Redundant Reactions of Indeterminate Beams by Principle of Quasi Work

Abstract

A new methodology for determining redundant reactions of beams is presented in this paper. This methodology is based on the principle of quasi work, which is a powerful pseudoenergy theorem deduced from Tellegen's theorem. It takes topography of a structural system as a variable in addition to the variables involved in conventional energy methods, variational principles, and finite element methods. The concept of topologically similar system lies at the heart of the principle of quasi work. This concept is explored for beams to define topologically similar beams and topologically equivalent beams. The principle of quasi work is validated for beams and subsequently used for determining redundant reactions of indeterminate and continuous beams. Further, a unique concept of reference beam is developed. Equation of deflection curve of this reference beam is used to solve redundant reactions of indeterminate beams. This methodology has an advantage of calculating redundant reactions mostly by simple multiplications without any integrations or differentiations and does not require any prior knowledge of writing bending moment expressions. The method is illustrated through examples. It is possible to develop an interactive graphic computer package for calculating reactions of indeterminate beams.