BETAI = -1.09, ALPHA2 parameters plus the probabilities of exceedance - = 24.00, BETA = -4.55 and non-exceedance for each discrete value of ) Cutoff magnitude = 6.8, breakpoint the ground parameter of interest (PGA discre- magnitude = 6.45 tized at 0.05g intervals) under the heading Line Source 2 (bi-linear recurrence relation- "Probability Distribution of Peak Ground Ac- ship) celeration". Figure D-17 shows a plot of the ALPHAI = 3.17, BETAI = -0.74, ALPHA2 complementary cumulative distribution func- = 79.15, BETA2 = -12.4 tion or hazard curve for the City 2. From figure Cutoff magnitude = 7.8, breakpoint D-16, magnitude = 6.50 Area Source I (bi-linear recurrence relation- P(A < 0.10g) = 0.7512 ship) Thus, for city 2, there is an approximately 75% ALPHAI = 0.14, BETAI = -0.07, ALPHA2 chance of exceeding 0.10g at least once during = 79.90, BETA2 = -13.04 the next 50 years, or 25% chance of not exceed- Cutoff magnitude = 6.5, breakpoint ing 0.10g during the same time period. Hence, magnitude = 6.15 All alpha values have been normalized with re- P(zero exceedance of 0.10g in 50 years) = 0.25 spect to time t = 50 years and the length (in (1) From the binomial probability law, it is degrees) or area of source, and the resulting known that for independent trials with proba- recurrence rates are used in the Poisson prob- bility of success p at each trail, the probability ability model (Step III). of r successes in n trials is given by

f. The attenuation parameters b1, b2, b3, and Pn (r) = (p) pr (1 p_)-r c in eq. 3-21 for PGA are as follows (Step IV): bi = 0.00429937 where r = 0, 1, 2, ... , n and (= r (n r)! b2 = 0.800 (2) Let each trial be a one-year duration for which we are observing the level of peak ground b3 = 2.000 ) acceleration. Define success as that event when c = 0.3673769 the peak ground acceleration for a given trial D-10 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A (year) exceeds 0.10g. Thus, the probability of (3) Similarly, using the complementary cu- zero successes in 50 years is the same as the mulative distribution function computed for probability of zero successes in 50 trials. Hence, "CITY2", a table of peak ground acceleration and return period can be developed and plotted P50(o) = (M) po (1-p) = (l-p) to obtain a curve referred to as an Acceleration Then having Z one Graph (AZG). Table D-I and figure D-18 0 show the values of Return Period versus PGA Pso = 0.25 = (1-p)5 and the AZG for "CITY2." Using this figure D- giving 18, the PGAI for EQ-I would be approximately p = 0.027 0.12g (corresponding to a 72-year return period); and the PGA11 value for EQ-I1 would be Therefore, for CITY2, there is a 2.7 percent 0.145g (corresponding to a 950 year return pe- chance that in any given year, a peak ground riod). These PGA values for EQ-I and EQ-II are acceleration of 0.10g will be exceeded. The cor- not very different in this example because the responding Return Period RP in "CITY2" for a example site has relatively low seismicity and peak ground acceleration of 0.10g is the three sources have low maximum magnitudes. 1/0.027 = 37 years

P1 I TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Untreated past seismic events gathered for the region (raw data file)

Treated past seismic events (data in complete form)

~~I , - _1 STAGE NO. 2

(Seismic source modeling of the region) )

Seismic Sources and recurrence relationships I

STAGE NO. 3

(Seismic Hazard Model)

,~ ~~ ,_ - 9 .- I

Future Seismic Loading

US Army Corps of Engineers

Figure D-7. Scheme of present seismic hazard methodology.

D12 27 February 1986 TM 5-809-1 0-1 /NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Obtain information regarding pact seismic events for the region of (0) Interest Store data on disk as card images

(Raw Data File)

I. Stage No. 1--Data Treatment

YES

(1)

Some records are mis- ( Disregard those sing information on both \ epicentral location ani records for direct magnitude } input

US Amy Corps of Engineeys

FigureD-8. General flow chart for seismic hazard analysis.

D-13 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

(MI) instead of magni-- "I tude I| I Use Program I R EGRESSION.ANALYSIS

(4USo ArmyCp / \ I ll~~~~~seProg~ram Some records are mis- GENRYESNIUDl sng information bot~h on _I magnitude and intensits <_

\ / § ~~~~~~UseProgramn \ / | ~~~~~REGRESSION.ANALYSIS |

US Army COrPS of Engineers

FigureD- 8 General Flow Chartfor Seismic HazardAnalysis-continued.

D-14 27 February 1986 TM 5-809-1Ol-1NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

(5)

.Supply information by judgement

II. State No. 2-Seismic Modeling of __ the Region

Use Frogram I System Dependent E 1~~vlz

(1) Locate seismic sources using geological information and judgement

- U r (2) l I *Use Program L OEGRESNSI.A:ALSIS

III. Stage No. 3--Seismic Hazard Model

US Army Corps of Engineers

FigureD-8. General Flow Chart for Seismic HazardAnalysis-continued.

D-15 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

US Army Corps of Engineers

Figure D-8. General Flow Chartfor Seismic HazardAnalysis-continued.

D-16 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

UN***u* VWNP W'N E *WE****P*EE**P*WM4a9aPaP"aE OEVW SPNaUpa P#nEam UKP s o n TY H n L C n R D 11 I n 5 o A O E o I A 0 L H A E SB a R 1 Y * U YT U U It T II A7DI D P t R T R R U 1 S I T 1 C H T T S U H 0 E C U T S L O U E D E

A.CRAN 17 t2 16.50 12 10 3S.SOON 07.4.00E 6.5 4.6W1 4.61 I A.CGAH 17 06 Iv03 00 24 36.500tl 07.FOOE 7.5 54S5 5.2S I A.GPAN 04 08 1005 02 11 36.400S 06.600E 0 8.0 5.10 5.10 A.GPAN 03 12 I 28 Vs 30 36.40Dtl 07.200E D 5.0o 5.O0 A.CFR?: 10 02 1t37 18 16 36.4001U 07.50E 0 9.0 5.40 5.40 A.GRAU CS 08 1947 09 46 36.30011 06.667E 0 8.5 5.30 5.30 A.GRAN 27 10 1947 It 29 37.60011 08.SOOE D 5.5 5.40 L A.GRAN 22 11 1930 02 43 36.1CON 07.200E E 5.0 4.10 L A.GRAN 01 04 19S2 04 El 36.500N 07.300E E 6.0 4.S0 4.50 A.GRAN 12 04 1952 16 23 36 SOON 07.300E [ 5.5 4.20 4.20 A.GRAtl 23 05 1956 06 37 36.400N 07.300E C 7.S 5.CO L A.GRAN 26 06 1956 O1 SO 36.000N 06.100E L 7.0 4.15 L A.GRAH 02 09 1953 12 26 36.500N 07.400E F 5.0 3.55 L A.GRAII 14 11 1959 16 10 36.40011 07.500E F 4.S 3.05 L A.GRAN 05 03 1960 04 '1 36.60ON 07.100E r 5.5 4.00 L A.GRAN 02 12 1961 12 40 36.500S 08.200E t.SO 5.50 A.GRAN 14 03 1963 12 25 36.200N 06.10DE 1 7.0 4.40 L A.GRAN 14 04 1967 23 44 36 S0ON 07.8O00 E 4.30 4.30

US Army Corps of Engineers

Figure D-9. Earthquakelisting for example 2.

D-17 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

IEGVES3s0N4 AMiLVSIS LUIErLRUI SCALE ?NC AREA Nttt SAIIPLE 12OLtfU I to *.3 4.10#

)UBCR OF RECORDS IIcLLEDce IS AREA 3.3 71111 IIANSO I25.03 1iltiA t&GoaI'uloEt i.os AG1IITWuE INCRESEHNTFOR COF 3.23 EARTHQUAKE HAGIhTnLES 4.03 3.23 3.13. 5.33 3.43 3.43 *.1t 0.30 0.23 3.03 4.1 1.50 3.03 4.03 3.S0 0.43 Rn INTERVAL CUMULATIVE FRtEl INTERVAL FREQUENCT OCCURRENCES AbOVI

3.00 - 3.09 3. 3.C3 - 3.39 l?. 3.03 *3.59 I I?. 1.63 -3.79 3 10. 3.80 - 3.99 I IA. 4.30 4.1, 3 1. 4.2 - 4.39 2a3. 0.43 - 0.59 I I. 0.03 - .79 I . 0.60 - 0.*9 3 3. 5.00 * 3.19 3 s.:e - 3.39 a.2 3.40 - 5.3 3 3. TM STRAIGHT LINES UILL St USED TO FIT THE DATA eREAK POINT I¶AGNITLUE .20 7 POINTS III THE FIRST LINE 7 POINTS IN Tllt SECO7.MLINE IThERCErT at0 SLPE OF 1.1! I STATISTICS ronn REGRESSIOI LINE SIEMNT a I ) X-MEAISM 3.31999 TfIEAI4' 2.777T7 XsVAR 3.13333 TVARS 1.30313 COVARXVS -0.03307 COEFF. OF VAR.. 0.705o2 VARMLIOIIS 3.00323 STDY(UIII'w 1.05723

ALPHA 3.5tIII5 BETA -v.:00079 D1LRCPT AT 35.0 . 7. 13.19374 t2.81303 9.78480 7.95"4 INTERCEPT A0.0SLOPE OF LINE t STATISTICS lOPrl RECCRE3310S SNCE SEIMr * I x-MEAN4 0.7;9994 7-MEANs 2.30304 XVARS 3.10003 TVA119 3.2342 COVARflTY -3.17041 CCEF. OF VANS 3.38753 YARI Ltu910 3.13311 3TOV1LNMI~S 3.14333

ALPHA ?.tt573s BETA -1.067,00 11ITERCrt AT 3. S. 0. 7. 32.5635 35.90710 t.31046 3.07737 IN'TERSEMTION POINT 0 AWITIE 0.0to U Of N 2.03

US Army Corps of Engineers

Figure D-10. Output for recurrence relationship, example 2.

D18 27 February 1986 TM 5-809-10-1INAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

7 J-.

-L S.

2 .

*. --.~. - - - --4 ------. - - - -

i - 7- i=__ __' I -%,I N -%, i . -, -7 in I IS, N N

@ . _ _ - I - - k .... _ -

I -- - .- _. - f - - - - ==I - M.:_ 6. .

, . z j-ZEa: - _4 :E- o_- tur :_;qx -Ftnt . C _ # * ._ E- * _ __ an,_ F _ w _

__ _ In

, .

1 _t I . I I- $1__+ 3 1-=___,:Z I=-I.-- LDn , . -._ - I i 3.=,__.. .9 _ I --Ml = - --_ _ M -EZ-. = : ------F4- === .B .

.6. =___ AM __= ::

Em A

3 4 5 7 8 Magnitude (M)

US Army Corps of Engineers

FigureD-11. Recurrence relationshipfor example 2.

D-19 -I C REGIESSI011 ANIALYSZS L.I11EIR-1.1 SCALE M4RC AREA RIHDK SAHIPLE PRCOLCII I la 0.9 0.0

I4UflER OF RECORDS INCLUDED IO AREA 0.0 TMElL (YEARS) 125.00 I11811fUl MIGNITUDL 3.00 IlAGIIITlE 14CREPI£NT FOR CWr 0.20 EARTHQUAKE HAGNIXTUOES z 4.60 5.20 5.10 5.00 5.40 5.30 S.14 4.10 C.50 4.20 S.00 4.10 3.50 3.00 4.00 5.50 4.40 4.30 P11 INTERVAL CUIWULArYVE FREQUENCY INTERVAL FREQUENCY OCCURRENCES ABOVE R" n

3.00 - 3.19 1- It 3.00 IP. 3.20 - 3.39 0 F. 3.20 3.40 - 3.59 1 E 3.40 UN 3.60 - 3.79 0 II 3.60 3.00 - 3.99 0 1I 16 4.00 4.00 - 4.19 3 4 .4 00 *In 4.20 - 4.39 2 I 5. 4.:0 4.40 - 4.59 2 11I.0 4.40 I 4.60 - 4.79 I . 4.60 3A 4.60 - 4.99 a0 4.00 3 5.00 5.00 - 5.19 i. 5.20 - 5.39 2 5.20 5.40 - 5.59 3 S. 5.40 INTERCEPT ANk SLOPE OF LIHE I STATISTICS FORH REGRESSION LINE S!GHIEN I X-MIEAN: 4.19999 Y-I1EANH 2.37704 XVA~v 0.S6004 YVAR0 0.27831 COVARXY8 -0.36135 COEFF. Of VAR.w 0.83776 VAUlUM4#1)3 0.05334 SIOV(LO"OI . Z3100 (It

ALPHA 5.036937 (A GCtA -0.64 5:2 S INTERCPt AT 3. S. 6. 7. a 23.36659 6.42923 5.37Z41 1.76898 90 X CO4FIOCENC INTERVALS

CONF. VALUE 2.20095 1ERROR INDIC.U 0 X v 3.000 3.200 3.400 3.600 3.800 4.000 *.200 4.400 4.600 4.800 30.502 35.987 22.190 19.009 16-363 14.103 lt.404 10.957 9.765 8.764 ONCNFX 17.930 16.231 14.68S 13.243 11.8a5 10.592 9.356 8.183 7.093 6.105 5.000 5.:00 5.400 UPCr:F a 7.903 7.150 6.433 0* OINCIAW2 5.230 4,466 3.805 C

US Army Corps of Engin~eers %0 co Figure D-12. Output for bilinearrecurrence relationship, example 2. 0% L (! t i,,

(K 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

.I --i . * - . - *-3- ..

7. _~~~~~~~~~~~~~~~~~~r

f . a .- - I a ;,. . -T -h .4: - - I ,~~~~.l- -":- .1.1 3 5 6 7 a )Hainitude CM) US Army Corps of Engineers

Figure D-13. Bilinearrecurrence relationshipfor example 2.

D-221 13, Section A 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter

30- 31. 32. 33- 33.

,Regi~on of Interest

32.

31- )

30. 30o 31I 32a 33. o Magnitude 4+ o Magnitude S+ 0 Magnitude 6+ 0 Magnitude 7+ Plot of epicenters (sample problem)

US Axry Corps of Engineers Figure D-14. Seismic sources for region of example 3.

D-22 27 February 1986 TM 5-809-O-10/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

EARTHQUAKE DATA SORTED BY SCYuMCEs ON*P**OO**%~* W*oP * %404 * %"w S D 1' IIL L. C n a 0 l II II S 0 0 0 L It 56 a R Y A E I A II A U Y A IU H 7 RL A 0 p I t 11 HT R R L IK C £ I T a C 11 7 *1 I S 1U N a E E Si 7 S L C U C C E

LINE S0LECE I 10 RECORDS) A.GRAN 0. 03 190 07 00 32.600H 30.75CE 3.50 3.50 A.CRAH 03 05 1902 05 00 32.50§ 30.900E 3.75 3.75 AA6RAII 05 03 1905 01 00 32.350N 30.90QE 4.75 4.75 A.GRAN 05 C3 1912 02 00 32.000N 30.S00E 3.25 3.25 A.ERAN 08 01 1920 02 30 32.200N 30.700E 6.00 S.00 A.GRAN 04 03 1965 09 30 32.000tl 30.600E 4.65 4.65 A.tRAN 03 03 1973 CS 30 32.400N 30.750E 5.00 5.00 A.GRSA 06 04 1976 05 00 32.150N 30.530E 3.:S 3.;5 LIE SCURRCE Z (9 PECO.05) A.GRAN 04 G9.1916 01 00 31.600N 30.530E S.50 3.50 A.XPAI 06 03 1921 09 10 31.70011 30.650E 4.50 4.50 A.GRAN 04 01 1935 IS 30 31.4500W 3t.0C0E 5.55 5.5S A.GRAN 10 CS 1937 01 15 31.2001 30.900E 3.60 3.60 A.CtRAIt 04 12 1940 03 0o 31.250N 31.O0CE 4.t0 4.10 A.ORAII 12 01 1972 It CS 31.75CG 30.900E 4.65 4.65 A.GRAPL It 05 975 01 15 31.5001 30.750E 6.30 6.30 A.GRAtl 01 08 1976 CS 12 30.500W 31.t50E 3.50 3.50 A.GRAN 01 07 1978 03 15 30.50N 32.420E 4.25 4.25 AREA SDORCE I I1S REQCDS) A.GRAN 17 02 1S93 Ot 00 31.0S011 32.35CE 4.35 4.35 A.GRAH 16 C I 1925 14 00 30.70011 32.700E 5.60 5.60 A.GRAFI 30 11 19S5 12 i5 31.500N 32.400E 3.50 3.50 A.GRAN 14 02 1945 01 00 31..SON 32.450S 5.60 3.60 A.GRAN 13 CZ 1950 13 30 31.150Wt 32.600E 3.60 3.60 A.VRAI 18 1 1 1S51 0: 15 31.3001 32.150E 7. 00 7.0o A.GOAN 15 06 1954 06 35 31.100H1 32.00GE 5.60 s.60 A.ERAN 02 12 1955 06 15 30.900C 31.e3CE 3.00 3.00 A.6RAl 18 01 1160 04 1e 30.62011 32.250E 4.65 4.65 A.GQRN 01 01 196S 13 14 30.S55N 32.5702 3.40 3.40 A.GRDJ4 04 10 1969 0t 00 30.650H 32.150E 3.15 3.15 A.GRA14 03 12 1970 10 12 30.350N 32.57CE 3.00 3.00 A.GRAtI 17 03 1972 13 CS 30.'50tl 32.460E 4.50 4.50 A.GRA?1 0C 11 1973 15 00 32.60011 32.750E 3.50 3.SO A.GRAtl 16 t0 1976 10 00 31.400D 32.650E 3.65 3.65

US Amy Corps of Engineers Figure -15. Earthquake listing for sources in example 3.

D-23 ITM 5-809-1 0-1I/NAFAC P-.355.1 /AFM 88-3, Chapter 13, Section A 27 February 1986

"O:OP.APLCC.*LXNH .ARA I 3IJPLE PROBLEM)P AITElJAUION CV15ThJ~tS D .312993700-O3 323 3.3000e000.03 US' 3.20000000401 33' 0.31737390433 IlIvAL 0 .5OO000*20-31 CELIAC a 8.50000000.31

Tmn PZrZws 50.00 ACCELCEATION 3.05 0.1t 9.13 3.20 0.25 3.30 3.35. 3.30 0.45 D.A 3.55 c.io .s 3.70 3.75 3.80 LV4~SOMMCES gaaaaa~a..a

LINE SmWCE I ALPHAI BETAS XCLI XLt ILI Y12 ML. 3.258000401 -3.109000,0I 3.305000.02 8.309200401 3.313700s02 0.3:6200.02 3.370000-SI SECOND REGRESSION CONSTAN73 ALPHAL? BETAL MM D.2'.000002 -3.3S5000.01 0.3*5000#01 3.380000#043 LINE SOtMCE 2 ALPHAl BITAI XLI XL2 ILI YU2 xi 0.31700D401 -0.740009000 3.30510906t 0.313000.00 31.317300.02 3.310000402 3.370000-31 StCOND REGRESSION CONSTANTS ALPHALZ DETAL! to 9.791S00.02 -0.12*000.02 S.350009.01 3.730000.01

AfEA SOUOCtS

AREA SOMCZII ALPNAI S ETAI Xv TO NA 3.143000900 -0.700000-01 0.323900.02 *.3tD0750. 3.739000.00 3.870000-31 SIC~tlD R.EGRESSIONI CWtSTA7ITS 9 ALPHAZ 3tTA2 13 3.799000.02 -3.130300.02 3.613009401 3.350000.01 I P X 0bSUPROA RI ITT 331S T It I U RION O F P IA rK S - OU N A C C IL EItA TZOU 04m

SITE OF INTEREST ICITY It GCOrMETRIC CONSTANTS ULU' 2 NAa I OI Lxv I M~rAXz I SETv I

SITE LOCATION Xx 32.000 To 38.010 TIlM PERtt0 a 50.00 IRS P0A * .0500 3.1000 I1.1300 3.2000 3.t500 0.3000 0.3500 3.43000 3.440 e.5000 PtT17)1 1.0000 3.7512 II.00.3 3.0 3.9 0.3 3. 3 3. 3 3. 3 3. 3 P(7Yt7) e.e0o0 I.t435 II*9957 1.0000 5.0000 1. 0000 5.0000 1.e000 1.0000 1.0000 PGA * 3.5500 0.1000 I1.3500 *.7000 0.7500 .5000 PtrVT91 3.3 3.0 I'.3 3.3 3.3 .e FItyOI 1.0000 1.0000 11.0000 1.e000 1.0000 5.0000

US Army Corps of Engineers

Figure D-16. Output for recurrencerelationships and site PGA probabilitydistribution for example 3.

'i)

D-24 27 February 1986 TM 5-809-1Ol-1NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

1.0

0. 9

0. 8 (1 - CDF)

0.7

0.6

0.5

0.4

I1 0.3

0.2

0.1

0.0 P.- Darameter 0.05 0.10 0.15 0.2) 0.30 u(P)und (P(IA in a,'s)

US Army Corps of Engineers FigureDo-1. Complementazr cumulative distributionfunction for example 3.

D-25 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Table D-o. Return period vs. PGA for CITY 2

PGA in g Return Period units In Years

0.06 18

0.075 23

0.100 37

0.110 63

0.120 87

0.130 141

0.140 358

0.150 10000

US Amy Corps of Engineers

D-26 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

;, oQo.._ * L * , v F-:3 ..6 iv *_ Z vr-,,:,,_ x t j j ! : 7- -. L- i-L ZF-t-l-_ - -' I ;- 4 :_ t ._ .. L _ _ _:a.t _- _ .._. = - *_ , _ __-- J -7 .z t , ,-t .-, _. _= ._ . - r _ .- i- _ F ==f ......

- . _F1_ z_:i - _ _ =.- c- :: ~--j =_* . ~ ~- =- F- ?- ~~~~~~~~~~~~~~~~~~~..t-3_ ' - : __ I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ____. __------r---- ; _ .,:--ei- - ~i. -- - - - _ _ o;; _ * -_ . . ;_ _ __ I gi=.I I ;-d i r . I- __

w_ _ _

_ _.

, OOQ

-I. - . *- _--- I _-:; ,j= .=-V _.: I -:-_ T:= _ -FE------F- U V

P.,P T: -- E ==D~~~~~~~~~~~~~~~~~~ -. I I_ i=_ _-.2.I _- 0 -.- . - : -I_ I.. I - .. = , i - - - , , __ I_ M- a ,_ J~u I I.I.j SII', . . - I . . , , ^-/tri A-f- v *- I, i i .4- M - I-H-I T . I . I I I j , ' U1 .00

=- _ _ _ - _ = -- . _ . * EE -

- == - - -- t=- ---.:

- -= * ..______I:A I~ - v -- 'r-1~q~-

= _ O_I =r_ _ _ - ,- 1 _ 22__-F - --. -- 1 -_ _ . _ ~=: - --1: a_ XFM-7-. Ei_ :-. -v--.l .-----I-R- -. _z I§ z ._wiII l- l--z -s- l l - l l l * -t 4 110F " 7:; :.*- rJ -. . --- J .- __. _-- . = . . t d_.,4_-_= -I n.__.._ ..j. . _ .II __s - _ _ __4r _- . _ _ t- I '- *-J - -' -- t'--' -T~t. 9 ._ ._:s .j-4m_..._ ._. ; - _...... , , ...... r to.. ; A-___ g. .). 7 _ _ . ______0 0.05 ' 0.10 0.15 I). 2) (PGA iato Z) US ArMy Corps of Engineers FigureD-18. Acceleration zone graph (AZG) for CITY 2.

D-27 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A APPENDIX E DESIGN EXAMPLES-STRUCTURES E-1. Purpose and scope. E-2. Use of appendix. This appendix gives illustrative examples for de- The design examples are purely advisory; they signing and analyzing various types of lateral are not intended to place super-restrictions on systems in accordance with the criteria and pro- the manual. This appendix is not a handbook cedures of chapters 4 and 5 of this manual. for the inexperienced designer. Neither the manual or the manual supplemented by the ap- pendices can replace good engineering judgment in specific situations. Designers are urged to study the entire manual.

Table E-1. Design Examples-Structures Fig. No. Example No. and Description E-1 E-1 Sample modal analyses. E-2 E-2 Box system. A 2-story building with bearing walls in concrete using a series of interior, vertical-load-carrying columns and girder bents. E-3 E-3 Steel ductile moment-resisting space frame and steel braced frame. A 3-story building with transverse ductile moment-resisting frames and longitudinal frames with K-bracing. E-4 E-4 Concrete ductile moment-resisting space frame. A 7-story building with a complete ductile moment-resisting space frame in concrete without shear walls.

E-1 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

DESIGN EXAMPLE: E-l

SAMPLE MODAL ANALYSES:

Purpose. This example is presented to illustrate the method of obtaining story forces, accelerations, and displacements from given building characteristics and ground motion response spectra. The results are-shown in a format similar to the sample format used in the equivalent static force procedure of the Basic Design Manual, table 4-4. Thus, a comparison of static force procedures and dynamic analysis procedures can be made. The data in this example serve as a back-up for the examples given in paragraph 2-Sc of this manual. The results are graphically displayed in figures 2-9 and 2-10 of this manual.

Description of Structure. The data on sheets 3 through 6 are based on the characteristics of a 7-story reinforced concrete moment- resisting space frame building. Sheet 7 represents a 30-story building. The model for this building was developed by expanding the 7-story building characteristics. Each story mass (w/g) of the 30-story building lumped mass model was assumed to represent 4 stories similar to those of the 7-story building (i.e., the indicated story plus one-and-one-half stories above and below). This was done only for illustrative purposes to demonstrate the influences of higher modes of vibration for taller buildings with longer periods of vibration (refer to para 2-Sc(3)).

Response Spectrum. The modal analyses were performed on the basis of the 5-percent damped response spectrum shown in figure 2-8 of this manual.

Masses, Mode Shapes, and Periods. Story masses were obtained from the calculated story weights of the building. A mathematical model of the building was developed from the section properties of the structural system. The building was modeled as a series of two- dimensional frames. A computer program that analyzes two-dimensional framing systems was used to determine the periods and mode shapes of the first three modes of vibration. In this computer program, each mode is normalized for E(w/g)02 = 1.0. The mode shapes are shown in figure 2-6 of this manual. In figure 2-6, the modes are normalized to a value of 1/2-inch at the top story.

LFSASpy Corps of Engineers

Example E-1 I of 7 Sample Modal Analyses

Figuzre El4. Sample modal analysis E-2 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Modal Analysis.-to Determine Total Base Shear and Story Acceler- ations. Sheet 3 illustrates a hand-calculation procedure to determine the total base shear and the story accelerations using mass, mode shape, period, and response spectrum data. Equations 4-1 and 4-2 are used to determine the participation factors. The spec;ral acceleration (Sa) for the period (T) of each mode is determined from the response spectrum. The story accelerations (a) are determined from equation 6-1 and the base shears (V) are determined from equation 4-4. The sum of the participation factors (P.F. and a) add up to 1.08 and 0.986, respectively. These values being close to the value of 1.0 indicate that most of the model participation is included in the three modes considered in this example (refer to paras 4-3cCl)(b) and 5-4c(2)). The storN accelerations and the base shears are combined by the square-root- of-the-sum-of-the-squares (SRSS) on the last column of the table. The modal base shears are 2408 kips, 632 kips, and 200 kips for the first, second, and third modes, respectively. These are used on the following sheets to determine story forces. The SRSS base shear is 2498 kips.

Story Forces, Accelerations, and Displacements. Sheets 4, 5, and 6 are set up in a manner very similar to the Basic Design Manual, table 4-4. In the static lateral force procedure, wh/1wh is used to distribute the force on the assumption of a straight line mode shape. In the dynamic analysis, the more representational wf/Ewt is used to distribute the forces for each mode. Story shears and overturning moments are determined in the same manner for each method. Modal story accelerations are determined by dividing the story force by the story weight. These are essentially the same values as shown on sheet 3 (slight differences are due to rounding off). The SRSS of the accelerations of sheet 3 are roughly estimated in the static procedure by the bracketed quantity in equation 3-9 of the Basic Design Manual and are listed in the last column of table 4-4 in that manual. Modal story displacements (6) are calculated from the accelerations and the period (equations 4-5 and 6-1 of this manual). Modal interstory drifts (A6) are calculated by taking the differences between the 6 values of adjacent stories. The values shown on sheets 4, 5, and 6 of this design example are summarized in table 5-3 and are plotted with the SRSS combination in figure 2-10.

Thirty-Story Example. Sheet 7 shows the model analysis for base shears and story accelerations for the 30-story example. This parallels the 7-story example on sheet 3. Parallel tables for sheets 4, 5, and 6 are not shown, but the results are summarized in figure 2-9.

US A,.y Corps of Engineers Example E-1 2 of 7 Sample Modal Analyses

Figure E-l. Sample modal analysis-continued. E-3 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 w

I7 STD.Y JUINFR~poCE CONCRF-Te rRAMie 6UILP1HC-;P ML1'hCMA0i7A Mo1del - CirPe1.4 Cowma 6tdEhO'Ib, 6trerL,

Pwd (T~)&d 7fl~4, 5hA~O15 (0) hixC been eIAleutrd I q A 1luv-ctim~m5nPt UnWWRtL AefZLP1. ,pctr. A eeflmb~mt /br .3 -modi obfA'ntd fr'ni PRopOnv,5pezfr

.R&G'L: .5Ybn 1 Aeeelir~ri*n (1) and. 65Au .5Awa. ifrrc, Cv)

U. 3 -- MoP I ModC 2 mOve 3 52SS LEVEL WA& ,Am &J~haLi-Al aL ,:63 J3 ~ 3 4. AX 4 I9 I (a) C() (1) 43A78 .0794 3~45 .27(, 0OyZ .0747 12-7 o.?A4 4a235 .040 1!M O.'Wm C'zo 0.418 7 45.34 .0745 .ZZ? O. W .0411 /-e O.L776' -~aIN -~X40 -. 16 .cO1 -0.W7 o.5a.4 CD 45.34 .o&" aioz. .eoi O.W+ -~M -. 1 0.001 0.0I.~ -c:o&44 -.2.4Z .I 0.118O 0.2I.' 5 £ 45.34 058 Z." ..141 O.7.54 -~047j -Z..14 0.101 a1.48 -. M -?.O& O.,cO -0ca, 0.314 414 .O4Z5 1.93 .052 mJ4 -07I8 -A~eo 0234 O.EZ -:XZl -..O1 xO ox "a?

.345.34 .oz-x, ,.t7 .035 0IZ7 -AA.7 -.IK./ ZZ .1 . 0*oO E.7+ 0.u& .. 0.10 O.Z7.5 2 f *t .0I4'1) 0.5 .013 0.045 -:oW,7 -2.c,50.'4 O.'47 a.a7 ~.55 0.?M a ig~ 0.7.03 I- a 0 a o 0 0 0 0 0 e0 0 DZU7.3 Ic,.4e61.00I I-.2-7 1,000 135 I.COI )

PT, 0.v8O4 0.= S0 0*24IG4 5.. ~0.ZC.A&) .5t 'j .a,

"AK __ .2 0.Of.'0 0.0/,1037

w ?/-aT.wj w .3fl,31x O?.2 w 'O-53., 111" eviIA;rl W&;Ihi- Siftc. 7~A At* .OQ5 kenIiFcter

MC.'AkL Ai4AL1'St5 TO PGTEAMINF6 lSTL ISASS SHEAIZ ; 5Tb-' ACI&e-aZ-KnON.S

US Army Corps of Engineers

Example E-1 3 of 7 Sample Modal Analyses

Figure E-g. Sample modal analysis-continued. E-4 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

It- a- * 0. #3 #3 .%. - 2 CD. a co 4 % F

k 101%16 9 . q E rz C, w 9 V.%Z OC Ir a vi

*-.0 I U) 45

*4.

'-S~ ~ ~ ~ t I.-

..k. 0 9- a M M - % %b 0~w ) UCz as %~ w vI a~ 6gr4 i 43 It #3 II~

r% I*~~.- 4% q%

1 ~~~1

I US Arny Corps of Engineers

Example E-1 4 of 7 Sample Modal Analyses

Figure B-I. Sample modal analysis-continued. E-5 TM 5-809-10-1 /NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

-3 I U A t2 13 )

"I3

US Armv Corps of Engineers

Example E-I 5 of 7 cses Sample Modal Anal%

Figure E-1. Sample modal analysis-continued. E-6 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

C13

.1: CZ 'I'

US Aty Corps of Engineers

Example E-1 6 of 7 Sample Modal Analyses

Figure E-1. Sample modal analysis-continued. E-7 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Mev¶6iie.LMWOd - C~rDO d0nrftL 5eJO=5, :Ppd.7rcI Gw' kx~eAd W%7 fr _51b AitvP~fn Mit-ho of 6"c fovx tfuriti IwAmptA'i.ft~o ayu. fvodto Cr) Md MobdL bh&9as (P V-C h&d ori *t mtu*', of c. io-d wntirii& etnmpttt prvjr~m. '5pcer&L A~dttM~tn'"fk M~OCU:P obtf fruvri QCV -'5Prm,

,We4v:. z~un Aje%-~dIAn (O.) an& &fjae OheO 7rxCe (V)

i 29 II. 181.4 4.X7 .003 .114 181.4 12.08 *805 .057 .0742 .079 '7 181.4 .075 .7W .13Z 7.7' * ,8 -.0718 *13.02 -. 4? 13 .0279 ~003 .141 *It,4 .0" 10%'C .i34 181.4 .04C1 .00 2.57 .0%0 MO.0f .1I(o 5 IB9.- .04.., .04 50 .09 9MD a a g I 0 0 0 0 0

1&51I ____3 1.1' 2j1 1e . 0;~CO6794% 13 436 44) -4 fM .0&84)0 2Zi0

5.60 8 3 O.Z40.9 O.44 6 It'W VI%~*) O.~jA0. 4 ~ (-.44)(Z40)a 0IC, (.217(,440) z O.094-9 .I1 V O 4I (10a 7 3 'A'Z4X4/2X) ' /03 8 (O02644.54 1to4Ia4 532 4

_ _ _V ______.0 W5 .0 /3 . 7 M2.9hr eresents At~ roof) njsZ and one.-h.If ft21s-4e.f f fhroulk zIS rset Oe ind~cAteal stor 1 pIus I71 StWrhes hbae ! beow.

US Amlay Corps of Engineers

Example E-1 7 of 7 Sample Modal Analyses

Figure EoI. Sample modal analysis-continued. 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

DESIGN EXAMPLE: E-2

BUILDING WITH A BOX SYSTEM:

Description of Structure. A 2-story hospital building with bearing walls in concrete, using a series of interior, vertical-load-carrying column and.girder bents. The structural concept is illustrated in the Basic Design Manual, Design Example A-1.

Initial Trial Structure. The building in Design Example A-1 of the Basic Design Manual was designed for Z = 1.0 and I = 1.0 with a base shear coefficient V/W = ZIKCS = 0.186. In order to utilize the same structure in this example, the following conditions are assumed: Seismic Zone 3, Z = 3/1 Hospital building, I = 1.5 Box building, K = 1.33 Soil factor, based on Ts = 2.5 sec Building period T < 0.3 sec CS = 0.133 ZIKCS = 0.20

The base shear, V, for this example is 0.20W, which is close enough to that design base shear in the building in Design Example A-1 so that uilding will be used for the initial trial design.

Seismic Design Criteria. The building is to be designed in accordance with the dynamic analysis procedures of this manual. The following conditions apply: Building classification: Essential facility Ground motion spectra: ATC 3-06 spectra with A = A = 0.30g Soil profile coefficient: Type S3

Design Procedure.

Sheet Introduction ...... 2 ite response spectra ...... 3 Q-I Seismic forces ...... 5 Capacities ...... 11 Deflections and period ...... 14 Commentary ...... 19 Q-II Seismic forces ...... 20 Torsion check ...... 22 Commentary ...... 23

US Army Corps of Engineers Example E-2 1 of 23 Box Svstem

Figure E-2. Building with a box system. E-9 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1IAFM 88-3, Chapter 13, Section A

INrPeo VUCXI0N

Tft . Sire fo-iV~~: qfcA- A64j Pvc-Lc-Pea 14 AC.Cc-'ftNc- WirM T11e flouCVDIE PVFc-cL,31-t ("'

ForL cq-T r A-4p 9-C1r MEE~V$owpJ ON4 SASET' 3 4, IP4mUUPaP4q T)tc CrFFecrS OF ViThr ;-VMZI1Tj SOL T(Pft,

'Mt STUr~UC1V. OF VAMLME A-1 114 Tft1,1-C. PfE5(qQ1 MANJLAL~ IS As$uwJE To 5e Tn14tJT1rL TRlAL. TFe51(61 AS -PSM1eDRj 110

QF V,%RA'rWN IS $t1*-'r , Afteo-ji~r~eviY .1 -,,2 c. v, ft~ Sfecr~./L A~~4-~?J Fo. rq'-T IS 2; ThiS ~* Vftt- IS TWICE Thir 'ZIC~. V4fre~ OF . 1 WtflC.t \Me. V,~ Fr4~ TM 1f4/r PcfltVI4 om Titf #Nf¶'-'eSA Fi-a Crq-T. WI(-L 79MCzr7 WiThjtm-

Th- E-)(A~-~iX !;pUCT1RCq2 IS A 1-6a( . lL.Pul4 Wh )

k~- L0Q~j~Ir1VMA-,r *PIP GflO'NS. T~fE Me-T77I. 'PeCK P- SYwreM fto-~t Pt 'FLt,(I3-e -Pift~rr-4A4fM WW1Le rftf MC47T.rL VCCrL MMT CONUAC-CT nL.L 1ro-9M& A ZdI' -vm-PttfA(,A A-r Ter Le-/rW FtM LEVEl-L-

IfJ C71LP TO ?eP.fbtM rT~r V*4AfrAKC fAOV,¶t AIALY'StS,

rM -e e-IC~II. Th*f T2AwJ\(M A?4P W rM,,P~mjLA. AMVrY.-S Al-C P(rXOa4e- Fo-t M7t 3Awt-P/r.Jc n- A- wffo-?c PSSa4.AAIIQj~ STP-A-I~ttr LINE /S~r Mc076 9tt?rPta /A 67~Ci

VISMrSutN4 -M N9PIL 1IPAL' WAl-LS 11S.MA-VE WfI~rZJM PIAPHIZA(IM fLM'SULTY A14 D AWD'AO r11ON-PCNTP-1a?~J ONJ 1RX-D'Mt- ION.

-US-Army Corps of Enzineers Example E-2 2. of 23 Box SN-stem

Figure E-2. Building Wit a box system-continued. E-10 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

PETerE~miNATioN- CF SiTS 1?EC-SotJS SPECT-r~A

FI4'vxEs ;-'io Th I-'43 .5HV' Thtv A ANPJ Av MWLLES Fe-P AN, ATC. S-O& VeCrAV"L. Se~te, F/jc4cW F02 CQ-T' At4D F,-rAL OfrAut-P VY 1ITEF,7'ct.Arno1? I;e-rWer VAftQS jiW Th-LE ?-4. YAWT~S VSCP W TfS CXAMPLE A~-Z A-S FrLL.Ow S

ATC. S-01~9e £- 3 EQ -IL

Av, 0.3O1 0.14q .3'

A v 0. 0 0__14 ______I

CoiiP"i,2 Coer-r-Ie.4,.Jr ~~ siSsuL4c !O1L F'r-ILE rvi'e Ss

.PA MP'NC., A-'DjvrSM EWr rFCrO_ PA&Mpli~q VALLTES FOUI ThW~ qI PAvmPiNq Fha-r' FRom TAfLE3-7

______VArMV~iw~j Pftu?INjj FAC-TM

EQ-T 57,1.0 EQ-11 Io0. O

qOVC&JI,%J3 EVAflC~NS (eq. -27, 3 29)

Eq -1: : S.L- W A, 6 /-r - i.22,60is/r-.25671/7 2. (A,) - .2.8 eq-Nfl : 52/ !-- I U.C) (.If) = . 5.& .

US Amy Corps of Engineers

Lxa~ple_ E-2 - 3-of 23-- Box Svstem

Figure E-2. Building with a box system-continued. E-I 1 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

PCSI4,4 1ZVoiJSF SFE.C.TRA FOIL UQ-1 AND4r EQ-f

5 a,, 1 .

0.1 0.0 L 0.0 1.0 1.0 £.0 to ?ERJOV I SECONDS

US Army Corps of Engineers Example E-2 4 of 23 Box svctem

FigureE-2. Building with a box system-continued. E-12 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

GFE CrLA L A tC.C.EI-9-Arn o o L Fi EST' MO0P E, 5o-,

PEciop T1** KIr ¶LAR4SIE.LE: (4-5) T'Iv,5(%)lq- 11A sec. Log Irl'vIiJ Im (e-'.) T-v522/V)2 - .01S,

SOL,,.2 F OLI E:QT SU TWVM FMR SOMh E-W A9V W-5

MOVE SHAPES , ort, A$SvME: A WrR..Airr fl l0 ULflJEi' MOVE SHAC.

-112,A -

(SEF, Fft. 4-St. FOIL APLJ FIL5T. . MOPE: SA'E: SHiEAP, . V.'. (.AVL.E EqUATiONS)

LLVEL W,, k MtI * .9 %fat rFL,~ &OrI) F%I~. I NI, k

. 514 16ii1. l.a Ib.10 I(. (P t,13s. .'4 2.00.0 Soo0.0 I io80 13' .S jJv* b.4 .wf. .167 2o,02 'uOZ ..o ': Ibi'q 60.1 13*Lf 25.0 4co2. o

£ . E1 tovEOVE A SE $tLP11- (5oJ) (26;.0) VFAfCTCAVAT~ION. FACTUE (EA-44)

cbI a 'et 50.1 " .$51 (.-Zs) g'U7MOPF, VA50E SHEAt CAE FFI CA.IE,.r

V, 11AI S.,.W,, (-.w - 402. IL t1- MovE SASE: SIEML (EQ.4-4)

US Army Corps of Engineers Example E-2 5 of 23 Box System

Figure E-2. Building with a box system-continued. E-13 TM 5-809-10-lINAYFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

PlsrLr1Lvr10 o,4 eisicI¾CFaza-s

(~I'A'LF04C;;5 FeCM. ILOOF PIRVl"I.A51M TZ) W'¶tLS 'BELOW

VIR-EeX StttA- : ~E .eoc1FS~t~trt IS PIS'~iSTep, Sy TxISQrA-f-Y AY1Eof (w,/f) slace~ 1w P1A?'HP-A4? IS FaX5ISLe .

iZISuIC~FbcIKS F0oM 2wv FLoot TD WAILLS BeLOW'

ACcrZPINq TD The. AT1%/E-ZPie or T-!'r wft-s ICL-ow (Yi/. IS

TH IOQ14 !~M. L: LP~tGIE-L COF Mtr- 'kCA-tMMLA-FD 1 T09r5IN CIL 11M "Ct-ivwEIr/m" TMSOWi, WE7 TD Etrhirg- iMr f- o. -N-S CnUflt9VA-4Z. iltC 'AtC41'eP4rACt TatLION IS COPte 9-1) V~¶i R C ThM eCCeNMICxTnS Wrt-LCA 7zt~4AYR'(V MDVIr'J4 nic CUNJTM Of ~AiS5'7.OF MMr 1%AAk1#A* U'3ILVIN.j~ Pi ANkcm~toN. 'TO ~IEhtg. 17P cF T1S CAU L ATtD ?-70'rk N. fTWC I10CIONP11. McO7CNJT 1S 1RXS41tD BY3'? Th N- A1r4v t-w WfLuA At¶CoeviNJ TD TttMIR

C~UIT~Z of fAcliprnrY. TM~-ratswonf VICA R S4AiZS. ~ 'wyr rt

-US-Army Corps-of Entineers Example E-2 6 of 23 Box System

FigureE2. Building with a box system-continued. E-14 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

CQ-T :'I'FI'V-q Of SEIMIC.Fof-C,6 FoM EorF ro WA-t.L 'FLOW/

E.Q~~~~ WALL~F,, -,~ ov t- r .t

IPi.e-cr-TS'eAE JTbZSIOPJAt._I SHEA.-. I_____ C

NWS I 3.2.5-(7 .

5 u(0q 3t% 1 . 4. 1 02. S5.5 3 b,2. ; .31 534 100o 2o0

A 24W 315.. 0 C. - I3sf, 0 534

I 0 5 169i 3T. i 0 102. 5S. T 0

WI~6 15.(v 100.0 100.0 534 A00.0 'ho0.0

N~o TbR.Stcij AS~wAEP. I

iiq! Arnv trnrn% nf r-naineers Example E-2 7 of 23 Box System

Figure E-2. Building with a box system-continued. E-15 TM 5-809-10-1 NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

15-T 2UDFLO7-LAt40 0 TrtCWON Pif.ewr Qtfl Au.JD TMS I Ot& L. W CPt IL. ratce s (SEEr SHEEr 10 FoVL WALL. ELEYATnoIJs) IQ) --- TQ 6 r

WorES : G±.M.' d9N'TEk. OF MASS

C.3- w4UJL OF ZI(Alipiy p.V PitffeX SiACO 'FoUZ (V %p. VR ) -r

MT4 Tb~.SNA1 MOVEW1

WEH- SCL&Th 'PJREfdn0N Fot. CAC.I WAIAL, VSC TMt C$LdL4AL~TV Ot Ac-EN77TTL borIAL ) McAcm1 Wvt1CM 7F-oPigZS T7tt IUG6tteS~ C7mlINEP P*Ic~. INJ Titts CASE) TMt TatS40WtJ,- t4A0 WILt. AtWA~YS TC AwnivE~/ Fin WN~LL I ¶3 At4p N&-g.eFo wftvS 5¶"7.

(,311 *r.-k 101-ri 4-k ZlTr Vx,(e,.;) -Vg (e;.o5-isr)-4vz ( &..0- Z462 it-k.

MASr-WECTr VECfloi . US~~A- eWTaer- -M S41-447 s~ear (wleirno la +)w

us Army Corps of Engineers ,Example F-2 8 of 23 Box System

Figure E-2. Building with a box system-continued. E-16 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

fgz vsTm-riow. oF sEisamic. F~CVJIE ff-cm 2NPFRctf- 1r WALLS 15ELc?,Av

T-OTAL. THEFIL 16L5w 21FLA.1PAPr1,eAm Fvj(E.), £1q02.K ¶O110SONA~L. MOMENfl IIr (Ns) LEc SteEr 8 M-r(r'-)- 3ts) At.-

VPiZECT_ StEAI-1LlN~L-rticMr 5H6ArZ. Pi____C rizety- WF~LONI"1 ILA6 Mr Wl IEQ- I WArLL W,-IL 1z SHCATotVI 'z

Al-S IT.O 41. 5 111.258 ;;q147- io 111 35.4 97.2.. 3 'h~~IN. 102.8 q7.7 102-Wi 'oil1 l 25.1. 128.0 q'4A 1o2. b l(,.3 11I 92' 24 5L. )..2. 10.T 7 59.8 134 A6 19.86 375 112. 24,52. -13.3 i 2.1.3

C. ___~35L 0 ;5S56 I1~9l 101-71 '3.9

E,-w I '21.o 0 m1.2b 1L3q347 19' 13.4 is.2,q 3 444*9 0 LJ7.7 102441 'HI9.O 9. 15 44.5 ~0 u&.3 h1I 2~ 3.; - 7 58.8 0 -19. 58 37 15l9 " 1.0 ;I.0

A 31*A, 201.0 235 I 174iq 2o4.8 C.. 36-, .20I.0 2.5.t iT714 *' . I 0q. B 11.2- f02.0 663'217

TItESE VALVE'S ALZ NOTI atrnC41L t T *CE !~ttcw,. ftiX Fv-k. C._AZry.

US Army Corps of Engineers Example E-2 9 of 23 Box S stern

FigureE-2. Building with a box system-continued. E-17 TM 5-809-1-1I/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Iw)

EQ - :VI5S1ZIUT1Of4 OF SEISMIC. StWARS AtJP L~RTVZXrj4q MOENT.fS OVEEtTANIi.JG Ij.~ ~ ~ ~~~SKEAiVr1Mmrr IT(4

1.---T 15.2.- .0 - -j a -Zc-j W W 124 A W

------7------;. .. , 0 --L 0 -...e - ... ri Q). M (1Z11.b

FILL h.ioo -- - I s - I kll38 2 1.3 I17.

31 f2 .8 - Ii)-'X

US Army Corps of Engineers Example E-2 10 of 23 Box System

FigureE-2. Building with a box system-continued. E-1 8 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

kAoMENT C.AACIrfl" - If STOt1' WftLS, ML~

M S~Ml, qf ; A,1 A- 2 WNLE ~* Aft V

41-4o (.DV(

4A. As4~/.(f~b

WALL TIMR. Al,

I 72. .&'I .12. *21' 2. qb A1 31 4.54, f 3 'It -. .12.L c 3.q 4' 41 .frI .12. 4so t. 172 .(,I .172. 6. 12.7.4 SASE51 (0 1. 2. ' 52. . 2 D&2

7 2.22 1.15$ 1.15 2.' I. lo $o.

'7 6 57(o 2.o 2.36 T72. 3q5D.

A, C, I 105 2.0 2.41 Io'q. 04 2 2.iv S.O .2.53 Il.12..6 I 21(. 3.0 2.55 ;I2.. 11o5. q lo 2.. 21; Iot 19z4.

-WPrA ftoMA VF.SteW IAAIPJVA-L r.%AMVX. A-1.

I US Army Corps of Engineers ,ExampleE-2 11 of 23 Box System

Figure E-2. Building with a box system-continued. E-1 9 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Eq-Ir : (-F-K V6AN.P/(.AACArY RAloS fot. FIEgS Im sr SrO-I'y WALLS t A)&f4u CMANP) -rYfl-ur. C = 2 +-P -22 rz; SffEAIL. ~C.Aw I Vot. M C,4,rowTY Z tic, = O ,A,(d -")A,2. J=4ok-,-I

__ ___- ~~.2V A 4 ~~i~ij, M As MC 1

E2Q-7. WALL ?Icz (i/.-) (N) (2) ; (I t-4 (2 1 va __

N-`S 11.1 3c.2. 710 49 91 A4! 12. .22. .12. 4. s I2.3 Ito 30 37 *.'l 83 *13 *45 4. D.*3 4?o 3o 3 7 .F~i 83 .13 .'5 .4 '.S '2.3 qfo 30o 37 (, I 3 I.13 *4;5 wi1. 30.2. 72.o 99 91 .4!0 1Z7 .22 .12.

I__ 5A5C V~.0 9!72. 57(,0 2.0 1'f1 I. . ZO fat .01 T7Z 3 co 3.7. o ITO 2i4o 3!1 1o3 2.0 rr7,+0 .1q .76 1i 11.5 51.0 21202 27 9(4 1.57 Ic~o *12 v 44*~~ iz~~s~o 214,7j ) 5 a 21.0 401o 2.14 0 ~ II2.3 2.0 ii4o .iij .45 7 121 4o-i 221o 21 -144 1.57 1030 *Q0 72. q44q 100.7 j 871

7 to I S.a I?I., S74 25 1193 2.o 1431~ .u I

E-W A1 c. 1 4.5 25l 6a 25 024 AG (424 .12 4. Z. 13.3 74.5 ;Io~,O 2. i22. 3.o I105, I') .4 5 133 '(. ;I _0__;5% 3..o Li.0o .1ii 4 4.Ai i25.9 1080 2b 24 2.0 (02q 12.-

VATA F1Oam VESIC9J FMAIJOAL- i:"PLV A-I. .tom t*XAmFLE A-1I fj '- ksb'/0 -4 kic., a.oozs

US Army Corps of Engineers Example E-2 12 of 23 30Ix System

FigureE-2. Building with a box system-continued. E-20 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

EQ- T. : C.4EC.AL WALL 3, Pielz 7 IMCWLVINC, W~AD L.OAP IFFFEC.TS

-rte K?_Viovs CALe.1LAT1ONS FCC VCM"VN POUE?'Tr WEP..e TUASED ot4 1rALTHqVAV.E PeMFI-JNI ONLYv, I ?JMNCj TIM PEAV LOADS. FO- WPCLS WM1$~ PrLEC W-ICtL'( SirUSSVP 2r TD -nrE FjLT~qv%.'~ LOAP~i.qje PiN ompPI¶ Al cAtCeefxL ct.&j uE MftVC -rD It4.JL'p TWC VFAV LOFAV. fo-ETWr SAIZIN45 WAktA ,'. IW'MS EXAATL4Y , 1H5 9ESvLTS W1A U T65AOT1IN. UVOC-'roM W, 'MtW VCMA?4V TO CAVMATY4'¶ PRrlo. (,VIS CAIZLILATIeOJ 1$ gNCLV)DO ftee FM~ ILLVSTIgA'TIN drP4L.' SINCX 7fl-M WA1LL'6 IN "lIS~FYAKATLE AxE NOT acfkSr-eZS5EV).

PEAD LOAP OW E14H$r TWL~ .o2.45 d x 32." 2 WAU.L .125 itsf'Ai2 'I21

WALL 5 * 0'. 06 * 25.85 on-11 i elC - .;)2.5'.. V * -2.1 1.7q £9It2.0. * CL.A~STIC. C.AACIr( (e.46 I(CO,.ILESS10r4 SIPE ) etC Ž: .81P + tOE. (Th'JsioN sive - mvsr c~twcx..)

C T+F-1 I5-~.oI-

fsf(I. - 1

M, - 0 [T(J-Y3.) - .9 [W. f(;17.'7')# - If 10 k- A

PC MAUP/tWacer( XA1IO "PIN v ?441mo-.4? c .?4

US Army Corps of Engineers Example E-2 13 of 23 Box System

Figure E-2. Building with a box system-continued. E-21 -

TM 5-809-10-1/NAYFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

CtEC.JC PEPL(CMONS i FMLOV A7 LoI~cSio1upipifk wACLLS A I C.

C.o~jaP9R. EAfcAs TIZL AS ANJ ujPjr?(j~pN'T, CANT22VEJL A4i~p ComvLrs TIM 'PEFLFC.TIoNs vs~'wqe vITvA-L woxK.. AS~vmC ThM StKASL is visrvJisur( TD ThE IKMiVVA- ?eiCRS IIQJ ALCCD"ANC-C Wi~h *TMtaa. ULATIVC Xi01l'iTIES.

E Iwoo 3''160 4 oo I-~~~~~~

rT as _W WALL A 10'lo J

PEt~S 1*4 ViEkS 2f3

?AovPeFTtFcS TiELS i4. FOLe COLNJ(L 1eR USE I rg.5(b /1. 1 IAJ. (Io/'c) (W A/,% 5~. 14 A-" A, u( 1l&) &5) r7T5 rf '

?ietLS 2.1.3 . XEC~rAINJ4LVLARTtE:L T4 '12,A,-%

I-. 73 I hk ' 'los 4 I A,," '("m)I B -12.5 Cft'

2ELA-nJE FicirpmeS~ A& . s?/n 'P/A. r- k.1/31 + -/*Av

rim i : & - o-)I(-,A4 +224'7-3 540o7 EA' .0185 ?I eIL 2..: 4, 2.'- I.07G o i .1588

US Army Corps of Engineers

Example E.-2 . 14 of 23 Box System \I)

Figure E-2. Building with a box system-continued. E-22 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

PFLeCXoNS CN7VP

SHELAL P.T.V1 LJTE1'VON ¶OVEfTVAW'PJe~MOM ENT

WAL.LA (r.eEr to) Ti ieE I~ tL ¶

VICLTUAL 5TRvcTueQ VoIL VPISEMmE~NS a) EOOF AWP 2"~

L2~a4-k. k

V FLECAXION OF Y IE.S I~ .VeNVuJG1 VeFLeL erIoNa Fir IS 1 !d, *2' ErL A1, AmMot L A, Fo- .- 'AGNo$#-6.

.op'*47 (810) 49

US Amty Corps of Engineers ILExample E-2 15 of 23 Box System

Figure E-2. Building with a box system-continued. TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

PEFL nrIoNS (CoWT1iVEp)

FRA t4kF A, l rh +'

GodI26IA)Ir , /E/ - ro0)2)9( ( .090)3)(1;)/?4 - .01__

* StAL. PEFLECON ris i 4

A, * 1.21L/AC, - ?1-/A,,C ' PL/A,,(.fC)

avow v 1°.1 (-)l)15.^)sto , ,0017"

.oo0 171 + .00 ab'3Z . 00X5

*OA PoCowFLccrwon PietR 'S

a 2w .ool4- ''oo I oo. .3 a

AMOpy 5 .0141 + .ooZe5 .oI4(o

US Army Corps of Engineers [Example E-2 16 of 23 Box System

FigureE-2. Building with a box system-continued. E-24 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

P'EVLeCrIoNJ (Cowriouep)

b!EFLtCXILPI OF rieps a2 f : '6ertJW'vC 5 Pe~FUMCXON E Ar

~ Ar "~e (4.;)e./5; Ao (q0 t

FoLf_ u A ,j IM51 "/.(f+') I~i

______I_ _ 4 5

bOArrn 4 AL W1z2(' fq)se~oo (4cS)

*SIMAPL 'PEFteCXvN FirE.5 .2.

A w.24 (i-i)~(. iqv .oo42'

t4LOFP -2.oql42. OO205' .00&.2.

*TOrAL VEpFLZCno.J 'PILS 2Z; 3

£~1NU . 36 -0 042-. - .00-7 *

AL-OI .0 l0b + .OO(,2. % j0970

USArmy Corps of Engineers Example E-2 17 of 23 Box System-

Figure E-2. Building with a box system-continued. E-25 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

?ceJU0D OF LN T-UPa,-4Pri. WA-u..S AfIG

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ASSUMEP C-ALtVLA-rev

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US Army Corps of Engineers Example E-2 18 of 23 Box System

Figure E-2. Building with a box system-continued. E-26 27 February 1986 TM 5-809-10-1/NAYFAC P-355.1/AFM 88-3, Chapter 13, Section A

CQ-tr CO L Me~rrA LY

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WiArES, WIL,4.. AL-SO ,66 USED Fak Th-E CQ-7n AALYSAS.

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US Army Corps of Engineers Example E-2 19 of 23 Box System

Figure E-2. Building with a box system-continued. TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

SPEC-TIZAt ACr.ELMATTCN faiL FtIL~r MCVE C,,

UME'fL&TS 7Tr JNELAi¶-C' SHCA4- VEWN17.J E~rTTO Ft-OM 7ABLE4,L1L fo9- CO0NCRE1-Er WALLS IN AP4 ESSENfrlAi._ FAC.ILITy.

TAAcpe P-S (NSti 4 - (17 .

L0Nqsrv~w1E (E-w)&TEaf125(*7V -0.

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£ u~i4~a~u 3.4 ~ zoil

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USArmyCorps of Engineer~1L.s.- LExanIple E-3, k 2rn09rof 23Bo Ss

I. 514 WFigur E-LBidigwt a box system -74on4tinued.

E-28 27 February 1986 TM 5-809-10-1 /NAVFAC P-355.1I/AFM 88-3, Chapter 13, Section A

ETQ-T[~~~~~~~~~~(Sa-

THEEFDEC, LL OF TKS XAr105 OF 14/14r Al'4P MP1/M-L AEE VOL&VL6V (SEE SHEEr 12 OF Z THE' £I4EAE 1&SIL.ASrtC PeMAi4tD IZATICS AZE Al-L LESS ThtAN 1.0 (rFof EYCAMIVLI - WA L-L I) PI E f I tr 2~,-7-.Z2 '.44 '4.o ). SOME MOMCNtr PEMAKIP Z*'TIOS ALC G1VEeArp-K TH~itJ 1.0 (Fot 6KA&APLE Wh.L T IMV. -7 :t/ 2.1,64 - 5 '-( o ) ROWEVE(.. WftJ PCA1P LCAD EFFEC~TS AIL 1tJC.LL'PE:P (Scr StieEr i34), TimC u'JLA~.V1 1EPUK~JI) UA~i OS, Age Si 4qI FIC rAJjhi.'lfpEuc+-6P - 6-.b THIAS, ¶t6 ST~verLeCV 9EMAWS,J ESSENTJ10AL.Lt r.L.A ST-nC. FoIL C-Q-7 FofGCE.S.

NOTV IF WALL I IHAP IgeLAsric. vemotip t~r11os

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US Army Corps of Engineers Example E-3 21 of 23 Box System

Figure E,-2. Building with a box system--continued. E-29 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

A~SSUME4 ' WAW,( I SniFJECI; RLPLCP TY i.15. - Wft. 3 SflFrNES ZEDVJC~ SY~ 1.5 v EC~CNrjUC,#TY, ec) I14ceepS-bM 1rm5.7' TD 29.o'

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A 15A(. 0 23.6 :l,4

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US Army Corp~s of Elgineers Example E-2 22 of 23 Box System

Figure E-2. Building with a box system-continued. 1-30 27 February 1986 TM 5809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

E-'Ir '-CO AAAENTA 1L

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US Army Corps of Engineers Example E-2 23 of 23 Box System

FigureE-2. Building with a box system-continued. E-31 TM 5-809-10-1INAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

DESIGN EXAMPLE: E-3

BUILDING WITH STEEL MOMENT-RESISTING SPACE FRAMES AND STEEL BRACED FRAMES:

Description of Structure. A 3-story hospital building with transverse ductile moment-resisting frames and longitudinal braced frames in structural steel, using nonstructural exterior curtain walls of flexible insulated metal panels. In addition, there are a series of interior vertical load-carrying column and girder bents. The structural concept is illustrated in the Basic Design Manual, design example A-3.

Initial Trial Structure. The building in design example A-3 of the Basic Design Manual was designed for a base shear (V = ZIKCSW) of 0.08W in the transverse direction and 0.14W in the longitudinal direction. In order to utilize the same structure in this example, the following conditions are assumed: Transverse Longitudinal

Seismic Zone 3 Z = 3/4 Z = 3/4 Hospital building I = 1.5 I = 1.5 Ductile frame/braced frame K = 0.67 K = 1.0 Soil period Ts = 1.0 sec Ts = 1.0 sec Building period T = 0.69 sec F = 0.3 sec CS = 0.116 CS = 0.140 ZIKCS = 0.087 ZIKCS = 0.157

The above base shears (0.087W and 0.157W) are reasonably close to the base shears of the building in design example A-3 of the Basic Design Manual so that building will be used for the initial trial design.

Seismic Design Criteria. The building is to be designed in accordance with the dynamic analysis procedures of this manual. The following conditions apply: Building classification: Essential facility Ground motion spectra: ATC 3-06 spectra with Aa = Av = 0.30 Soil profile coefficient: Type S2

US Army Corps of Engineers Example E-3 1 of 34 Steel Frames

Figure E-3. Building with steel moment-resisting frames and steel braced frames. E-32 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

-z~~~~~~~~~~~~ Design Procedure. The site response spectra are developed in accordance with the procedure described in chapter 3. The governing equations and spectra for EQ-I and EQ-II, shown on sheets 3 and 4, include the effects of site severity, soil type, and structural damping. The structure of Basic Design Manual design example A-3 is assumed to be the initial trial design (para 5-3a). The EQ-I design spectrum is compared to the static base shear coefficients ZICS as follows: T, period S S Ratio (estimate) a(g) ZICS a - ZICS Transverse 0.69 sec 0.35 0.130 2.7 Longitudinal 0.3 sec 0.41 0.157 2.6

These ratios of Sa to ZICS are greater than 2. This is an indication that the structure may have to be modified for the higher force level. Because the ratio is less than 3, it has been decided to continue with the procedure without modifying the structure at this time.

The example building is a steel frame structure with lateral forces resisted by ductile frames in the transverse direction and braced frames in the longitudinal direction. The metal deck roof system forms a flexible diaphragm while the metal deck with concrete fill forms rigid diaphragms at the second- and third-floor levels. The procedure used to distribute the forces is discussed on sheet 5.

An outline of the procedures for the transverse direction and the longitudinal direction are given below: Sheet Transverse direction - Frame 4 Modal analysis ...... 6 Load combinations .10 Element stress check .12 Interstory drift check .is Commentary .16 Method 2 analysis ...... 17 Suggested modifications. . 23

Longitudinal direction - Frame A Modal analysis .24 Load combinations .27 Element stress check .29 Interstory drift check. , 32 Commentary .33 Suggested modifications .34

US ArtY Corps' of Eniineers Example E-3 2 of 34 Steel Frames

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-33 TM 5-809-1O0-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

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US Army Corps of Engineers

Example E-3 3 of 34 Steel Frames

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-34 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

PC•~Lr'J Z.ESPCNC.C *ECTZ~A Fcrf E4Q-1 Ar?'I E-Qjl

0.9. 0.8

0.7

50.5

0.1

0.5

0.1

0.0

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US Army Corps of Engineers

Example E-3 4 of 34 Steel Frames

FigureE-3. Building with steel moment-resisting frames and steel braced frames-continued. E-35 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

TII-E Cri-fc'J0Fc-R7CCS -Th 1rKE FWAME WM"l&

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US Army Corps of Engineers

Example E-3 5 of 34 Steel Frames)

Figure E-3. Building wIth steel moment-resisting frames and steel braced frames--continued. E-36 27 February 1986 TM 5-809-10-1INAVFAC P-355.1IAFM 88-3, Chapter 13, Section A

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US Amy Corps of Engineers

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-37 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

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US Army Corps of Engineers Example E-3 7 of 34 Steel lrames

Figur EZ- Building with steel moment-resisting frames and steel braced frames-continued. E-38 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

mcPA1. ANALY'SIS. TRA,%JSVERZSE NLt-SnPit.ncJ - fr.mg

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US Army Corps of Engineers Example E-3 8 of 34 Steel Frames

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-39 TM 5-809-10-INAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

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M61(ittk KiCVES O'V 9IMPONCE' 'C&C'M6 1NJC Pv:PCeLf lAP01Th~.z

ASf TMS zteiL&PIN -qeTSmre1tMv ,~r Tr IS 17"A-Tr, Tnj-a (,t ZA-L %Z~foJ45C. h Ca~Ael~a-? aF T-r~ W.(dA-L 9¶r1Y 5VT7WS ANP~-rMrr- WgS5 ST-)?X

lt4~AVE Qtlr4tS ifirP m4rr L7CP ';;M AJerVYiS, MTS eg(~P~r3M¶1 OF 1?tE 5,5 ~t A-T ThT gou6r, 19 AT- TrtE 3,' npv A?,Ip q577 A-WTmE 29, r-Lov-. V4MiLE' 11r210 MOVE( SfftWR-. A-T iVtF 9&P JS 50o7 d-F 7ntr 15-r M~ow 5At WihrN Ca~-g6,brp OW Am gaS SlrejAS VWE V~rM676 Accouf4TS F~t 117. aF hr~ 50&$ £e-nATN-E wrn1 -2olo rvi Tffr Z""' A~o-PE A-rqp OA.7. rvi Tr1r 'APcE-.

Mav FS I MOVE 2.- mope 3 L~~Wu~~ V~ V,/,/tS (v,/A,5S VI_. I~/ ~ V (Y'a

2- 1. 0 (,. 1 *g'j. *-y -?*iq *1o2. 5. m 113-3 112..' .911 .9f 5.2. .o00. -19,3 .0IT 2. 1313 132.7 *¶5 .11 4fo.7-. .0?3 13. 0 *oa0I

IW EFFEMVIF MLVfrL, WEI , FtFVCTCM I C<,,, vsao Adcws M 1tXL" \ IMPO-7k JCC Cf EdAC) MoRE. IF 1tlS F XMUPg., (@Aao.o+, d.I'IitqVI=.off), 7o.0+% OF 7Tr 6UIL>1lIq MOS5S iAnTiCI'rAtS WI7f Pr MoPe l4.c?7. f TEr a2. move- itNP 4 .1 N rm 3 M 7e(.

US Anmy Corps of Engineers Example E-3 9 of 34 Steel Frames

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-40 27 February 1986 TM 5-809-10,1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

EQ-3X ELEMFN-r Fzces: TnaIsygesE (N4-S)PUMC.noW -F-RAIIE A/

L a LL %ESVL¶5S Pg.OM PES14tN MA 14Vft LrAIApLE A-5 sicrt is oi -34.

SCISWC. ae$VLTrsr2Ok N~S /,MVT-

* UN1T5 AEC IC, t4i.

50n So M .9.. 12 _27 C4 40 W~0 a %3 * 7b *16 a :t lb fr c ___I I-I C ('a V

QECAD L-OAD I-IVyE LOA D

Xk.> f>

M 117 1qq~~( - ti 105 101 ______. . 10 7 91q a,~ lt a t28#

4,00

~46 460~ r_ _ _ _

Dl S.-I qg.~~ ~ ~ ~ .~ -1 '41

SEISM1C. - EQ-! StS5

US Army Corps-of Engineers

Example E-3 10 of 34 Steel r B w s l fra mes al S t e el,-rameFrames s

Figure E-3 Building with steel momnent-resisting frames and steel braeed frarmes-continued. E-41 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

EQ-IE ELEMEN'r FoICES : -rXASVE#.S5 (N 4,) p~tecflocm - nAE _4

17 LL ZESV'LTS FIZOL4 P7E$ISI J MA IN&L CMAJA ME A- 3 aftriB aa 34. SCISmIC, 9ZSVuU5 ?I2o4 C.OMW~TCIZ. AMALY'SIS. ALL eWV -MOMENTS Ai1JD SWC1AIS, ~ivE7 AT F~c oFSPo UNIT5 AZE K) It#.

XQ. XmpTLU> . X7 M 50 It H 1.11 27 o a

'% so 113 o _ __ ~~o a~ '4 0~~T

a 3:0 0

240 ;0 ______DEAD LOAD C. ) 0555

Fl ir4 176 ______v

0190

Nj 4q 4 _ _ _ __A

r4 A at xi1 0, N -aOe- U. I I3.

SEISMir. - eq-fl StS5 Tro7ALvI.OD+.25L*I.O0 Ee.,

us Army Corps of Engineers

Example E-3 11 of 34 Steel Frames I

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-42 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

r tcI.- eLrewANr ~,ese

~56L E Q-T u~e 1.7 W- ALLOWABLE SrR.E5ES (SEE A15C., 6' EpinoN, Secnol I~.'s1 ) OIL USE Sff-LN~ri VEI;IJ CftIMThI4. ccemft-~e b Pf-AtMiP VvtCES TO C-ArPef~cTY FictC.Z k'Nv £CViCAJ Fe- E. LAS~TJL.,67F HIrELY E-TL/'-T1e.

201,. C-F TNlE UCAIA MOg 10% 0o: TbH COtLVAANS Al- ANY' STri-1Y IA.E A-LLcWE' -TD E-/CtEP -ntC FLeXLWkA-L.. I-MENIT-H f-t~,-EAeNS Y vP To 257.. Fb, nTrM ?U& F-MAS IN TritC Lok~erTMP~JAz. 171R re~ ( IL..I. 0) )zo%. o- i-ite Fo AWP 10%, OFTITE CCLUMNS A-r Aw74r SCty'

QrPeN(crH 1ZqvP~eNTrs ?VY Lf 7 10 7.. ~jo 0I,4S-mess 15 ftu.cwep TMt Tlte .- 5 ZA-CZ5 .

VcrL eq-IL CCM(A-F-C YVeMrNND 'FCt-cS To 7rer PLAr7nc.. LAEAA'EFL CHAfPC-irIC IM oeyZP Tm CCMP'-A7E

F'CqvE 4-1 F"t QirTi -;ftrc Aw' n~vE q-2 FML =E COUwrAjS. TatC 1ftL'WA6FLC 'VU4CrLL71E'S ak jt4C~teeTIC. 'PMA-ND f-ATfcS PA-f &+c-wtj IN T-ABLE- 4-2. Fat MEt TV-4¶N~eV&e;- PMKSF, flE frLLowAIL46 TA71cS AIP-E' 2.0

,/P" AkUr YE LCSS TrA74 I-C). kc lr-tt ?FgA*CC

I251.VS FOR. COLOMAJ, AIJD 1.0 FOR. K-9ACES.

US Army Corps of Engineers

Example E-3 12 of 34 Steel Frames

FigureE-3. Building with steel moment-resisting frames and steel braced frames-continued. E-43 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

LEteMEreN;- SAC~SS S- FgAMw 4-+ (-P AAeS r-

~'3VM ELEMENTS (EQ. 4-f.) q- IC LCC I .Ob42D-1.dL -0-1. 06 (tub+* I)

.~~~sI~ ~ Z1L MDM,. Mv

IDM ______~I- (C 2 (9-4) (0-4) MiC. 'k*W) (k I

zccp %a4#3o l1 .3 Ii1) i42,. 1.4o 2't2 14lZ 1.70a 2I0

3 wit '55 I 1. 437 33(. 1.3o 553 33(, r.5G 2.0

2. Wlb'(9o I V~ 4fe 30. 1.2.S5 581 3(. 1(90 2.0

"'US# ML.)rM, 1 vlIF7 , - 36 js;

VV- £L.A~rle. !CMAWR yEATO KP.om TATLS 4-L.

CC UIOMMNTr .froIL. eQ..TI T"E ?..T10 cF- mOJmEi4T V ANV TD M3PAer4J- C*9AOiTY' IS LiTE ID1.0 FCFL MoSXr ELeMEW'1S BuT 15 ALLOWeP TO £EAC-14 VP ThO 1.2.5 FOR. A LIMrreo NuIAIsEZ OF LLEJ.EI~rS IN ACC01ZIANCE W~flH MEtt '4 EARL'r eLi¶5T1C C.LU'rERJA (S~EE FALA, T~3()A)lteSE LIMITS ItAve S~EEN 614C.EEVE Fait Eq- T.

US Army Corps of Engineers

Example E-3 13 of 34 Steel Frames

FigureE-3. Building with steel moment-resisting frames and steel braced frames-continued. E-44 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

6LEMEN'r SMME~S~ - FR1AUE ((CNT' J e.D~)

STEELCO~a.MNS ,, sro~r 0 3AS6 ScEL VE$I4P MAIJUAL- E'iAMILE A-3N

A S§ 't Mv Fe. F S 17E6 (r"') (;-V) (r) (r4.) ( () (rL'-- (i'.-) ( QlC.)E a QAA.,&101h`

w i4t,4? 4.i 70.3 i55 I2.1 11.0 'I6.3 17.2 j.'f 341 0.84 /41j3

WI L I% IT. 9Z.2. 2.264 VT a 425.3 1?.%~24 377 0aiS i.4

ER i. . d IC-(:¶) Eq'.Ci-!b 1 £. Li F~~~,- I.~17(.~F 7) 11 FL1

E -~~~VCU> I.OP 2.'lL+I-CC

A Z. .MD M" 11'AFc~t~,?I1-tF p:4M,, ±1 'rT9

wlq"i~ 1 1.'i 102.. I5S OL *10IMq 6H . 'W72 33274 v.8 1.25

tlSer n4vC q-1 P Mr/MCfXq,-L '~AI,PI

US Army Corps of Engineers I Example E-3 14 of 34 Steel Frames

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E45 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

CefeLL NMSrosy vP-I~r-

ftLd W& fi V'LzF~r FbiL MeNTIPrt- r-A-UwnES : .0 * WCi4Hr Fole. Cq-r (Pa'e. q-vomwj) .010 * trVICIrfT rm eq - -Ir (e.

-MAN~SIELS (Q.-s) Vpt.LC.A1Ot4 - F.AMF At

CTMI4'Jrr. EQ -r en - r

R..Oorr JWi I.l I .733 Z.78a /.,.44'S 13 132. j.0 14f .(40 2.339 1.32.0 2. Izf 4?340 1.18IIo.2b0

* s~ VALVES FXoM sitter 8. ) * THE MLLOWAILE PLIFr LIPArS AU rxC.Egp N-r L /Egr AVA61. OF ?g.AMI 4 Frot. som cq-r A4D SenIL.

US AMy Corps of Engineers Example E-3 15 of 34 Steel Frames

FigureE-3. Building with steel moment-resisting frames and steel braced frames-continued. E-46 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

FR..A ~U ~-"Mp CcMiJT-e

VQ-T TK ' CLASTirc ft--(SI I~ CF Ff-Am E 4 Fcf u-q -r SHrCW5 ThIAT 1'WM fiR-CT FL&CIZ COLL)MIAJS ANJ A¶LL. OF T1tC 1SEAMS AI¶F.E OV SPe~f> AiqD Trm ftt~cw4?r:E- Pf-irr UmAITS tt?~VE VEEIJ MEEP -rrrE -p- nu 6- I-A$5 EXCEeEPI Thi `P4EAZL' 'ELA!Sric.. C.&IrElLiA L~wcc i-rH- ovec- es Thn s~ Foic want -gcAiv S AWDl CCLvMAJS ftEW q-C'A¶T TWAn7J TH-t It S ftLL..WEP 6M ThIAMLE FJE*MIPJ4 S-r4AA. FMJ1MF ' gc VIES 1/ OF lTH- C-1r1P.4sC, 1?Cc--N FL(rMFr5J IN TM1 TitftN 'etS -pP-eC-(-c77 4,¶i4P w~s WrMlrLY ;CL're-P FrtiL ,¶NftLYjs ?ECA'vF IT- Cn t IE MCP-E LO-ft Th-? f lMro C7: ThtEE-DEr "e CS. A CL4'L*~ tA,-YiIS ft9 FCA-MES I 7 MIcwr IZCS4(ALT

E9uvi~v9q AS~ A WI+CtE VfLL W&Lt4L17 NorF MRAET- THE * NEAILLY ELASTIC-' CJTC$Li A .

EQ-IIZ - MeThtl' I iTM EC;-]l AIVAL7r.IS FO'LLCWE-P ¶I E LASTIC- ?FAOPvL~e PESCrgC-p~ fAS METHt I wi 'Pfr.AVA-et 4-..L 'ThE INLCLASr1C VM~'wJ, ?A-floS F 7Wnr Fits4r m..cI- Cnt.,~ArsJ AtCe Irfun-r TH1'rw Thtr 1.2.5 vqttC44 IS ftLLCWED 4N1 Tflt 'P-FT L'AAilS "rVE: 'Fce1w c'xcpcp~.

1Q- M: A T*eC 2. WMtLC K~,4E 4 -Pat-. No0r ftArVE'

Eq-jLI A r7PrftE7?- OCttc WA-S ?'Pfct~MOrz7T S~w - nfrImPLEC C MrrtVP 2 TPeCej-r-Z ?"t-IirTif -q-q4 rMS. is ~,fro-wN ON~' trhC.

US Army Corps of Engineers

Exainple E-3 16 of 34 Steel Frames

Figure E-3. Building with steel moment-resisting frames and steel braced frames--continued. E-47 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

MIEflo'D Z * CArAC.1 r%( 'S?64iZUw MCT400 Far I-'p.A.&$VEZSe tyjCcTj0o4 Re5FbMS& Tob - 'RIWCi To ?ALA 4-4-J A#- ?pAtA 9-rb

WTERMIN~r ft&STIC. C4WAI1Y RATIO T0.'LI-.

L~VOL SI-'L EC V sZ5L Nrip' L.El~ V-00oF W 14 147. 54I7 7 % 7 Si w iSS~ 336 1i's 13 Z1 2 uD WOO4 S3al Ml 14- 2V2 4o (a 00DsSO.' *netr eg-riiQ a eArts cA?AcIh i y = EC. -D -b.Sa L (ej 5.I)

?W'bic&1is f1ite-T %(Aft hr Ra -TZA 64CY -rie COLU.13N5 COL14t*14 UfxMEiNTS S 'Rr To SA*07S JO - 14-

-"11 -U O&1 Da--I ;U L UM-1 1 t~1 W1 4 45 'PipoI ~M og ; a 13 I ri .M Il4

w~he I ~v1 w" 15024 I2 I I 'Li I . I'~ %.0(IA

A " ' * * 4 S 0 7 a p e R ~ l 7

FILT'9V: "-4- 0. (.6 Trlm~r C -T. (tmTO A j Mists I~oe Z ftoS. 3 ~i ME SWJXa COLEF, C*s M-I c.,Lo'a o.oml ae ozs' T1ELD hT .6 0.13I'S$ O A 0.013 014 Cl*?ACITY Cx'A~S V&T t Y,"ei. M CR$,C.:O.

4 %se vkw" -ro VLa? CC.Lft , SE6 sweet IR,0,10

US Arny Corps of Engineers Example E-3 17 of 34 Steel Frames

Figure E-3 Building with steel moment-resisting frames and steel braced frames-continued. E-48 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

It has been determined that the seismic base shear coefficient (in terms of first mode values) could reach a value of 0.13 before any yielding would occur in the structural frame. For seismic forces applied towards the north (towards the right on sheet 19), the base of the north (right) column and the center column will yield in flexure (the column bases were assumed fixed). The south (left) column does not yield because both the dead and live load stresses are counter- balancing some of the lateral load stresses. At a base shear coefficient of 0.13, the spectral acceleration is 0.161g, the spectral displacement is 1.43 inches, the roof displacement is 1.93 inches, and the period is 0.97 second (refer to sheet 20). A new mathematical model is constructed that allows the base of two columns to yield in flexure. A nominal lateral force is applied. The relative distribution of beam moments will vary from the distribution of beam moments shown on sheet 10 for seismic forces. New values for periods, mode shapes, and participation factors are calculated. The forces are proportionally adjusted until a number of additional structural elements begin to yield (t5to of calculated yield capacity). At an additional equivalent base shear coefficient of 0.06, yielding occurs at the base of the third (left) column, the tops of the other two first-story columns, the top and bottom of the second-story center column, and the north end of the first- and second-story beams (model 3 on sheet 19). The period of this revised model is 1.14 seconds and the roof displacement is 1.10 inches for the base shear of 0.06. When the results of this model are superimposed on the initial model, the following results are obtained: base shear is 0.19 (0.13 + 0.06), spectral acceleration is 0.224g, spectral displacement is 2.27 inches, the roof displacement is 3.02 inches, and the effective period is 1.02 seconds. These results are summarized on sheet 20.

The mathematical model is revised again to allow the newly formed hinges to yield. These hinges were given sectional properties roughly equal to 5% of their fully elastic value. An additional set of periods, mode shapes, and participation factors are calculated. New increments of force are applied until additional hinges form and a mechanism forms at the first floor (see model 4 on sheet 19). The period for this last increment of displacement is 2.29 seconds, the base shear coefficient is 0.04, and the roof displacement is 2.69 sec- inches. When these results are superimposed on the previous results, the following values were obtained: base shear is 0.23, spectral acceleration is 0.257g, spectral displacement is 4.45 inches, roof displacement is 5.71 inches, and the effective period of vibration is 1.33 seconds (refer to sheet 20).

US Army Corps of Engineers Example E-3 18 of 34 Steel Frames

FigureE-3. Building with steel moment-resisting frames and steel braced frames-continued. E-49 ..TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Q j ®D 07 10, LI-0 - it I-. ..- . I I I I - 0.3

0 "4 &I 0.2 co Id S '-4 ONOlI SHUTs U0 120 FLo ki V 0.1 U 1031-10. luVII "4 0.

W. I I I. . . . 0 . _ 1.0 2.0 3.0 4.0 5.0 6.0 Spectral Displacement, Sd (in.)

CAPACITY CURVE

0 First Yield, I-2DR

O2nd I-3DR MODELS METHOD 2 HODELS AND CAPACITIES US Arby Corps of Engineers . IExample'E-3 19 of 34 Steel Frames

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-50 27 February 1986 TM 5-809-1 0-1NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

DEFLECTED SWES (INCEES)

LEVEL Model + Model - 12 + Model 13 v I-1 1-2D I-3DR W (3) R00 137 (5.31)

3RD; 236 (7.32)

2ND k

(7.32)

IST I...

W-6 5 9 k2 :£2- 39.35 r12 81.46 (Int.20. 45)k-Sec /ft. (EwL - 89.3) (Em: -362.4)

a (±n) 1.93 1.10 3.02 2.69 5.71

T(sec) 0L. 1.14 2.29

CD 0.13 0.06 0.19 0.04 0.23

C S/ 0.305 0.897 0. 348 0.934 0.895

0.161a 0.224i 0.25 7 i

1.345 1.298 1.331 1.219 1.283 $a 1.43 2.27 4 .45

0.95 1.02 sec. 1.33 sec.

CAPACITY SURMARY US Amy Corps of Engineers

Example *rrnesE-3 20 of 34 Steel

FigureE-3. Building with steel moment-resisting frames and steel braced frames-continued. E-I1 ..TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

1.0

0.8

0.6

a- . 4

Oz. )

0 0 0.5 1.0 1.5 2.0 2.5 FEt.eOD, -r (SEC.

sviEEr 4 Fo3. ES'7cNSE 5?EC..IA

CAPACITY SPEC.TPVMI METHOD

US Army Corps of Engineers IExample E-3 21 of 34 Steel Frames

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-52 27 February 1986 TM 5-809-10-1INAFAC P-355.1/AFM 88-3, Chapter 13, Section A

Lme-,Hop 2. (coN1rimuJct)

SUMMAI

I. Vrtif STEOGTVR.C YIELD7S Ar eq-z.

2. ThE FIEtST- YIVLV OC4L'LS rT- 0.(o+ E-Q-I; 1 vHov.F091rrVoE$ N4T HAVF Tht CAPAC4rY TO SATIS~FY TitE NEAtLY CLASTIC CLTMA

3. ThE. CAPAAc~1rY SPECCTrE.LJA VOES NOT CLOSS TIM r,Q-U PEMAiN.J UESFOISC SPECrl~v~ (stmer 2ij); 1,tezzFveLC flte STmv(tC.Thte paES N.OT S.AlS-~Fy 4? Q -U f.JTU..4A. EEef TO ?A-EAkqPAPFH 6-5'(2.()AMPD Tb FivacLt 6-Ca..

US Army Corps of Engineers Example E-3 22 of 34 Steel Frames

Figure E"3. Building with steel moment-resisting frames and steel braced frames-continued. E-53 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

FLAME ~ ('MI.SF) - MODIFIC.ArioNS

Th-E TIZAP4SVJERLSE FF-AMES MVST 'DE, Mo&viiEV tJ CT-PEZ. Thd tQ~ASE TiteOL CA¶?AC-AW -rr, teSiSr S-CiSMIC LOAviI44;. rHEE.C FOSSI1?LC maOpitgC-rfoY4 ss4imas AtE ViSCOLSSeD ISLOWI.

• Ttt6 1501tLPINiJc ACTUAW( C-OuJT1AuS 7 -rV-NSVMCS F-gA 4EsSOIJL'1 3 OF WRItCM~ IAVE 'SEEN VETAILC- &S 'PVr17L.EV MAOOENr IMESflNGq FRAAAes. v'CnA1MqItq Thug CoJitJreCloN L'PT-AIL-S FoR..T~f1+ WrEJR.D-4rD ATF Fe2AMCS AtL I FIZANeS MAY De vsev 70 ft5tsr 1TEMILAThE.A1.. LOAPS.

* 11tg M'elAiM SiZIS foL Sg mi ^NP CaLvMJS i, FRIZAPIE5 )IfAwD 7 CAN V( IN~tEASCP To i"A?gP-*4 TW~tIQ LATrRJI.ft 1VS1Sr~r1CE. Fb-e CA-M'LF7 TK-E U-OcF 3F-&m ttAS A PC MA-W 0 K~omerJT' Mi211~4 A, ¶,CxON Wtrn S4JFFiC.4eIr VLt~e t"fqc4Ty mo IAt)trVC A flAiSrt4L SC-Tn o W MOP VL'WS Z~r I II 2)/1 (, - .(.3 ;,' *A w i4 -4 3 (Ze' i.1.')) oit. A Wi16-35 (WG4(.5) WOUVLP '5 APCQLAT7E. AFTI!P. ThM

ANP EQ-71 S"VtWVle IM PEAZIP. WCREASINCI Tflt SI1FFtICSS

OF h15t FAME: MAY !EeSVT IN A 1(jqfttR. 1Vr 1 47 SFCC~T'AL AC&ELLEAflc? AND R 11144eItr*51 PeiJ ASI S1tePH2.

* m TRAr4SMEfSI FEAMES CA'J IC MNcjnr"ME'P ~4mt Tit AVVrfloN OF' A TR.ACZ'P FRAM~E- SysrF~i.. TliiS WILL. ST11IFFE. TrM STrE.uTVR9 AJ'P IW~CeeA$Lr TWE SCISp~tC_. POIL"cS So Th-r~ TntV C-r AVNP eq-ir AAIJItYses 3E-r'BiZCPCAiZ. SEE T)tE FOILLOViA/Nq SccTichJ FOR.. 'NWJ E.KAM?L-t OF: h '3ZA"P FO--Me &I~rLYSI-S.

US Amy Corps of Engineers Example E-3 23 of 34 Steel Frames

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. 27 February 1986 TM 5-809-1Ol-INAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

~o~J~I1VINF~ (E- PecnJf) : FRAme A - fAcer, Figj'-mC

M CP lgtt fES (01) t'rr4P -FM C` S (-r,) Ff-o-L Cam Pv-Tr AiN&LY~iS arF .Ak4ME A. MAS5 CALCAJLATh-P F9o4W/4

MASS m~OPET I MJOVE. 2. MOPE

LEVEL ('~ --

~~ Io.V~~ 2.3oo *qj1 AO2. MA p..O s25%" 51

'O"7.7 V 6o+I23 *702 -l-afm 1.001 .V 1 -'Io317.5

PF,~~~~~ ~1.057 .031 -. 015

su. .2..¶ .0st -0,07

~AS A CMEFCAJLOCIcTE TMAt AN.P ~o~wo

0.02f1 jf

.14I 451 . . I fs l

MCPC '2

-MOP9 I mAove z

US Army Corps of Engineers Example E-3 72 nf 'a Steel Frames

FigureE-3. Building with steel moment-resisting frames and steel braced frames-ontinued. E-55 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Sedion A 27 February 1986

1ijp46r~TV'INPWAt (E.-W) V~TICUTIO- Si'e CAT At~ELMA-naNS. ~

Eck I~~~~AO0PE Mov e 7. move '3

(p'7/.')SanT,4) .41' Al') .31 ~ *0b2. .004

aoar: As SWv 1w T7nr8 4-2., TWZ I#4EUfr'%Tn1C PEMA70> RA-Tlo f-L K-B3RCkS IN A Cflnc-fr, SScwnTA-L FhCALir1 IS 1.0 . THUSTt-C LON ITaPINrA ?JoD IS 7HC SNEF T-a.j;gen R-T ft4' Eq-11 MID rtWe sZme COUNTM KOTL WA-S VS-E FO9 -&Tn

US Arzy Corps of Engineers Example E-3 25 of 34 Steel Frames

FigureE-3. Building with steel moment-resisting frames and steel braced frames-continued. E-56 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

IACPFO PjAN~v(iSe L0,JGITVPWAiL. (E-YLrcJ-_ FkrLme A

- EV- LI ttgWn (K) (ff4.k' (A)U..ic viv ____ I.,

'4' I-co5T .45(o 15.1- 2650.1 27O I10 *q33 .31& .I0 0- 2 ~.585 .153 .JIJ WAPL 35')01 If .14o .2.05 *2.o'1

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- = - ,q~-~~~~~i. -7 I ..L{22&.74, -

US Army Corps of Engineers Example E-3 26 of 34 Stecr1 F'rames

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-57 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

E~Q-I FLEM-Eb.JT FOKCe5S LOIJqI7VVINAL (6-W)-F7RAME A_ see Nores opi~ stierT to.

o a 0 I Z- T1 .1 vz- I vy ~--W

.7 0 i

%.3 I. w 'U 0 U.. 44 4 1N -J &W 9. ~ % 0 4

V- 4 10 a

w0 .%A

Q~ N-

jI S l.IO *I C1 r US Army Corps of Enzineers Example E-3 27 of 34 Steel Fraw-e

Figure E-3. Building th steel moment-resisting frames andsteel braced frames-continued. Ea58 27 February 1986 rTM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-59 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

ELCMFW'r Sr-e - FP-AME Pr (?;Atce-'P-fWME (v'F,-46s;)

STEEL A r ~L Fa. I .P 2 LA.. i'p21FI IL.. imP -rvs E (I.j G3. r (10 CIL) ?C, L M) _____

5~5'q. q* 1 I~) 12I1.'2 10.13 ItI. 12..8 I.(4c 232. 2.5, I-O

0 BAM ELLEMETS Nt "BP-Acg!' wPr-es

F a - T I______

Z, M V . M j D Mv ti C. M., Ir!e LEvJEL SvLE (L.;.) (L-4') MC (k 4i) (IL-) 1M1C,

d,) 2. witt4o ~1?.L in2 i;3 .G5 mI 2Z;5 .47 i.5

*.jLNLAsTIC. Z£mArIp g"io FibDt mAcue 4-2.

US Arly Corps of Engineers Example E-3 29 of 34 Steel Frames

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-60 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

E~eAAcNT SrReS,'D - FP.AVE A ((c-NPNvED

-TArM CLMEVNT'& IN 1gP-P(rcc efrrS (Crfs-CV. IN4T-E-CA.TloN erqT-OrNs , SU AS fvf~Ccrt Ltme j s) L-[(,' b E~~~~IEC1 I-P I.CIL'I.Ce

W,¾-jc ?.is '113 ck.i7 5- 3. 13r.& . A7~ 0 7 .11,;

vji8 *q O 11,.q 7?.' 19,.5 I II' 9b o q14 , 9c-.2 1 2,. j 3 5 .

US BAmy Corps of Engineers Example E-3 30 of 34 Steel Frames

FigureE-3. Building with steel moment-resisting frames and steel braced frames-continued. EI61 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

ELeizerJT SUE~S~SE - 'FgimE A~ (caPo vo,

S3rEEL CZLL'MNS Iw ~i-TM (Z 'TAWE

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w04?_ 14.1 1 2.1 132 10 9%3 , ¶.3? 11.2- .27 37V• .92

"MCTpiFeD uNRIA)A. tNM ACTICN EqJAr'Ct.JS -see F9AMeF4 SttE9ET 114.

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S Any FCorV-seo 4-E.e I M,1AfI / - (/"rlpx)

US Amay Corps of Engineers Example E-3 31 of 34 Steel Frames

FigureE-3. Building with steel moment-resisting frames and steel braced frames-continued. E-62 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1 AFM 88-3, Chapter 13, Section A

04WAL IMTM;;,.r VP-IF7-

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US Army Corps of Engineers Example E-3 32 of 34 Steel Framnes

Figure E-3. Building with steel moment-resisting frames and steel braced frames-continued. E-63 TM 5-809-10-1INAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

~ in-c En~snc- JwMX-(5I INPrC&iEs Thi- lTr ?&: -

AL.T1-ovrqi- 7M1 St-AAS AMPD COLVMt.JS AT' rM1% LEVEL.

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US ArM Corps of Engineers Example E-3 33 of 34 Steel Frames

Figure E-3. Building with steel moment-resistingframes and steel braced frames-.continued. E-64 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

1:AME- A - MOPTIC&T-71NS

flELc,'T12vLP,rJiAL. f.~fAIF E-EQQJtEP 1AO'PVIATION

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I tPL".0 TOIL0 -fAME A M#AIVFIEV Go A

US Amy Corps of Engineers I Example E-3 34 of 34 Steel Frames ,F--

Figure E-3. Building with steel moment-zesisting frames and steel braced frames--continued . E-65 TM 5-809-10-1INAVFAC P-355.1/AFM 88-3, Chapter 13, SectIon A 27 February 1986

DESIGN EXAMPLE: E-4 ' J

SEVEN-STORY DUCTILE CONCRETE FRAME BUILDING:

Purpose. This example is presented in order to illustrate the modal analysis of a multistory building and the procedure for checking the ductility of beams and columns in a reinforced concrete frame.

Description of Structure. Design example E-4 is based upon a building with the same characteristics as the one that was used for design example E-1 and for the examples given in paragraph 2-Sc of this manual. The building is a 7-story, reinforced concrete moment-resisting space frame building as shown on sheet 2. The computer program TABS was used to model the structure for the seismic analyses. The section properties for the model were based on gross concrete sections and the properties for the spandrel beams around the perimeter were increased by 50% to approximate the influence of the slab.

Modal Analysis, The transverse modal analysis of the structure is shown in example E-1. The site response spectra for EQ-I and EQ-1I were provided by the soils engineer. The spectrum for EQ-I was based on 5% structural damping and a soil profile similar to type S2. The EQ-I spectrum has a peak ground acceleration of 0.20g and a maximum spectral acceleration of 0.50g. The seismic analyses included three modes of vibration from which the SRSS responses were determined. ) Ductility Check. One beam and one column section were selected from the sixth-floor level of frame B in order to illustrate the ductility check procedure. The properties of these sections and appropriate dead load, live load, and seismic analysis results are shown on sheets S and 6. The beam ductility check is presented on sheets 6-8 and the column ductility check is on sheets 9-12.

US Army Corps of Engineers

Example E-4 1 of 12 Concrete Frame

Figure E-4. Seven-story ductile concrete frame building. E-6 27 February 1986 TM 5809-1 O1w /NAVFAC P-355.1 /AFM 88-3, Chapter 13, Section A

1'STIDT-' ot¶.FLAM6EIE~~~' 6A1L.4VL1N~

R II - -11 11 I---- I 7 II - -II I I 11 11 if 11 5 -11 -II-- - I 3 11 It - II If 11 z _-II - 11 11 11 11 I.1015M - TF it __ it IL__ -II

SOUTHSou~~hFLEV-F-LEVATI . .O._ ON

US Army COrDS of. Engineent Example E-4 2 of 12 Concrete Frame Fure_ _t S d I e f ..g_ P _

'Figre ". Seven-story ductile concrete frame building-ontinued. E-67 TM 5-809101/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

pwk

MOVAL AJAINYSl - IJFWENCZ~r 1415*eti M.ov~s Cw VkM. 54L

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vM A s~~Q- r

MOVE' I ___ MVV 2.. mev '3

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4 MODAL SI4Ag. FLQM PES$UiN EXAM4&LZ E-1I SHE(Th 4, ?4.

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Trf SrLSS EuLTL~~ f0MA rfti 3-HoRE: Ai4AitS WitLE4? VS~CP lb COtZCXK Tlt U6AM AtJP COLUIAJi4 1r TYC i

Example E-4 3 of 12 I Concrete Frame

F'gure E-. Seven-story ductile concrete frame buflding--continued. E-68 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-, Chapter 13, Section A

rev- 'jtsir' Ecy~MpVe , aNe U~A-M A c~tcCcw.NviLK~ C'~Vtx ~~AP~t AiJ Nor- Ff. rr S40 -W r~gOC-cpPLr, i*Te UOT-TIES OFFrttV SEL(~p

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us Army Corps of Engineers Example E-4 4 of 12 Concrete Frame

FigureE-4. Seven-story ductile concrete frame building-continued. E-69 TM 5-80910l1/NAVFAC P-355.1/AFM 88-3, Chapter 13, SectIon A 27 February 1986

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EQ-I.

US Army Corps of Engineers I Example E-4 5 of 12 Concrete Frame V

Figure E-4. Seven-story ductile concrete frame building-continued. 1-70 27 February 1986 TM 5-809-10-1/NAYFAC P-355.1I/AFM 88-3, Chapter 13, Section A

Se&M FCZZs A-IJp LoAp COMAZINAflONS (ON ITS:kjf4)

FR AM e (E FI.&ot~(P Fegom

M V ~M M V VEA'! LOAP G-OP~) -1i +W -320 i.12

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.8v I'l I-oe --- #fl02 *-I3 -414 +7C, -BP + - DCO~ -6(.oL +. +1 1 +117 + 2+

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US Army Corps of Engineers Example E-4 6 of 12 Concrete;Frame

Figue E-4. Seven-stor-Y ductile concrete frame building-continued. B-71 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

Puc-nILrY' C~iteu. V-LfMTrAM

Tftf E"MO OP 'CMAA1 MAMENrU - UMiAkTE MOUA EsTJ L4ffXIr~Y A1 7ft~ f'PrM LS CeiteCz.D As F=±.owS- eq -r Mr14 e 1.0 Elq-r M,/MI / I (TARLC V-2)

UI-rIM4rT-E MOMENTr C*ACAC.r1 " k.= M e- 0-a-.9 J * fL-4 - As k /. r5 F,'

US Army Corps of Engineers

Exampl2Concrete Frame

Figure E-4. Seven-story ductile concrete frame building-continued. 1-72 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

pVICTI-rrY ciiECK. (coJni~vep) - PCMAIJr' gArlos

TOP SAR-5 ____roTTm twts-

EQ M~ f1~ ~I M__ EQ-I END 0 i7'4 583 1.2.8 lb2 358 .OI 1.0 SPAN - - - 2.28 I7Z .Yb 1.0 END(~ 620M &"1 ii, 117 358 .33 9.0

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"FojL. eq-W TWE PEMANP EAxioS Ate WIThIN Tft AU.OW/AILE (UJILASTIC VtM*P CtnTI91A IN 1hsWE 4-2, avr TRt VLLPPJ~ AS A WftaL MO.T 'It CiIECjLP FMt MPEC*NIJSMA AAIP vuNSMMfM~.C4;2

US Army Corps of Engineers Example E-4 8 of 12 Concrete Frame

Figure.E-4. Seven-story ductile concrete frame building-continued. E-73 TM 5-809-10-1/NAVFAC P-355.1I/AFM 88-3, Chapter 13, Section A 27 February 1986

COLUMN~ FPc-g"c AN LOADP CqM5IrJA-1ol)4S (UPOIrs : Y.04.)

COLUMPJ 102. ;ETWEN, SW" i (,Tb Roots

1' ro P wBo-rm -o? soWTom VPEAP LGAP (iLOP) V14 -c, - -, 45 LIVC- LOAV (I-oL0 Ir1 -z -f 2 - I

1.2.p4L*I~oe443 f J-?27 P-31 -71 1. .L4o0 El] 37c. -3I3 (a5 51 .$b '1.09 --- 24 -WO - S24 -85 -4bC

iszusmc~ (1.ot) ± i±5o7 ±L7 tIOl1 8

I.0D..2~LiOC ~ " 4iI -'p2. -U -73a

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US ArMY Corps of Engineers Example E-4 9 of 12 Concrete Frame

Figure E-4. Seven-story ductile concrete framie building-continueoL E-74 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Sedtion A

)VC.T I ITY Ci+0 Ec- FCK.'FCcT~ CLE 1- CLUL wAA 4

rite 1IiAi)jAl. CA-PACATY OF CO1.uMIhJ Z-2. WILL, 79 CnU-ED V LOAPS ?(ALt-Tjh4 'Fgc- Am. 7.h.t- I AFPL-ICE7D INTWE E-VVPIE~'C~nON. Fri 6u - 4~-5 9RP.cArT-S ittE qVA-T70N S 1ZeQ(, I40 &- A '61A'Lf.. WtTLITYV CtttCK. ,F A COCII ft fJ 17OL.E 4~- 2- UCXS RW. INVLA-5-IC 'PPAADJPtMO aF 1.2.5 FM~2w~~ IN A CCf,4(ieTt DA4.SF INJ N, C$W155ETIL LI

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F:,4 lk*-& M nYt Q1 -1 .7jF E 2

US Amy Corps of Engineers

Example E-4 10 of 12 Concrete Frame

Figure E-4. Seven-story ductile concrete frame building-continued. E-75 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

1 PUCTILITY C4t!rCJY - C-OLUMM 53-7 (Jt-bjnLrv) FMt ThiS eOmV14 f4, v4 ks'

6 p0.-17 10 1T.241 -2 -. 02&4

eQ-r. eq -,m ACC PrA6C01A

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r . ~A 2.0~4(4o/-f *357 -- 9

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:.wFVIE-~ rQ-1 IN~rcfOLATC Ft&.i . ( IRi rq- P } VCA 'TAILE 5

US Army Corps of Engineers Example E-4 11 of 12 Concrete Frame

Figure E-4. Seven-story ductile concrete frame building-continued. E-76 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A

'PV(-TILITY -CULVIAN 'V2- (CO14riAlve-D)

-0-13,fft Y Ve-tjVjWq ' "IAt CU FEKSm q OL 1)4. 11 . . 50 e 1.0 Eaq-1 AP 55 1

-U1 1II V .(.q 41.2's EQ-Jr 1161 S14 I

El%.+ 1y (4 4oi +. qi I.3 . 63 < 1.0 EQ-t P CIA 14,0Y P

S17 + III : . f\) 4 1.25 cQ-Z .F- 54

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TKN71NC, Wtfl"N THC EA-fT114vArE IS~ APLLf:7' ;'JJ

US Army Corps of Engineers [ Example E-4 12 of 12 Concrete Frame

Figure E-4. Seven-story ductile concrete frame building-continued. E-77 TM S-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 APPENDIX F DESIGN EXAMPLES-EQUIPMENT IN BUILDINGS

F-1. Purpose and scope. F-2. Design examples. The design examples in this appendix are to il- The following design examples are representa- lustrate principles, factors, and concepts de- tive of typical mechanical or electrical equip- scribed in chapter 6 of this manual for the ment supported on the roof or on a floor of any anchorage or bracing of mechanical or electrical building. The various examples illustrate the equipment in buildings. procedures for the analysis and design of both rigid and flexibly mounted equipment.

Table F-1. Design Examples-Equipmentin Buildings. Fig. No. Example No. and Description 4 F-1 F-1 Cooling tower in building: presents analysis for a rigidly mounted cooling tower in a multi-story building. F-2 F-2 Unit heater-flexible brace: analysis of a unit heater not rigidly braced. F-3 F-3 Unit heater-rigid support: demonstrates the reduction of the lateral seismic load by rigidly bracing the unit heater of design example F-2. F-4 F-A Tank on a building: demonstrates the seismic analysis of a storage tank on a building. Emphasis is placed on the period determination.

F-I TM 5-809-10-1INAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986

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F-1 5 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A BIBLIOGRAPHY

Chapter 3 (I) Aki, K., "Generation and Propagation of G Waves from the Niigata Earthquake of June 16,1964. Part 2.tEstimation of Earthquake Moment, Released Energy, and Stress-Strain Drop from the G Wave Spectrum," Bulletin of the Earthquake Research Institute, Tokyo University, Vol. 44, 1966, pp. 73-88. (2) Algermissen, S. T., and Perkins, D. M., "A Probabilistic Estimate of Maximum Acceleration in Rock in the Con- tiguous United States," U.S. Geological Survey Open File Report No. 76-416, 1976. (3) Algermissen, S. T., "Seismic Risk Studies in the United States," Proceedings of the 4th World Conference on Earthquake Engineering, Santiago, Chile, Vol. I, Section A-1, 1969, pp. 14-27. (4) Archuleta, B. J., and Frazier, G. A., "Three-Dimensional Numerical Simulations of Dynamic Faulting in a Half Space," Bulletin of the Seismological Society of America, Vol. 68, No. 3, 1978, pp. 541-572. (5) Barstow, N. L., Brill, K. G., Nuttli, 0. W., and Pomeroy, P. W., "An Approach to Seismic Zonation for Sitting Nuclear Electric Power Generating Facilities in the Eastern United States." Technical Report NUREG/CR-1577, Nuclear Regulatory Commission, 1981. (6) Benjamin, J. B., "Probabilistic Models for Seismic Force Design." Journal of the Structural Division, ASCE, ST5, No. 94, 1968, pp. 1175-1196. (7) Berareuter, D. L., Mortgat, C. P., and Wight, L. H., "Seismic Hazard Analysis: Site Specific Response Spectra. Sensitivity Results," Nuclear Regulatory Commission Report No. NUREGICR-1582, Vol. 4, 1981. (8) Bollinger, G. A., "Reinterpretation of the Intensity Data for the Charleston, S.C., Earthquake," U.S. Geological Survey, Professional Paper 1028, 1977. (9) Bollinger, G. A., "A Catalog of Southeastern United States Earthquakes 1754 through 1974," Virginia Polytechnic Institute and State University, Blacksburg, Va., Research Division Bulletin 101, 1975. (10) Bollinger, G. A., "The Giles County, Va., Seismic Zone: Configuration and Hazard Assessment," Proceedings of the Conference on Earthquakes and Earthquake Engineering: Eastern United States, Knoxville, Tenn., Vol. 1, 1981, pp. 277-308. (11) Bonilla, M. G., and Buchanan, J. M., "Interim Report on Worldwide Historic Surface Faulting," Open File Report, US. Geological Survey, 1970. (12) Boore, D. M., and Joyner, W., "The Influence of Rupture Incoherence on Seismic Directivity," Bulletin of the Seismological Society of America, Vol. 68, No. 2, 1978, pp. 28-300. (13) Boore, D. M., Joyner, W. B., Oliver, A. A., and Page, B. A., "Estimation of Ground Motion Parameters," United States Geological Survey Circular No. 795, 1978. (14) Campbell, K. W., "Near-Source Attenuation of Peak Horizontal Attenuation," Bulletin of the Seismological Society of America, Vol. 71, No. 6, 1981, pp. 2039-2070. (15) Chung, D. H., and Bernreuter,D. L., "On the Regionalization of Ground Motion Attenuation in the Conterminous United States," Second U.S. National Conference on Earthquake Engineering, Stanford, California, 1979, pp. 753- 762. (16) CIT., "Analysis of Strong Motion Earthquake Accelerograms," California Institute of Technology, Earthquake Research Laboratory Reports, Vol. I-IV, 1969-1975. (17) Cluff, L. S., "Geological Perspectives on Earthquake Hazards and Dam Safety," Seminar Workshop Lecture Notes on New Perspectives on the Safety of Dams, Stanford University, 1978. (18) Cornell, C A., "Engineering Seismic Risk Analysis," Bulletin of the Seismological Society of America, Vol. 58, No. 5, 1968, pp. 1583-1606. (19) Cornell, C. A., and VanMarcke, E. H., "The Major Influences on Seismic Risk," Proceedings of the Fourth World Conference on Earthquake Engineering, Santiago, Chile, Vol. I, Section A-1, 1969, pp. 69483. (20) Cornell, C. A., Banan, H., and Shakal, A. F., "Seismic Motion and Response Prediction Alternatives," Journal of Earthquake Engineering and Structural Dynamics, Vol. 7, 1979, pp. 295-315. (21) Dalal,J. S., "Probabilistic Seismic Exposure and Structural Risk Evaluation," Technical Report No. 169, Depart- ment of Civil Engineering, Stanford University, 1973. (22) Der-Kiureghian,A., and Ang, A.H-S., "A Fault Rupture Model for Seismic Risk Analysis," Bulletin of the Seis- mological Society of America, Vol. 65, No. 4, 1975, pp. 1023-1027. (23) Dong, W. M., Shah, H. C, and Bao, A. B., "Use of Maximum Entropy Principal in Earthquake Recurrence Rela- tionships," Final Report to the U.S. Geological Survey, The John A. Blume Earthquake Engineering Center, Stanford University, 1982. (24) Geller, A. J., and Kanamori, H., "Magnitudes of Great Shallow Earthquakes from 1904 to 1952," Bulletin of the Seismological Society of America, Vol. 67, 1977, pp. 587-598. (25) Gupta, L. N., and Nuttli, 0. W., "Spatial Attenuation of Intensities for Central U.S. Earthquakes," Bulletin of the Seismological Society of America, Vol. 66, No. 3, 1976, pp. 743-751. (26) Gutenberg, B., and Richter, C F., "Earthquake Magnitude, Intensity, Energy, and Acceleration," Bulletin of the Seismological Society of America, Vol. 46, 1956. (27) Hadely, J. B., and Devine, J. F., "Seismotectonic Map of the Eastern United States," U.S. Geological Survey, Report No. MF-620, 1974. (28) Haskell, N. A., "Total Energy and Energy Spectral Density of Elastic Wave Radiation from Propagating Faults, Part 11: Statistical Source Model," Bulletin of the Seismological Society of America, Vol. 56, No. 1, 1966, pp. 125- 140.

Bibliography 1 TM 5-809-10-1 /NAVFAC P-355.1 /AFM 88-3, Chapter 13, Section A 27 February 1986 (29) Haskell, N. A., "Total Energy and Energy Spectral Density of Elastic Wave Radiation from Propagating Faults, Part 1," Bulletin of the Seismological Society of America, Vol. 56, No. 1, 1964, pp. 125-140. (30) Idriss, L. M., "Characteristics of Earthquake Ground Motions," Proceedings of the ASCE Specialty Conference on Earthquake Engineering and Soil Dynamics, Pasadena, California, 1978. (31) Joyner, W. B., and Boore, D. M., "Peak Horizontal Acceleration and Velocity from Strong Motion Records Including Records from the 1979 Imperial Valley, California, Earthquake," Bulletin of the Seismological Society of America, Vol. 71, No. 6, 1981, pp. 2011-2038. (32) Kiremidjian,A. S., and Shah, H. C, "Seismic Hazard Mapping of California," Technical Report No. 21, the John A. Blume Earthquake Engineering Center, Stanford University, 1975. (33) Kiremidjian, A. S., and Shah, H. C, "Probabilistic Site-Dependent Response Spectra," Journal of the Structural Division, Proceedings of the ASCE, VoL 106, No. STI, January 1980, pp. 69-86. (34) Liu, S. C, and Fagel, L. W., "Seismic Risk Analysis-Comparison of Three Different Methods for Seismic Region- alization," Bulletin of the Seismological Society of America, VoL 65, No. 4, pp. 1023-1027. (35) McCann, M. W. Jr., "A Bayesian Geophysical Model for Seismic Hazard," Technical Report No. 47, The John A. Blume Earthquake Engineering Center, Stanford University, 1981. v (36) McGuir, A. K., "Effects of Uncertainty in Seismicity on Estimates of Seismic Hazard for the East of the United States," Bulletin of the Seismological Society of America, VoL 67, No. 3, 1977, pp. 827-848. (37) McGuire, B. K., "Seismic Structural Response Risk Analysis, Incorporating Peak Response Regressions on Earth- quake Magnitude and Distance," Massachusetts Institute of Technology, Department of Civil Engineering, Tech- nical Report No. R74-51, 1974. (38) McGuire, R. K., and Barnhard,J. A, "Magnitude, Distance and Intensity Data for C.I.T. Strong Motion Records," U.S. Geological Survey, Journal of Research, VoL 5, No. 4, 1977, pp. 437-443. (39) Mertz, H. A., and Cornell, C. A., "Seismic Risk Analysis Based on a Quadratic Magnitude-Frequency Law," Bulletin of the Seismological Society of America, Vol. 63, No. 6, 1973, pp. 1999-2006 (40) Molinar, P., "Earthquake Recurrence Intervals and Plate Tectonics," Bulletin of the Seismological Society of America, Vol. No. 1, 1979, pp. 115-133. (41) Mortgat, C P., and Shah, H. C, "A Bayesian Approach to Seismic Hazard Mapping," Technical Report No. 28, The John A. Blume Earthquake Engineering Center, Stanford University, 1978. (42) Mortgat, C. P., Zsutty, T. C, Shah, H. C., and Lubetkin, L., "A Study of Seismic Risk for Costa Rica," Technical Report No. 25, The John A. Blume Earthquake Engineering Center, Stanford University, 1977. (43) Murphy, J. E., and O'Brian, L. J., "Analysis of a Worldwide Strong Motion Data Sample to Develop an Improved Correlation Between Peak Acceleration, Seismic Intensity, and Other Physical Parameters," Nuclear Regulatory Commission, Report, No. NUREG-0402, 1978. (44) Newmark, N. M., and Hall, W. J., "Earthquake Spectra and Design," EERI Monograph Series, 1982. (45) Nishioka, T., and Shah, H. C, "Application of the Markov Chain on Probability of Earthquake Occurrence," Proceedings of the Japan Society of Civil Engineers, No. 298, June 1980, pp. 137-145. (46) Nuttli, 0. W., and Zollweg, J. E., "The Relationship Between Felt Area and Magnitude for Central United States Earthquakes," Bulletin of the Seismological Society of America, Vol. 64, No. 1, 1974, pp. 73-83. (47) Nuttli, 0. W., "Similarities and Differences Between the Western United States Earthquakes and Their Conse- quences for Earthquake Engineering," Proceedings of the Conference on Earthquakes and Earthquake Engi- neering in the Eastern United States, VoL 1, Knoxville, 1981, pp. 25-51. (48) Nuttli, 0. W., "The Relationship of Sustained Maximum Ground Acceleration and Velocity to Earthquake Intensity and Magnitude," Report No. 16, Miscellaneous Paper S-73-1, U.S. Army Engineer Waterways Experiment Station, 1979. (49) Nuttli 0. W., "The Mississippi Valley Earthquakes of 1811 and 1812, Intensities, Ground Motion, and Magnitudes," Bulletin of the Seismological Society of America, Vol. 63, 1973, pp. 227-24& (50) Patwardbam,A. S., Kulkari, B. B., and Tocber, D., "A Semi-Markov Model for Characterizing Recurrence of Great EaTthquakes," Bulletin of the Seismological Society of America, Vol. 70, No. 1, 1980, pp. 323-347. (51) Savage, J. G., "Radiation from a Realistic Model of Faulting," Bulletin of the Seismological Society of America, VoL 56, No. 2, 1966, pp. 577-52. (52) Savy, J. B., Shah, H. C, and Boore, D., "Non-Stationary Risk Model with Geophysical Input," Journal of the Structural Division, Proceedings of the ASCE, Vol. 106, No. STI, January 1980, pp. 145-163. (53) Savy, J. B., "Determination of Seismic Design Parameters: A Stochastic Approach, Technical Report No. 34, The John A. Blume Earthquake Engineering Center, Stanford University, 1979. (54) Schnabel,P. B., and Lysmer, 3., "SHAKE-A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites," Report No. EERC 72-12, University of California, Berkeley, 1972. (55) SEAOC, "Suggested Procedures for Developing Seismic Ground Motions," Structural Engineers Association of California, 171 Second Street, San Francisco, 1979. (56) Seed, H. B, et aL "Site-Dependent Spectra for Earthquake Resistant Design," Report No. EERC 74-12, University of California, Berkeley, 1974. (57) Seed, H. B., et al. "Characteristics of Rock Motions During Earthquakes," Report No. EERC 68-5, University of California, Berkely, 1968. (58) Shah, H. C, Mortgat, C. P., Kiremidjian, A S., and Zsutty, T. C, "A Study of Seismic Risk for Nicaragua, Part I," The John A. Blume Earthquake Enginering Center, Technical Report No. 11, Stanford University, 1975. (59) Shah, H. C, Zsutty, T. C, Krawinkler, H., Mortgat, C. P., Kiremidjian, A. S., and Dizon, J. O., "A Study of Seismic . Risk for Nicaragua, Part II, Commentary," The John A. Blume Earthquake Engineering Center, Technical Report No. 12A, Stanford University, 1976.

Bibliography 2 27 February 1986 TM 5-809-10-1INAVFAC P-355.1IAFM 88-3, Chapter 13, Section A (60) Sieh, K. E., "Prehistoric Large Earthquakes Produced by Slip on the San Andreas Fault at Pallet Creek, California," Journal of Geophysics Research, Vol. 83, 1978, pp. 3907-3939. (61) Slemmons, D. B., "Fault and Earthquake Magnitude," State-of-the-Art for Assessing Earthquake Hazards in the United States, Report No. 6, Miscellaneous Paper S-73-1, U.S. Army Engineer Waterways Experiment Station, 1977. (62) Stepp, J. C, "Analysis of Completeness of the Earthquake Sample in the Puget Sound Area and its Effect on Statistical Estimates of Earthquake Hazard," Proceedings of the First Microzonation Conference, Seattle, 1974. (63) Tera Corporation,"Seismic Hazard Analysis: Solicitation of Expert Opinion," Nudear Regulatory Commission Report No, NUREG/CR-1582, Vol. 3,1980. (64) Tera Corporation,"Seismic Hazard Analysis-Solicitation of Expert Opinion," Nuclear Regulatory Commission, NUREG/CR-1582, Vol. 4, 1980. (65) Tera Corporation,"Seismic Hazard Analysis: Results," Report to Lawrence Livermore National Laboratory, 1981. (66) Trifunac, M. D., and Brady, A. G., "On the Correlation of Seismic Intensity Scales with the Peaks of Recorded Strong Ground Motion," Bulletin of the Seismological Society of America, Vol. 65, No. 1, 1975, pp. 139162. (67) U.S. Geological Survey CircularNo. 898, "Summary of Workshops Concerning Regional Seismic Source Zones of Parts of the Conterminous United States," Convened by the US. Geological Survey, 1979-1980, Golden, Colorado. Edited by Paul C. Thenhaus. (68) Vagliente, V. N, "Forecasting the Risk Inberent in Earthquake Resistant Design," Ph.D. Dissertation, Department 1, of Civil Engineering, Stanford University, 1973. Also published as Technical Report No. 174, Department of Civil Engineering, Stanford University. (69) Wiggins, J. H., "Procedure of Determining Acceptable Risk Ground Motion Design Criteria," Technical Report. No. 75-1229, J. H. Wiggins Company, Redondo Beach, California, 1975. (70) Woodward Clyde Consultants, "Offshore Alaska Seismic Exposure Study," in six volumes, prepared for Alaska Subartic Offshore Committee (OASES), 1978. (71) Yegian, M. K., "Probabilistic Seismic Hazard Analysis," Report No. 17, Miscellaneous Paper S-73-1, US. Army Engineer Waterways Experiment Station, 1979. (72) Zaback, M. D., et al, "Major Fault Zone Associated with the Main New Madrid Fault Seismic Trend Shown by Seismic-Reflection Profiling," 51st Annual Meeting, Eastern Section of the Seismological Society of America, 1979. Chapters 4 and 5 (73) Applied Technology Council, "An Investigation of the Correlation Between Earthquake Ground Motion and Build- - ing Performance," ATC-10, Palo Alto, California, 1983. (74) Blume, J. A., et aI, "Design of Multistory Reinforced Concrete Buildings for Earthquake Motions," Portland Cement Association, Skokie, Illinois, 1961. _ - (75) Chopra, Anil, K., "Dynamics of Structures-A Primer," Earthquake Engineering Research Institute, Berkeley, California, 1981. - (76) Freeman, S. A., "Prediction of Response of Concrete Buildings to Severe Earthquake Motion," Douglas McHenry International Symposium on Concrete and Concrete Structures, American Concrete Institute, SP-55, Detroit, Michigan, 1978. (77) Freeman,S. A., Nicoletti, J. P., and Tyrrell, L. V., "Evaluation of Existing Buildings for Seismic Risk-A Case Study of Puget Sound Naval Shipyard, Bremerton, Washington," Proceedings of the US. National Conference on Earth- quake Engineering-1975, Earthquake Engineering Research Institute, Berkeley, California, 1975. (78) Hudson, D. E., "Reading and Interpreting Strong Motion Accelerograms," Earthquake Engineering Research Institute, Berkeley, California, 1979. (79) Jeing, J. C, "Problems in the Use of Root-Sum-Square Solutions for Three-Dimensional Dynamic Analysis of Buildings," Proceedings of the Seventh World Conference on Earthquake Engineering, Istanbul, Turkey, 1980. (80) Murphy, L. M., Scientific Coordinator,"San Fernando, California, Earthquake of February 9, 1971," Effects on Building Structures, Vol. 1, US. Department of Commerce, National Oceanic and Atmospheric Administration, Washington, DC, 1973. (81) Newrmark, N. M., and Hall, W. J., "Procedures and Criteria for Earthquake Resistant Design," Buildings Practices for Disaster Mitigation, Building Sciences Series 46, National Bureau of Standards, Washington, DC, 1973. (82) Seismology Committee, "Recommended Lateral Force Requirements and Commentary," Structural Engineers Association of California, San Francisco, California, 1980. (83) URS/John A. Blume & ASsodates, Engineers, "Effects Prediction Guidelines for Structures Subjected to Ground Motion," JAB-99-115, San Francisco, California, 1975. Appendix C (84) Ambraseys, N. N., "The Correlation of Intensity with Ground Motions," Advancements In Engineering Seismology in Europe, Trieste, Italy, 1972. (85) Chinnery, M. A., and Rodgers D. A., "Earthquake Statistics in Southern New England," Earthquake Notes, Vol. XLIV, No. 304, 1973. (86) Chopra, A. K., "Dynamics of Structures-A Primer," EERI Monograph, 1981. (87) Gutenberg, B., and Richter, C. F., "Earthquake Magnitude, Intensity, Energy, and Acceleration," Bulletin of the Seismological Society of America, Vol. 46, No. 2, 156, pp. 1054145. (88) Gutenberg, B., and Richter, C. F., "Earthquake Magnitude, Intensity, Energy, and Acceleration," Bulletin of the Seismological Society of America, Vol. 32, No. 3, 1942, pp. 163-191.

Bibliography 3 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1IAFM 88-3, Chapter 13, Section A (89) Hershberger,J., "A Comparison of Earthquake Acceleration with Intensity Ratings," Bulletin of the Seismological Society of America, Vol. 46, No. 2,1956, pp. 317-320. (90) Hudson, E. E., "Readings and Interpreting Strong Motion Accelerograms," EERI Monograph, 1981. (91) Krinitzsky, E. L., and Cbang, F. K., "Specifying Peak Motions for Design Earthquakes," Report No. 7 in the Series, State-of-the-Art for Assessing Earthquake Hazards in the United States, U.S. Army Engineer Waterways Exper- iment Station, Miscellaneous Paper S-73-1, 1977. (92) Krinitzsky, E. L., and Chang, F.K, "Earthquake Intensity and the Selection of Ground Motion for Seismic Design," Report No. 4 in the Series, State-of-the-Art for Assessing Earthquake Hazards in the United States, U.S. Army Engineer Waterways Experiment Station, Miscellaneous Paper S-73-1, 1975. (93) Lysmer, I., Udaka, T., Tsai, C F., and Seed, H. B., "FLUSH-A Computer Program for Approximate 3-D Analysis of Soil-Structure Interaction Problems," Report No. EERC 75-30, University of California, Berkeley, 1975. (94) McGuire, R. K., "FRISK: Computer Program for Seismic Risk Analysis Using Faults at Earthquake Sources," U.S. Geological Survey Open File Report No. 78-1007, 197& (95) Newmark, N. M., and Ha, W. J., "Earthquake Spectra and Design," EERI Monograph, 1982. (96) Richter, C F., "An Instrumental Earthquake Magnitude Scale," Bulletin of the Seismological Society of America, Vol. 25, No. 1, 1935, pp. 132 (97) Richter, C F., "Elementary Seismology," W. H. Freeman & Company, San Francisco, 1958. (98) Schnabel,P. B., andLysmerm J., "SHAKE-A Computer Program for Earthquake Response Analysis of Horizontally Layered Sites," Report No. EERC 72-12, University of California, Berkeley, 1972. (99) Seed, H. B., and Idriss, I. M., "Influence of Soil Conditions on Ground Motions During Earthquakes," Journal of Soil Mechanics and Foundation Division, ASCE, Vol. 95, No. SMI, 1969, pp. 99-137. (100) Shah, H. C, "Earthquake Engineering and Seismic Risk Analysis," Class Notes by the John A. Blume Earthquake Engineering Center, Stanford University, 1979. (101) Slemmons, D. B., "Faults and Earthquake Magnitude," Report No. 6 in the Series, State-of-the-Art for Assessing Earthquake Hazards in the United States, U.S. Army Engineer Waterways Experiment Station, Miscellaneous Paper S-73-1, 1977. (102) Tera Corporation,"Seismic Hazard Analysis: Solicitation of Expert Opinion," NRC Report No. NUREG/CR-1582, Vol. 3,1980. (103) Trifunac4 M. D., and Brady, A. G., "On the Correlation of Seismic Intensity Scales with the Peaks of Recorded Strong Motion," Bulletin of the Seismological Society of America, Vol. 65, No. 1, 1975, pp. 139-162.

,, Bibliography 4 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A GLOSSARY TERMS FOR PROBABILISTIC SEISMIC RISK AND HAZARD ANALYSIS Acceptable Risk-a probability of social or economic consequences due to earthquakes that is low enough (for example in comparison with other natural or manmade risks) to be judged by appropriate authorities to represent a realistic basis for determining design requirements for engineered structures, or for taking certain social or economic actions. Active Fault-a fault that on the basis of historical, seismological, or geological evidence has a high probability of producing an earthquake. (Alternate: a fault that may produce an earthquake within a specified exposure time, given the assumptions adopted for a specific seismic-risk analysis.) Attenuation Law-a description of the behavior of a characteristic of earthquake ground motion as a function of the distance from the source of energy. B-Value-a parameter indicating the relative frequency of occurrence of earthquakes of different sizes. It is the slope of a straight line indicating absolute or relative frequency (plotted loga- rithmically) versus earthquake magnitude or meizoseismal Modified Mercalli intensity. (The B- value indicates the slope of the Gutenberg-Richter recurrence relationship.) Coefficient of Variation-the ratio of standard deviation to the mean. Damage-any economic loss or destruction caused by earthquakes. Design Acceleration-a specification of the ground acceleration at a site, terms of a single value such as the peak or rms; used for the earthquake-resistant design of a structure (or as a base for deriving a design spectrum). See "Design Time History." Design Earthquake-a specification of the seismic ground motion at a site; used for the earthquake- resistant design of a structure. Design Event, Design Seismic Event-a specification of one or more earthquake source parameters, and of the location of energy release with respect to the site of interest; used for the earthquake- resistant design of a structure. Design Ground Motion-see "Design Earthquake." Design Spectrum-a set of curves for design purposes that gives acceleration velocity, or displacement (usually absolute acceleration, relative velocity, and relative displacement of the vibrating mass) as a function of period of vibration and damping. Design Time History-the variation with time of ground motion (e.g., ground acceleration or velocity or displacement) at a site; used for the earthquake-resistant design of a structure. See "Design Acceleration." Duration-a qualitative or quantitative description of the length of time during which ground motion at a site shows certain characteristics (perceptibility, violent shaking, etc.). Earthquake-a sudden motion or vibration in the earth caused by the abrupt release of energy in the earth's lithosphere. The wave motion may range from violent at osme locations to imper- ceptible at others. Elements at Risk-population, properties, economic activities, including public services etc., at risk in a given area. Exceedence Probability-the probability that a specified level of ground motion or specified social or economic consequences of earthquakes, will be exceeded at a site or in a region during a specified exposure time. Expcted-mean, average. Expected Ground Motion-the mean value of one or more characteristics of ground motion at a site for a single earthquake. (Mean ground motion.) Exposure-the potential economic loss to all or certain subset of structures as a result of one or more earthquakes in an area. This term usually refers to the insured value of structures carried by one or more insurers. See "Value at Risk." Exposure Time-the time period of interest for seismic-risk calculations, seismic-hazard calculations, or design of structures. For structures, the exposure time is often chosen to be equal to A the design lifetime of the structure. Geologic Hazard-a geologic process (e.g., landsliding, liquefaction soils, active faulting) that during an earthquake or other natural event may produce effects in structures. Glossary 1 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A 27 February 1986 Intensity-a qualitative or quantitative measure of the severity of seismic ground motion at a specific site (e.g., Modified Mercalli intensity, Rossi-Forel intensity, Housner Spectral intensity, Arias intensity, peak acceleration, etc.). Loss-any adverse economic or social consequence cause by one or more earthquakes. Maximum-the largest value attained by a variable during a specified exposure time. See "Peak Value." Maximum Credible Maximum Expectable Maximum Expected Maximum Probable-These terms are used to specify the largest value of a variable, for example, the magnitude of an earthquake, that might reasonably be expected to occur. These are mis- leading terms and their use is discouraged. (The U.S. Geological Survey and some individuals and companies define the maximum credible earthquake as "the largest earthquake that can be reasonably expected to occur." The Bureau of Reclamation, the First Interagency Working Group (Sept. 1978) defined the maximum credible earthquake as "the earthquake that would cause the most severe vibratory ground motion capable of being produced at the site under the current known tectonic framework." It is an event that can be supported by all known geologic and seismologic data. The maximum expectable or expected earthquake is defined by USGS as "the largest earthquake that can be reasonably expected to occur." The maximum probable earthquake is sometimes defined as the worst historic earthquake. Alternatively, it is defined as the 100-year-return-period earthquake, or an earthquake that probabilistic determination of recurrence will take place during the life of the structure.) Maximum Possible-the largest value possible for a variable. This follows from an explicit assumption that larger values are not possible, or implicitly from assumptions that related variables or functions are limited in range. The maximum possible value may be expressed deterministically or probabilistically. Mean Recurrence Interval, Average Recurrence interval-the average time between earthquakes or faulting vents with specific characteristics (e.g., magnitude a 6) in a specified region or in a specified fault zone. Mean Return Period-the average time between occurrences of ground motion with specific characteristics (e.g., peak horizontal acceleration n 0.1 g) at a site. (Equal to the inverse of the annual probability of exceedance.) Mean Square-expected value of the square of the random variable. (Mean square minus square of the mean gives the variance of random variable.) Peak Value-the largest value of a time-dependent variable during an earthquake. Response Spectrum-a set of curves calculated from an earthquake accelerogram that gives values of peak response of a damped linear oscillator, as a function of its period of vibration and damping. Root Mean Square (rms)-square root of the mean square value of a random variable. Selsmic-Activity Rate-the mean number per unit time of earthquakes with specific characteristics (e.g., magnitude a 6) originating on a selected fault or in a selected area. Seismic-Design-Load Effects-the actions (axial forces, shears, or bending moments) and deformations induced in a structural system due to a specified representation (time history, response spectrum, or base shear) or seismic design ground motion. Seismic-Design Loading-the prescribed representation (time history, response spectrum, or equivalent static base shear) of seismic ground motion to be used for the design of a structure. Seismic Event-the abrupt release of energy in the earth's lithosphere, causing an earthquake. Seismic Hazard-any physical phenomenon (e.g., ground shaking, ground failure) associated with an earthquake that may produce adverse effects on human activities. Seismic Risk-the probability that social or economic consequences of earthquakes will equal or exceed specified values at a site, at several sites, or in an area, during a specified exposure time. Seismic-Risk Zone-an obsolete term. See "Seismic Zone." Seismic-Source Zone-an obsolete term. See "Seismogenic Zone" and "Seismotectonic Zone." Seismic Zone-a generally large area within which seismic-design requirements for structures are constant. Seismic Zoning, Seismic Zonation-the process of determining seismic hazard at many sites for the purpose of delineating seismic zones. Glossary 2 27 February 1986 TM 5-809-1O-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A Seismic Mlcroxone-a generally small area within which seismic-design requirements for structures are uniform. Seismic microzones may show relative ground motion amplification due to local soil conditions without specifying the absolute levels of motion or seismic hazard. Seismic Microzoning, Seismic Microzonaftion-the process of determining absolute or relative seismic hazard at many sites, accounting for the effects of geologic and topographic amplification of motion and of soil stability and liquefaction, for the purpose of delineating seismic microzones. Alternatively, microzonation is a process for identifying detailed geological, seismological, hy- drological, and geotechnical site characteristics in a specific region and incorporating them into land-use planning and the design of safe structures in order to reduce damage to human life and property resulting from earthquakes. Seismogenic Zone, Seismogenic Province-a planar representation of a three-dimensional domain in the earth's lithosphere in which earthquakes are inferred to be of similar tectonic oi ..i. A seismogenic zone may represent a fault in the earth's lithosphere. See "Seismotectonic Zone." Selsmogenic Zoning-the process of delineating regions have nearly homogeneous tectonic and geologic character, for the purpose of drawing seismogenic zones. The specific procedures used depend on the assumptions and mathematical models used in the seismic-risk analysis or seismic- hazard analysis. Seismotectonic Zone, Selsmotectonic Providence-a seismogenic zone in which the tectonic processes causing earthquakes have been identified. These zones are usually fault zones. Source Variable-a variable that describes a physical characteristic (e.g., magnitude, stress drop, seismic moment, displacement) of the source of energy release causing an earthquake. Standard Deviation-the square root of the variance of a random variable. Upper Bound-see "Maximum Possible." - Value at Risk-the potential economic loss (whether insured or not) to all or certain subset of structures as a result of one or more earthquakes in an area. See "Exposure." Variance-the mean squared deviation of a random variable from its average value. Vulnerability-the degree of loss to a given element at risk, or set of such elements, resulting from an earthquake of a given magnitude or intensity, which is usually expressed on a scale from 0 (no damage) to 10 (total loss).

Glossary 3 27 February 1986 TM 5809- 10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Secton A INDEX Paragraph Accelerations ...... 5-4g, 6-3b, 6-4b Accelerograms ...... , 2-3b Active fault approach ...... 3-4a(1) All other buildings ...... 4-c 4 , -2d(3),5-3d Allowable stresses .. 4-3f Alterations .. 1-lb Annual risk .. 3-8a Approval authorities .l...... I-lb Architectural elements...i. 6-5 Area source .3-40)(c),3-4b(2)(a) Attenuation. 3-3c(4), 3-5c, 3-5d Background area source. 3-4b(l)(e) Base shear .-...... 43c(i)(1) Basic Design Manual. I-l, 4-1,4-2 Basis of design .1-3 Bibliography .1-4 Buried structures .7-7 Capacity .4-4c(3), 5-24 5-4e(2), 5-5b Capacity Spectrum Method ... 4-4 5-5b Coefficient of variation .3-7a(1) Combining modes . 22-5 44-3c(i)(i), 5-4d(l)(c) Communications ...... 6-7d Concrete ...... 4-3f(l) Connections ...... 4-3f(5) Damping Ratio ...... 2-5a, 3-8d, 4-3b(table 4-1), 4-4b, 7-2a(table 7-1) Definitions ...... 4-2b Deflection ...... 4-S3c 4-S3c(l)(h), 4-3e(7), 4-4e(2), 5-4f, S-5c Demand ...... 4-4c(2), 5-5a(4), 5-5b Design procedures ...... 5-3 Design response spectrum ...... 3-8c 4-3b, 4-4b, 5-2a Deterministic approach ...... 3-3c(2) - Diaphragms ...... 5-4c(5) Dippling plane source. 3-4b(1)(d) Drift ...... '-3c,4 4-3e(7), 4-4e(2), 5-4f, S-5c Dynamic amplification factor ...... 3-6b Dynamic analysis procedures ...... 2-2a, 2-5, 4-2d, 5-3b, c; d Economic life ...... 3-le Effective peak acceleration ...... 3-8a Effective peak velocity ...... 3-8a Effective response spectra ...... 3-6h, 3-8e Elastic Capacity (EC) ...... 4-3e(2), 4-3f, 5-4e(2), 5-Sb(2) Elastic design provisions ...... 4-3, 5-4 Electrical elements ...... 6-1,6-6 Elevators ...... 6-7e Emergency power ...... 6-7c Envelope ...... 3-7a(2) EQ-1*...... --...... 3-le, 4-2d, 4-S3, S-2a(I), S4, 6-2a. 6-3 EQ-I1 ...... 3-le, 4-2d, 4-4, 5-2a(2), 5-5, 6-2b, 6-4 Equipment .. Chp...... Chap 6 Essential facilities ...... I-ld(2), 4-la, 4-2d(1), 5-3b, 6-7 Exposure time ...... 3-le Fire protection systems ...... 6-7a Floor response spectra ...... 2-6a, 6-3c Floor spectral acceleration ...... 6-3c(2) Forecasting models ...... 3-4d Foundations ...... 2-4c, 5-2d Frequency of vibration ...... 2-5a Graphical procedure ...... 4-4d Ground failure ...... I-lb Hazard ...... 3 -7c Hazardous critical facilities ...... I-ld(l) Hazardous materials ...... 6-7b High-rise buildings ...... 5"4a(4) High risk facilities ...... I-id(3), 4-ib, 4-2d(2), 5-3c I-factor .. 4.....4-la,4lb Index 1 TM 5-809-10.- N.A FAC P-355.1 /AFM 88-3, Chapter 13, Section A 27 February 1986 Inelastic response ...... 2-Se Inelastic-demand ratio ...... 4-4c(4), table 4-2, 5-5a(4) Initial trial design ...... 5-3a Interstory displacement ...... 2-6b, 4-3e(7), 5-4a (table 5-3), 6-3d, 6-4d Irregular buildings ...... I-ld(4), 2-5d, 4-3c Lateralforce ...... 4-)(e) Liquefaction ...... I-lb Load combinations ...... 4-3e(2), 4-4e(1), 5-4e Low-rise buildings ...... 5-4a(2) Masonry ...... 4-3f(3) Mathematical models ...... 4-3c(l)(a), 5-4b Maximum earthquake ...... 3-4c(2) Mechanical elements ...... 6-1, 6-6, 6-7f Median ...... 3-5e Method 1: elastic analysis procedure ...... 4-4c, 5-Sa Method 2: capacity spectrum method ...... 4-4d, 5-Sb (fig 5-6) Minimum lateral forces ...... 4-3d Modal analysis ...... 2-Sc, 4-3c, 5-4a Multi-degree-of-freedom (MDOF) system ...... 2-5b Moderate-rise buildings ...... 5-4a(3) Modes of vibration ...... 2-Sb, 4-3c(1) (b), 5-4c(2), 5-4d(2) Nearly elastic behavior ...... 4-3e(1) Nonlinear response ...... 2-Se Nonstructural elements ...... 2-6, 4-2e, 6-1 Normalization ...... 3-4c(1)(a), 3-4c(1)(b) Normalized response spectra ...... 3-6b Notations ...... 4-2c Orthogonal effects ...... 4-3e(4) Overturning ...... 4-3c(1)(g),4-3e(6),5-4h P-delta effects ...... 4-4e(2) (c), 5-5d Participation factors ...... 4-3c(l)(c), (d), 5-3a(3)(c), 5-4c(2), 5-4d(2) Periods of vibration ...... 2-Sa, 4-3c(1)(b) Point source ...... 3-4b(1)(b) Poisson probability model ...... 3-3a(3), 3-4d(l), 3-7c Post-yield analysis ...... 4-4 Preliminary design consideration ...... 5-2...... 2 Probabilistic approach ...... 3-3c(2) Recurrence relations ...... 3-4c(l)(e), 3-4ct1)(f) Regional geology ...... 3-6b(4) Reliability ...... 3-7b Response spectra ...... 2-3c, 3-6 Response spectrum shape ...... 2-4(a) Retaining walls ...... 7-4 Return period ...... 3-4d(1) Risk levels ...... I-Ic Seismic moment ...... 3-4c(3) Separations ...... 4-3e(7), 4-4e(2), 5-4f, 5-5c Single-degree-of-freedom (SDOF) systems ...... 2-5 Single-story buildings ...... 5-4a(1) Site soil conditions ...... 3f(3) Soil column response ...... 3-6d Spectral acceleration, S...... 2-3 (fig 2-4), 4-3c(l)(e), 5-4a(3)(e), 5-5b (table 5-4), 5-Sb(2)(h) Spectral displacement, S ...... 2-5c (fig 2-7), 4-3c(1)(h), 5-Sb (table 5-4), 5-5b(2)(h) Spectral.shape factor ...... 3-Ba Square-root-of-the-sum-of-the-squares (SRSS) ...... 2-Sc STASHA program ...... 3-3d Steel ...... 4-3f(2) Structural systems ...... 5-2b Structures other than buildings ...... 4-2f, Chap 7 Symbols ...... 4-2c Symmetry ...... 4-3c Tanks ...... 7-3,7-4,7-5 Tectonic province approach ...... 3-4a(1) Three-dimensional models ...... 4-3c(2), 5-4d Time history ...... 2-3b Torsion ...... 2-Sd, 4-3e(5), 5-4c(4), 5-4d(l)(b), 5-4i, 5-Sa(4)(d) Transmission path ...... 3-5a(1) Tripartite plots ...... 3-e1) Index 2 27 February 1986 TM 5-809-10-1/NAVFAC P-355.1/AFM 88-3, Chapter 13, Section A Two-dimensional models ...... 443c(1), 5-4c Two-level approach ...... 1-2d, 4-2d, 5-3b U ncertainty ...... 3- Se,3-7a Vertical acceleration. 4-3e(3) Wood.. 4--3f(4)

Index 3 27 February 1986 TM 5-809-10-1/NAYFAC P-355.I/AFM 88-3, Chapter 13, Section A

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By Order of the Secretaries of the Army, the Air Force, and the Navy:

JOHN A. WICKHAM, JR. General, United States Army Official: Chief of Staff MILDRED E. HEDBERG BrigadierGeneral, United States Army The Adjutant General CHARLES G. GABRIEL General, USAF Official: Chief of Staff NORMAND G. LEZY Colonel, USAF Director of Administration J. P. JONES, JR s BRear Admiral, CEC, U.S. Navy Commander, Naval Facilities Engineering Command Distribution: Army: To be distributed in accordance with DA Form 12-34B, Requirements for Seismic Design for Buildings. Air Force: F Navy:

* U.S OVWRNMENTPUM0IG 0fCE: 1987 0-181-421 (701161