Study On Hysteretic Model Of The Unstiffened CHS X-joints Under In-plane Bending

As a major type of steel tubular joint,the unstiffened CHS joint is widely used in engineering practice due to its superiority,which is embodied in the convenience of manufacture and the clear path of load transmission.Up to now,scholars at home and abroad have done a lot of research on the unstiffened CHS joint,among which scholars have focused more on its ultimate bearing capacity than on its hysteretic behaviour.In the past two decades,domestic scholars have mainly researched the unstiffened CHS X-joint’s hysteretic behaviour under axial compression and out-of-plane bending,but seldom looked into its hysteretic model under in-plane bending,especially when multiple loads are applied simultaneously.Even fewer studies have considered the condition of crack growth and joints failure.This study adopted Abaqus for modeling and analysis to study X-joint’s semi-rigid behaviour and hysteretic behaviour.The non-linear multiple regression technique is used to build the semi-rigid connection model and the hysteretic model.On this basis,the X-joint’s hysteretic model under in-plane flexure is constructed,while considering the axial compression of both the branch and the chord.First,this study adopted variable-controlling method to study the impact of 7 different geometric parameters（f_y、D、τ、β、γ、θ、φ）on the X-joint under in-plane bending（M_i-Ψ_icurve）.The result shows that while the size of the chord and branch keeps unchanged,the non-orthogonality（θ）of the chord and branch can greatly improve the bearing capacity of X-joints,which also demonstrated the feasibility of using a four-parameter exponential function to simulate the M_i-Ψ_i curve.Afterward,three performance parameters(k_ii、k_ipand M_ip)of the semi-rigid connection model（i.e.the four-parameters exponential function）were extracted by analyzing parametric FE models of 190 X-joints.Through single-parameter analysis and multiple regression techniques,the arithmetic expression of the three parameters and the relationship between k_ii and k_ip were established.The accuracy and applicability of the model are verified by comparing the model with the result of the finite element analysis（FEA）.By using the semi-rigid connection model as the skeleton of the hysteretic model as well as using Ramberg-Osgood function as the unloading path,an accurate unstiffened CHS X-joint bending hysteresis curve model was built.This model,which is also highly accordant with the FEA result,contains a concise expression with parameters of definite physical meaning.The smooth curve also helps avoid the stiffness mutation at the turning point of the multi-folded line model.Furthermore,the influence of the axial force coming from the branch and chord was taken into consideration.By modeling and analyzing 60groups of X-joints with different axial force levels,the performance parameter M_ip was improved.Therefore,the model of in-plane flexural hysteresis under the effect of the main axial forces was built.Besides,the hysteresis model of this study can also reflect the declination of the bending moment curve under the large axial force of the branch and chord.Finally,by adopting the Extended Finite Element Method（XFEM）of Abaqus,the impact of the crack growth on X-joints under in-plane bending was studied,whose result was then compared with both FEA without crack and the semi-rigid connection model.The outcome of comparison demonstrated that as the chord turns thicker,the crack growth’s impact on the bending resistance of the joint grows simultaneously.