A Study on the Mechanism of Impact between Curved Bridge Segments Using Nonsmooth Dynamics

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.

Energy Losses of Impacts With Friction

Many machine and mechanism processes are accompanied by impacts with friction. They arise by short-time contacts between two or more bodies, and they generate energy losses mainly due to friction in tangential contact directions. During the last two decades a couple of impact models based on the theory of rigid body contact were established connected with the names of Moreau, Fremond and Glocker, which all work quite satifactorily with respect to practical applications, although some examples indicate deviations requiring more investigations with respect to the impact models and the type of examples considered. We shall focus on Glocker’s model, for which some experimental verifications are available by Beitelschmidt. A missing link are energy considerations, which are available, but nevertheless do not provide us with a complete information for all possible cases. The paper tries to fill a bit this gap by founding the investigations on a combined phenomenological and theoretical basis.