First-order computation of the statistics of joint moments in partially restrained steel structures

Abstract

The flexibility of connections affects the performance of steel frame structures. Therefore, it must be considered in order to analyze the structure accurately. This flexibility is best described by the moment-rotation ( M- θ) curve of the connection which is modeled quite well by the Richard model. This model characterizes the M- θ relation by four parameters. The variation in the four parameters governing the M- θ curves for similar connections is mainly due to differences in fabrication and field conditions. This results in the moment predicted by the Richard M- θ model being a random variable. For a specific value of joint rotation, the probability distribution of the moment is dependent on the four parameters which define the model. This distribution should be determined in order to account for the variability in joint behavior in the analysis of flexible steel frames, and to assess the reliability of the structures. In this study, the distribution of the moment is found from the distributions of the four parameters which completely characterize the Richard model. Statistical simulation is used to generate values of the four parameters from their respective distributions. These values are used to calculate values of the moment for a range of values of rotation. The results are used to compute the statistics of the moment and to fit an appropriate probability distribution to its value. Finally, in order to provide a practical means of estimating the mean value and variance of the moment, a first-order Taylor series approximation is used and its results are compared to those of the simulation.