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- Numerical methods to predict human induced vibrations on low frequency stairs. Part 1: literature review, modellingPublication . Andrade, Pedro; Santos, José; Maia, LinoRecent 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.
- Numerical methods to predict human induced vibrations on low frequency stairs. Part 2: evaluation by comparing with experimental dataPublication . Andrade, Pedro; Santos, José; Escórcio, PatríciaNowadays, vibration serviceability criteria are becoming the governing factor in the design of most modern staircases, because their increasing susceptibility to human induced vibrations. Although more awareness have been raised to the dynamic design of new staircases, there are still few studies found in the literature that compare the different results of numerical methods for predicting vibrations with experimental data, in order to validate the same. Hence, this paper employs the main existing numerical methods to an actual staircase with known liveness, by comparing the predicted results with the experimental data, to evaluate their accuracy when designing flexible staircases. This paper is Part 2 of a set of two papers. In Part 1, the different numerical methods are presented and details are given of how to apply them. To accomplish this, an in-situ staircase dynamic characterisation and several walking tests are performed. The measured vibrations are initially compared with different proposed acceptable limits to confirm that the vi brations exceed the limits. The different numerical methods are then employed and the predicted results are compared with the experimental results. Lastly, the main findings of this work are discussed together with those of diverse researchers who also applied one of these procedures to estimate vibrations. The results obtained showed that, with two of the numerical procedures applied (footfall force time histories and simplified vibration evaluation), it was possible to effectively predict the vibrations, while with the remaining two (Fourier series walking models and steady-state analysis), in general, overestimated responses were predicted.