Abstract
It has been observed in many previous earthquakes that impact often occurs between the main girders in curved bridges. An earthquake can result in deck-unseating leading to catastrophic destruction of the structure. In this paper, the nonsmooth multirigid body dynamics method and the set-valued formulation were used to model and analyze the mechanism of impact between the curved bridge segments. The analysis demonstrated that these impacts are the major cause of segment rotation. The main contribution of this paper is to use Newton’s impact law and Coulomb’s friction law to describe the interaction between the curved bridge segments in the form of a set-valued function and to express impacts with friction as a linear complementary problem. For frictionless and frictional contact, the paper considers the single-point and multipoint impacts using the linear complementary formula to detect the unique actual slip-stick conditions of these states. A variety of criteria for distinguishing each case are presented and the results provide the kinetic characteristics of each contact case. The analysis has shown that the impact between the segments of a curved bridge and the tendency of the segments to rotate (and thus detach) are related to the overall geometry, the coefficient of restitution, the coefficient of friction, and the preimpact conditions in the plane of motion. Finally, a theoretical relationship diagram of the impact, rotation slip, and stick condition of the curved bridge segments at the contact point is given. The presented results will be useful for the seismic design of curved bridges.
Highlights
Impact occurs when two or more bodies contact for a brief time, which is mainly determined by the material characteristics, geometry, and preimpact conditions of the bodies
By solving the linear complementarity problem (LCP) equation, the normal and transverse stickslip contact cases of curved bridge segments are studied for different preimpact conditions. e overall geometry influences significantly the postimpact deck responses, which again depended on the preimpact conditions. is complex phenomenon is analytically studied for a single-impact case during deck-to-deck pounding between two curved bridge segments
Linear Complementarity Problem. e LCP method can encapsulate many of the physical phenomena occurring during bridge segment impacts in a curved bridge
Summary
Impact occurs when two or more bodies contact for a brief time, which is mainly determined by the material characteristics, geometry, and preimpact conditions of the bodies. Using the Karnopp friction model, Amjadian and Agrawal [11] investigated the influence of pounding on rigid-body motion of horizontally curved bridges during strong earthquakes. Ere are many impact simulation methods [4, 15], such as the restitution coefficient method, the stereo-mechanical approach, the compliance method, and the linear complementarity problem (LCP) method. Is paper studies in detail the impact on curved bridges based on their method In this formalism, the deck is assumed to be a rigid body. By solving the LCP equation, the normal and transverse stickslip contact cases of curved bridge segments are studied for different preimpact conditions. Based on a previous investigation [12] on the impact between the abutment and the deck of a curved bridge, this paper studies the problem of impact between bridge segments of a curved bridge. The classification boundary of slip and stick after two adjacent bridge segments make contact is established from a kinematic consideration
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