Using VBA in Excel to analyze plane beam reactions by the matrix method

Abstract

A simple computational tool for planar beam analysis is developed in Excel using VBA based on the Matrix Structural Analysis (MSA) method. This method describes the relationship between nodal forces, nodal displacements, and structural stiffness through a matrix-form equilibrium equation. The program automates the calculation process, including stiffness matrix formulation, conversion of distributed loads into equivalent nodal forces, and solving the system of equations to determine displacements, support reactions, and internal forces of the beam. The results are presented visually through tables and shear–moment diagrams. In addition, the study compares the results of MSA with those of the Finite Element Method (FEM), highlighting the simplicity, transparency, and applicability of MSA in teaching and linear structural analysis research.