Chapter 47: Theory and Analysis of Structures
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Lecture Notes on Structural Analysis - I
www.jntuhweb.com JNTUH WEB LECTURE NOTES ON STRUCTURAL ANALYSIS - I Department of Civil Engineering Skyupsmedia JNTUH WEB www.jntuhweb.com JNTUH WEB CONTENTS CHAPTER 1 Analysis of Perfect Frames Types of frame - Perfect, Imperfect and Redundant pin jointed frames Analysis of determinate pin jointed frames using method of joint for vertical loads, horizontal loads and inclined loads method of sections for vertical loads, horizontal loads and inclined loads tension co-effective method for vertical loads, horizontal loads and inclined loads CHAPTER 2 Energy Theorem - Three Hinged Arches Introduction Strain energy in linear elastic system Expression of strain energy due axial load, bending moment and shear forces Castiglione’s first theorem – Unit Load Method Deflections of simple beams and pin - jointed plain trusses Deflections of statically determinate bent frames. Introduction Types of arches Comparison between three hinged arches and two hinged arches Linear Arch Eddy's theorem Analysis three hinged arches Normal Thrust and radial shear in an arch Geometrical properties of parabolic and circular arch Three Hinged circular arch at Different levels Absolute maximum bending moment diagram for a three hinged arch CHAPTERSkyupsmedia 3 Propped Cantilever and Fixed beams Analysis of Propped Cantilever and Fixed beams including the beams with varying moments of inertia subjected to uniformly distributed load central point load eccentric point load number of point loads uniformly varying load couple and combination of loads JNTUH WEB -
CE301 BASIC THEORY of STRUCTURES Teaching Scheme
CE301 BASIC THEORY OF STRUCTURES Teaching Scheme: 03L+ 00 T, Total: 03 Credit: 03 Evaluation Scheme: 15 ISE1 +15 ISE2 + 10 ISA + 60 ESE Total Marks: 100 Duration of ESE: 03Hrs --------------------------------------------------------------------------------------------------------------------- Deflection of Beams: Relation between bending moment, slope and defection, introduction to double integration method, concept of moment area method, Mohr's theorems, use of moment area method to calculate slope and deflections of beams such as simply supported, over hanging and of uniform cross sections and different cross sections. Conjugate beam method, application of conjugate beam method to simply supported, overhanging and compound beams. Slope and Deflection: Castiglione’s first theorem and its application to find slope and deflection of simple beams and frames, deflection in determinate trusses. Analysis of redundant trusses by Castiglione’s second theorem, lack of fit and temperature changes in members, sinking of supports (degree of indeterminacy up to 2) Fixed Beams:- Concept, advantages and disadvantages, nature of bending moment diagrams, fixed end moment due to various types of loads such as point, uniformly distributed, uniformly varying, couples for beams, effect of sinking of support, plotting of bending moment and shear force diagrams. Continuous Beams:- Analysis of continuous beam by three moment (Clapyeron's theorem) up to three unknowns, effect of sinking of supports, plotting of bending moment and shear force. Three Hinged Arch: - Concept of three hinged arch as a hunched beam, support reactions, B.M., S.F. and axial thrust diagrams for circular and parabolic three hinged arches. Two Hinged Arches:- Horizontal thrust at supports. shear, normal thrust and BM at a point, BM diagrams for parabolic arch due to concentrated load and uniformly distributed load. -
Use of Principle of Contra-Gradience for Developing Flexibility Matrix [ ]
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 05 Issue: 01 | Jan-2018 www.irjet.net p-ISSN: 2395-0072 Use of Principle of Contra-Gradience for Developing Flexibility Matrix Vasudha Chendake1, Jayant Patankar2 1 Assistant Professor, Applied Mechanics Department, Walchand College of Engineering, Maharashtra, India 2 Professor, Applied Mechanics Department, Walchand College of Engineering, Maharashtra, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - Flexibility method and stiffness method are the computer program based of flexibility method is increased two basic matrix methods of structural analysis. Linear because the procedure of the direct stiffness method is so simultaneous equations written in matrix form are always mechanical that it risks being used without much easy to solve. Also when computers are used, matrix algebra is understanding of the structural behaviours. very convenient. Matrix algebra required in new approach of flexibility method When static degree of indeterminacy is less than the kinematic is also very simple. So the time required for manual degree of indeterminacy, flexibility method is advantageous in calculations can be reduced by using MATLAB software. structural analysis. The final step in flexibility method is to develop total structural flexibility matrix. The new approach 1.1 Principle of Contra-gradience to develop total structural flexibility matrix, requires force– deformation relation, transformation matrix and principal of Consider the two co-ordinate systems O and O’ as shown in Contra-gradience. Subsequently compatibility equations are fig 1. The forces acting at co-ordinate system O are F , F required to get the value of unknown redundants. This new X Y approach while using flexibility method is useful because and M and the forces acting at co-ordinate system O’ are ' ' ' simple matrix multiplications are required as well as order of FX , FY and M . -
Syllabus of Semester Wise Departmental Subjects
SYLLABUS OF SEMESTER WISE DEPARTMENTAL SUBJECTS First Year Second Semester BUILDING MATERIAL AND CONSTRUCTION Building Materials: Brick, Stones, Lime, Sand, Cement, Admixtures and Plasticizers, Paints and Primers: properties and specifications. Preparation and use of Cement and Lime mortars, Plane and Reinforced Concrete. Building elements: foundation, floors, walls, roofing and wood work. Roof treatment, finishing items for floors, walls, and woodwork. Brick bond: English and Flemish bond, Expansion joint, Prefabricated Constructions, Shuttering and Staging, Details of reinforcements in slab, beam, column, staircase, foundation, lintel and chajja. Plumbing and Fixtures. Corporation / Municipality rules and regulations SURVEYING-I Introduction to surveying: Fundamental Definitions, Errors and Accuracy, Linear measurement and corrections, Chain survey, Prismatic compass survey, Traversing: Principles and Adjustments of Traverse, Plane table surveying, Leveling: Ordinary, Reciprocal, Contouring, Area and volume measurements, Mass diagram. STRUCTURAL MECHANICS- I Introduction to structural elements, Stress-Strain relationship, Relation between different Elastic moduli, Composite section, Thermal stress. Bending moment and Shear force analysis of statically determinate beams. Simple theory of bending of beams: Bending stress, Shear stress and Shear flow. Torsion of circular shafts. Principal stress, Principal planes, Mohr's circle diagram. Combined stress problems. Determinate Plane trusses: Method of joints, Method of section and Graphical -
Analysis of Statically Indeterminate Structures by Matrix Force Method
Module 2 Analysis of Statically Indeterminate Structures by the Matrix Force Method Version 2 CE IIT, Kharagpur Lesson 7 The Force Method of Analysis: An Introduction Version 2 CE IIT, Kharagpur Since twentieth century, indeterminate structures are being widely used for its obvious merits. It may be recalled that, in the case of indeterminate structures either the reactions or the internal forces cannot be determined from equations of statics alone. In such structures, the number of reactions or the number of internal forces exceeds the number of static equilibrium equations. In addition to equilibrium equations, compatibility equations are used to evaluate the unknown reactions and internal forces in statically indeterminate structure. In the analysis of indeterminate structure it is necessary to satisfy the equilibrium equations (implying that the structure is in equilibrium) compatibility equations (requirement if for assuring the continuity of the structure without any breaks) and force displacement equations (the way in which displacement are related to forces). We have two distinct method of analysis for statically indeterminate structure depending upon how the above equations are satisfied: 1. Force method of analysis (also known as flexibility method of analysis, method of consistent deformation, flexibility matrix method) 2. Displacement method of analysis (also known as stiffness matrix method). In the force method of analysis, primary unknown are forces. In this method compatibility equations are written for displacement and rotations (which are calculated by force displacement equations). Solving these equations, redundant forces are calculated. Once the redundant forces are calculated, the remaining reactions are evaluated by equations of equilibrium. In the displacement method of analysis, the primary unknowns are the displacements. -
Structural Analysis by C.S
2/4 B.Tech. FOURTH SEMESTER CE4T6 STRUCTUAL ANALYSIS – I Credits: 3 Lecture: 3 periods/week Internal assessment: 30 marks Tutorial: 1 period /week Semester end examination: 70 marks ____________________________________________________________________________ Pre-requisites: Mechanics of Solids-I, Mechanics of Solids-II Learning objectives: To get practice in doing the analysis of propped cantilever, fixed and cantilever beams. Knowing the application of slope deflection method for various beams. To draw Influence Line Diagrams (ILDs) and to know the application of ILDs for the analysis of simply supported girders. To understand the analysis of trusses and Castiglione’s theorems Course outcomes: At the end of course the student will be able to: 1. Analyse the trusses by method of joints and method of sections 2. Draw ILD for all components, calculate Max. SF and BM at a given section, Equivalent UDL and focal length 3. Determine the horizontal thrust, max. bending moment, normal thrust and radial shear for a 3 hinged arch 4. Calculate the shear forces, bending moments and deflections in a propped cantilever beam and a fixed beam. 5. Analyse the continuous beam by using clapayron’s theorem of three moments with or without sinking of supports UNIT – I ANALYSIS OF PIN-JOINTED PLANE FRAMES: Determination of Forces in members of pin-jointed trusses by (i) method of joints and (ii) method of sections. Analysis of various types of cantilever and simply – supported trusses. UNIT – II INFLUENCE LINES AND MOVING LOADS: Definition of influence line for reactions, SF, Influence line for BM- load position for maximum SF at a section-Load position for maximum BM at a section, single point load, U.D.L longer than the span, U.D.L shorter than the span. -
The Column Analogy; Analysis of Elastic Arches and Frames
I LL IN I S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN PRODUCTION NOTE University of Illinois at Urbana-Champaign Library Large-scale Digitization Project, 2007. ~> UNIVERSITY OF ILLINOIS BULLETIN SISSUD WMmKT V1. XXVIII October 14, 1930 No.7 - [Entered as senad-clase matter December 11, 1912, at the post office at Urbana, Illinois, under the Act of August 2, 1912. Acceptance for mailing at the pecal rate of postage provided for in section 1103, Act of Oetober 8, 1917, authorized July 31, 1918.] THE COLUMN ANALOGY BY HARDY CROSS BULLETIN No. 215 ENGINEERING EXPERIMENT STATION PUWaB.is.ex Byr stvrmieM or Ii4tol, UeAxA Piacs: Fodft CNa . HT-HE Engineering Experiment Station was established by act of the Board of Trustees of the University of Illinois on De- cember 8, 1903. It is the purpose of the Station to conduct investigations and, make studies of importance to the engineering, manufacturing, railway, mining, and other industrial interests of the State. The management of the Engineering Experiment Station is vested in an Executive Staff composed of the Director and his Assistant, the Heads of the several Departments in the College of Engineering, and the Professor of Industrial Chemistry. This Staff is responsible for the establishment of general policies governing the work of the Station, -including the -approval of material for publication. All members of the teaching staff of the College are encouraged to engage in scientific research, either directly or in cooperation with the Research Corps composed of full-time research assistants, research graduate assistants, and special investigators. To render the results of its scientific investigations available to the public, the Engineering Experiment Station publishes and dis- tributes a series of bulletins. -
Structural Analysis.Pdf
Contents:C Ccc Module 1.Energy Methods in Structural Analysis.........................5 Lesson 1. General Introduction Lesson 2. Principle of Superposition, Strain Energy Lesson 3. Castigliano’s Theorems Lesson 4. Theorem of Least Work Lesson 5. Virtual Work Lesson 6. Engesser’s Theorem and Truss Deflections by Virtual Work Principles Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method................................................................107 Lesson 7. The Force Method of Analysis: An Introduction Lesson 8. The Force Method of Analysis: Beams Lesson 9. The Force Method of Analysis: Beams (Continued) Lesson 10. The Force Method of Analysis: Trusses Lesson 11. The Force Method of Analysis: Frames Lesson 12. Three-Moment Equations-I Lesson 13. The Three-Moment Equations-Ii Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method..............................................................227 Lesson 14. The Slope-Deflection Method: An Introduction Lesson 15. The Slope-Deflection Method: Beams (Continued) Lesson 16. The Slope-Deflection Method: Frames Without Sidesway Lesson 17. The Slope-Deflection Method: Frames with Sidesway Lesson 18. The Moment-Distribution Method: Introduction Lesson 19. The Moment-Distribution Method: Statically Indeterminate Beams With Support Settlements Lesson 20. Moment-Distribution Method: Frames without Sidesway Lesson 21. The Moment-Distribution Method: Frames with Sidesway Lesson 22. The Multistory Frames with Sidesway Module 4. Analysis of Statically Indeterminate Structures by the Direct Stiffness Method...........................................................398 Lesson 23. The Direct Stiffness Method: An Introduction Lesson 24. The Direct Stiffness Method: Truss Analysis Lesson 25. The Direct Stiffness Method: Truss Analysis (Continued) Lesson 26. The Direct Stiffness Method: Temperature Changes and Fabrication Errors in Truss Analysis Lesson 27. -
Course Descriptor
INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad -500 043 CIVIL ENGINEERING COURSE DESCRIPTOR Course Title STRUCTURAL ANALYSIS Course Code ACE008 Programme B.Tech Semester V CE Course Type Core Regulation IARE - R16 Theory Practical Course Structure Lectures Tutorials Credits Laboratory Credits 4 - 4 - - Chief Coordinator Mr. Suraj Baraik, Assistant Professor Mr. S. Ashok Kumar, Assistant Professor Course Faculty Mr. Suraj Baraik, Assistant Professor, I. COURSE OVERVIEW: Civil Engineers are required to design structures like buildings, dams, bridges, etc. This course is intended to introduce the basic principles to impart adequate knowledge and successfully apply fundamentals of Structural Engineering within their chosen engineering application area. A structural engineer must be able to design a structure in such a way that none of its members fail during load transfer process. This course is intended to introduce analysis of various structural members using different methods. For this, the concept of trusses, arches, determinate and indeterminate structures are covered in depth. Deflections by energy methods of propped cantilevers, fixed and continuous beams under various load combinations. Through this course content engineers can analyze the behavior of various structural members under different loading conditions for design, safety and serviceability. II. COURSE PRE-REQUISITES: Level Course Code Semester Prerequisites Credits UG ACE004 IV Strength of material-II 4 Page | 1 III. MARKS DISTRIBUTION: CIA Subject SEE Examination Total Marks Examination Structural Analysis 70 Marks 30 Marks 100 IV. DELIVERY / INSTRUCTIONAL METHODOLOGIES: V. ✘ Chalk & Talk ✔ Quiz ✔ Assignments ✘ MOOCs ✔ LCD / PPT ✔ Seminars ✘ Mini Project ✔ Videos ✘ Open Ended Experiments V. EVALUATION METHODOLOGY: The course will be evaluated for a total of 100 marks, with 30 marks for Continuous Internal Assessment (CIA) and 70 marks for Semester End Examination (SEE). -
CE-311 Structural Analysis
CE-311 Hall Ticket Number: III/IV B.Tech (Regular) DEGREE EXAMINATION November , 2015 (First Semester) Structural Analysis - I (CIVIL ENGINEERING) Time: Three Hours Maximum : 60 Marks Answer Question No.1 compulsorily. (1X12 = 12 Marks) Answer ONE question from each unit. (4X12=48) A1. Answer all questions (1X12=12 Marks) 1. a) What do you mean by virtual work? b) Write the expression for strain energy in members under bending. c) State max wells law of reciprocal deflection d) What is the effect of sinking of support in a fixed beam? Draw a sketch indicating the effects e) A fixed beam of span ‘l’ is subjected to a uniformly distributed load of w/unit length . Draw the bending moment diagram. f) State the applications of Castiglionos theorems g) What is the difference between cantilever and propped cantilever beam? h) A pin-jointed plane truss is deficient. How to make it redundant? i) A fixed beam is subjected to a clock-wise couple at the centre? Draw the shear force diagram. j) Can a fixed beam be analyzed by Clapeyron’s theorem of three moments? Give the reason k) What do mean by redundancy ? l) Practically where do you observe sinking of support? UNIT I 2. A beam ABC of length 8m is supported at A and B 6m apart with an overhang BC of 2m. it carries two point loads of 60kN and 20kN at distances 2m and 8m respectively support A. using virtual work method find out deflections under load points. Take E= 2 x105 N/mm2, I= 2x108 mm4. -
Ace004 Strength of Materials
INSTITUTE OF AERONAUTICAL ENGINEERING (AUTONOMOUS) Dundigal – 500 043, Hyderabad Regulation: R16 (AUTONOMOUS) Course code: ACE004 STRENGTH OF MATERIALS – II B.TECH IV SEMESTER Prepared By SURAJ BARAIK Assistant Professor 1 Unit I Deflection in Beams 2 Deflection in Beams • Topics Covered Review of shear force and bending moment diagram Bending stresses in beams Shear stresses in beams Deflection in beams 3 Beam Deflection Recall: THE ENGINEERING BEAM THEORY M E y I R Moment-Curvature Equation v (Deflection) y NA x A B A’ B’ If deformation is small (i.e. slope is “flat”): 4 1 d R dx R y and (slope is “flat”) x B’ y 1 d2y A’ R dx 2 Alternatively: from Newton’s Curvature Equation y d2y dy2 R if 1 1 dx 2 dx 3 y f (x) R 2 dy 2 2 1 1 d y dx x R dx 2 5 From the Engineering Beam Theory: M E 1 M d2y I R R EI dx2 d2y EI M dx 2 Flexural Bending Stiffness Moment Curvature 6 Relationship A C B Deflection = y dy Slope = dx d2y A C B Bending moment = EI 2 y dx d3y Shearing force = EI dx3 d4y Rate of loading = EI dx4 7 Methods to find slope and deflection Double integration method Moment area method Macaulay’s method 8 Double integration method d2y 1 M Curvature Since, dx 2 EI dy 1 M dx C Slope dx EI 1 1 y M dx dx C1 dx C 2 Deflection EI Where C1 and C2 are found using the boundary conditions. -
Introduction to Matrix Methods Module I
Structural Analysis - III Introduction to Matrix Methods Module I Matrix analysis of structures • Definition of flexibility and stiffness influence coefficients – development of flexibility matrices by physical approach & energy principle. Flexibility method • Flexibility matrices for truss, beam and frame elements – load transformation matrix-development of total flexibility matrix of the structure –analysis of simple structures – plane truss, continuous beam and plane frame- nodal loads and element loads – lack of fit and temperature effects. 2 Force method and Displacement method • These methods are applicable to discretized structures of all types • Force method (Flexibility method) • Actions are the primary unknowns • Static indeterminacy: excess of unknown actions than the available number of equations of static equilibrium • Displacement method (Stiffness method) •Displacements of the joints are the primary unknowns •Kinematic indeterminacy: number of independent translations and rotations (the unknown joint displacements) • More suitable for computer programming Types of Framed Structures a. Beams: may support bending moment, shear force and axial force b. Plane trusses: hinge joints; In addition to axial forces, a member CAN have bending moments and shear forces if it has loads directly acting on them, in addition to joint loads c. Space trusses: hinge joints; any couple acting on a member should have moment vector perpendicular to the axis of the member, since a truss member is incapable of supporting a twisting moment d. Plane frames: Joints are rigid; all forces in the plane of the frame, all couples normal to the plane of the frame e. G rids: all forces normal to the plane of the grid, all couples in the plane of the grid (includes bending and torsion) f.