Deriving analytical solutions using symbolic matrix structural analysis: Part 2 – Plane trusses

This study extends the use of symbolic computation in matrix structural analysis to plane trusses, expanding on previous work that focused on continuous beams. We present a fully open-source MATLAB program, available on GitHub, that performs symbolic analysis of 2D trusses subjected to point loads, applicable to any truss configuration. Using the Symbolic Math Toolbox, the program derives closed-form analytical expressions for displacements, support reactions, and axial forces, providing deeper insight into structural behavior. A key advantage of the symbolic approach is its ability to perform sensitivity analysis efficiently by computing partial derivatives of structural responses with respect to input parameters. This feature enhances design exploration and optimization by allowing direct evaluation of parameter influences. Moreover, the framework is highly scalable, capable of generating symbolic solutions even for large-scale truss structures, something previously unattainable using traditional methods due to computational limitations. The tool serves both engineering practice and education, offering clear insights into parameter relationships and strengthening conceptual understanding in structural mechanics. To ensure accuracy, the symbolic results were rigorously validated against two commercial finite element software programs and results from the literature, with complete agreement. These validations confirm the reliability, scalability, and general applicability of the proposed methodology.