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Application of Castigliano's theorem in the analysis of semi-circular arch deflection

Date
2025-07-02
Abstract
The article presents an analytical solution for determining the vertical deformation of a three-hinged arch subjected to a point load at its apex. The theoretical approach is grounded in Castigliano's theorem and utilizes the principle of superposition of strain energy along the arch. A parametric study is included, examining various curvature radius-to-beam thickness ratios to assess when the contributions of strain energy from shear and axial forces must be considered. The parametric study is based on varying the ratio R/h, which ranges from a value of 100 to 0.25. The findings are validated through finite element analysis (FEA) computational models and experimental measurements.
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Civil and Environmental Engineering
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School of Engineering
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Cosgrove_2025_Application.pdf
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Keywords
Castigliano´s theorem, deflection, three-hinged arch, strain energy, semi-circle
ULRR Identifiers
https://researchrepository.ul.ie/handle/10344/31421
 https://doi.org/10.34961/18936
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Sustainable Development Goals
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Article
Rights
http://creativecommons.org/licenses/by-nc-sa/4.0/
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