# MATRIX METHODS OF STRUCTURAL ANALYSIS

~~₹400.00~~ ₹360.00

By **DR. A. S. MEGHRE **& **S. K. DESHMUKH**

2nd Edition 2016 (First Reprint) (Paperback)

ISBN : 9788192869278

540 + 12 = 552 Pages

Size : 17 cm × 23.5 cm × 2 cm

Weight : 0.680 kg

## Description

This book is intended for a beginner with elementary knowledge of structural mechanics

and Fortran Programming. Stiffness and flexibility methods are commonly known as matrix

methods. Of these, the stiffness method using member approach is amenable to computer

programming and is widely used for structural analysis.

The emphasis in the book is on explaining basic fundamentals of this approach and on developing programs. This is achieved through extremely simple style of presentation in lucid

language and proceeding in stages from simple to complex structures. Unified theory with a

single complex program is totally avoided. Instead, each skeletal structure is discussed in a

separate chapter with simple, short and transparent program. Theory is presented in matrix

notations along with clear mention of scalar components for proper understanding of the

physical quantities. Illustrative solved examples explain data preparation, data file and interpretation of the results. Alternate possibilities of data preparation are mentioned and used.

The information about data generation, skyline storage, variable dimensioning and frontal

technique is intentionally presented separately at a later stage to help reader in modifying

initial simple programs.

The treatment of flexibility and direct stiffness method is limited to introduction of elementary concepts. Transfer matrix method, plastic analysis by stiffness method and sub-structure

method are included as additional topics of interest. A chapter is devoted to present an alternate view of stiffness method as a variational approach. Non-linear structural behaviour and

techniques commonly adopted to evaluate non-linear response are discussed. Formulae for

displacements in beams and restraining actions are included in Appendices A and B. Appendix C discusses various methods of solution of simultaneous algebraic equations. Exercises

are included at the end of each chapter.

The book will be useful to undergraduate and postgraduate civil engineering students and

also to those preparing for competitive examinations.

## Additional information

Weight | 0.68 kg |
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Dimensions | 17 × 2 × 23.5 cm |

Author Name | |

Book Edition | |

ISBN |

## Content

1 : INTRODUCTION

2 : FLEXIBILITY METHOD

3 : STIFFNESS METHOD

4 : PLANE TRUSS

5 : SPACE TRUSS

6 : PLANE FRAME

7 : GRID

8 : SPACE FRAME

9 : ADDITIONAL TOPICS – I

10 : ADDITIONAL TOPICS – II

11 : ADDITIONAL TOPICS – III

12 : NON-LINEAR ANALYSIS

APPENDIX A

APPENDIX B

APPENDIX C

BIBLIOGRAPHY

INDEX

## Details Content

**Chapter 1 INTRODUCTION**

1-1 General

1-2 Classification of structures

1-3 Conditions of structural analysis

1-4 Methods of analysis

1-5 Degree of static indeterminacy

1-6 Degree of kinematic indeterminacy

1-7 Force and displacement

1-8 Force displacement relations

Exercises I

**Chapter 2 FLEXIBILITY METHOD**

2-1 General

2-2 Flexibility method

2-3 Calculation of displacements

2-4 Examples of statically indeterminate structures

2-5 General approach in flexibility method

2-6 Examples

2-7 Concluding remarks

Exercises II

**Chapter 3 STIFFNESS METHOD**

3-1 General

3-2 Continuous beam (I)

3-3 Frames without sway and axial deformations

3-4 Total joint load

3-5 Bar assembly

3-6 Spring assembly

3-7 Shaft

3-8 Continuous beam (II)

3-9 Concluding remarks

Exercises III

**Chapter 4 PLANE TRUSS**

4-1 General

4-2 Stiffness matrix of a member

4-3 Joint equilibrium equations

4-4 Member force

4-5 Examples

4-6 Member stiffness matrix – alternate approach

4-7 Preliminaries to program

4-8 Flow chart

4-9 Data

4-10 Data file

4-11 Results

4-12 Computer program TRUSS1.FOR

4-13 Listing of program TRUSS1.FOR

4-14 Stiffness matrix in half band form

4-15 Computer program TRUSS2.FOR

4-16 Examples using TRUSS2.FOR

4-17 Listing of program TRUSS2.FOR

4-18 Reactions and boundary conditions

4-19 Data type II

4-20 Computer program TRUSS3.FOR

4-21 Examples using TRUSS3.FOR

4-22 Listing of program TRUSS3.FOR

4-23 Analysis of symmetric trusses

4-24 Inclined support

Exercises IV

**Chapter 5 SPACE TRUSS**

5-1 General

5-2 Stiffness matrix of a member

5-3 Equilibrium of a joint

5-4 Axial force in member

5-5 Illustrative example

5-7 Listing of program STRUSS.FOR

5-8 Examples using program

5-9 Stiffness matrix of a member – alternate approach

5-10 Establishing member axes

Exercises V

**Chapter 6 PLANE FRAME**

6-1 General

6-2 Stiffness matrix of a member

6-3 Joint equilibrium conditions

6-4 Member forces

6-5 Numerical example

6-6 Flow chart

6-7 Computer program PFRAME.FOR

6-8 Listing of program PFRAME.FOR

6-9 Examples using program

6-10 Internal hinge in member

6-11 Neglecting axial deformations

6-12 Inclined roller support

6-13 Cable supported beam

Exercises VI

**Chapter 7 GRIDM**

7-1 General

7-2 Stiffness matrix of a member

7-3 Joint equilibrium conditions

7-4 Member forces

7-5 Torsion constant

7-6 Examples

7-7 Computer program GRID.FOR

7-8 Listing of program GRID.FOR

7-9 Examples using program

Exercises VII

**Chapter 8 SPACE FRAME**

8-1 General

8-2 Stiffness matrix of a member

8-3 Joint equilibrium conditions

8-4 Fixed end reactions

8-5 Member end forces

8-6 Data type III

8-7 Computer program SFRAME.FOR

8-8 Listing of program SFRAME.FOR

8-9 Example

8-10 Examples using program SFRAME

Exercises VIII

**Chapter 9 ADDITIONAL TOPICS – I**

9-1 General

9-2 Half band width

9-3 Joint-code relations from fixity data

9-4 Joint load data and load vector

9-5 Groupwise data

9-6 Data generation

9-7 Storage schemes and memory requirement

9-8 Out-of-core methods

9-9 Frontal solution method

9-10 Variable dimensioning

Exercise IX

**Chapter 10 ADDITIONAL TOPICS – II**

10-1 Effects of member loads, temperature and lack of fit in trusses

10-2 Elastic supports

10-3 Direct approach in stiffness method

10-4 Super element

10-5 Sub-structure method of analysis

10-7 Transfer matrix method

Exercises X

**Chapter 11 ADDITIONAL TOPICS – III**

11-1 Stiffness method as a variational approach

11-2 Strain energy

11-3 Potential of loads

11-4 Total potential energy

11-5 Minimum potential energy theorem

11-6 Loaded member – strain energy and potential of loads

11-7 Equilibrium equations and energy minimisation conditions

11-8 Interpolation and shape functions

11-9 Member stiffness matrix using assumed displacements

11-10 Equivalent joint loads using shape functions

11-11 Introduction to finite element method

11-12 Triangular element for plane stress analysis

Exercises XI

**Chapter 12 NON-LINEAR ANALYSIS**

12-1 Linear and non-linear response

12-2 Secant and tangent stiffness matrices

12-3 Non-linear analysis

12-4 Non-linear behaviour of a truss

12-5 Non-linear analysis of truss

12-6 Program steps for non-linear analysis of truss

Exercise XII

**APPENDIX A**

(A1) Slopes and deflections in beams

(A2) Combination of standard formulae

**APPENDIX B**

(B1) Restraining actions in restrained member

**APPENDIX C**

(C1) Simultaneous linear algebraic equations

(a) Determinant method

(b) Elimination methods

(b1) Gauss elimination method (rowwise)

(b2) Row exchanges in Gauss elimination method

(b3) Gauss elimination for half banded matrix [HA]

(b4) Gauss-Jordon elimination method

(b5) Gauss method – columnwise reduction of symmetric matrix [A]

(b6) Column wise reduction in skyline storage

(c) Methods based on decomposition of [A]

(c1) Cholesky square root decomposition

(c2) Cholesky decomposition of half banded matrix

(c3) Gauss-Doolite decomposition of symmetric [A]

(c4) Gauss-Doolite decomposition of [HA]

(c5) Gauss-Doolite decomposition of [ASKY]

(d) Iteration methods

(d1) Gauss-Seidel iteration method

(d2) Iteration method with half banded matrix [HA]

(e) Use of inverse

(f) Multiple and subsequent right sides

**Bibliography
Index**

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