Compared to unstiffened circular hollow section (CHS) X-joints, CHS X-joints stiffened with external ring stiffeners and gusset plates have exhibited much higher bearing capacity. To gain insight into the effects of the chord pre-loads on ultimate bearing capacity, this paper presents results of finite element (FE) analyses of the stiffened X-joints with braces under compression and chord under (i) axial load, (ii) in-plane bending moment, or (iii) combinations of axial load and in-plane bending moment. Precision of the FE model under combined brace and chord loads is validated by test results. The ultimate bearing capacities attained by using proportional loading and non-proportional loading respectively are presented, and the results indicate that the differences due to loading path are negligible. The validated FE modelling technologies are then employed in a parametric study on the effect of chord pre-load. A total of 4560 stiffened X-joints are examined in the parametric study. The theoretical analysis presented herein provides a reasonable explanation for the significant reduction in strength of stiffened X-joint when the chord is under axial tension. Finally, a chord stress function with corresponding boundary conditions is proposed, in which the coefficients for different chord load cases are determined through regression analysis. Furthermore, a lower-bound multiplier is given for the function to ensure a conservative design.

Introduction

It has been well recognized that chord load plays an important role in ultimate bearing capacity of tubular joints. Therefore, it is necessary to take into account the effect of chord load in the design of tubular joints. In companion paper [1], an innovative stiffened X-joint with external ring stiffeners and gusset plates is introduced, as shown in Fig. 1. This paper extends the investigation into the effects of chord loads on ultimate bearing capacity of stiffened X-joint. To account for the effects of chord loading, chord stress/load function is usually adopted. The early study on the function can be traced back to the work by Togo [2], in which the effects of axial chord load on bearing capacity of X-joint were experimentally investigated. After that, Boone et al. [3] presented results of ten tests on identical large-scale double-tee (DT) specimens that were used to investigate the effect of uniform axial and bending chord stresses on strength of tubular joint. In addition, chord stress functions in terms of the combination of axial and bending stress were correspondingly proposed. Using the same chord nominal dimensions as in Boone’s tests, Weinstein and Yura [4] completed thirteen tests to examine the effect of the ratio of brace diameter to chord diameter, β.