Non-linear equivalent frame modelling:- Assessment of a two storey perforated unreinforced masonry wall

The highly non-linear behaviour of unreinforced masonry walls makes linear static analysis methods inadequate and inaccurate and therefore for both academics and practicing engineers non-linear analysis of masonry buildings is preferable. Although accurate predictions of the structural response and cracking pattern can be generated by complex finite element (FE) meso models, the computational skill and high time cost often discounts this approach for everyday use. Alternatively, Equivalent Frame models are able to represent the essential characteristics of perforated wall response with minimal computational expense and can evaluate the key design parameters of ultimate strength, maximum displacement and failure mode. The main features of the Equivalent Frame model used to represent the non-linear behaviour of unreinforced masonry perforated walls in SAP2000 are detailed. Closed-form solving of sectional equilibrium equations to evaluate the flexural strength of pier and spandrel components using a stress-strain relationship specific to New Zealand URM material behaviour which incorporates strain softening, is presented and used to define the coupled axial-moment hinge. Spandrel failure modes are developed and equations to capture the shear strength for each mode are presented. Finally a comparison between the modelled force-displacement response, and the experimentally obtained force-displacement response for full scale sub-structures and a two storey perforated wall previously experimentally tested is discussed.