Universal response spectrum procedure for predicting walking-induced floor vibration

Floor vibrations caused by people walking are an important serviceability problem both for human occupants and vibration-sensitive equipment. Present design methodologies available for prediction of vibration response due to footfall loading are complex and suffer from division between low and high frequency floors. In order to simplify the design process and to avoid the problem of floor classification, this paper presents a methodology for predicting vibration response metrics due to pedestrian footfalls for any floor type having natural frequency in the range 1–20 Hz. Using a response spectrum approach, a database of 852 weight-normalised vertical ground reaction force (GRF) time histories recorded for more than 60 individuals walking on an instrumented treadmill was used to calculate response metrics. Chosen metrics were peak values of 1 s peak root-mean-square (RMS) acceleration and peak envelope one-third octave velocities. These were evaluated by weight-normalising the GRFs and applying to unit-mass single degree of freedom oscillators having natural frequencies in the range 1–20 Hz and damping ratios in the range 0.5–5%. Moreover, to account for effect of mode shape and duration of crossing (i.e. duration of dynamic loading), the recorded GRFs were applied for three most typical mode shapes and floor spans from 5 m to 40 m. The resulting peak values as functions of frequency i.e. spectra are condensed to statistical representations for chosen probability of being exceeded over a wide range of applications. RMS (acceleration) spectra show strong peaks corresponding to the first harmonic of pacing rate followed by clear minima at approximately 3.5 Hz, a second much smaller peak corresponding to the second harmonic and a steady decline with increasing frequency beginning around 5 Hz. One-third octave spectra show asymptotic trends with frequency, span and damping. A comprehensive validation exercise focusing on the acceleration RMS spectra was based on a representative range of floor samples for which modal properties had been identified and walking response studied during experimental campaigns of vibration serviceability evaluation. Due to the statistical approach an exact validation would not be possible, hence measured peak RMS values were matched to distributions for the equivalent idealised structure. In the vast majority of cases the measured values, intended to represent worst-case conditions, fitted the upper decile of the corresponding simulated spectra indicating consistency with the proposed approach.