Keywords: spectral method, rhythmic crowd loads, floor vibration.

This paper provides a spectral method for evaluating floor vibration generated by rhythmic crowd movements where jumping is involved. The method combines a theoretical method developed earlier and the harmonic analysis of a convenient finite element package. This provides a global picture of the floor vibration and effectively speeds up the prediction and assessment. The method is developed from the spectral response of a floor for a harmonic load to that for several harmonic loads (rhythmic crowd loads) at a selected point and then to the peak responses at all points of the floor. This method does not explicitly require the use of the modal load and modal mass (or modal stiffness) and the consideration of combining the responses from several modes of vibration. The method provides other advantages that the concerned modes of vibration and the critical load frequencies can be quickly appreciated and that the maximum response at any location of a floor can be identified as well as the vibration transmission between floor panels. Two practical examples are given to demonstrate the formation and application of the method.

The spectral method is proposed to fulfil practical design requirements and is inspired by the spectral method used in earthquake resistant design. In earthquake engineering, spectra are obtained based on a single degree-of-freedom (SDOF) model while the ground input to the model is complete, i.e. real earthquake records. This requires a combination of the responses from several SDOF models and the square root of the sum of squares method is used. In this paper, spectra are obtained based on a real floor model where the vibration of all related modes are included, while the load input is incomplete, i.e. a single harmonic load. This requires a combination of the responses from several harmonic components. The method in Reference [1] can be used where the phase lags between the load components are considered. The method uses ANSYS and the spectral values of all points on a floor can be quickly established to produce contours for the maximum displacements and acceleration of the floor.

1

B.R. Ellis, T. Ji, "The Response of Structures to Dynamic Crowd Loads", BRE Digest 426, Building Research Establishment Ltd, 2004.

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