Deflection of Structures using Principle of Quasi Work

A new methodology for obtaining deflections of structures is presented in this paper. It is based on Principle of Quasi Work, which connects two topologically similar systems thereby leading to a unique concept of standard elements for every category of structural problems. Using a priory known equation of deformation/deflection of elastic axis of these elements, solution for equation of deformed/ deflected elastic line of other structural members of similar category having different loading and boundary conditions is presented here. This methodology is easy to use as deflection of a given structure is obtained mostly by simple multiplications and it also eliminates the use of internal force/bending moment expressions unlike conventional methods. Even though this methodology can be applied to any structure, its use is illustrated for one dimensional structural elements (viz. axial bars, torsion rods and beams) for the sake of conciseness and clarity. The concept of topologically similar system is explored for each category of elements as it lies at the heart of the principle of quasi work.