AN ANALYSIS OF INTERNAL FORCES IN A SIMPLE TRUSS STRUCTURE: GAUSS-JORDAN ELIMINATION METHOD AND THE EFFECT OF NUMERICAL ERRORS

Abstract

This study analyzes the internal forces in a simple truss structure using the Gauss-Jordan method. The truss structure is analyzed through a mathematical approach by formulating a mathematical model of the simple truss structure in the form of a system of linear equations based on the equilibrium of forces at each joint. The resulting system of force equations is transformed into a coefficient matrix and solved using the Gauss-Jordan method to determine the internal forces in each truss member. This study also evaluates the impact of numerical errors in computation. The results indicate that the Gauss-Jordan method is effective for small-scale structures, but it is sensitive to rounding errors and near-zero coefficients, thus highlighting the need for careful application of numerical methods in civil structural analysis.   Keywords: Internal Force Analysis, Truss Structure, Gauss-Jordan Method, Numerical Error