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basic structural analysis

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Basic Structural Analysis. Encouraged by the tremendous response to the first edition, this book has been revised keeping in mind the valuable suggestions received from the reviewers, publishers, readers and colleagues. Keeping the basic approach of the first edition intact, the second edition has been written to make the book broad-based and gain wider acceptance amongst teachers and students.



(81 Units - Second Edition - Principal KSRM College of Engineering Cuddapah)



Encouraged by the tremendous response to the first edition, this book has been revised keeping in mind the valuable suggestions received from the reviewers, publishers, readers and colleagues. Keeping the basic approach of the first edition intact, the second edition has been written to make the book broad-based and gain wider acceptance amongst teachers and students.


Chapter 3 on Theory of vectors and matrices has now been removed from the main text and placed in Appendix A. Chapter 7, Rolling loads-Influence lines has been completely revised and a number of illustrative examples have been added for better conceptual understanding.


This edition incorporates new chapters on Cables and suspension bridges (Chapter 8), Column analogy (Chapter 14), and Plastic analysis of steel structures (Chapter 18). Chapter 12 on Moment distribution methods has been expanded by including topics like No sheer moment distribution, and adding concept building illustrative examples.


Chapters 17 and 18 on Flexibility and stiffness matrix methods of analysis have been rewritten to include a large number of worked-out examples. In these chapters, the emphasis has been laid on computer applications for which flow charts for flexibility and stiffness have been provided.


I hope that the above changes in the second edition will widen the scope of the book and meet the approval of the students, teachers and practising engineers. Further suggestions for the improvement of the book are welcome. In the end, I wish to express my sincere thanks to the publishers for their expert guidance in bringing out this revised edition. I also appreciate the ardous effort of Shri K Subba Reddy in typing the manuscript.


The use of computers for structural analysis has completely altered the method of presentation of structural theory. While the student is expected to be familiar with this presentation, it is far more important that he understands the basic principles of tructural analysis.


This book endeavours to present in one volume, the classical as well as matrix methods if structural analysis. It is expected that for sometime to come, the student win be required to study both these approaches, for the matrix methods are not very different from classical methods-the only difference is in the emphasis laid in formulating them so as to be suitable for computer programming. An understand ing of the basic principles in both these methods necessarily requires the solving of simple problems using hand computations.


This book is intended for a course in structural analysis following the usual course inmechanics of solid or, as it is more commonly called, strength of materials.


It aims to provide a smooth transition from the classical approaches that are based on physical behaviour of structures in terms of their deflected shapes to a formal treatment of a general class of structures by means of matrix formulation.


Chapters I and 2 deal with basic principles of structural analysis of simple structures using only equilibrium equations. Chapter 3 is devoted to the theory of vectors and matrices. This review is intended to provide the background material for the analysis of space trusses in Chapter 5 and matrix methods of structural analysis later in Chapters 14 to 17. Chapter 4 deals with the analysis of plane trusses.


Chapters 6 and 7 deal with displacement calculations by geometric and energy methods respectively. Chapter 8 is devoted to the approximate analysis of statically indeterminate structures, while Chapter 9 discusses the analysis for moving loads by influence lines.


Chapters 10 to 13 are devoted to the analysis of statically indeterminate structures using classical methods, such as consistent displacement, slopedeflection and moment distribution. Kanis method is presented in some detail in


Chapters 14 and 15 discuss the preliminaries required for the formulation of matrix methods of structural analysis. The flexibility and stiffness methods of analysis are presented in Chapters 16 and 17. Simple examples needing only hand computations have been illustrated in these chapters. However, the matrix formulation of the problems and computation techniques employed are suitable for computer programmes.


A book such as this, devoted to basic aspects of structural analysis cannot claim to contain any original work, and only material collected over the years is presented. The author gratefully acknowledges the sources he has consulted.


The author sincerely thanks all his colleagues and students who helped in writing this text. The author is grateful to his wife for her understanding and forebearance during the long hours he spent working on the manuscript. A word of appreciation is due to his children who refrained from disturbing him. The author also thanks Usharanjan Bhattacherjee for typing the manuscript and S. P. Hazra for makiQg the final diagrams.







1.1 Forms of Structures

1.2 Analysis and Design

1.3 Loads and Forces

1.3.1 Dead Load

1.3.2 Imposed Loads and Forces

1.3.3 Load Combinations

1.4 Idealizatiod of Structures

1.5 Supports and Connections-Conventional Representation

1.6 Elastic and Linear Behaviour of Structures

1.7 Principle of Superposition


2.1 Equations of Equilibrium

2.2 Free-body Diagrams

2.3 Sign Convention

2.4 Simple Cable and Arch Structures

2.4.1 Cables

2.5 Arches

2.5.1 Theoretical Arch or Line of Thrust

2.5.2 Actual Arch

2.5.3 Types of Arches

2.6 Graphic Statics

2.6.1 General

2.6.2 Resultant of 1\vo Concurrent Forces

2.6.3 Resultant of Sewnl Forces in a Plane

2.6.4 Equilibriant

2.6.5 Funicular Polygon

2.6.6 Funicular Polygon through 1\vo Points


3.1 Introduction

3.2 Plane Truss

3.3 Geometric Stability and Static Determinancy of Trusses

3.4 Analysis of Trusses

3.4.1 Assumptions

3.4.2 Methods of Analysis

3.4.3 Subdivided Truss

3.5 Compound and Complex Trusses

3.6 Graphical Analysis of Trusses

3.6.1 Analysis of a Simple Truss

3.6.2 Analysis of a Fink Roof. Truss


4.1 Introduction

4.2 Simple Space Truss

4.3 Types of Supports

4.4 Equilibrium and Stability Conditions

4.5 Analysis of Space Trusses •


5.1 Deflected Shapes

5.2 Moment-area Method

5.3 Conjugate Beam Method

5.4 Deflection of Trusses-Graphical Method

5.4.1 Williot-Mohr Diagram


6.1 Introduction

6.2 Forms of Elastic Strain Energy

6.2.1 Axial Stress

6.2.2 Shearing Stress

6.2.3 Multi-Axial State of Stress

6.3 Strain Energy in Members

6.3.1 Axially Loaded Members

6.3.2 Members Under Bending

6.3.3 Members Under Shearing

6.3.4 Circular Members in Torsion

6.4 Energy Relations in Structural Theory

6.4.1 Law of Conservation of Energy

6.5 Virtual Work

6.5.1 Virtual Work on a Rigid Body

6.5.2 Virtual Work on an Elastic Body

6.6 Bettis and Maxwells Laws of Reciprocal Deflections

6.7 Applications of Virtual Work

6.8 Deflection of Trusses and Frames

6.9 Castiglianos Theorems


7.1 Introduction

7.2 A Single Concentrated Load

7.3 Unifomlly Distributed Load Longer Than the Span

7.4 Uniformly Distributed Load Shorter Than Span

7.5 1\vo Concentrated Loads

7.6 Series of Concentrated Loads

7.6.1 Maximum S. F. At a Section

7.6.2 Maximum Bending Moment Under a Given Load

7.6.3 Maximum Bending Moment at a Given Section

7.6.4 A9solute Maximum Shear and Moment in Beams

7.7 Equivalent U. D. L

7.8 Influence Lines

7.8.1 Introduction

7.8.2 Influence lines

7.8.3 Uses of Influence Lines

7.8.4 Distributed Loads

7.8.5 Influence Lines for Statically Determinate Framesand Beams with Hinges

7.9 Influence Lines for Panelled Beams

7.10 Influence Lines for Truss Members

7.11 Influence Lines for Three-hinged Arches

7.11.1 Influence Line for Horizontal Reaction H

7.11.2 Influence Line Diagram for Moment

7.11.3 Influence Line Diagrams for Radial Shear and Normal Thrust

7.11.4 Absolute Maximum Moment in a Three-Hinged Parabolic Arch

7.12 Influence Lines from Deflected Shapes


8.1 Introduction

8.2 Cables

8.2.1 Equation of the Cable

8.2.2 Horizontal Tension in the Cable

8.2.3 Tension in Cable Supported at Different Levels

8.2.4 Length of the Cable

8.2.5 Effect on Cable Due to Change of Temperature

8.3 Stiffening Girders

8.4 Three-hinged Stiffening Girder

8.4.1 Single Concentrated Load

8.4.2 Influence Line for H

8.4.3 I. L. For B. M. At Section X

8.4.4 Maximum B. M. Under U. D. L. Longer than Span

8.5 Influence Lines for Stiffening Girder

8.5.1 Influence Line for Shear Force

8.5.2 Uniformly Distributed Load Longer than Span

8.6 Livo-hinged Stiffening Girder

8.6.1 Influence Lines for a Single Concentrated Load Rolling Over the Girder

8.6.2 Uniformly Distributed Load Longer than Span


9.1 Introduction

9.2 Methods of Analysis

9.2.1 General

9.2.2 Indeterminate Trusses

9.2.3 Mill Bents

9.2.4 Portal Frames

9.2.5 Continuous Beams and Building Frames

9.3 Portal Method

9.4 Cantilever Method


10.1 Introduction

10.2 Degree of Indeterminancy and Stability of Structures

10.3 Analysis of Indeterminate Structures

10.4 Flexibility Coefficients

10.5 Theorem of Three Moments

10.6 The Method of Least Work

10.7 Invo-hinged Arches

10.8 Influence Lines for Continuous Members


11.1 Introduction

11.2 Sign Convention

11.3 Development of Slope-deflection Equations

11.4 Analysis of Continuous Be. Ams

11.5 Analysis of Frames With No Lateral Translation of Joints

11.6 Analysis of Frames With Lateral Translation of Joints


12.1 Introduction

12.1.1 Absolute and Relative Stiffness of Members

12.1.2 Carry Over Factor (C. O. F.)

12.1.3 Distribution Factor (D. F.)

12.2 Devewpmem of Method

12.3 Analysis of Frames With No Lateral Translation of Joints

12.4 Analysis of Frames With Lateral Translation of Joints

12.5 Symmetrical Frames

12.6 Multistorey Frames

12.7 No-shear Moment Distribution

Chapter 13: KANIS METHOD

13.1 Introduction

13.2 Basic Concept

13.3 Frames Without Lateral Translation of Joints

13.4 Frames With Lateral Translation of Joints

13.5 General Case-Storey Columns Unequal in Height and Bases Fixed or Hinged


14.1 Introduction

14.2 Development of the Method

14.2.1 Sign Convention

14.2.2 Stiffness and Carry-over Factors

14.3 Analysis of Frames by the Column Analogy Method

14.3.1 Closed Frames

14.4 Gable Frames

14.5 Analysis of Unsymmetrical Frames


15.1 Introduction

15.2 Stiffness and Flexibility Coefficients

15.3 Member Stiffness and Flexibility Matrices

15.4 Energy Concepts in Structures

15.5 Maxwells and Bettis Reciprocal Deflections

15.6 Strain Energy in Elements and Systems


16.1 Transformation of System Forces to Element Forces

16.2 Transformation of System Displacements to Element Displacements

16.3 Transformation of Element "Flexibility Matrices to System Flexibility Matrix

16.4 Transformation of Element Stiffness Matrices to System Stiffness Matrix

16.5 Transformation of Forces and Displacements in General

16.6 Tranformation of Information from Member Coordinatesto Structure Coordinates and Vice versa


17.1 Introduction

17.1.1 Flexibility Method-Steps to be Followed

17.1.2 Sign Convention

17.1.3 Effect of Displacements at Releases

17.2 Generalised Method of Analysis

17.3 Statically Determinate Structures

17.3.1 Computer Programme for Statically Determinate Structure

17.3.2 Flow Chart

17.4 Statically Indeterminate Structures

17.4.1 Computer Programme for Statically Indeterminate Structures

17.4.2 Flow Chart

17.5 Temperature Stressses, Lack of Fit, Support Settlements,, etc


18.1 Introduction

18.1.1 Stiffness Method-Steps to be Followed

18.1.2 Effect of Support Displacements, Temperature Changes, etc.

18.2 Development of Stiffness Matrix for a Pin-jointed Structure

18.2.1 Member Forces

18.3 Development of Method for a Structure Having Forces atall Degrees of Freedom

18.3.1 Computer Programme for the Stiffness Analysisof Kinematically Determinate System

18.4 Development of Method for a General Case

18.4.1 Computer Programme for the Stiffness Analysis of Kinematically Indeterminate Structures

18.4.2 Temperature Stresses, Lack of Fit, Support Settlements, etc.

18.5 Direct Stiffness Method

18.6 Analysis by Tridiagonalization of Stiffness Matrix

18.7 Comparison of Flexibility and Stiffness Methods


19.1 Introduction

19.2 Stress-strain Curve

19.3 Plastic Moment

19.3.1 Plastic Modulus, Shape Factor

19.3.2 Load Factor

19.3.3 Mechanism of Failure

19.4 Methods of Analysis

19.4.1 Statical Method of Analysis

19.4.2 Mechanism Method of Analysis

19.5 Gable Frames or Frames with Inclined Members

19.6 Bay Portal Frame

Appendix A

Appendix B

Appendix Cl

Appendix C2

Select Bibliography Answers to Problems for Practice



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