Seismic reliability of non-linear frames with PR connections using systematic RSM

An effective, efficient, and robust reliability analysis algorithm is proposed for non-linear structures, where seismic loading can be applied in the time domain. The method is developed specifically for steel frame structures considering all major sources of non-linearity, including geometry, material, and partially restrained (PR) connections. The non-linearity due to PR connections is modeled by moment-relative rotation curves using the four-parameter Richard model. For seismic excitation, the loading, unloading, and reloading behavior at PR connections is modeled using moment-relative rotation curves and the Masing rule. The proposed algorithm intelligently integrates the response surface method, the finite element method, the first-order reliability method, and an iterative linear interpolation scheme. The uncertainties in all the random variables including the four parameters of Richard model are considered. Two unique features of the proposed algorithm are that (1) actual earthquake time histories can be used to excite structures in the presence of major sources of non-linearity and uncertainty and (2) it is possible to estimate the risk corresponding to both the serviceability and strength limit states. The algorithm is verified using the Monte Carlo simulation technique. The verified algorithm is first used to study the reliability of a frame structure in the presence of PR connections with different degrees of flexibility. Then the algorithm is used to estimate the reliability of a frame structure excited by 13 actual recorded earthquake time histories, 12 of them recorded during the Northridge earthquake of 1994. As expected, the reliabilities of the frame are found to be quite different, when excited by several time histories of the Northridge earthquake.