By M.R. Willford, P. Young

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1 above. 19. 07mm/sec respectively. 9. 9 Predicted response at middle of bay using modal properties derived by FE analysis. 19 Response in each mode to a single footfall Response in Each Mode to a Single Footfall Predicted response in each mode using modal properties derived by FE analysis. 20 Total response to a single footfall Predicted total velocity using modal properties derived by FE analysis. 15 Time (secs) As the FE model contains the full spatial distribution of mode shapes, it is possible to perform the response calculation for every node on the floor model.

The modal mass of each mode derived by the rectangular plate calculation is one quarter of the total mass. 55. 16 First four mode shapes of the floor. A finite element model of the floor was constructed including the back span and the columns. 16. It can be seen that the natural frequencies from the FE analysis are slightly higher than from the rectangular plate calculation. This is due to the influence of the back span and the inclusion of the columns in the analysis. The measured frequency of the first mode is slightly higher than that predicted by the FE analysis.

2. 12) 3. 13: N ∑v (t) v(t) = where v(t) is the total velocity at time t and N is the number of modes. 14) 4. 7. e. T is smaller), which increases the overall RMS response. The relationship between vRMS and footfall rate is therefore not quite linear, having an exponent slightly greater than 1. To calculate the maximum possible response, it is only necessary to calculate the response at the fastest walking speed. 7 Graph of impulsive response versus footfall rate. 4 Simplified and approximate methods for floors Whilst the detailed methods of the previous sections enable responses to be predicted for any structure, simplified methods are included below for certain regular rectangular floor bays of uniform properties which can be approximated reasonably well as simply supported plates having equal or different stiffnesses in the two orthogonal directions.

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A Design Guide for Footfall Induced Vibration of Structures by M.R. Willford, P. Young
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