Numerical methods to predict vibration serviceability on high frequency stairs

Abstract

With the increasingly deepen knowledge on structural dynamic behaviour, nowadays, monumental staircases and their steps are usually designed with high stiffness and low mass, obtaining high fundamental frequencies, out of the interval of step frequencies excitable by the human walking. However, neglecting the structure’s mass can also result in with high levels of impulsive responses. Furthermore, often the connection between the staircase and its steps experience an almost null rotational stiffness, which can cause local vibrations in steps, where the structural behaviour of two elements is nearly independent from each other. In this scenario, steps will most likely exhibit undesirable vibrations. Hence, intending to improve future designs, this paper compares different numerical methods that can be used to predict human induced vibrations in this type of structures, applying them to a real staircase with a high local liveness. The results showed that the footfall force time histories method could realistically predict the vibrations for almost all tested step frequencies, while the effective impulse could accurately estimate the vibrations for descents at different step frequencies. The walking models defined by Fourier coefficients only generated close vibrations for descents at 3.3 Hz.