Matrix methods of structural analysis
Meghre, A. S.
Matrix methods of structural analysis theory, examples and programs - Anand Charotar Publishing House Pvt. Ltd. 2003 - xii,540p.
CONTENTS
Chapter 1: INTRODUCTION 1-26
1-1 General 1
1-2 Classification of structures 2
1-3 Conditions of structural analysis 4
1-4 Methods of analysis 5
1-5 Degree of static indeterminacy 7
1-6 Degree of kinematic indeterminacy 13
1-7 Force and displacement 15
1-8 Force displacement relations 15
Exercises I 22
Chapter 2: FLEXIBILITY METHOD 27-66
2-1 General 27
2-2 Flexibility method 27
2-3 Calculation of displacements 36
2-4 Examples of statically indeterminate structures 37
2-5 General approach in flexibility method 42
2-6 Examples 44
2-7 Concluding remarks 61
Exercises II 61
Chapter 3: STIFFNESS METHOD 67-110
3-1 General 67
3-2 Continuous beam (I) 67
3-3 Frames without sway and axial deformations 81
3-4 Total joint load 85
3-5 Bar assembly 87
3-6 Spring assembly 91
3-7 Shaft 93
3-8 Continuous beam (II) 94
3-9 Concluding remarks 105
Exercises III 106
Chapter 4: PLANE TRUSS 111-206
4-1 General 111
4-2 Stiffness matrix of a member 111
4-3 Joint equilibrium equations 115
4-4 Member force 117
4-5 Examples 118
4-6 Member stiffness matrix - alternate approach 124
4-7 Preliminaries to program 128
4-8 Flow chart
4-9 Data
4-10 Data file
4-11 Results
4-12 Computer program TRUSS 1.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
5-6 Computer program STRUSS.FOR
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 254
6-10 Internal hinge in member 260
6-11 Neglecting axial deformations 263
6-12 Inclined roller support 268
6-13 Cable supported beam 273
Exercises VI 277
Chapter 7: GRID
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 10-6 Plastic 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
Linear and non-linear response
Secant and tangent stiffness matrices
Non-linear analysis
Non-linear behaviour of a truss
Non-linear analysis of truss
Program steps for non-linear analysis of truss
Exercise XII
Appendix A (Al) (A2)
Slopes and deflections in beams Combination of standard formulae
Appendix B
(Bl) Restraining actions in restrained member
Appendix C
Bibliograph
Index
Appendix C
Simultaneous linear algebraic equations
(a) Determinant method
(b) Elimination methods
(bl) Gauss elimination method (rowwise)
(b2) Row exchanges in
Gauss eliminationmethod (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 ] (cl) 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
(dl) Gauss-Seidel iteration method
(d2) Iteration method with
half banded matrix [ HA ]
(e) Use of inverse
(f) Multiple and subsequent right sides
9788185594088
624.171 / MEG
Matrix methods of structural analysis theory, examples and programs - Anand Charotar Publishing House Pvt. Ltd. 2003 - xii,540p.
CONTENTS
Chapter 1: INTRODUCTION 1-26
1-1 General 1
1-2 Classification of structures 2
1-3 Conditions of structural analysis 4
1-4 Methods of analysis 5
1-5 Degree of static indeterminacy 7
1-6 Degree of kinematic indeterminacy 13
1-7 Force and displacement 15
1-8 Force displacement relations 15
Exercises I 22
Chapter 2: FLEXIBILITY METHOD 27-66
2-1 General 27
2-2 Flexibility method 27
2-3 Calculation of displacements 36
2-4 Examples of statically indeterminate structures 37
2-5 General approach in flexibility method 42
2-6 Examples 44
2-7 Concluding remarks 61
Exercises II 61
Chapter 3: STIFFNESS METHOD 67-110
3-1 General 67
3-2 Continuous beam (I) 67
3-3 Frames without sway and axial deformations 81
3-4 Total joint load 85
3-5 Bar assembly 87
3-6 Spring assembly 91
3-7 Shaft 93
3-8 Continuous beam (II) 94
3-9 Concluding remarks 105
Exercises III 106
Chapter 4: PLANE TRUSS 111-206
4-1 General 111
4-2 Stiffness matrix of a member 111
4-3 Joint equilibrium equations 115
4-4 Member force 117
4-5 Examples 118
4-6 Member stiffness matrix - alternate approach 124
4-7 Preliminaries to program 128
4-8 Flow chart
4-9 Data
4-10 Data file
4-11 Results
4-12 Computer program TRUSS 1.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
5-6 Computer program STRUSS.FOR
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 254
6-10 Internal hinge in member 260
6-11 Neglecting axial deformations 263
6-12 Inclined roller support 268
6-13 Cable supported beam 273
Exercises VI 277
Chapter 7: GRID
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 10-6 Plastic 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
Linear and non-linear response
Secant and tangent stiffness matrices
Non-linear analysis
Non-linear behaviour of a truss
Non-linear analysis of truss
Program steps for non-linear analysis of truss
Exercise XII
Appendix A (Al) (A2)
Slopes and deflections in beams Combination of standard formulae
Appendix B
(Bl) Restraining actions in restrained member
Appendix C
Bibliograph
Index
Appendix C
Simultaneous linear algebraic equations
(a) Determinant method
(b) Elimination methods
(bl) Gauss elimination method (rowwise)
(b2) Row exchanges in
Gauss eliminationmethod (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 ] (cl) 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
(dl) Gauss-Seidel iteration method
(d2) Iteration method with
half banded matrix [ HA ]
(e) Use of inverse
(f) Multiple and subsequent right sides
9788185594088
624.171 / MEG