Seismic risk analysis of frames with uncertain support and PR connection conditions

Abstract

A hybrid reliability evaluation procedure is proposed to estimate the risk of steel frames considering the rigidity of connections and supports as accurately as possible. Nonlinearities due to geometry, material, partially restrained (PR) connections, and flexible supports are considered in the proposed algorithm. The four-parameter Richard model is used to represent the flexibility of connections and supports. All major sources of uncertainty in the loading and resistance-related parameters and the parameters in the Richard model are incorporated in the algorithm. The unique feature of the algorithm is that the earth-quake loading can be applied in the time domain, providing an alternative to the random vibration approach. The proposed algorithm intelligently integrates the concepts of the finite element method, the response surface method, the first order reliability method, and the iterative linear interpolation scheme. The algorithm is verified using Monte Carlo simulation. With the help of an example, it is shown that the proposed algorithm can be used to estimate risk for both the serviceability and strength limit states. The presence of PR connections and/or flexible supports alters the dynamic properties (stiffness and damping) of the structure and adds a new and major source of energy dissipation. The serviceability limit state may become the controlling limit state, particularly for seismic loading. Thus, the common practice of considering all connections and supports to be rigid and designing the frame for the strength limit state may not be appropriate. The flexibility of connections and supports and the uncertainty in modeling them have a considerable influence on the overall behavior of frames, particularly under seismic loading. An efficient, robust, and accurate method is proposed to evaluate the reliability of such frames.