Large-deflection analysis of prismatic and tapered beam-columns using the Differential Transform Method

Abstract

The large-deflection analysis of a tapered beam-column under transverse loadings and restrained axially is presented. The proposed method is based on the Differential Transform Method (DTM) but with improved efficiency. This is achieved by separately analyzing and incorporating the differential transform of the trigonometric functions sinθ and cosθ with θs-=∑k=0muks-k being the solution to the problem making possible to work with series of order m = 20 without incurring into excessive computational effort and calculation time. The transformed equations convert the governing integro-differential equation of the problem into a polynomial equation with the coefficients ukfound by recurrence with its solution much easier to determine. The accuracy of the improved DTM depends on the order m of the series becoming the “exact” solution to the differential integral equation as m tends to infinity. The minimum value of m required in the expansion depends on the applied loads on the beam-column, its support conditions and geometry. Two classic beam-columns are analyzed herein using the proposed method: 1) a simple-supported beam-column partially restrained axially subject to a uniformly distributed transverse load; and 2) a tapered cantilever beam-column subject to a concentrated transverse load at the free end. The obtained results are compared with those reported by other researchers with excellent agreement showing the validity and simplicity of the proposed method and its corresponding equations.