THE UTILIZATION OF LOAD AND RESISTANCE STATISTICS IN A WIND SPEED ASSESSMENT by TIMOTHY PATRICK MARSHALL, B.S., M.S. A THESIS IN CIVIL ENGINEERING Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN CIVIL ENGINEERING Approved / IXrre^nff^rí May, 1983 '7--V.. ACKNOWLEDGMENTS I would like to thank Dr. James McDonald for his support and en- couragement throughout my stay in the Civil Engineering program as well as his constructive comments and guidance in helping me complete my thesis. I would also like to express my appreciation to the rest of my committee, Drs. Joseph Minor, Kishor Mehta and Richard Peterson for their suggestions on my thesis and knowledge gained both in and out of the classroom. It has also been a pleasure to be a part of the Institute for Disaster Research and to be on the forefront of engineering research. My thanks and love also go to my wife, Kay, for her love, patience and encouragement and for believing in me. I dedicate this thesis to the memory of Dr. Jack Villmow: a teacher and friend who devoted his life to meteorology and who inspired me to seek higher education in the sciences. n ACKNOWLEDGMENTS I would like to thank Dr. James McDonald for his support and en- couragement throughout my stay in the Civil Engineering program as well as his constructive comments and guidance in helping me complete my thesis. I would also like to express my appreciation to the rest of my committee, Drs. Joseph Minor, Kishor Mehta and Richard Peterson for their suggestions on my thesis and knowledge gained both in and out of the classroom. It has also been a pleasure to be a part of the Institute for Disaster Research and to be on the forefront of engineering research. My thanks and love also go to my wife, Kay, for her love, patience and encouragement and for believing in me. I dedicate this thesis to the memory of Dr. Jack Villmow: a teacher and friend who devoted his life to meteorology and who inspired me to seek higher education in the sciences. n TABLE OF CONTENTS Page ACKNOWLEDGEMENTS ii LIST OF TABLES vi LIST OF FIGURES vii I. INTRODUCTION 1 1.1 Background 1 1.2 Purpose 2 1.3 Outline 2 II. THE CONCEPT OF VARIABILITY 3 2.1 Factor of Safety 3 2.2 Load and Resistance Equations 5 2.3 Binary Operations 6 2.4 Confidence Levels 11 III. STRUCTURAL RESISTANCE STATISTICS 13 3.1 Steel 13 3.1.1 Steel Sections 13 3.1.2 Bending Resistance 14 3.1.3 Steel Connections 16 3.2 Concrete 18 3.3 Masonry 20 3.3.1 Tensile Bond Strength 20 3.3.2 Strength Properties of Masonry 23 3.4 Wood 24 3.4.1 Nailed Connections 28 3.5 Window Glass 28 m Page 3.5.1 Types of Window Glass 30 3.5.2 Window Glass Strength 30 IV. WIND LOAD STATISTICS 34 4.1 Wind Load Variables 34 4.1.1 The Air Density Term 34 4.1.2 Pressure Coefficients 34 4.1.3 Pressure Coefficient Reduction 36 4.2 Summary of Load and Resistance Statistics 39 4.3 Load and Resistance Wind Speed Compared to F-scale. 42 V. WIND SPEED CALCULATIONS USING LOAD AND RESISTANCE STATISTICS 50 5.1 Altus Tornado Damage Path 50 5.2 Parachute Drying Tower Wind Speed Calculation ... 50 5.2.1 Overall Wind Loading 54 5.3 Dining Hall Wind Speed Calculation 57 5.3.1 Cafeteria Roof 58 5.3.2 Roof Over Offices 64 5.3.3 Interior Roof Section 66 5.4 Recreation Building Wind Speed Calculation .... 67 5.4.1 Windward Roof Corner 67 5.4.2 Windward Roof Section 72 5.5 Communication Building Wind Speed Calculation ... 73 5.5.1 Windward Roof 76 5.5.2 Windward Wall 79 5.6 Summary 80 IV Page VI. CONCLUSIONS 82 6.1 General Conclusions 82 6.2 Future Research 83 LIST OF REFERENCES 84 APPENDIX I 87 LIST OF TABLES Table Page 1 Summary of Binary Operations for Combining Two Normal Probability Distributions 8 2 Factors Which Affect the Strength of Steel 15 3 Summary of Resistance Statistics for Steel 17 4 Factors Which Affect the Strength of Concrete 19 5 Summary of Resistance Statistics for Concrete 21 6 Factors Which Affect the Strength of Masonry Walls . 22 7 Summary of Resistance Statistics for Masonry 25 8 Factors Which Affect the Strength of Wood 26 9 Summary of Resistance Statistics for Wood 27 10 Summary of Resistance Statistics for Nailed Connections . 29 11 Factors Which Affect the Strength of Window Glass ... 31 12 Summary of Resistance Statistics for Window Glass ... 33 13 Summary of Wind Load Variable Statistics 40 14 Credence Levels for Wind Speed Calculations Based on Variability 41 15 Limits in Accuracy in Wind Speed for Various Materials. 43 16 Factors Which can Influence the F-scale Rating .... 45 17 Comparison of F-scale Wind Speed to Load and Resistance Wind Speed 47 18 Comparison of the Performance of Housing Wind Speed to Load and Resistance Wind Speed 49 19 Characteristics of the Altus Tornado 52 20 Summary of Wind Speed Estimates in the Altus Tornado . 81 21 Summary of Strength Data for 8d Nailed Connections ... 90 22 Summary of Strength Data for 16d Nailed Connections. 91 vi LIST OF FIGURES Figures Page 1 A typical load and resistance probability distribu- tion. The shaded region indicates the probability of failure 4 2 Mean GC ^ values for flat roof and wall sections .... 38 3 Tornado damage path through the Altus Air Force Base. Gradations of damage is shown by F-scale 51 4 Plan view of the Parachute Drying Tower and Building 279 . 53 5 Wind loading on the Parachute Drying Tower at Altus Air Force Base 56 6 Plan view of Dining Hall showing windward roof damage (unshaded portion) 59 7 Windward roof-wall detail of the Dining Hall at section A . 60 8 Plan view of the roof sections of the Dining Hall over a) cafeteria and b) offices as divided into ANSI-A58.1 1982 wind regimes 61 9 Plan view of the Recreation Building showing windward roof corner damage (unshaded portion) 68 10 Windward roof-wall detail of the Recreation Building at section B 69 11 Plan view of the failed roof section of the Recreation Building as divided into ANSI-A58.1 1982 wind regimes . 70 12 Plan view of the Communications Building showing windward roof damage (unshaded portion) 74 13 Windward roof-wall detail of the Communications Building . 75 14 Sections of the Communications Building used to determine wind speed calculations a) roof as divided into ANSI-A58.1 1982 wind regimes and b) windward wall 78 15 The types of nailed connections used in the tensile tests a) toenailed and b) straight. Nails were driven into grade two, 2x4, white pine lumber 88 16 View of the Reihle testing machine used to pull apart the nailed connections 89 vn• • CHAPTER I INTRODUCTION 1.1 Background A significant natural disaster in terms of a wind event provides an opportunity for engineers and meteorologists to conduct a damage survey and assess the performance of structures in the path of the storm. The knowledge gained in estimating wind speeds responsible for causing the damage can be used to better design structures to resist the wind. Before 1950, few studies appeared in the literature on wind speed estimates derived from damaged structures. Most notably, the Dallas tornado in 1957 provided the first significant opportunity to study the damage caused to many structures with different types of construc- tion. Segner (1960) presented wind speed estimates from an engineering analysis of the damaged structures. More recently, wind speed estimates have been derived from engineering analyses of damage caused by the Lubbock tornado (Minor et al., 1971) and the Xenia, Ohio tornado (Mehta et al., 1974). In all the above cases, a wind speed was calcu- lated based on average characteristics of the structure. A problem arises in that several variables may be responsible for deviations from the calculated wind speed. Material strength properties, construction practices, orientation of the structure and pressure co- efficients are a few of the variables which are subject to uncertainties. These variables may, in turn, lead to an overestimate or underestimate of the calculated wind speed to cause the damage. In order to quantify the degree of error in a wind speed estimate, statistical properties of the load and resistance behavior of the structure must be known. Within the past several years, a new concept has emerged in the design of engineered structures which enables engineers to account for the variations in the strength and types of loading on structures. The concept is termed Load and Resistance Factor Design (LRFD). LRFD treats the load and resistance properties of structures in terms of continuous probability distributions. In contrast, nominal strengths or loads are discrete values. 1 2 1.2 Purpose The purpose of this study is to utilize recently published load and resistance data in conjunction with statistical methods to place a degree of confidence in a calculated wind speed. 1.3 Outline The theory of variability applicable to load and resistance equa- tions is discussed in Chapter II. Structural resistance statistics are presented in Chapter III along with a brief discussion of the major un- certainties. Chapter IV contains wind load statistics. The methodology for handling highly fluctuating pressure coefficients in a turbulent wind flow is addressed.