Ultimate capacities formulae of collar and doubler plates reinforced SHS X-joints under in-plane bending

•FEA models of collar and doubler plates reinforced SHS X-joints were setup.•FEA models of SHS X-joints were in good agreement with the corresponding test.•An extensive parametric study on plates reinforced SHS X-joints was carried.•Formulae of plates reinforced SHS X-joints under in-plane bending were proposed.

This paper presents two finite element model of collar and doubler plates reinforced SHS X-joints under in-plane bending, which were verified by the corresponding test results. The parametric study was carried out to reveal the failure modes and plasticity propagation of collar and doubler plates reinforced SHS X-joints under in-plane bending. The effects of SHS brace width to SHS chord width ratio (β), reinforced plates thickness to SHS chord wall thickness ratio (λ), and reinforced plates length to SHS brace width ratio (Δ) on the ultimate capacities of collar and doubler plates reinforced SHS X-joints were evaluated. The typical failure modes of collar and doubler plates reinforced SHS X-joints under in-plane bending were obtained from the finite element analysis, which included braces inclination, chord face concave in compression stress zone, convex in tension stress zone, collar or doubler plates bending. The ultimate capacities of joints with large β value significantly increased with the increase of reinforcement plates thickness. The in-plane bending ultimate capacity increased with the increase of β value. The ultimate capacities formulae are proposed by using multiple linear regressions for collar and doubler plates reinforced SHS X-joints under in-plane bending based on the current design equations of unreinforced SHS X-joints given in the Eurocode 3. It is shown from the comparison that the joint strengths of collar and doubler plates reinforced SHS X-joints under in-plane bending calculated using the proposed formulae agreed well with the finite element analysis results, which means the proposed formulas are verified to be accurate and safe.