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

By M.R. Willford, P. Young

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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.

P. , Theory of Plates and Shells, 2nd edition, McGraw-Hill International Book Company, 1981. 13 ROARK, T. J. & YOUNG, W. , Formulae for Stress and Strain, 5th edition, McGraw-Hill Kogakusha, 1975. 14 2003 ASHRAE Handbook – HVAC Applications : Chapter 47 Sound and Vibration Control. Publisher ASHRAE. 15 EWINS, D. , Modal Testing, 2nd edition, Research Studies Press Ltd, 2000. 61 Footfall Induced Vibration of St61 61 06/12/2006 16:30:38 Glossary Damping Damping is a general term used to describe the dissipation of energy in a vibrating system.

13 ROARK, T. J. & YOUNG, W. , Formulae for Stress and Strain, 5th edition, McGraw-Hill Kogakusha, 1975. 14 2003 ASHRAE Handbook – HVAC Applications : Chapter 47 Sound and Vibration Control. Publisher ASHRAE. 15 EWINS, D. , Modal Testing, 2nd edition, Research Studies Press Ltd, 2000. 61 Footfall Induced Vibration of St61 61 06/12/2006 16:30:38 Glossary Damping Damping is a general term used to describe the dissipation of energy in a vibrating system. It is described in section 4 of Appendix A. In this guide damping is quantified numerically as the fraction of critical damping, ζ.