Comparison of Analytical and Computational Methods for the Analysis of Hyperstatic Structures

Abstract

This article aims to compare analytical and computational methods applied to the analysis of hyperstatic structures, focusing on understanding the advantages, limitations, and practical applicability of each approach. Hyperstatic structures, having more constraints than necessary for equilibrium, require specific methods for accurate analysis. The main theoretical foundations of analytical methods, such as the force method and the displacement method, traditionally taught in engineering courses, are addressed. Subsequently, the role of computational methods is analyzed, with emphasis on the Finite Element Method (FEM), widely used in structural engineering software such as SAP2000, Robot Structural Analysis, and Ftool. The adopted methodology included the analysis of a beam with double supports at each end, initially solved using analytical methods and later modeled in a computational environment. The results showed that, although both methods lead to similar solutions in terms of internal forces and displacements, execution time and calculation complexity differ significantly. Analytical methods offer greater transparency in the processes and are useful for conceptual understanding,but become impractical for complex structures. Computational methods, on the other hand, provide agility and versatility, although they require proficiency with the tools and critical validation of the results. It is concluded that the combined use of both methods is essential for the education of engineers, uniting solid theoretical foundations with current technological practice.

Introduction

Structural analysis is essential in engineering to understand how structures respond to various loads. Statically indeterminate structures, which have more constraints than required for equilibrium, need special analysis methods. Traditional analytical methods like the force method and displacement method offer accurate solutions but become impractical for complex structures.

With advances in computational technology, Finite Element Method (FEM)-based software (e.g., SAP2000, ANSYS, Ftool) enables faster and more detailed analysis of such structures. This article compares traditional analytical methods and modern computational approaches by applying both to a case study, focusing on internal forces, displacements, and computation time to evaluate their advantages and limitations.

Analytical Methods:

• Based on classical mechanics, suitable for simple or low indeterminacy structures.

• Advantages: deep understanding and accuracy for simple cases.

• Limitations: mathematically complex and error-prone for larger, complex structures.

Displacement Method:

• A key analytical technique based on nodal displacements and stiffness matrices (F = K•u).

• Builds a global stiffness matrix by assembling elemental stiffness matrices derived from material and geometric properties.

• Applies boundary conditions to solve for displacements, then calculates internal forces.

• Grounded in principles like virtual work and energy minimization ensuring stable, unique solutions.

Applications:

• Used for continuous beams, frames, indeterminate trusses, and structures with semi-rigid connections.

• Particularly effective for highly indeterminate systems where force methods are difficult.

Advantages of Displacement Method:

• Provides clear insight by focusing on structural deformations.

• Accurate under linear, elastic assumptions.

• Forms the theoretical basis for computational FEM methods.

Limitations:

• Grows complex with increased degrees of freedom.

• Requires advanced theoretical and mathematical knowledge.

• Limited to linear elastic behavior; nonlinear problems require extensions.

Conclusion

This comparative study shows that both analytical and computational methods are complementary in the analysis of statically indeterminate structures. A strong grasp of theoretical fundamentals ensures greater safety in interpreting numerical results, while computational methods significantly improve efficiency and scope of analyses. The ideal balance lies in combining conceptual knowledge with digital tools. Civil engineering education should continue to value the teaching of classical methods, while also promoting digital literacy through modern structural simulation tools.

References

Published journal articles: [1] Batista, M. A., & Silva, J. R. (2019). Comparative Study Between Analytical and Numerical Methods for Structural Analysis. Engineering Structures, 198, 109491. [2] Mendes, F., & Costa, P. (2020). Accuracy of Classical Methods in Hyperstatic Frame Analysis. International Journal of Civil Engineering, 18(5), 527–538. Research reports: [3] Instituto Superior Técnico. (2017). Technical Report on the Analysis of Statically Indeterminate Structures. Department of Civil Engineering. Dissertations and theses: [4] Ferreira, M. J. (2020). Comparative Analysis of Methods for Statically Indeterminate Structures (Master\'s Thesis). University of Porto. Web pages: [5] University of Aveiro. (2023). Support Material for the Structural Analysis Course. Available at: https://www.ua.pt Software: [6] Ftool – Structural Analysis Software. Developedby Prof. Luiz Fernando Martha, Pontifical CatholicUniversityof Rio de Janeiro, https://www.ftool.com.br ORCID David Filipe Pereira Fernandes

Copyright

Copyright © 2025 J.M. Gouveiaa, D.F.P. Fernandes. 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.