Stress Analysis in Straight and Inclined Sections of Continuous Beams and Frames Using the Force Method:

Abstract

This Master’s thesis presents a detailed comparative study between two essential approaches used in the analysis of statically indeterminate structures: the classical Force Method and the Finite Element Method (FEM). The investigation focuses on continuous beams and planar frame structures, exploring their theoretical principles, step-by-step procedures, and practical implementation. Through a series of carefully developed case studies and numerical evaluations, the Force Method is highlighted for its exact analytical solutions and pedagogical value, while the Finite Element Method is distinguished by its computational versatility and its capacity to handle structures with complex geometries and varied loading scenarios. The results of this study demonstrate the complementary nature of both methods: the Force Method provides precise, physically meaningful outcomes, whereas FEM offers highly accurate approximations supported by detailed graphical outputs of internal forces, stress and structural deformations. By combining traditional analytical techniques with modern numerical tools, this work underscores the value of integrating classical and contemporary methods to enhance structural analysis, promote deeper understanding, and support more robust engineering decisions.