Structural Analysis Homework Help | TutorBin.com

# Structural Analysis

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In structural analysis, we find the reactions, shear force, bending diagram, deformations so as to know what internal forces will be generated for the loads the structure is subjected to. For any safe structure, these internal forces should be effectively resisted by the material thus the design should be such that the strength of a material is greater to the maximum load the structure is subjected to. One has to also limit the deformations in a structure so that the structure is functionally fit to use, so we draw elastic curve for structural elements so as to know what will be the maximum deflection in the structure.

Structural analysis is the pre-requisite for structural design. Once analysis is done, materials are chosen so as to resist the internal forces such that the structure is same. Choice of materials also depends upon the economy of the material but in any case, the strength of the chosen material should be greater than the internal forces developing in the structure. Thus, a proper factor of safety is required depending on the type of material, structure and uncertainty in the estimation of loading.

Structural analysis utilizes the knowledge of applied mechanics, applied mathematics to find out the stress functions. It finds its application in finding shear force, reactions, bending moment, analysis of truss, analysis of cables, analysis of arches, analysis of determinate and indeterminate structures.

Practical structures are indeterminate in nature but analysis of such structures can’t be done just by using static equilibrium conditions only. Additional equations have to be developed which are also known as compatibility equations to find the unknowns. To analyze indeterminate beams and frames, we can use moment-distribution method, slope-deflection method, unit load method, strain energy method etc. Methods like moment distribution method, slope deflection method are iterative in nature. To analyze indeterminate trusses one can, use strain energy method and unit load method effectively to find the unknown forces.

To fulfil the serviceability criteria, one has to limit the slope and deflection of structural elements. There are different methods of calculating slope and deflection like double integration method, Macaulay Theorem, Castigliano’s theorem, Moment-area method, conjugate-beam method etc. It should be noted that the above methods are applicable for linear-elastic structures because value of E (modulus of elasticity) will be constant. In case of non-linear structures or plastic structures one can use virtual work method.

In structural analysis, we utilize principle of superposition to analyze the structure but this valid only for linear-elastic models or structures. For non-linear structures, sophisticated modeling has to be done through computer software like ANSYS etc. For non-linear analysis one has to properly define the material non-linearity, element non-linearity and structural non-linearity on a whole. For very simple structures, one can use static analysis. But for a good and efficient analysis, dynamic and non-linear analysis has to be done.

Dynamic analysis offers a fairly good degree of estimation of dynamic loads but the accuracy depends on the method of analysis though. For example- for earthquake loads time history method provides better estimation of loading which is more economical to use rather than equivalent static load method or response spectrum method. Non-linear dynamic analysis is the best method for analyzing any structure but this is very tedious method thus it finds the application in the complex structures. STAAD Pro software is fairly good in analysis of residential buildings, structural elements with certain loading. Any analysis software is just a application of structural analysis methods but since a large number of iterations are required these software are helpful in analyzing a structure at each instant but basic knowledge of structural analysis is required so as to understand and visualize the structure and take the assumptions accordingly which will be in valid in that particular situation.

Structural analysis also deals with the analysis of moving loads on a structure like a moving train on a bridge etc. For this we need to draw the influence line diagram so as to see analyze the structural elements at each instant of loading and we design the elements considering the maximum load by using a suitable factor of safety. We see iconic structures like Burj Khalifa, Eiffel Tower, The Taj Mahal and the list is countless which fills us with utter amazement and excitement. These beautiful megastructures demand a great degree of understanding of structural analysis. To turn a dream of an architect in to a beautiful reality, a structural engineer is the link.

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