Evaluation of the dynamic behaviour of steel staircases damped by the presence of people

People acting on a slender structure can affect the dynamic behaviour of the structure they occupy, in addition to being a source of forcing. In such cases, the use of the dynamic properties of the empty structure to estimate the structural response can lead to an erroneous estimation of the amplitudes of vibration. This work proposes an approach to improve the prediction of the structural response due to the presence of people. The method is based on the identification of an equivalent set of frequency response functions to represent the dynamic behaviour of the joint structure-moving people system. The method starts from the modal model of the empty structure, i.e., natural frequencies, damping ratios and mode shapes. No restriction on the number of degrees of freedom of the structure is required. Each subject is modelled through an equivalent apparent mass and is introduced on the model of the empty structure to obtain a model of the joint structure-moving people system. An active force is then applied to the equivalent model to obtain a prediction of vibration levels. The effectiveness of the approach was verified through experimental tests performed in controlled conditions. Two lightly damped steel staircases were used as test cases. A comparison between the amplitudes of the measured vibration and those predicted using the proposed methodology is presented. The results show that the use of the empty structure model can lead to a high overestimation of the vibration amplitudes. Conversely, the results obtained with the proposed approach are in agreement with the experimental data.