MATRIX METHODS OF STRUCTURAL ANALYSIS [THEORY, EXAMPLES AND PROGRAMS] by Dr. A. S. Meghre and S. K. Deshmukh

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.

1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8

General Classification of structures Conditions of structural analysis Methods of analysis Degree of static indeterminancy Degree of kinematic indeterminancy Force and displacement Force displacement relations Exercises Top>>

Chapter 2 : FLEXIBILITY METHOD

2-1 2-2 2-3 2-4 2-5 2-6 2-7

General Flexibility method Calculation of displacements Examples of statically indeterminate structures General approach in flexibility method Examples Concluding remarks Exercises Top>>

3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9

General Continuous beam (I) Frames without sway and axial deformations Total joint load Bar assembly Spring assembly Shaft Continuous beam (II) Concluding remarks Exercises Top>>

4-1 4-2 4-3 4-4 4-5 4-6 4-7 4-8 4-9 4-10 4-11 4-12 4-13 4-14 4-15 4-16 4-17 4-18 4-19 4-20 4-21 4-22 4-23 4-24

General Stiffness matrix of a member Joint equilibrium equations Member force Examples Member stiffness matrix – alternate approach Preliminaries to program Flow chart Data Data file Results Computer program TRUSS1.FOR Listing of program TRUSS1.FOR Stiffness matrix in half band form Computer program TRUSS2.FOR Examples using TRUSS2.FOR Listing of program TRUSS2.FOR Reactions and boundary conditions Data type II Computer program TRUSS3.FOR Examples using TRUSS3.FOR Listing of program TRUSS3.FOR Analysis of symmetric trusses Inclined support Exercises Top>>

5-1 5-2 5-3 5-4 5-5 5-6 5-7 5-8 5-9 5-10

General Stiffness matrix of a member Equilibrium of a joint Axial force in member Illustrative example Computer program STRUSS.FOR Listing of program STRUSS.FOR Examples using program Stiffness matrix of a member - alternate approach Establishing member axes Exercises Top>>

6-1 6-2 6-3 6-4 6-5 6-6 6-7 6-8 6-9 6-10 6-11 6-12 6-13

General Stiffness matrix of a member Joint equilibrium conditions Member forces Numerical example Flow chart Computer program PFRAME.FOR Listing of program PFRAME.FOR Examples using program Internal hinge in member Neglecting axial deformations Inclined roller support Cable supported beam Exercises Top>>

7-1 7-2 7-3 7-4 7-5 7-6 7-7 7-8 7-9

General Stiffness matrix of a member Joint equilibrium conditions Member forces Torsion constant Examples Computer program GRID.FOR Listing of program GRID.FOR Examples using program Exercises Top>>

8-1 8-2 8-3 8-4 8-5 8-6 8-7 8-8 8-9 8-10

General Stiffness matrix of a member Joint equilibrium conditions Fixed end reactions Member forces Data type III Computer program SFRAME.FOR Listing of program SFRAME.FOR Examples Examples using program SFRAME Exercises Top>>

9-1 9-2 9-3 9-4 9-5 9-6 9-7 9-8 9-9 9-10

General Half band width Joint-code relations from fixity data Joint load data and load vector Group wise data Data generation Storage schemes and memory requirement Out-of-core methods Frontal solution method Variable dimensioning Exercises Top>>

10-1 10-2 10-3 10-4 10-5 10-6 10-7

Effects of member loads, temperature and lack of fit in trusses Elastic supports Direct approach in stiffness method Super element Sub-structure method of analysis Plastic analysis Transfer matrix method Exercises Top>>

11-1 11-2 11-3 11-4 11-5 11-6 11-7 11-8 11-9 11-10 11-11 11-12

Stiffness method as a variational approach Strain energy Potential of loads Total potential energy Minimum potential energy theorem Loaded member – strain energy and potential of loads Equilibrium equations and energy minimisation conditions Interpolation and shape functions Member stiffness matrix using assumed displacements Equivalent joint loads using shape functions Introduction to finite element method Triangular element for plane stress analysis Exercises Top>>

12-1 12-2 12-3 12-4 12-5 12-6

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 Exercises Top>>