Comparative Study of Structural Analysis Methods with Practical Application

Abstract

This article intends to compare two classical methods of analyzing statically indeterminate structures: the force method and the displacement method. The analysis is based on the theoretical description of the principles, advantages, and limitations of each approach, considering different application contexts. The study explores the formulation of the main unknowns, the complexity of the solution procedures, and the suitability of each method for both simple and complex structures. The comparison is illustrated through the application of both methods to various example structures, demonstrating the differences in formulation and the results obtained. The results show that, although both methods remain relevant, the displacement method stands out due to its applicability in modern software, offering greater efficiency and flexibility in more complex analyses. It is concluded that a deep understanding of both methods remains essential for professional practice in civil engineering, enabling a careful choice of the most appropriate approach for each situation.

Introduction

Structural analysis is vital for ensuring the safety and stability of constructions, particularly for statically indeterminate structures. Two primary methods for analyzing such structures are the Force Method and the Displacement Method, each with distinct approaches and applications.

The Force Method (or compatibility method) focuses on finding internal redundant forces by applying equilibrium and compatibility conditions. It is effective and straightforward for simple structures with few supports and uniform loads but becomes cumbersome and inefficient for complex structures with many redundancies or irregular loadings. It offers transparent calculations and good control but often requires software support for more complex problems.

The Displacement Method uses nodal displacements and rotations as primary unknowns. It is well-suited for complex, statically indeterminate structures like frames, continuous beams, and multi-story buildings. Its systematic and algorithmic nature makes it ideal for computer implementation and forms the theoretical basis for the Finite Element Method widely used in modern software. However, it can be more complex to apply to simpler structures or those with movable supports.

A comparative analysis of two similar statically indeterminate beam structures was performed: one analyzed with the Displacement Method focusing on nodal displacements and rotations, and the other with the Force Method focusing on internal forces. This illustrates the practical differences, strengths, and limitations of each approach.

Conclusion

The study successfully applied the Force Method to a statically indeterminate structure of degree two, composed of four simple supports and subjected to three concentrated loads. It was possible to determine the support reactions, internal forces, and the bending moment and shear force diagrams based on equilibrium conditions and deformation compatibility. It was observed that, although the Force Method is more demanding in algebraic terms, it remains a relevant tool in structural analysis, especially for structures with low degrees of indeterminacy. The practical application of the method demonstrated its usefulness in both academic and professional contexts, corroborating the theoretical foundations described by Soriano (2015) and other classical authors such as Timoshenko (1961). From a scientific perspective, this work contributes to the consolidation of knowledge related to the analysis of statically indeterminate structures, providing a basis for future comparisons with the Displacement Method and with numerical methods. Pedagogically, it reinforces the importance of thoroughly understanding classical methods before relying on advanced computational tools.

References

Books [1] H.L. Soriano, S.S. Lima, Análise de Estruturas: Método das Forças e Método dos Deslocamentos, 2ª ed. atualizada, Editora Ciência Moderna, Rio de Janeiro, [s.d.]. Web Pages [2] L.F. Martha, Métodos básicos da análise de estruturas. http://www.tecgraf.puc-rio.br/~lfm, [s.d.] (acesso em 12 maio 2025). Journal Articles [3] K.M. Santos Duarte, P.V.R. Fernandes, A utilização do método das forças na determinação de diagramas de esforços de vigas em concreto armado, Rev. Gest. Conhec., 17(2) (2023) 190–213. Software [4] L.F. Martha, Ftool - Two-Dimensional Frame Analysis Tool (Version 3.00), PUC-Rio, Rio de Janeiro, 2000. http://www.tecgraf.puc-rio.br/ftool (acesso em 12 maio 2025).

Copyright

Copyright © 2025 J.M. Gouveia, M.B.G. Coimbra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.