Static Analysis Methodology

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Chapter Methodology This chapter includes some basic information related with structures. These include static and dynamic analysis, linear static and static nonlinear analysis i.e. pushover analysis. Also it include time history analysis. The contents are described in a systematic manner to help in better understanding of the problem statement. We will begin by defining the static analysis. Static Analysis Structural analysis focuses on the changes that occurs in a structure when forces or loads are applied on the structure. Sometimes these loads are quasi that is they change very slowly with time and hence called static analysis. “Static analysis is a type of analysis in which the rate of change of force with respect to time is negligible …show more content…

Static structural analysis methods include: Static linear analysis Static nonlinear analysis Static Linear Analysis In a static linear analysis, the forces included are static that is either they are already present on the structure or else they are applied very slowly. Along with that analysis is linear that is with increase in force, deformation varies linearly. The deflections and rotations involved are small and the material behaves as linear elastically. Hence linear static analysis can be defined as: “the type of static analysis in which the behavior of the material is linear and elastic i.e. material after removal of force come back to its original shape and doesn’t undergo permanent deformations.” Figure 1 Material behaviour of different …show more content…

After yielding the material enters perfectly plastic region. When loading is removed the material should come back to its original position in a linear fashion. Figure 4 elastic perfectly plastic stress vs strain curve Figure 5 Plastification of cross section. Collapse Mechanism “When a system of loads is applied to an elastic body, it will deform and will show a resistance against deformation. Such a body is known as a structure. On the other hand if no resistance is set up against deformation in the body, then it is known as a mechanism.” Figure 6 Formation of collapse mechanism of a fixed beam. Theorems of plastic collapse The theorems of plastic collapse are given below. Lower bound or Static theorem “A load factor ( λs ) computed on the basis of an arbitrarily assumed bending moment diagram which is in equilibrium with the applied loads and where the fully plastic moment of resistance is nowhere exceeded will always be less than or at best equal to the load factor at rigid plastic collapse (

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