GENERAL ANALYTICAL SOLUTION OF AN ELASTIC BEAM UNDER VARYING LOADS WITH VALIDATION

Abstract

In this paper, we take into account the system of differential equations with boundary conditions of a fixed elastic beam model (EBM). Instead of finding a solution of EBM for a particularly specified load, which is the usual practice, we derive the general analytical solution of the model using techniques of integrations. The proposed general analytical solutions are not load-specific but can be used for any load without having to integrate successively again and again. We have considered load in a general polynomial form and obtained a general analytical solution for the deflection and slope parameters of EBM. Direct solutions have been determined under two types of loads: uniformly distributed load and linearly varying load. The formulation derived has been validated on the known cases of uniformly distributed load as appears frequently in the literature.