Structural Analysis of 2D Frame Using the Stiffness Matrix Method in Python with Validation Against SAP2000 - Samsul Abdul Rahman Sidik Hasibuan (JOURNAL OF CIVIL ENGINEERING BUILDING AND TRANSPORTATION, 2025)
Structural analysis is a critical aspect of civil engineering design, ensuring the safety and performance of structural systems under various loading conditions. The stiffness matrix method, as a fundamental numerical approach in structural analysis, is widely implemented in commercial software such as SAP2000. However, the reliance on proprietary tools often limits transparency and understanding of the underlying computational process. This study aims to develop a Python-based implementation of the stiffness matrix method for analyzing a two-dimensional (2D) frame structure and to validate its accuracy against SAP2000 results. The methodology involves modeling the structure, formulating element and global stiffness matrices, applying boundary conditions, and solving the system of equations to obtain nodal displacements, support reactions, and internal member forces. The results show that the Python model produces highly consistent outcomes compared to SAP2000, with discrepancies in nodal displacement and support reactions generally less than 2%. The deformation pattern, reaction forces, and internal force diagrams, including bending moment, shear, and axial force, demonstrate strong agreement between both approaches. These findings confirm that the stiffness matrix method implemented in Python is capable of accurately representing structural behavior. The study highlights the potential of open-source computational tools as reliable alternatives to commercial software for structural analysis. It is recommended that future studies extend this approach to nonlinear analysis and larger structural systems. The implications of this research support the integration of transparent and reproducible computational methods in engineering education and professional practice.