Vol. 3, No. 7, 2008

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ISSN: 1559-3959
Analysis of the run-in effect in fiber-reinforced isolators under vertical load

James M. Kelly

Vol. 3 (2008), No. 7, 1383–1401
Abstract

Previous work on experimental and theoretical studies on fiber-reinforced bearings has shown the feasibility of using them as lightweight low-cost elastomeric isolators for application to housing, schools and other public buildings in highly seismic areas of the developing world. The theoretical analysis covered the mechanical characteristics of these bearings where the reinforcing elements, normally steel plates, are replaced by fiber reinforcement. The fiber in the fiber-reinforced isolator, in contrast to the steel in the conventional isolator (which is assumed to be rigid both in extension and flexure), is assumed to be flexible in extension, but completely without flexural rigidity. This leads to an extension of the theoretical analysis on which the design of steel-reinforced isolators is based that accommodates the stretching of the fiber-reinforcement. Several examples of isolators in the form of long strips were tested at the Earthquake Engineering Research Center Laboratory.

The theoretical analysis suggests, and the test results confirmed, that it is possible to produce a fiber-reinforced strip isolator that matches the behavior of a steel-reinforced isolator. The fiber-reinforced isolator is significantly lighter and can be made by a much less labor-intensive manufacturing process. The advantage of the strip isolator is that it can be easily used in buildings with masonry walls.

The main difference between the behavior of a fiber-reinforced and a steel-reinforced bearing is the degree of run-in under vertical loading. In this context we mean by run-in that a certain amount of vertical load must be applied to the bearing before its vertical stiffness can be developed.

The most likely source of the run-in is that the fibers are initially not straight and as they have no bending stiffness, the vertical stiffness cannot be developed until they have been straightened by the action of the applied vertical load. Straightening the fibers requires them to push against the surrounding rubber. This causes an increasing force in the fiber, and as it is straightening, there will be a transition to the stretching of the fiber and to the consequent stiffness of the composite system. These bearings can be used in a wide range of applications in addition to seismic protection of buildings including bridge bearings and vibration isolation bearings, so there is a need to be able to predict how much vertical load or vertical displacement is needed before the full vertical stiffness can be achieved. In this paper a theoretical analysis of the effect has been developed in an attempt to formulate a prediction for the transition from the initially bent to the finally straight fiber.

The method takes the already formulated analysis for the straight fiber and modifies it by treating the fiber as a curved string on an elastic foundation, adds to this an estimate of the subgrade reaction of this foundation, and, using the basic equations of the fiber-rubber composite, calculates the effective compression modulus as a function of the vertical compression strain or pressure.

Keywords
seismic isolation, fiber-reinforced isolators, elastomeric bearings, bearing mechanics
Milestones
Received: 22 April 2008
Accepted: 23 July 2008
Published: 1 September 2008
Authors
James M. Kelly
University of California at Berkeley
Pacific Earthquake Engineering Research Center
1301 South 46th St., Bldg. 451
Richmond, CA 94804
United States