Transcription
Matrix Methods of Structural Analysis
Matrix Methods ofStructural AnalysisP.N. GODBOLEFormer ProfessorDepartment of Civil EngineeringIndian Institute of Technology RoorkeeR.S. SONPAROTEAssociate ProfessorDepartment of Applied MechanicsVisvesvaraya National Institute of Technology, NagpurS.U. DHOTEAssistant ProfessorDepartment of Civil EngineeringYeshwantrao Chavan College of Engineering, NagpurDelhi-1100922014
Matrix Methods of Structural Analysis (with CD-ROM)P.N. Godbole, R.S. Sonparote, and S.U. Dhote 2014 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may bereproduced in any form, by mimeograph or any other means, without permission in writing from thepublisher.The authors and the publisher make no warranty of any kind, expressed or implied, with regard to programs containedin this companion CD. The authors and publisher shall not be liable in any event for incidental or consequentialdamages in connection with, or arising out of, the furnishing, performance, or use of these programs.ISBN-978-81-203-4984-1The export rights of this book are vested solely with the publisher.Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, PatparganjIndustrial Estate, Delhi-110092 and Printed by Rajkamal Electric Press, Plot No. 2, Phase IV, HSIDC,Kundli-131028, Sonepat, Haryana.
ContentsPreface xi1. Introduction1.11.21.31.4Why Matrix Methods 1Types of Framed Structures 2Forces and Displacements 3Basic Structural Principles 41.4.11.4.21.51–12Condition of Equilibrium 5Compatibility of Deformations 6Static and Kinematic Indeterminacy 61.5.11.5.2Static Indeterminacy 6Kinematic Indeterminacy 91.6Flexibility and Stiffness Methods of Analysis 101.7Stiffness vs Flexibility Method 11Problems 12Part 1—Basics2. Matrix ions 15Matrix 3.72.3.8Addition and Subtraction 17Multiplication 17Transpose of Matrix 18Determinant of Matrix 19Inverse of Matrix 19Orthogonal Matrix 20Differentiating a Matrix 20Integrating a Matrix 20v
viContents2.4Some Typical Matrix ication of Two Column Vectors (Matrices) 20Transpose of Product of Two Matrices 21Differentiating Expression of Quadratic Form 21Differentiating Product of Two Vectors 22Partitioning of Matrices 23Problems 233. Solution of Equations3.13.2Introduction 25Assembly and Storage of Equations 253.2.13.2.23.3Band Storage 26Skyline or Profile Storage 29Application of Boundary Condition 293.3.13.3.23.3.33.425–40First Method 29Second Method 30Third Method (Penalty Method) 31Solution of Equations 323.4.13.4.2Method of Gauss Elimination 33Cholesky’s Method (Crout’s Reduction) 353.5Frontal Method of References 404. Stiffness and Flexibility4.14.2Introduction 41Stiffness and Flexibility 414.2.14.2.24.2.34.341–54The Elastic Spring 41A Bar Subjected to Axial Force 42A Cantilever Beam 42Flexibility Matrix and Stiffness Matrix Methods 454.3.14.3.2A Propped Cantilever Beam 46Structure with more than One Indeterminacy 48Problems 53Part 2—Structure (System) Approach5. Flexibility Matrix Method5.15.25.35.4Introduction 57Description of the Method 57Evaluation of Flexibility Coefficients 59Steps in the Analysis 5957–81
�60Plane Frames 69Pin-Jointed Plane Truss 74Truss for Lack of Fit/Temperature �796. Stiffness Matrix ription of the Method 83Steps in the lysis of Beams 88Analysis of Plane Frame 95Analysis of Pin-Jointed Plane �104Part 3—Stiffness Matrix Method—Member Approach7. Basic Steps of Stiffness �109Stiffness Matrix: The Elastic Spring 110Spring Assemblage 111Some Properties of Stiffness Matrix 113Assembly of [K] by Superposition (Direct Method) 114Method of Solution 1157.6.1Force in the Spring 1157.7Stiffness Matrix of a Bar Member 1167.8Steps in the 1218. Beams8.1Introduction 1228.2Stiffness Matrix of a Beam Member 1238.3Equivalent Nodal Load Vector 1258.4Steps in the �142122–143
viiiContents9. Plane 144Global Coordinate System 144Local Coordinate System 144Transformation Matrix or Rotation Matrix 145Stiffness Matrix of Plane Truss Member 1459.2.19.2.29.2.39.2.4Stiffness Matrix of Truss Member: Local Axis 145Transformation Matrix 147Stiffness Matrix of Truss Member: Global Axis 148Force in the Member 1499.3Steps in the Analysis 1509.4Examples 1519.5Some Important Features of Stiffness Matrix Method 167Problems 17410. Plane Frames176–20010.1 Introduction 17610.2 Stiffness Matrix of a Plane Frame Member 17610.2.1 Stiffness Matrix in Local Axis 17710.2.2 Transformation Matrix 17810.2.3 Stiffness Matrix and Nodal Force Vector with Respect to Global Axis 17910.3 Steps in the Analysis 18010.4 Examples 181Problems 20011. aviour of Grid Member 201Stiffness Matrix of a Grid ness Matrix of a Member in Torsion 202Stiffness Matrix of a Grid Member in Local Axis 204Transformation Matrix 205Stiffness Matrix in Global Axis 207Equivalent Nodal Loads 20711.4 Steps in the Analysis 20711.5 Comparison between Grid and Plane Frame 212Problems 21212. Space Trusses and Space Frames12.112.2Introduction 214Space Trusses 21412.2.112.2.212.2.312.2.4Stiffness Matrix of Member: Local Axis 215Transformation Matrix (Rotation Matrix) 216Stiffness Matrix of Member in Global Axis 217Steps in the Analysis 218214–230
Contentsix12.3Space 6Stiffness Matrix and Load Vector in Local Axis 222Transformation Matrix (Rotation Matrix) 224Stiffness Matrix and Load Vector in Global Axis 225Equivalent Nodal Force Vector 225Determination of Transformation Matrix [T] of a Member 225Steps in the Analysis 22712.4 Conclusions 229Problems 22913. Additional Topics13.113.213.3Use of Symmetry and Anti-Symmetry 231Inclined Supports (Oblique Supports) 235Beams with Shearing Deformations 245231–25813.3.1 Deformation in Beam due to Shear 24513.3.2 Stiffness Matrix of Beam with Shearing Deformation 24613.4Member end Releases in Beams and Frames 24813.4.1 Moment Discontinuity (Moment Release in the Form of Hinge) 24813.5 Temperature Changes and Prestrains 251Problems 256Part 4—Educational Program14. Computer Program and Illustrative Examples14.114.214.314.414.5261–284Introduction 261Structure of the Program 262Important Variables in the Program 264Explanation of Subroutines/Functions 265FORTRAN Program 26514.5.1 Guide to Input Data 26614.5.2 Illustrative Examples 26714.6C Program 28114.6.1 Guide to Input Data 28114.6.2 Illustrative Examples 282AppendicesA. Methods to Find Deflections287–297B. Slopes and Deflections in Beams298–299C. Fixed End Forces in Beams300–301D. Properties of Plane Areas302–303Index305–309
Matrix Methods Of Structural Analysis30%OFFPublisher : PHI LearningISBN : 978812034 984 1Author : GODBOLE, P.N. ,SONPAROTE, R.S., DHOTE,S.U.Type the URL : http://www.kopykitab.com/product/7611Get this eBook
5.5.1 Analysis of Beams 60 5.5.2 Analysis of Plane Frames 69 5.5.3 Analysis of Pin-Jointed Plane Truss 74 5.5.4 Analysis of Truss for Lack of Fit/Temperature Changes 77 5.6 Conclusions 78 Problems 79 6. stiffness Matrix Method 82-106 6.1 Introduction 82 6.2 Description of the Method 83 6.3 Steps in the Analysis 88 6.4 Examples 88 6.4.1 .
