Transcription
Matrix Methods of Structural Analysis
MATRIX METHODS OFSTRUCTURAL ANALYSISTheory and ProblemsC. NatarajanProfessorDepartment of Civil EngineeringNational Institute of TechnologyTiruchirappalliP. RevathiAssistant ProfessorDepartment of Civil EngineeringPondicherry Engineering CollegePondicherryDelhi-1100922014
MATRIX METHODS OF STRUCTURAL ANALYSIS: Theory and ProblemsC. Natarajan and P. Revathi 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.ISBN-978-81-203-4900-1The 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 Mohan Makhijani at Rekha Printers Private Limited,New Delhi-110020.
Dedicated toour beloved parents
ContentsForeword xiPreface xiii1. BASIC CONCEPTS1.1 Introduction 11.2 Classification of .71–17Axial and Bending Structures 1Plane and Space Structures 2Two-dimensional and Three-dimensional Structures 2Discrete Elements and Continuum Systems 2Stable and Unstable Structures 2Determinate and Indeterminate Structures 3Supports and Restraints 31.3Levels of Structural Analysis 41.3.1 Static and Dynamic Analysis 51.3.2 Linear and Nonlinear Analysis 51.3.3 Deterministic and Probabilistic Analysis 61.4 Static Indeterminacy 61.5 Kinematic Indeterminacy 12Review Questions 162. DETERMINANTS AND MATRICES2.1 Introduction 1818–272.1.1 What is a Matrix? 182.1.2 What is a Determinant? 192.22.32.4Matrix Addition and Subtraction 20Matrix Multiplication 21Matrix Inversion 222.4.1 Adjoint Method of Matrix Inversion 222.4.2 Inverse of Second Order Matrix 24vii
viiiContents2.5Solution of Linear Simultaneous Equation 242.5.1 Inverse Method of Solution 262.6 Condition of Matrices 26Review Questions 273. STIFFNESS AND FLEXIBILITY CHARACTERISTICS OF STRUCTURES3.1 Introduction 283.2 Behaviour of Structures 2828 – 563.2.1 Elastic and Inelastic Behaviour 283.2.2 Linear and Nonlinear Behaviour 293.3Flexibility and ibility Matrix 35Stiffness Matrix 36Flexibility and Stiffness Matrices in n Co-ordinates 373.6.1 Flexibility Matrix in n Co-ordinates 383.6.2 Stiffness Matrix in n Co-ordinates 383.6.3 Force Displacement Relations 38Structure with a Single Co-ordinate 32Springs in Parallel 34Springs in Series 34Structure with Two Co-ordinates 353.7 Constrained Displacement Measurements 393.8 Constrained Force Measurements 403.9 Stiffness Matrix for a Prismatic Beam Element 453.10 Properties of Stiffness Matrix 493.11 Stiffness and Flexibility Matrices Relationship 493.12 Closure 55Review Questions 554. TRANSFORMATION MATRICES4.1 Introduction 574.2 Co-ordinate Systems 574.2.1 Global Co-ordinates and System Co-ordinates 584.2.2 Local Co-ordinates and Element Co-ordinates 584.3 Transformation of Information 594.4 Force Transformation 594.5 Flexibility Transformation 614.6 Displacement Transformation 624.7 Stiffness Transformation 644.8 General Transformation of Forces and Displacements 654.9 General Transformation of Stiffness and Flexibility Matrix 664.9.1 Transformation of Flexibility Matrix 664.9.2 Transformation of Stiffness Matrix 67Review Questions 6757– 69
Contentsix5. CONCEPTS IN MATRIX METHODS OF ANALYSIS5.1 Introduction 705.2 Methods of Structural Analysis 7070 – 855.2.1 Force Method 715.2.3 Displacement Method 715.3 Equivalent Joint Loads and Fixed End Moments 715.4 Flexibility Method Applied to Statically Determinate Structures 735.5 Flexibility Method Applied to Statically Indeterminate Structures 745.6 Internal Forces Due to Secondary Stresses: Flexibility Approach 765.7 Step-by-Step Procedure in Flexibility Matrix Method 785.8 Choice of Redundant in Flexibility Method 785.9 Stiffness Matrix Method of Analysis 805.10 Internal Forces Due to Secondary Stresses: Stiffness Approach 815.11 Step-by-Step Procedure in Stiffness Matrix Method 825.12 Choice of Suitable Method of Analysis 825.13 Degree of Static and Kinematic Indeterminacy 835.14 Computation of Flexibility and Stiffness Matrices 835.15 Computational Effort 845.16 Suitability for Computer Programming 84Review Questions 856. ANALYSIS OF PIN-JOINTED FRAMES6.1 Introduction 866.2 Flexibility Method 866.3 Frames with Lack of Fit and Temperature Stresses 1366.4 Stiffness Method 1466.5 Frames with Lack of Fit 1866.6 Comparison of Methods 191Review Questions 19186 –1947. ANALYSIS OF CONTINUOUS BEAMS7.1 Introduction 1957.2 Flexibility Method 1957.3 Continuous Beams with Support Settlement 2567.4 Stiffness Method 2707.5 Continuous Beams with Support Settlement 3147.6 Comparison of Methods 329Review Questions 329195 – 3318. ANALYSIS OF RIGID-JOINTED FRAMES8.1 Introduction 3328.2 Flexibility Method 3328.3 Frames with Temperature Effects 381332 – 438
Matrix Methods Of Structural Analysis:Theory And Problems30%OFFPublisher : PHI LearningISBN : 978812034 9001Author : NATARAJAN, C.,REVATHI, P.Type the URL : http://www.kopykitab.com/product/764 5Get this eBook
Contents ix 5.CONCEPTS IN MATRIX METHODS OF ANALYSIS 70 - 85 5.1 Introduction 70 5.2 Methods of Structural Analysis 70 5.2.1 Force Method 71 5.2.3 Displacement Method 71 5.3 Equivalent Joint Loads and Fixed End Moments 71 5.4 Flexibility Method Applied to Statically Determinate Structures 73 5.5 Flexibility Method Applied to Statically Indeterminate Structures 74
