Numerical methods to predict human induced vibrations on low frequency stairs. Part 1: literature review, modelling

Recent trends towards slender construction with prominent and exigent architectural requirements often result in low frequency staircases that are significantly flexible and susceptible to unacceptable vibrations, which may promote safety concerns for their users. For structural engineers, however, there is still a lack of understanding, available information and specific design guides for predicting the dynamic behaviour of staircases due to human induced vibrations. To address this problem, this work reviews and applies the main existing numerical methods for predicting vibrations, to evaluate their precision and provide practical guidance when designing flexible staircases. The work developed is presented in a two-part paper. In Part 1, the actual paper, several numerical methods are introduced and a detailed description is given of how these can be employed in a design stage. The distinction between low and high frequency staircases is explained, since it directly influences the structure’s behaviour and, subsequently, the selected method. A description is given of how to simulate walking dynamic loads, which forms the basis of all methods. The group effect is also discussed because it tends to considerably amplify the staircase response. Finally, the different numerical procedures are applied to a practical case and compared. It was observed that, although the four numerical methods were employed with the same staircase, their results were different. The reasons for the higher results of Fourier series walking models are explained. In Part 2, the follow-up paper, the numerical methods are employed on a real staircase, comparing the estimated and experimental results.