When data is insufficient to support a probabilistic assumption, the structural seismic performance evaluation results with probabilistic approach are suspicious. In this paper, the convex set theory, which requires much less information, is employed to model the uncertainties of peak acceleration and frequency characteristics of earthquake ground motions. The bounds of shear forces are first derived with Chinese seismic code, and then a lateral bound load method for Push-over analysis is conducted. Then the convex analysis is integrated into Push-over analysis to study the bounds of structural capacity. Furthermore, the bounds of earthquake demand are deduced with the bounded convex set model and Chinese seismic code. The bounds of target displacement are obtained using capacity spectrum method. The seismic performance of structure is then evaluated with an interval. Finally, seismic performance evaluation of a three-storey RC building is given to demonstrate the benefits of the proposed method.
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