Numerical Simulation of Unreinforced Masonry Buildings with Timber Diaphragms

Though flexible diaphragms play a role in the seismic behaviour of unreinforced masonry buildings, the effect of the connections between floors and walls is rarely discussed or explicitly modelled when simulating the response of such buildings. These flexible diaphragms are most commonly timber floors made of planks and beams, which are supported on recesses in the masonry walls and can slide when the friction resistance is reached. Using equivalent frame models, we capture the effects of both the diaphragm stiffness and the finite strength of wall-to-diaphragm connections on the seismic behaviour of unreinforced masonry buildings. To do this, we use a newly developed macro-element able to simulate both in-plane and out-of-plane behaviour of the masonry walls and non-linear springs to simulate wall-to-wall and wall-to-diaphragm connections. As an unretrofitted case study, we model a building on a shake table, which developed large in-plane and out-of-plane displacements. We then simulate three retrofit interventions: Retrofitted diaphragms, connections, and diaphragms and connections. We show that strengthening the diaphragm alone is ineffective when the friction capacity of the wall-to-diaphragm connection is exceeded. This also means that modelling an unstrengthened wall-to-diaphragm connection as having infinite stiffness and strength leads to unrealistic box-type behaviour. This is particularly important if the equivalent frame model should capture both global in-plane and local out-of-plane failure modes.

Equivalent frame modelling of an unreinforced masonry building with flexible diaphragms

A case study was conducted to investigate the applicability of the equivalent frame modelling for the nonlinear time-history analysis of unreinforced masonry buildings with flexible diaphragms. The dynamic responses calculated from the equivalent frame models were compared against shake table test results of a full-scale two-storey stone masonry building. The investigated modelling approach reflected the simplifications commonly assumed for the global analysis of buildings; namely, considering the diaphragms to behave elastically and neglecting the stiffness and strength contributions of the out-of-plane responding walls. The sensitivity of the analysis to different idealisations of the equivalent frame, as well as to the diaphragm stiffness values, were also investigated. Discussions are provided on the accuracies and limitations of the investigated modelling approach, which may serve as a useful guidance for practical application.