A Direct Finite Element Limit Analysis for Assessing the Structural Safety of Masonry Under Anisotropic Behavior

ABSTRACT The proposed study presents a finite element direct formulation of limit analysis, allowing the application of the classical method of limit design to complex structures in two and three‐dimensional environments. The main result of the proposed method is to recognize the admissible stress in a structure as a function of a finite number of nodal parameters that allow defining the optimal program to implement the lower bound theorem in the Melàn form. Direct limit analysis, devoted to calculating the collapse load, does not depend on the detailed knowledge of the load time history that is generally unknown. Specific formulation for masonry structure is described, focusing on the two‐step approach at the constituent scale, mortar and brick fabric, and at the structural scale. Namely, at first, limit analysis has been applied to Representative Volume Elements describing the masonry fabric and has been used to calculate the limit strength along the principal axes of the material anisotropy. A second step involves applying the procedure to a structure composed of the material obtained from the previous analysis. The proposed examples describe a typical masonry building where the anisotropic behavior of the material, both in the elastic and plastic ranges, has been considered, highlighting the feasibility of the method and the accuracy of the obtained results. Finally, a literature case, the Prestwood bridge, whose experimental collapse load is obtained from a full‐scale test by Page, has been analyzed to compare the method with experiment and different numerical approaches, confirming its feasibility and robustness.