16 Vibration Testing and Analysis of A Monumental Stair 167 Fig. 16.6 Measured and analytical first mode shapes of the structure. (a) Measured, (b) analytical Fig. 16.7 Comparison of the measured and analytical FRFs 16.7 Comparison of the Analytical and Measured Responses To check the level of accuracy of the analytical model to predict the structural response of the stair, the SAP2000 model was subjected to the same dynamic excitation during the modal testing and the responses were compared. To achieve this, a steady-state analysis of the structure was conducted by applying a harmonic excitation with a unit amplitude at the corner of the landing. The excitation frequency was varied in order to compute the frequency response functions (FRF) of any desired point on the stair structure. The measured first mode damping ratio was used to compute the responses of the analytical model. Figure 16.7 compares the largest measured and computed FRFs in the landing area. As can be noted, the responses are different by about 23 %, which can be considered within the acceptable range. It has to be noted that further refinement of the analytical model, in particular inclusion of the folded geometry of the stair, may result in improvements in the estimation of the dynamic properties of the structure and accuracy in prediction of its response subjected to dynamic loads (such as people’s footfalls).
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