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Introduction

Analysis by the Strain Energy Method

Analysis by the Virtual Work Method

Deflection of Beams

Influence Lines for Simple Structures

Statically Determinate Arches

Suspension Cable Systems

Structural Analysis and Different Kinds of Software

Types of Structures
Structures can be classified on the basis of materials used as follows:

  • Steel structures
  • Concrete structure
  • Masonry structure
  • Wooden structures
  • Plastic structures

Structural Mechanics
Structural mechanics is the branch of mechanics that deals with the forces and motion of structural systems. it is the computation of deformations , deflections, and internal forces or stresses within the structure for the evaluation of existing structures. Approaches to structural Analysis : The two basis approaches of structural analysis are as follows:

  • Force Method
    In this method, the number of independent unknown forces (both external and internal ) is found and is compared with the number of an independent equation of static equilibrium that can be written involving these unknown forces. if the number of unknowns is equal to the number of independent equations, the unknown forces can be directly determined . But if the number of unknown forces exceeds the number of equilibrium equations, a number of unknown forces in excess of the equilibrium equations are designated as redundant forces and are assumed to be removed as restraints to obtain a statically determine residual structure called primary structure .
    For each redundant, one equation is written in which the displacement of the point of application of redundant is expressed in terms of known forces and the unknown redundant forces. Finally, these equations are solved to get the unknown redundant forces.
  • Displacement Method
    In this method, the independent unknown displacement components involved in the structure are estimated and these are considered as the unknown to be found .
    The internal forces in the structure are then expressed in terms of these unknown displacement, using the stress-displacement relations. For each unknown displacement component, a corresponding equilibrium is written in terms of known external forces and unknown internal forces which are expressed in terms of the displacement. These equations are solved to find the unknown displacement. Finally, internal forces are calculated from the displacements.

Linear and Non-linear Elastic Structures
A system is called a linear system if its materials have linear stress-strain relationship i.e it obeys Hook’s and undergo a small deflection of deformation. For linear system principle, superposition can be satisfactorily applied
The non-linear system is the system in which its material does not have linear stress-strain relationships i.e. it does not obey Hook’s law and the deformation is so large that a change of geometry cannot be neglected in the analysis. Superposition principle doesn't hold good. If the nonlinearity is due to stress- strain relationship ,it is called material nonlinearity and if the nonlinearity is due to considerable change in the geometry, it is called geometric nonlinearity

Computer Based Methods

  • SAP (Structure Analysis Program ): This is a general purpose finite element program which is used for linear static and dynamic analysis of structures. The boundary condition can be assigned.
  • STAAD pro : It is the most widely used structure analysis and design software. It supports several steel, concrete, and timber design codes. it can be used for static analysis , geometric nonlinear analysis or buckling analysis.
  • NISA ( Nonlinear Incremental structural Analysis ): This software is used for nonlinear analysis and buckling can be studied as well
  • ETABS : This software is mostly used for building (3-D analysis ). Static earthquake loads can be considered in the analysis of structures.

Bibliography
Khurmi, R.S. (1987). Theory of structure. India.


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