Upper bound limit analysis of meso-mechanical spandrel models for the pushover analysis of 2D masonry frames

摘要

In this paper, a numerical model for the pushover analysis of in-plane loaded unreinforced masonry walls is presented. For the analysis of the walls, which consist of vertical piers connected by horizontal masonry spandrels, an equivalent frame model is adopted. The analysis approach consists of two steps: In Step I, ultimate bending moment-shear force strength domains of the masonry 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 the spandrels correctly is crucial for the ultimate resistance of masonry walls that are loaded in-plane. Heterogeneous limit analysis is particularly suitable for computing the failure load of unreinforced masonry members since it permits a distinct modelling of bricks and mortar joints. Appropriate static and kinematic boundary conditions are imposed to account for the complex interaction of internal forces and deformed shapes of the spandrel beams at failure. In Step II. a frame model of the masonry wall is assembled. In this frame model the spandrels are modelled as elastic Timoshenko beams. At each analysis step it is checked that the internal forces of these coupling beams are smaller than the failure loads stored in the database created in Step I. If the capacity is exceeded, flexural hinges are introduced at both ends of the coupling beam. The resistance of the element is set to zero when a limit chord rotation is exceeded. The piers are modelled in a similar manner. The shear force and bending moment capacity of the piers are, however, simply estimated according to the Italian Design Code. Pushover analysis results compare favourably with computationally expensive 2D nonlinear heterogeneous FE analyses, but also confirm that the ultimate lateral resistance of masonry walls is very sensitive to the assumed spandrel strength if an equivalent frame model is used.