Keywords: dynamics, vibration, steel structures, composite floors, human comfort, dynamic structural design, rhythmic dynamical loads, human rhythmic activities.

The ever more competitive world market trends have forced structural engineers to develop minimum weight and labour cost solutions. These structures should also be capable to incorporate an extra increase in the construction's speed, factor that substantially influences the global construction's cost. This process produced very slender structural solutions altering the ultimate and serviceability limit states that controlled their design.

A direct consequence of this new design trend is a considerable increase in problems related to unwanted floor vibrations. This phenomenon is very frequent in a wide range of structures subjected to rhythmic dynamical load actions[1,2,3]. These load actions are generally caused by human rhythmic activities such as: musical and or sporting events, dance or even gymnastics. Another examples of structures subjected to vibration problems can be found in floors used to support electrical engines and impact load actions.

The significant growth in floors subjected to unwanted vibrations is caused by the fact that the great majority of structural engineers disregards, or even do not know how to incorporate the dynamical actions in the structural analysis. This procedure limits current structural designs to a simple static analysis, fact that can, in extreme cases, compromise the structure's behaviour and reliability.

Proper consideration of all the aspects mentioned earlier pointed out to an investigation of the structural behaviour of commonly used composite floors subjected to rhythmic dynamical load actions. The main objective of this paper is to verify the use of these structural systems taking into account the possibility of occurrence of unwanted vibrations that could cause human discomfort or in extreme cases structural failure.

In order to evaluate the acceptable vibration level of a structural system a complete knowledge of the dynamical behaviour is required. Reasonable estimations of the acceptable floor vibration levels can be calculated based on empirical formulae having as main parameters: structures natural frequencies, accelerations, velocities, displacements and excitations frequencies. Although these formulae are very simple an indiscriminate use should be avoided due to their inherent applicability limitations.

First a characterisation of the structural natural frequencies are presented and discussed. This is followed by a comparison with the acting excitation frequencies. With this analysis in hand, a computational analysis focused in the evaluation of the structures dynamical response in the time domain based on the generation of time functions associated with accelerations, velocities and displacements was performed.

The computational results were obtained with the aid of a finite element linear elastic analysis trough the ANSYS program[4]. A composite floor used for gymnastics[5] was simulated to calibrate the proposed methodology. In this example the concrete slab was represented as plate finite elements while the steel beams were modelled through three dimensional beam elements.

An additional assessment was made against formulae present in major current design standards[6]. The main conclusions of this paper are related to alert structural engineers to the possible distortions in structural response generated by the misuse or even disregard of the dynamical load actions.

1

Ellis, B.R., Ji, T., "Floor Vibration Induced by Dance-Type Loads: Theory and Verification", The Structural Engineer, Vol. 72, 1994.

2

Bachmann, H., Ammann, W., "Vibrations in Structures Induced by Man and Machines", Structural Engineering Document 3e, International Association for Bridges and Structural Engineering, 1987.

3

Murray, T.M., Howard, J.N., "Serviceability: Lively Floors - North American and Britsh Design Methods", Journal of Constructional Steel Research, 46 (1- 3), Paper N0 251, 1998. doi:10.1016/S0143-974X(98)00155-2

4

ANSYS, "Swanson Analysis Systems", Inc., P.O. Box 65, Johnson Road, Houston, PA, 15342-0065, Version 5.5, Basic Analysis Procedures, Second Edition, 1998.

5

Vecci, M.A.M, Fakury R.H, Mendon�a, P.V.P., "Análise de Vibraç ões de Pisos Submetidos a Excitaç ões R�tmicas. Aplicação de Critérios para Conforto em Edificações", Encontro Nacional de Conforto no Ambiente Constru�do,Brasil, (In Portuguese), 1999.

6

Supplement to the National Building Code of Canada, Commentary on Serviceability Criteria for Deflections and Vibrations, National Research Council of Canada, Ottawa, 1995.

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