RESPONSE ANALYSIS OF STEEL FRAMES BASED ON A SIMPLE HYSTERESIS RULE : Accuracies and errors in predicting inelastic responses of steel frames subjected to severe earthquakes (Part 2)
1988 Volume 394 Pages 37-48
Details
1988 Volume 394 Pages 37-48
1. Introduction Recent progress of efficient computer algorithm can provide a precise prediction of inelastic earthquake response, once an appropriate mathematical model of a structural behavior is constructed. Also an experimental study becomes still more indispensable to construct such model but also to check its validity. The preceding paper (Part 1) reported an outline of 19 cases of earthquake response tests on scaled steel.frame models (Ref. 1). The inelastic behaviors observed in the tests are approximated herein by a simple hysteresis model, and the response analyses are carried out by use of the model. The correlations between the test results and the computed are discussed. 2. Summary of Response Tests (Ref. 1) The response tests reported in Ref. 1 consist of 5 shaking table tests and 14 pseudo-dynamic tests. Various types of steel frame models were tested under uni-directional horizontal ground motions. The profiles of the frame models are summarized again on Table 2. The N-S component of El Centre 1940 and the E-W component of Hachinohe Harbor 1968 were scaled both in time and amplitude and used as input ground motions. Test parameters of 19 cases are summarized on Table 1. 3. Approximation by 4-component Hysteresis Model Story drift vs. story shear curves observed in the tests except No. 17 were approximated by the 4-component hysteresis model. As for the test No. 17, the hysteresis loops in the modal coordinates were studied as shown in Fig. 5. As illustrated in Fig. 2, the 4-component hysteresis model consists of a elastic element, two elasticperfectly plastic ones, and a slip-type one. The final values of the model parameters were determined after several trials to improve the two indicators of fitness, ν_1, and ν_2, which were evaluated for a trial curve approximated under the same drift history in the test. The test curves and the approximated ones are shown in Figs. 4 (1) and (2), respectively. 4. Prediction of Stiffness and Strength Parameters Stiffness and yield strength parameters of the test frames were calculated under the following assumptions, and they were compared with the test values in Fig. 9. Elastic stiffness of moment resistant frame was calculated by considering only flexural deformation of beam and column members, while the shear and the axial deformation were ignored. As for the braced frame, the contribution of the compression side bracings to the total stiffness were ignored. Yield strength of moment resistant frame was derived from a simple plastic-hinge analysis, where a hinge moment was set to the full-plastic moment corresponding to the yield stress in the coupon test. It was assumed for a pair of bracing, respectively, a tension-side one carried its yield force, and a compression-side one carried a post-buckling stable force smaller than its initial buckling strength. Past proposals about the post-buckling stable force are shown in Fig. 8. The formula proposed in Ref. 5 was adopted herein. 5. Correlation of Computed Responses and Test Results A numerical response analysis based on the approximated model was carried out under the same excitation in the test. Story drift vs. story shear curves computed are shown in Figs. 4 (3), and the computed curves for No. 17 test are shown in Figs. 5 (2) and (4). It is noteworthy that a mathematical model approximated in the above manner does not always provide a good prediction of the drift history, while its hysteresis curve under the same drift history in the test seems to match well with the test curve. Computed response quantitines, such as peak story drift, permanent set after earthquake, energy absorption, and so on, are compared with the test results in Figs. 10 (1) to (5). It is found that energy absorption at the most damaged story and the total energy absorption can be fairly well predicted by the present analysis even if it fails to predict the permanent set and the peak drift. 6.
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