It is well recognised that the dynamic response of unreinforced masonry buildings with flexible timber diaphragms typically contains multiple dominant modes associated with the excitations of the diaphragms and the in-plane walls. Existing linear analysis methods for this type of structure commonly account for the multi-mode behaviour by assuming the independent vibrations of the in-plane loaded walls (in-plane walls) and the diaphragms. Specifically, the in-plane walls are considered to be rigid and the unmodified ground motion is assumed to be transmitted up the walls to the diaphragm ends. While this assumption may be appropriate for many low-rise unreinforced masonry buildings, neglecting the dynamic interaction between the diaphragms and the in-plane walls can lead to unreliable predictions of seismic demands. An alternative analysis approach is proposed in this paper, based on the mode properties of a system in which (1) the mass ratios between the diaphragms and the in-plane wall are the same at all levels, and (2) the periods of the diaphragms are the same at all levels. It is proposed that under these conditions, two modes are typically sufficient to obtain the peak seismic demands of the in-plane walls in elastically responding low-rise regular buildings. The applicability of the two-mode analysis approach is assessed for more general diaphragm configurations by sensitivity analysis, and the limitations are identified. The two-mode approach is then used to derive a response modification factor, which may be used in conjunction with a linear static procedure in the seismic assessment of buildings with flexible diaphragms.
A novel macroelement for seismic analysis of unreinforced masonry buildings based on MVLEM in OpenSees
