Abstract Summary
Vibration serviceability of floors due to walking loads has become an important design criterion as a result of advancements in construction technology that lead to more slender and lightweight building floors. Current design guidelines require the assessment of the vibration performance of floors based on a single walking pedestrian, modelled as a fixed load, expressed as the summation of deterministic harmonic components. However, the effect of the walking path on the dynamic response of floors has not received any attention in the guidelines that generally consider the walking force as a stationary load applied to the antinodes of the floor mode shapes. Furthermore, due to the stochastic nature of the pedestrian walking force, the deterministic approaches adopted by the current guidelines can give unreliable vibration response estimation. The present paper aims to investigate the dynamic response of simply supported rectangular floors under a single walking pedestrian. At first, a deterministic loading model is assumed; then a probabilistic approach is adopted taking into account the stochastic nature of pedestrian walking force. From the deterministic standpoint, the present study reports an exact closed-form solution to calculate the dynamic response of floors subjected to a pedestrian walking load modelled as a summation of harmonic loads moving along a generic walking path. The critical walking paths which can provide the maximum dynamic response are derived and expressed analytically as a function of floor dimension and mode shape. Then, an approximated closed-form solution is proposed to calculate the vibration response of floors due to a moving resonant harmonic load along the critical walking paths. Results showed that considering the worst-case loading scenario as a design criterion could be conservative due to the fact that there is a low probability that pedestrians walk along the critical walking paths at the perfect resonant condition. Thus, it is essential to consider a probability-based vibration analysis to assess the vibration serviceability of floors. The probabilistic approach takes into account the randomness of several parameters such as step frequency, pedestrian velocity, dynamic force amplitude, pedestrian weight, and walking path. Monte Carlo simulations are carried out for floors with different geometric and dynamic characteristics to provide simplified procedures which allow the probabilistic prediction of the vibration response of floors. According to the numerical results, the present study introduces cumulative probability functions that allow estimating the probability that the maximum acceleration is higher than a certain percentage of the peak acceleration corresponding to the worst-case loading scenario, obtained through the approximated closed-form solution.
