Abstract
In earthquake design philosophy non-linear inelastic damage is concentrated at predetermined locations in a structure, with the 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. It is particularly important to identify the parameters that will allow for the accurate replication of the degrading and pinching qualities of the force-displacement relationships. The authors summarise 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 to model the links, from previous research, is described. This process considers the initial elastic stiffness, the force-displacement curve up to ultimate-strength, the post ultimate-strength degrading stiffness, and the reversing stiffness. The procedure can be adopted for both linear and rotational cyclic excitation. 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 walls. The authors apply cyclic loading to a model wall, and then for a separately designed wall apply seismic ground accelerations associated with the 2011 Canterbury earthquakes in New Zealand, and the results are presented. While the examples provided in this paper involve timber shear walls, the numerical modelling method will be equally useful for a variety of structures of different material types and configuration.
Highlights
This paper provides an overview of a methodology developed by which allows for the rapid numerical modelling of a common form of non-linear relationship under seismic excitation - pinched hysteresis loops
While pinched hysteretic behaviour can be associated with braced frames, concrete shear walls, and the beam-column connection of reinforced concrete structures, it almost invariably occurs in timber structures with slender steel connectors
An example of a model nail connection is subjected to cyclic loading, with the resulting hysteresis behaviour providing an excellent representation of an experimentally obtained result
Summary
This paper provides an overview of a methodology developed by which allows for the rapid numerical modelling of a common form of non-linear relationship under seismic excitation - pinched hysteresis loops. Pinched hysteretic behaviour can be observed at the reinforced concrete beam column joints [1], reinforced concrete shear walls [2], and are the characteristic behaviour of structures with compressive members that buckle, such as structures with conventional steel bracing [2]. In timber structures, it is the interaction of the steel connectors, primarily nail connections, with wood that provides ductility (wood in itself being brittle) [3], and in the case of timber shear walls it is the sheathing to-framing-nail connections that govern the overall force-displacement behaviour.
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