Verificação do estado limite de vibração em uma escada com degraus em balanço submetida ao caminhar humano

Abstract

In the design of structures submitted to the action of human walking such as footbridges, floors and staircases, must be subjected to a dynamic analysis in order to verify their limit states related to the discomfort caused by excessive vibration. It is not uncommon to find cases of staircases with problems of vibration, those that have cantilever steps are among the most sensitive to vibration due to the structural scheme of their steps. The current design standards do not provide criteria for checking excessive vibrations specifically for staircases. Some authors suggest limits for maximum accelerations and natural frequencies. In this work a review was done on the criteria for the limit of vibrations and a numerical modeling to exemplify the application of such criteria in a self-supporting staircase with cantilever steps. Two models were tested, both has the support beam with rectangular section made of reinforced concrete, one has metallic steps composed of sections made of cold-formed steel in a u-stiffened profile and another with rectangular steps made of reinforced concrete. A finite element computational model was assembled in the software SAP 2000 version 21 Evaluation. The determination of the static loads acting on the staircase and the dimensioning were done according to the Brazilian standards. The dynamic load used for human walking was the obtained in Meinhardt et al. (2014). In the staircase with metallic steps the acceleration values exceeded the limit values present in the bibliography, whereas in the staircases with concrete steps the acceleration was smaller than the limits for the comfort of the user.