•Under the tensile test, bolted spherical joints suffered three failure modes.•Factors influencing the stiffness and ultimate strength of bolted spherical joints.•Behaviours of bolted spherical joints were predicted by XFEM method.•Formulas were proposed to evaluate the tensile strength of bolted spherical joints. Aiming at evaluating the reliability of the high-strength bolts’ fake tightened-up phenomena of the bolted spherical joints in a spatial grid structure, this research studied the tensile strength, stiffness, and failure modes of the bolted spherical joints with different bolt types and screwing depths using a combined method of the lab experiments and numerical simulations. A total of 40 axial tension tests of the bolted spherical joints were conducted with five different bolt types and eight different screwing depths. The test results showed that the bolted spherical joints with the different bolt screwing depths of high strength bolts suffered three failure modes, namely, the thread failure, bolt fracture failure, and sphere rupture failure. Validated by its feasibility and accuracy, the proposed numerical simulation method of the bolted spherical joints can estimate the ultimate strengths and failure modes, as well as the detailed stress distribution and failure development process. According to the test and numerical analysis results, a group of calculation formulas was developed for predicting the tensile strength of bolted spherical joints with different bolt screwing depths.