Reconciling Elastic and Equilibrium Methods for Static Analysis

We examine two widely used classes of methods for static analysis of masonry buildings: linear elasticity analysis using finite elements and equilibrium methods. It is often claimed in the literature that finite element analysis is less accurate than equilibrium analysis when it comes to masonry analysis; we examine and qualify this claimed inaccuracy, provide a systematic explanation for the discrepancy observed between their results, and present a unified formulation of the two approaches to stability analysis. We prove that both approaches can be viewed as equivalent, dual methods for getting the same answer to the same problem. We validate our observations with simulations and physical tilt experiments of structures.