Impact Response of Simply-Supported Beams

The most fundamental problem that should be considered in thestudy of vehicle-induced vibrations on bridges is the dynamic responseof a simply-supported beam subjected to a single movingload. This problem is important in that the solution can be given inclosed form. In this chapter, impact formulas will be derived for thedeflection, bending moment and shear force of a simple beam undera single moving load. By the principle of superposition, the solutionobtained for a single moving load will be expanded to deal with a seriesof identical, equi-distant moving loads, by which the key parametersdominating the dynamic response of the beamcanbeidentified.Furthermore, based on the conditions of resonance or cancellationfor the waves generated by a series of moving loads, optimal designcriteria for suppressing the resonant response of beam structures willbe presented. In designing a high-speed railway bridge, such criteriaare useful for the selection of the span length and cross section of agirder bridge, if the car length, axle distance and operating speed ofthe train are already decided.