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- Vibrações induzidas por peões em escadas metálicasPublication . Andrade, Pedro; Santos, José; Escórcio, Patrícia
- Direct integration methods versus modal superposition method, on predicting staircases vibrationsPublication . Andrade, Pedro; Santos, José; Escórcio, PatríciaThe majority of Finite Element software’s present two different solutions methods to perform time history analysis of the equations of motion due to dynamic (time-varying) loads: Direct Integration and Modal Superposition. This paper aims to assess which method should be employed in the design of modern flexible staircases, to more efficiently predict human induced vibrations. This was verified by estimating vibrations on a real staircase using the two time domain analysis methods and, then, comparing with vibrations experimentally measured. The results indicate that Direct Integration could yield to overestimated responses due to the limited capacity, as the vibration modes increase, of FE numerical models to realistic predict natural frequencies and modal shapes of a real structure. Therefore, Modal Superposition is suggested to be used for design routines, excluding, for the same reason, the vibration modes with higher frequency content. © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo Keywords: Modal Superposition; Direct Integration; Duhamel Integral; Human Walking Vibrations; Flexible Staircases. * Corresponding author. Tel.: +351 291 705 197. E-mail address: jmmns@fe.up.pt Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2019) 000–000 www.elsevier.com/locate/procedia 2452-3216 © 2020 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the European Structural Integrity Society (ESIS) ExCo 1st Virtual European Conference on Fracture Direct Integration Methods versus Modal Superposition Method, on Predicting Staircases Vibrations Pedro Andradea , José Santosb,c,*, Patrícia Escórciob a University of Madeira, 9020-105 Funchal, Portugal b University of Madeira, Faculty of Exact Sciences and Engineering, Department of Civil Engineering and Geology, 9020-105 Funchal, Portugal c CONSTRUCT-LABEST, Faculty of Engineering (FEUP), University of Porto, Portugal Abstract The majority of Finite Element software’s present two different solutions methods to perform time history analysis of the equations of motion due to dynamic (time-varying) loads: Direct Integration and Modal Superposition. This paper aims to assess which method should be employed in the design of modern flexible staircases, to more efficiently predict human induced vibrations. This was verified by estimating vibrations on a real staircase using the two time domain analysis methods and, then, comparing with vibrations experimentally measured. The results indicate that Direct Integration could yield to overestimated responses due to the limited capacity, as the vibration modes increase, of FE numerical models to realistic predict natural frequencies and modal shapes of a real structure. Therefore, Modal Superposition is suggested to be used for design routines, excluding, for the same reason, the vibration modes with higher frequency content.
- Application of the effective impulse approach to stairsPublication . Andrade, Pedro; Santos, José; Escórcio, PatríciaOne of the most commonly used simplified methods for predicting man induced vibrations in floors with high fundamental frequencies is the Effective Impulsive approach, first developed by the ARUP's company and later modified by the design guide SCI P354. Since the Effective Impulse approach was designed to be used in floors, its use in stairs can be arguable. To better understand the effectiveness of this method in stairs, in this paper are experimentally measured vibrations on a staircase with a poor dynamic behavior and then compared to the vibrations predicted using the Effective Impulse approach. The results indicate that this approach can be used, especially in the stair descends. The serviceability of the analyzed staircase was also verified by comparing the measured and predicted vibrations with the acceptable limits proposed by various authors and design guides.
- Pre-design of laterally supported stair stepsPublication . Santos, José; Andrade, Pedro; Escórcio, PatríciaIt is becoming increasingly common to design monumental staircases and their steps with elevated stiffness and low mass, obtaining high natural frequencies, off the range of frequencies that are excitable by pedestrians. However, this sometimes leads to unacceptable levels of vibration, with impulsive responses. In many cases the dynamic behaviour of steps is almost independent from the rest of the staircase, causing a phenomenon de signated as local vibrations, which could be much more severe than the global vibrations of the staircase. In order to avoid this problem, this paper presents a simplified expression to pre-design stair steps which guarantee that excessive vibrations will not occur, without the need to perform a dynamic analysis. The ex pression was deduced based on the results of an experimental campaign, several numerical analyses and a theoretical analysis. During this study it was necessary to define an acceptable limit of vibrations specific for this type of vibration, which affects mainly the feet of pedestrians. The expression deduced is easy to apply because it depends only of vertical stiffness of the step. Finally, the pre-design expression is also applied to the staircase used in the experimental campaign, and it was concluded that it would be easy to avoid excessive vibrations, with a negligible cost increase.
- 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.
- Improvement of staircases vibration serviceability to human ergonomics: a case studyPublication . Andrade, Pedro; Santos, José; Maia, LinoContemporary, slender and lightweight monumental staircases are often highly susceptible to resonance phenomena, due to typically low fundamental frequencies, which can considerably amplify their responses, raising major serviceability problems and causing discomfort and unsafety concerns to its users. This paper presents a case study of a low fundamental frequency steel staircase with known high levels of vibration since the beginning of its construction, in which various improvement solutions were proposed in order to increase its vibration serviceability. In total, six improvement measures were proposed, being tested using the Finite Element (FE) software SAP2000. The initial FE staircase model was first calibrated with the vibrations experimentally measured on the real staircase. Then, the original FE model was modified with the six improvement measures and the resulting vibrations were compared with those initially obtained and the acceptable limits suggested by the design guide SCI P354, to verify their viability. The most efficient numerical improvements were those that increased the staircase fundamental frequency, off the range of frequencies excitable by pedestrians walking.
- 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.
- Reinforcement measures to reduce the human induced vibrations on stair steps: a case studyPublication . Andrade, Pedro; Santos, José; Maia, LinoThe human induced vibrations seen on stairs are usually a global phenomenon, however in some cases, if the connection between the treads and the rest of the structure has a very low rotational stiffness, a so-called local vibration phenomenon can happen, i.e. the vibrations in the treads may be independent from those verified on the staircase that it supports them. This paper presents a case study of a particular metal staircase in which the local vibrations were high. The objective of this study was to measure the vibrations experimentally and then to propose several reinforcement measures in order to reduce them. A total of eight reinforcement measures were proposed, being tested through the construction of several numerical models using the software SAP2000. The numerical accelerations obtained with each reinforcement measure were compared with those obtained initially and with the design guide SCI P354 to verify their effectiveness. The most effective reinforcement measures were those that significantly increased the stiffness of the treads.