Numerical modelling of the static and seismic behaviour of historical buildings: the church of San Francesco in Lucca

This paper describes the numerical modelling of the structural behaviour of the church of San Francesco in Lucca, Italy. The constitutive equation for the various types of masonry employed in historic buildings views masonry as a nonlinear elastic material with zero tensile strength and infinite or bounded compressive strength. As such an equation has proven to be able to realistically model the most significant aspects of masonry behaviour, it has been implemented in the finite element code NOSA-ITACA for solving equilibrium and evolution problems of solids not withstanding tension, as well as for modelling restoration and consolidation operations. Numerical analyses of the church of San Francesco have been conducted using the NOSA-ITACA code. The church, which dates back to the thirteenth century, presents evident fractures and deformations mainly due to the large dimensions of its nave. It has been studied under two different conditions: in its actual state and in the presence of reinforcement structures. In particular, an assessment has been made of the effects of a metal framework, applied atop the longitudinal walls, on the behaviour of the structure subjected to its own weight and horizontal actions modelling an earthquake. The case study described in the paper highlights the important role of mathematical models and numerical tools in assessing the mechanical behaviour of historical masonry buildings in the presence of earthquakes, as well as in planning strengthening operations on such structures.