Pedestrian-induced actions on footbridges are commonly schematized, at the design stage, as a resonant sinusoid moving across the bridge with speed related to the walking frequency. In this paper, the equation of motion of a footbridge crossed by a moving sinusoidal load, representing a pedestrian, is solved by a perturbation technique, the method of multiple scales. Based on such a method, the solution is expressed as a harmonic with slow time-varying amplitude; thus, the maximum dynamic response coincides with the maximum of the amplitude. For simple beams, analytical expressions of the mode shapes are available and the maximum dynamic response can be provided in closed-form. However, the solution here proposed can also be adopted to estimate the maximum response of generic bridges knowing their modal shape, without requiring burdensome step-by-step dynamic analyses.

Vibration serviceability of footbridges: a closed-form solution

TUBINO, FEDERICA;PICCARDO, GIUSEPPE
2008-01-01

Abstract

Pedestrian-induced actions on footbridges are commonly schematized, at the design stage, as a resonant sinusoid moving across the bridge with speed related to the walking frequency. In this paper, the equation of motion of a footbridge crossed by a moving sinusoidal load, representing a pedestrian, is solved by a perturbation technique, the method of multiple scales. Based on such a method, the solution is expressed as a harmonic with slow time-varying amplitude; thus, the maximum dynamic response coincides with the maximum of the amplitude. For simple beams, analytical expressions of the mode shapes are available and the maximum dynamic response can be provided in closed-form. However, the solution here proposed can also be adopted to estimate the maximum response of generic bridges knowing their modal shape, without requiring burdensome step-by-step dynamic analyses.
2008
9789727521029
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/252108
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