A macroelement for the nonlinear analysis of in-plane unreinforced masonry piers

This paper presents the formulation and validation of a macroelement capable of simulating the in-plane response of unreinforced masonry (URM) piers and spandrels. The modeling approach adopted was originally developed for the in-plane analysis of reinforced concrete walls in the 1980s, and involves placing nonlinear shear springs in series with rotational springs to simulate both shear and flexure response. For this study, the modeling approach was extended to explicitly address the in-plane failure modes unique to URM. Specifically, the proposed macroelement includes an axial spring, three shear springs, and two rotational springs to simulate the axial, bed joint sliding, diagonal tension, and rocking/toe crushing failure modes observed during past URM pier tests. The validation of this macroelement involved comparison with 21 past experimental studies of URM pier behavior, and focused primarily on ultimate strength and failure mode simulation. Overall the macroelement properly simulated 67% of the reported failure modes and provided strength estimates with an average absolute error of 19.1%. These errors are primarily attributed to the variability of URM response as well as the uncertainty associated with using default material properties in the absence of reported material properties. Following the ‘calibration’ of the default diagonal tension strength of masonry, the average absolute error was reduced to 11.9%; however, the number of failure modes predicted remained unchanged. Finally, the proposed macroelement was used to carry out parametric studies of vertical stress, aspect ratio, and boundary conditions.