Effect of Uncertainties in Design Variables on the Hysteresis Response of 2D Steel Moment-Resisting Frames

Reliability theory considers the effect of uncertainty in the modeling and design of structures. Uncertainty in variables such as the material properties, geometric dimensions, and external loads during the analysis of steel moment-resisting frames can have significant effects on structural safety. This study evaluated the safety probability of two two-dimentional steel moment-resisting frames and examined the effect of uncertainly on each design parameter on the maximum frame drift using sensitivity analysis. It also evaluated the robustness index of energy dissipated in the stories of the frames. The uncertainties were modeled with normal probabilistic distribution of random variables. The Monte Carlo simulation method and the maximum story drift constraint were used to calculate the probability of safety and define the limit state function, respectively. Nonlinear time-history analysis was performed on the frames under seven ground motion records having an exceedance probability of 10% in 50 years. The modified Ibarra-Krawinkler behavioral model has been used to define the potential plastic hinges of the frame. The results indicated that the values of the probability of safety may be appropriate for evaluation of the 3-story frame, but be undesirable for a design based on reliability assessment. Sensitivity analysis showed that the steel modulus of elasticity and yield stress values having the greatest effects, whereas the web thickness of the sections and gravity loads applied to the stories had the least effects on the maximum drift of the structure. Using the probability of safety and robustness index, this study has produced useful information for the seismic rehabilitation of structures relating to design variable uncertainty on the hysteresis response for steel moment-resisting frames.

The application of appropriate safety coefficients for parameters with uncertainty and the modeling of these uncertainties have been extensively studied in recent years. Because there are uncertainties in the design parameters of existing structures, it is better to examine the effect of these uncertainties on the response of the structure. There is a special gap in rehabilitation studies that can be used to evaluate the existing structures. Therefore, a practical approach is required to evaluate the structures undergoing structural rehabilitation to investigate the effect of uncertainties in the design parameters on the hysteresis response of steel moment-resisting frames. In this regard, it is also better to evaluate the probability of safety and the robustness of the hysteresis response of steel moment-resisting frames. Also, the sensitivity of the desired output value to the parameters with uncertainty using nonlinear time-history analysis for this type of structures was one of the items preferred by the authors to be estimated.