Deriving Analytical Solutions Using Symbolic Matrix Structural Analysis: Part 1 -- Continuous Beams

Abstract: This study investigates the use of symbolic computation in Matrix Structural Analysis (MSA) for continuous beams, leveraging the MATLAB Symbolic Math Toolbox. By employing symbolic MSA, analytical expressions for displacements, support reactions, and internal forces are derived, offering deeper insights into structural behavior. This approach facilitates efficient and scalable sensitivity analysis, where partial derivatives of outputs concerning input parameters can be directly computed, enhancing design exploration. The development includes an open-source MATLAB program, hosted on GitHub, enabling symbolic analysis of continuous beams subjected to point and uniform loads. This approach is invaluable for both engineering practice and pedagogy, enriching the understanding of structural mechanics and aiding in education by illustrating clear parameter relationships. The program supports deriving influence lines and identifying maximum response values.