Abstract: The stiffness of semi-rigid joints in socket-and-disk cuplock steel tube formwork supports gradually decreases with increasing joint bending moment， showing an obvious nonlinear relationship. When multiple bending cross bars are connected to the buckle joint at the same time， stress overlap occurs at the buckle root， leading to reduced joint stiffness. This study investigates the variation law of stiffness values in semi-rigid joints of socket-and-disk supports under the combined action of one， two， three， and four cross bars through experimental testing and ABAQUS finite element numerical simulation. The mathematical statistical methods of the two-parameter logarithmic model and the trilinear model were used to process the test and finite element data， facilitating numerical analysis of joint stiffness and bending resistance in frame structures. The results showed that when the buckle joint connected two adjacent cross bars at a right angles， the stress overlap at the buckle root reduced the joint stiffness. Specifically， when the bending moment of the joint was 0-200 N·m， the stiffness value of semi-rigid joints should be 20-30 kN·m/rad；when the joint bending moment was 200-600 N·m， the stiffness value of semi-rigid joints should be 9-11 kN·m/rad；when the joint bending moment exceeded 600 N·m， the stiffness value of semi-rigid joints should be 2-6 kN·m/rad。