A cracked elastic collapse model for slender masonry arches

Paper in proceeding, 2026

We present a simple cracked elastic model that can be used for the analysis of slender masonry arches where elastic deformation and cracking significantly reduce the load capacity. The aim of this work is to produce results that can be compared with those obtained from more sophisticated numerical methods such as the finite element method and the discrete element method. The proposed formulation uses Euler-Bernoulli beam theory and considers only the compressed part of the cross-section. The arch is discretised using three-node quadratic B-spline beam elements and solved using dynamic relaxation. Using displacement control, we investigate how Young's modulus and cracking affect the peak load under a point load. The results of our formulation are compared with the collapse loads predicted by the rigid circular arch and by a discrete element analysis, as well as the stiffness of the linear elastic circular arch in the case when there are no cracks. The preliminary results of a relatively slender arch show that the collapse load is affected by elastic deformation when the Young's modulus is below 10 GPa. However, further work is needed to investigate why the stiffest arches with a Young's modulus above 80 GPa had a collapse load slightly higher than that of the rigid arch, which should not be possible.