Abstract
A procedure is proposed to evaluate the dynamic out-of-plane stability of cracked unreinforced masonry (URM) walls located in multi-storey URM buildings. The equations of dynamic motion are derived from first principles and representative single-degree-of-freedom (SDOF) models are proposed. The models have nonlinear stiffness properties that correspond to the restoring gravitational forces. A method is suggested to transform the nonlinear problem to a corresponding linear equivalent so that conventional spectral methods can be used to calculate wall response.
 The dynamic interaction between the URM building as the main structural system and the out-of-plane loaded walls as secondary elements is addressed by developing floor response spectra. Several buildings were assumed in a parametric study and subjected to code-compatible ground motion records. The absolute acceleration response at floor levels was calculated and the response spectra for that modified acceleration were subsequently obtained.
 The results from the study suggest that modifications should be made to the equations proposed for the Parts response spectra in the New Zealand seismic loading standard, NZS 1170.5:2004, in order to calculate the spectral response of out-of-plane loaded URM walls. Several worked examples are presented to demonstrate application of the procedure.
Highlights
Unreinforced masonry (URM) walls possess limited out-ofplane strength due to the inherent weakness of masonry in tension
Post-earthquake observations (Figure 1) consistently reveal the significance of the out-of-plane failure mode, and the development of a technique to predict wall out-of-plane instability is an essential part of a URM building detailed seismic assessment procedure
For simplicity of analyses it is often assumed that walls are supported only along their top and bottom edges, so that wall failure is generally in the form of a horizontal crack located above the wall mid-height, and any wall penetrations are ignored in the analysis
Summary
Unreinforced masonry (URM) walls possess limited out-ofplane strength due to the inherent weakness of masonry in tension. For simplicity of analyses it is often assumed that walls are supported only along their top and bottom edges, so that wall failure is generally in the form of a horizontal crack located above the wall mid-height, and any wall penetrations are ignored in the analysis. These assumptions lead to a lower bound result and have been adopted in the current study, but it is acknowledged that most existing walls have supports along at least one of their vertical edges
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