The Earthquake Engineering Online Archive

Investigation of the elastic characteristics of a three story steel frame using system identification

Kaya, Izak; McNiven, Hugh D.

UCB/EERC-78/24, Earthquake Engineering Research Center, University of California, Berkeley, 1978, 116 pages (555.3/K3/1978)

In this report, three different models in increasing order of complexity are used to identify the seismic behavior of a three-story steel frame subjected to arbitrary forcing functions, all of which excite responses within the elastic range. In the first model, five parameters have been used to identify the frame. Treating the system as a shear building, one stiffness coefficient is assigned to each floor and Rayleigh-type damping is introduced 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 acceleration or displacement. 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. An integral squared error function is used to evaluate the discrepancy between the response of the model and the structure when both are subjected to the same excitation. Different quantities, such as displacements, accelerations, rotations, etc., are used in different combinations to form the error function in an effort to determine the best set of measurements that need to be made to identify the structure properly. The final eight-parameter model is the last of three. The discoveries that were made between the first and the third models are significant. Measured and predicted quantities are compared. 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 considered. The stiffness of the symmetrical springs at the base of the table is introduced as a ninth parameter in the model. The match between measured and predicted response is slightly improved over the eight-parameter model.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-78-24.pdf (8 MB)