Hysteretic models

Mualem Y (1976) Hysteretical models for prediction of the hydrauhc conductivity of unsaturated porous media. Water Resour Res 12 1248-1254... 

Using a model with lumped masses at two characteristic levels (top and level 1), a nonlinear dynamic analysis was performed with a complex hysteretic (IZIIS) model (Fig. 8.5, Shendova 1998). To calibrate the computations in defining the capacity degradation in hysteretic models, the results from seismic shaking table testing of the model were used. With this, an attempt was made to model the dynamic response in a simple way, suitable for everyday analyses, resulting however in satisfactory final results on the behavior at individual levels. 

Table 8.4 summarizes the knowledge gained in the form of input parameters defining the envelope points from the hysteretic model as empirical relationships between storey stif iess (K), storey height (H) and ultimate storey shear force (Q). In this way, knowing the values of K and Q, it is possible to analyse the dynamic response of an actual structure without previous experimental testing. 

A nonlinear dynamic analysis has been performed for the three monuments (Sect. 8.2.3), with the masses lumped at characteristic levels and applying a corresponding storey hysteretic model obtained by summing up the elastoplastic characteristics of each of the bearing walls, with the load-bearing capacity of each of them limited to the bending and shear capacity, whichever is less. 

The analytical investigations involved definition of the seismic response of the structure in the nonlinear range of behavior. To model the behavior of the structural system in the elastic phase, at the beginning of nonlinearity (occurrence of cracks) and deep nonlinearity, the IznS three-linear hysteretic model with stiffness degradation and pinching effect was used (Fig. 8.5). 

Dynamic analysis With the masses lumped at two characteristic levels, a nonlinear dynamic analysis has been performed with storey hysteretic model obtained by summing up the elastoplastic characteristics of each of the bearing walls, whereas the load-bearing capacity of each of them has been limited to the lower value of bending and shear capacity (according to Sect. 8.3.3). To obtain the dynamic response, three different types of earthquake (Petrovac 1979, Ulcinj 1979 and El Centro 1940) with maximum input acceleration of 0.24g and return period of 1,000 years have been applied. Obtained as the results from the dynamic analysis are the storey displacements and ductility ratios required by the earthquake that have to comply with the design criteria defined in Sect. 8.3.4. 

Fig. 19.7 Hysteretic model for axial (steel and concrete) and shear springs, (a) Steel spring, (b) Concrete spring, (c) Shear spring...

Regarding the shear springs, it is assumed that shear has no effects on the axial force and bending interaction. The hysteretic model for the shear spring is assumed to be multi-linear model, as shown in Fig. 19.7c, where Q is shear force and y the deflection of the shear wall due to shear deformation. The value of the shear force and deflection at cracking and yielding can be calculated according to the formulations proposed by the Architectural Institute of Japan. 

Balan, T.A., Filippou, EC. Sc Popov, E.P. 1998. Hysteretic model of ordinary and high-strength reinforcing steel. Journal of Structural Engineering 124(3) 288-297. 

Hurtado, J.E. Barbat, A. 2000. Equivalent linearization of the Bouc-Wen hysteretic model. 

Figure 1. Bilinear hysteretic model of the lead rubber bearings used in this study...

FEMA-695 (2009) Quantification of building seismic performance factors. FEMA, Washington, DC Genshu T, Yongfeng Z (2007) Seismic force modification factors for modified-Clough hysteretic model. Eng Struct 29(11) 3053-3070... 

Lee EH, Han SW (1999) Determination of ductility factor considering different hysteretic models. Earthq Eng Struct Dyn 28(9) 957-977... 

Most isolation devices are characterized by effective stiffness, and equivalent viscous damping For LR bearings, the effective stiffness assuming the above bilinear hysteretic model is computed as... 

The load-displacement relationship of the WPD under an arbitrary cyclic loading pattern can be predicted with a simple hysteretic model, and a procedure for predicting its failure. In this hysteretic model, the shape of the skeleton part and the shape of each segment of the Bauschinger are determined as follows. 

Seismic Collapse Assessment, Fig. 8 Basic deteriorating hysteretic models (a) bilinear, (b) peak oriented, and (c) pinching (Modified from Ibarra and Krawinkler 2005)... 

Ibarra LE, Medina RA, Krawinkler H (2005) Hysteretic models that incOTporate strength and stiffness deterioration. Earthq Eng Struct Dyn 34 1489-1511... 

With a robust and relatively efficient algorithm devised in section System Identification, a differential model of hysteresis of any degrading system may be identified from a given load-displacement trace. Suppose a hysteretic model is generated with a given load-displacement trace. It will be shown that, under fairly broad conditions, the model predicts the response of the same structure when driven by other cyclic loads. This can be carried out experimentally by building a number of identically configured structural joints... 

Each specimen of the identically configured T-connections is driven by a cyclic excitation and 1,000 s of load-displacement data are recorded. Using any of these load-displacement traces, a model of hysteretic evolution can be identified. Two issues will now be examined. (1) Can a hysteretic model identified with a given cyclic load predict the future structural response if the same cyclic load continues beyond the duration used for identification (2) Can a hysteretic model identified with a given cyclic load predict the structural response due to a different cyclic load ... 

In identifying a hysteretic model of the T-connection, the experimental load-displacement trace associated with excitation C has been used... 

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