The determination of the deflection of the beam with continuously varying cross-section by the finite difference method

Abstract

Amongst others, the deformation criterion is to be fulfilled in the process of steel structure design. Often, it can be more restrictive than the stress criterion. Although the stress state is within the permissible limit, excessive structure deformation can lead the additional load to emerge in the carrying structure and cause improper operation and shorter life of attached devices and equipment. For that reason, besides other requirements, the allowable deformation limits of the steel carrying structure are defined. The stress-strain analysis of the structure is usually conducted by utilization of finite element method (FEM) in the early phase of the design process. Alternatively, this paper shows the application procedure of the finite difference method (FDM) for the deflection determination on the simple elastically restrained cantilever beam with continuously varying box-like cross-section and linear change of section height. Dependence of the deflection on the design parameters is obtained through programming in MATLAB and the comparison is made with the results from the finite element model built in ANSYS. The results from both numerical approaches showed excellent compliance.