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.

翻译：本研究探讨了在连续梁的矩阵结构分析中运用符号计算的方法，并利用了MATLAB符号数学工具箱。通过采用符号矩阵结构分析，推导出位移、支座反力和内力的解析表达式，从而为结构行为提供更深入的理解。该方法促进了高效且可扩展的灵敏度分析，其中输出关于输入参数的偏导数可直接计算，增强了设计探索能力。研究开发了一个开源MATLAB程序，托管于GitHub，支持对承受集中荷载和均布荷载的连续梁进行符号分析。该方法对于工程实践和教学均具有重要价值，通过阐明清晰的参数关系，深化了对结构力学的理解并有助于教学。该程序支持推导影响线并识别最大响应值。