A simple and rapid approach for the numerical simulation of non-linear elements and examples of its application

In earthquake design philosophy non-linear inelastic damage is concentrated at predetermined locations in a structure, with the ultimate aim being to keep structural members critical for collapse avoidance, elastic. Non-linear elements can include the beam column joints in steel and reinforced concrete moment resisting frames, the nail connections of timber sheathing-to-framing shear walls, and the hold-down connectors of shear walls. To numerically model the seismic behaviour of these structures, it is critical to be able to quickly and simply model their respective hysteretic behaviours. In particular, this requires identifying the necessary parameters that will allow for the accurate replication of the degrading and pinching qualities of the force-displacement relationships. The authors propose the use of a proprietary multi-linear plastic link, available in most finite element packages, in order to achieve this. A step-by-step process is provided to model the links, taking into account the initial elastic stiffness, the force-displacement curve up to ultimate-strength, and the post ultimate-strength degrading stiffness, and the reversing stiffness. The procedure can be adopted for both linear and rotational cyclic excitations. The modelled individual elements are subjected to a series of displacement controlled time-history schedules, and validated against the results from experimental tests. These elements, representing non-linear behaviour, are in turn implemented in various numerical models of shear wall and moment frame structures. The structures are subjected to cyclic loading and seismic excitation, and the non-linear characteristics of the individual elements are reflected in the overall response of the respective structures