2141 Modeling Guidelines

The development of analytical models must account for all possible aspects of behavior while still working within the limitations of the analytical tools being used to carry out the evaluation of seismic demands. Both commercial and noncommercial software is available to assist engineers in estimating seismic demands, and the modeling requirements vary from one tool to the next. Most programs employ simple hinge-based inelastic models with multilinear characterization of force-deformation behavior. In general, it is necessary to model three commonly recognized aspects of cyclic behavior: stiffness degradation, strength deterioration, and pinching response. Hysteretic models that incorporate some or all of these behavioral aspects have been proposed by numerous researchers (Kunnath et al. 1997; Sivaselan and Reinhorn 2000). There is also a large body of work on degrading force-deformation models developed by Japanese researchers, many of which are summarized in a report by Umemura and Takizawa (1982).

A general hysteretic model that incorporates all three elements is shown in Figure 21.5. This basic model, which is implemented in the inelastic damage analysis of RC structures (IDARC) (Kunnath et al. 1992; Kunnath 2004) series of programs, uses several control parameters to establish the rules under which inelastic loading reversals take place. A variety of hysteretic properties can be achieved through the combination of a nonsymmetric trilinear curve and certain control parameters that characterize the shape of the force-deformation loops. For example, a, which can be expressed as a function of the deformation, controls the amount of stiffness loss; f and w control the initiation and degree of pinching respectively; and the slope s and the change in expected peak strength (M to M*) control the softening due to system deterioration. A sample simulation of observed behavior using this model is shown in Figure 21.6. The hysteresis curves in this case were obtained from tests of a precast concrete connection with a hybrid combination of mild steel and posttensioning steel (Cheok et al. 1998). However, the specification of hysteretic rules in an actual analysis is rather empirical and should be based on available experimental data. Even so, a parametric study to evaluate the sensitivity ofthese parameters is necessary.

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