A vehicle, of weight (F_{0}), moving at a constant speed on a bridge (Fig. 8.43(a)) can be

Question:

A vehicle, of weight \(F_{0}\), moving at a constant speed on a bridge (Fig. 8.43(a)) can be modeled as a concentrated load traveling on a simply supported beam as shown in Fig. 8.43(b). The concentrated load \(F_{0}\) can be considered as a uniformly distributed load over an infinitesimal length \(2 \Delta\) and can be expressed as a sum of sine terms using Fourier sine series expansion (of the distributed load). Find the transverse displacement of the bridge as a sum of the responses due to each of the moving harmonic load components. Assume the initial conditions of the bridge as \(w(x, 0)=\partial w / \partial t(x, 0)=0\).

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