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. The second order effects are often neglected in the evaluation of the global seismic response of masonry buildings. Pier in-plane response is often governed by shear failure modes, particularly in case of rather squat panels and relatively high compression. Shear failure is usually associated with a limited deformation capacity which makes acceptable an approach based on the undeformed geometry of the structure. In case of structural members with a prevailing bending behaviour, the displacement capacity can be significantly increased and second order effects may no longer be negligible. Indeed, experimental tests on panels with a marked rocking behaviour show a gradual reduction of lateral strength for increasing lateral displacements, also in the absence of significant toe-crushing effects. The 2-node macro-element model implemented in the TREMURI computer program concentrates in the two extremities the coupled axial and flexural behaviour allowing for a rigorous representation of flexural cracking and toe-crushing effects. The shear response is concentrated in the central body of the element and the interaction between shear and bending-rocking behaviours is allowed by two internal degrees of freedom. The kinematic formulation of the macroelement and in particular the presence of the additional internal degrees of freedom easily allowed the introduction of P-delta effects in the nonlinear element response. Numerical results obtained with the upgraded macro-element model showed a very good agreement with experimental results. The new feature implemented in the macro-element model makes its use in the equivalent frame modelling further reliable and opens new perspectives and applications in other fields such as the analysis of rigid or quasi-rigid block systems.

A MACRO-ELEMENT MODEL FOR THE NONLINEAR ANALYSIS OF MASONRY MEMBERS INCLUDING SECOND ORDER EFFECTS