Reliability Analysis of Floors for Vibration Performance

In this paper, the vibration serviceability of a two-bay composite floor under walking excitation was evaluated via both deterministic and stochastic methods. The floor framing was irregular with one bay being about 25 % longer than the other. Using the deterministic approach recommended by a widely recognized design guide, it was predicted that the vibration levels in both floor bays due to footfall were deemed acceptable in terms of human comfort in an office environment. The stochastic approach took account of random variations in the floor modal properties, the loading and the tolerance vibration limit. Statistical properties of the random variables were determined by reference to contemporary floor vibration guidelines as well as a modal analysis of the finite element model of the floor. Close-formed formulas for use with the first-order reliability method were developed to predict the failure probability of the floor. Reliability analysis using Monte Carlo simulation with a sufficiently large number of trials was also performed. Both of the analytical and numerical reliability analyses revealed an exceedance probability of around 36 % for the longer floor bay, which was in marked contrast to the deterministic method. For the shorter floor bay, a failure probability of practically zero was found by the random procedures. Furthermore, the excellent agreement between the results acquired from the first-order reliability method and the Monte Carlo simulation highlights the effectiveness of the former approach which requires much less computation effort.