Application of Castigliano's Theorem in the Analysis of Semi-Circular ARCH Deflection

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.