Study on out-of-plane flexural stiffness of unstiffened multi-planar CHS X-joints

•Develop a ring model for elastic out-plane flexural stiffness of the CHS X-joints.•A simplified elastic out-plane flexural stiffness formula for the joints is obtained.•A series of numerical parametric study about CHS X-joints is conducted.•Comparison among FEA, tests and formula proves reasonability of the proposed formula. Although the stiffness of different kinds of unstiffened circular hollow section (CHS) joints have been well studied, only few literatures about out-of-plane flexural stiffness of multi-planar CHS X-joints can be found. In this paper, firstly a ring model is developed to establish a theoretical formula of elastic out-of-plane flexural stiffness of the CHS X-joints. Then based on the Taylor series and taking the polynomials as intermediary, the complex expression of the theoretical formula could be simplified to the product of exponential function, power function and trigonometricfunction. After this, numerical parametric study is conducted by calibrated finite element (FE) models with software ABAQUS, and an elastic out-of-plane flexural stiffness parameterized formula for the X-joints is established. Finally, a comparison among the stiffness values of CHS X-joints from the FE results, tests and the parameterized formula is made, which proves the reasonability of the derived formula.