| Abstract: | In this report, three different models in increasing order of complexity have been used to identify the seismic behaviour of a three-storey steel structure subjected to arbitrary forcing functions, all of which excite responses within the elastic range. All of the models are constructed using system identification. In the first model, five parameters have been used to identify the frame. Treating the system as a shear building, we assign one stiffness coefficient to each floor and introduce Rayleigh-type damping with two additional parameters. The mass, assumed to be concentrated at a floor level, is kept constant throughout the study. The parameters are established using a modified Gauss-Newton algorithm. The match between measured and predicted quantities is satisfactory when these quantities are restricted to floor accelerations or displacements. To remove the constraint imposed by assuming that the frame deforms as a shear building, a second model with eight parameters is introduced, allowing rotations of the joints as independent degrees of freedom. Six of the eight parameters are related to the stiffness characteristics of the structural members while the remaining two are related to damping as before. In constructing the eight-parameter model, we learned that it is the effective lengths of the members that change during optimization. We also found that the independent response quantities, floor accelerations and joint rotations, must be used in the cost function for the optimization algorithm to converge. The match between measured and predicted quantities for the eight-parameter model is excellent. The set of parameters derived from the minimum squared error gives a model that shows very good correlation using information on the full duration of the pulse or only a portion of it. Also the same correlation exists between the coefficients obtained from different excitations. In an effort to explain the values of the parameters associated with the girders, an additional degree of freedom, namely, the pitching motion of the shaking table, is introduced as an additional degree of freedom. The paper presents, therefore, a five-, an eight- and, finally, a nine-parameter model. |
