Collapse capacity of masonry domes under horizontal loads: A static limit analysis approach

TL;DR

This paper introduces a static limit analysis method for evaluating the collapse capacity of masonry domes under horizontal loads, utilizing shell theory, optimization, and validation against experimental data.

Contribution

It develops an original computational strategy combining shell stress analysis and convex optimization to assess masonry dome stability under horizontal forces.

Findings

The method accurately predicts collapse multipliers and failure mechanisms.

Validation confirms reliability against experimental results.

Parametric analysis shows influence of geometric and friction parameters.

Abstract

A static limit analysis approach is proposed for assessing the collapse capacity of axisymmetric masonry domes subject to horizontal forces. The problem formulation is based on the sound theoretical framework provided by the classical statics of shells. After introducing the shell stress tensors on the dome mid-surface, integral equilibrium equations are enforced for its typical part. Heyman's assumptions of infinite compressive and vanishing tensile strengths are made, with cohesionless friction behavior governing the shear strength, to characterize the admissible stress states in the dome. An original computational strategy is developed to address the resulting static limit analysis problem, involving the introduction of a mesh on the dome mid-surface, the interpolation of the physical components of the shell stress tensors on the element boundaries, and the imposition of equilibrium and admissibility conditions respectively for the elements and at the nodes of the mesh. The descending discrete convex optimization problem is solved by standard and effective optimization tools, automatically providing collapse multiplier of horizontal forces, incipient collapse mechanism and expected crack pattern. Convergence analysis, validation with experimental results available in the literature, and parametric analyses with respect to geometric parameters and friction coefficient, are presented for spherical and ellipsoidal masonry domes, proving the reliability of the proposed approach for estimating the pseudo-static seismic resistance of masonry domes.