Analysis of a frictional oblique impact observed in skew bridges

The oblique contact/impact of skew bridges triggers a unique rotational mechanism which earthquake reconnaissance reports correlate with deck unseating of such bridges. Building on the work of other researchers, the present study adopts a fully non-smooth rigid body approach and set-valued force laws, in order to analyze in depth this oblique multi-impact phenomenon. A linear complementarity formulation is proposed which yields a great variety of (multi-) impact states, depending on the initial (pre-impact) conditions, such as “slip” or “stick” at one corner (single-impact) or two corners (double-impact) of the body. The pertinent existential conditions of those impact states reveal a complex dynamic behavior. With respect to the rotational mechanism associated with double-impact, the physically feasible impact states as well as, counter-intuitive exceptions are recognized. The study proves that double oblique impact, both frictionless and frictional, may or may not produce rotation of the body and proposes criteria that distinguish each case. Most importantly, it is shown that the tendency of skew bridges to rotate (and hence unseat) after deck-abutment collisions is not a factor of the skew angle alone, but rather of the overall geometry in-plan, plus the impact parameters (coefficient of restitution and coefficient of friction). The study also provides a theoretical justification of the observed tendency of skew bridges to jam at the obtuse corner and rotate in such a way that the skew angle increases. Finally, counter-intuitive trends hidden in the response are unveiled which indicate that, due to friction, a skew bridge may also rotate so that the skew angle decreases.