Analysis of Loaded Beam, Cantilever, and Elongated Vertical Column via Integral Rohit Transform

Abstract

Structural analysis is a branch of solid mechanics which utilizes straight forward models for solids. The main objective of Structural analysis is to find out the effect of loads on the physical structures and their components. A beam is a structure with a constant cross-section and is described by its significant length in comparison to its thickness and width. A cantilever, on the other hand, is a slender beam with a uniform cross-sectional shape that is fixed horizontally at one end and subjected to a load at the other end. Columns, which serve as vertical compression members in building frames, are susceptible to buckling and failure when subjected to relatively small axial loads. The analysis of loaded beams, cantilevers, and elongated vertical columns is typically carried out using the principles of calculus. However, this paper introduces the integral Rohit transform for the analysis of loaded beam supported at ends, cantilever, and elongated columns with low buckling axial loads. It is found that the depression grows as the cantilever and beam lengths that are loaded in the middle and supported at both ends rise. An attempt has been made to analyze the elongated column with low axial buckling loads and derive the Euler's formula for buckling load. The obtained solutions are graphically represented, and the results demonstrate accuracy, capability and effectiveness of the integral Rohit transform technique when compared to existing methods in the literature. The Rohit transform involves simple formulation and less computational work compared to other me­thods available in the literature.