Historical masonry buildings located in the Southern Italy are usually built with irregular stones joined with mortar with poor mechanical properties. Therefore, piers and spandrels ultimate resistance is not always well predicted by simplified formulas suggested by codes of practice, which typically are tailored to regular patterns. In this framework, we present a two-step numerical model –within the equivalent frame approach assumption– for the pushover analysis of in-plane loaded historical masonry walls constituted by an irregular assemblage of stones. In Step I, ultimate bending moment-shear force strength domains of piers and spandrels are derived by means of a heterogeneous upper bound FE limit analysis and the results are stored in a database. Assessing the capacity of both piers and spandrels is crucial for correctly predicting the ultimate resistance of masonry walls acted upon by in-plane loads. Heterogeneous limit analysis is particularly suitable for computing failure loads, since it permits a distinct modeling of stones and mortar joints. Appropriate static and kinematic boundary conditions are set to account for the complex interaction of internal forces and deformed shapes of single elements. At Step II, a frame model of the masonry wall is assembled, where piers and spandrels are modeled as elastic Timoshenko beams. At each analysis step it is checked that the internal forces in each structural element are smaller than the failure loads stored in the database created at Step I. If the capacity is exceeded, suitable flexural hinges are introduced at the end of the structural elements. The resistance of the element is then set to zero when a limit chord rotation is exceeded. With the numerical tool developed, a real scale old masonry oil-mill located in the Southern Italy is analyzed in the inelastic range under increasing static loads.
Piecewise rigid displacement (PRD) method: a limit analysis-based approach to detect mechanisms and internal forces through two dual energy criteria
