Deriving Analytical Solutions Using Symbolic Matrix Structural Analysis: Part 2 -- Plane Trusses

Abstract: This study extends the use of symbolic computation in Matrix Structural Analysis (MSA) to plane (2D) trusses, building on previous work that focused on continuous beams. An open-source MATLAB program, hosted on GitHub, was developed to perform symbolic analysis of 2D trusses under point loads for any configuration. Using MATLAB's Symbolic Math Toolbox, the program derives analytical expressions for displacements, support reactions, and axial forces, providing a deeper understanding of truss behavior. The symbolic approach also supports efficient and scalable sensitivity analysis by directly computing partial derivatives of outputs with respect to input parameters, enhancing design exploration and optimization. This tool serves as a valuable resource for both engineering practice and education, offering clear insights into parameter relationships and enriching the understanding of structural mechanics. The accuracy of the symbolic results has been rigorously validated against two commercial finite element software programs and results from the literature, with full agreement, confirming the validity and generality of the methodology.