A numerical approach to the evaluation of collapse load multiplier of masonry curved structures

Heyman’s safe theorem is a powerful tool for the evaluation of the load-carrying capacity of curved masonry structures. According to such a theorem, a lower bound of the collapse load multiplier is computed by searching for a statically admissible state of stress that is compatible with the applied loads. The estimation of lower and upper bounds of the collapse load is not easy for masonry elements featuring arbitrary geometry and curvature. Several recent, theoretical and numerical approaches to the limit analysis of masonry structures can be found in [1][5]. The present work proposes a numerical approach to the collapse load multiplier of curved structures that moves from an accurate in-situ modelling of the three-dimensional geometry. The proposed procedure searches for a lower bound of the collapse multiplier and the corresponding thrust surface, by using a NURBS (Non Rational Uniform B-Splines)-based approach. A NURBS model of a curved structure with general geometry is studied via a lumped stress method (LSM) that reduces the structure to a 3D network of truss elements working only in compression. Such a compressive truss network is researched in the region comprised within the intrados and the extrados of the vault via an iterative procedure.