Structural systems often show nonlinear behavior under severe excitations generated by natural hazards. In that condition, the restoring force becomes highly nonlinear showing significant hysteresis. The hereditary nature of this nonlinear restoring force indicates that the force cannot be described as a function of the instantaneous displacement and velocity. Accordingly, many hysteretic restoring force models were developed to include the time dependent nature using a set of differential equations. This survey contains a review of the past, recent developments and implementations of the Bouc-Wen model which is used extensively in modeling the hysteresis phenomenon in the dynamically excited nonlinear structures.

The Hysteresis Bouc-Wen Model, a Survey

Optimum lead–rubber isolation bearings for near-fault motions

The response of bridges seismically isolated by lead-rubber bearings (L-RB) to bidirectional earthquake excitation (i.e., 2 horizontal components) is presented. The force-deformation behavior of L-RB is considered as bilinear, and the interaction between the restoring forces in 2 orthogonal horizontal directions is duly considered in the response analysis. The specific purpose of the study is to assess the effects of seismic isolation on the peak response of the bridges, and to investigate the effects of the bidirectional interaction of restoring forces of isolation bearings. The seismic response of the lumped mass model of continuous span isolated bridges is obtained by solving the governing equations of motion in the incremental form using an iterative step-by-step method. To study the effectiveness of L-RB, the seismic response of isolated bridges is compared with the response of corresponding nonisolated bridges (i.e., bridges without isolation devices). A comparison of the response of the isolated bridges obtained by considering and ignoring the bidirectional interaction of bearing forces is made under important parametric variation. The important parameters included are the flexibility of bridge piers and the stiffness and yield strength of the L-RB. Results show the bidirectional interaction of the restoring forces of the L-RB has considerable effects on the seismic response of isolated bridges. If these interaction effects are ignored, then the peak bearing displacements are underestimated which can be crucial from a design point of view.

Seismic response of isolated bridges

Seismic performance of highway bridges

An innovative isolation device for aseismic design

Dynamic tests on two lead-rubber bearings, 280 x 230 x 113 mm, are described in which a dynamic actuator was used to apply shear displacements of ±10 to ±140 mm at frequencies of 0.1 to 3 Hz, giving shear strains in the rubber of up to ±200%. The weight of the structure on the bearing was applied by a vertical jacking system and ranged from 35 to 455 kN. Sequences of cycles were performed to simulate earthquake conditions and force-displacement hysteresis loops were obtained.
It was concluded that at strains approaching 200% in the rubber, the force-displacement hysteresis loop could be represented by the linear elastic slope of the rubber component plus a rectangle appropriate to the plastic shear of the lead, with some rounding of the corners of the hysteresis loop. There was a decrease in the area of the hysteresis loop of 20% after six cycles at 1 Hz with a maximum shear strain of 125% in the rubber; but recovery followed within minutes. In one bearing an attempt was made to locally confine the lead by screwing external plates to the first internal plate within the bearing at the top and the bottom, but no difference in performance between the two bearings was noted. The scope of the tests indicated that, with peak strains in excess of 100% in the rubber, the bearings would continue to perform satisfactorily for a sequence of very large earthquakes.

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W. H. Robinson

Papers

High-strain tests on lead-rubber bearings for earthquake loadings