Probability distribution functions for the ultimate strength of X-joints with collar plates in compressive load at room and fire conditions

Abstract

In this paper, the results of performing finite element (FE) analysis on 360 tubular X-joints reinforced with collar plates have been used to propose a probability distribution model for ultimate strength at ambient and fire conditions. As far as the authors know, no study has been conducted on the probability distribution of the ultimate strength in X-joints with collar plates. Consequently, according to the reinforced X-joints, a total of ultimate capacity data sets was generated. The FE models were validated and compared with 35 experimental tests and numerical models. Also, in the present FE models, the welds connecting the plates to the chord member were created. Moreover, the contacts between the outer surfaces of the chord member and the inner surfaces of the reinforcing plates were modeled. In addition, nonlinear material and geometry properties were applied. In the following step, twelve theoretical probability density functions (PDFs) were fitted to relative frequency histograms of five databases. The maximum likelihood method was applied to determine the parameters of each distribution. Investigating the goodness-of-fit according to the Kolmogorov-Smirnov, Anderson Darling, and Chi-square tests showed that the Generalized Petro distribution is the best for the ultimate capacity values in collar plate retrofitted X-joints at ambient and different fire conditions. In the following step, six fully defined theoretical PDFs and cumulative distribution functions (CDFs) were established. Also, probability-probability graphs indicated that the proposed theoretical probability distributions are near the given data sets.