An Approach to Elastic Curve and General Flexibility Function using Virtual Work Method

Abstract

Calculation of deformations and flexibility forms an important part of structural analysis. One of the powerful tools used for this purpose is virtual work method; it can find deformation at a particular point of structure with any load combinations. However, there is room for improvement of virtual work method: standard textbooks in strength of materials or theory of structures do not depict the calculation of elastic curve equation by virtual work method. The purpose of this paper is to develop a theoretical approach to use virtual work method in calculating elastic curve equation. By expressing the point of application of the unit force in terms of variable dimension, equations for elastic curves can be developed. This approach is further extended to define and obtain a general flexibility function for structural systems. It is found that each of flexibility, elastic curve and deformation is a particular case of general flexibility function.