CHAPTER 1 Force Analysis. Deformation Analysis. INTRODUCTION The Structures are basically built to withstand the applied loads. The application of these loads develops internal forces and deformations within the structural components. Structural analysis is related with the determination of forces and deformations experienced by the structure. It is divided into two types. Force Analysis. Deformation Analysis. 1.1FORCE ANALYSIS Force Analysis involves the calculation of reactions of the supports and the determination of variation of internal actions (Normal forces, Shear forces, Bending moments etc.) within the structure. 1.2 DEFORMATION ANALYSIS: Deformation Analysis involves the evaluation of deformation (displacements and strains) of the elements of the structure as well as of the whole structure. 12/5/2018

1.3 METHOD: The analysis can be carried out either by classical methods or by matrix methods. These matrix methods are best suited for the process of obtaining the behavior of a series of elements into which the structure has been subdivided. This idea is based on the finite element concept that enables the step by step build up of the force deformation relationship of a structure of which the structure is consisted. Study of the classical methods followed by a study of the matrix methods provides a better understanding of the behavior of a structure. The matrix methods are presented in the present text. These methods can be easily implemented for the analysis using computer. These methods are becoming more and more popular as the advancements are going on in the computational field by using high speed microcomputer. The computers are now in the reach of almost every engineer and use of computer for the analysis of structure is now more realized. 1.4 REQUIREMENT: Following main requirements are to be satisfied by any method of analysis for any structure. These are: 1-Equilibrium of forces. Equilibrium between the internal forces and external loads. 2-Compatibility of displacement. Displacement of a structure at a particular point must be compatible with the strains developed within the structure at that point. 12/5/2018

1.5 FORCE AND DISPLACEMENT METHOD 3-Force displacement relationship. specified by geometric and elastic properties of the elements. 1.5 FORCE AND DISPLACEMENT METHOD The various methods of analyzing indeterminate structure generally fall in two classes. Force method (Flexibility method) Displacement method (Stiffness method) 1.6 FORCE OR FLEXIBILITY METHOD: In this method redundant constraints are removed and corresponding redundant forces (or moments) are placed. An equation of compatibility of deformation is written in terms of these redundant and the corresponding displacements. The redundant are determined from these simultaneous equations. Equations of static's are then used for the calculation of desired internal action. In this method forces are treated as the basic unknowns. 1.7 DISPLACEMENT OR STIFFNESS METHOD: In this method the rotations or the nodal displacements are treated as unknowns. These are then related to corresponding forces. Stiffness method is discussed in this book in detail. This method can be extended to finite element method. 12/5/2018