Investigation on probability model of bending moment-rotation relationship for bolt-ball joints

As a representative semi-rigid connection, accurately predicting the mechanical properties of bolt-ball joints is of significant importance for structural design. The impact of axial load should be considered in the derivation for the initial stiffness of bolt-ball joints and its bending moment capacity. Because of the variability of geometric dimension and stochastic mechanical property of material, there is a degree of randomness in the actual mechanical behavior of the joints. In order to quantify the randomness in the bending performance, theoretical study was first carried out for the initial stiffness and bending moment capacity of the joint considering effects of axial load, which can accurately predict the bending mechanical performance of bolt-ball joints. Furthermore, the Monte Carlo method was utilized to study the impact of uncertainties in material mechanical properties, joint geometric dimensions, and assembly tightness on the bending performance. Utilizing the Latin Hypercube Sampling (LHS) methodology, a dataset comprising 10,000 samples were systematically extracted for each of the five distinct sizes of bolt-ball joints, and their stochastic responses for initial stiffness and bending moment capacity were obtained using Matlab software. Moreover, the additional variability in initial stiffness and bending moment capacity due to model uncertainty was considered and quantified. By combining the randomness of initial stiffness and bending moment capacity with the additional variability, a three-parameter power function model with random parameters was developed to establish a probabilistic model for the bending moment-rotation relationship of bolt-ball joints.