The determination of the deflection of the stepped column by the finite difference method

Abstract

Besides the strength criterion, steel structures must also meet the deformation criterion, which in some cases may be critical. Excessive deformation of the structure may lead to additional loads and improper operation of the installed equipment. The most common practice in steel structure design involves using the finite element method (FEM) to calculate the stress and deformation of the current model. However, this is usually limited to the case study for the particular structural model. The paper demonstrates the application of the finite difference method (FDM) to determine the deflection of a stepped column, enabling a broader parametric study and analysis of a variety of solutions that satisfy the deformation criterion. The application of FDM yields a scheme convenient for coding in MATLAB while showing the dependence between the column deflection and the design parameters. The results from the finite element analysis (FEA) are in excellent agreement with those from the FDM.