GENERAL ANALYTICAL EXPRESSIONS FOR DEFLECTION AND SLOPE OF EULER-BERNOULLI BEAM UNDER DIFFERENT TYPES OF LOADS AND SUPPORTS

Abstract

In this research paper, we solve the Euler-Bernoulli beam (EBB) differential equations by taking the general boundary conditions. Instead of finding a solution for the EBB model for a particular load and its particular boundary conditions, we derive the general analytical solution with general boundary conditions by using techniques of integration. The proposed general analytical solutions are neither load specific nor dependent on specific boundary conditions but can be used for any load and any boundary condition without having to integrate again and again. We have taken a general polynomial load function with general boundary conditions, and get the general analytical solution for the deflection and slope parameters of EBB. We find the direct solution for uniform distributed load and linearly varying load for a fixed beam.