The weld form of intersecting joints in a steel tubular truss structure changes with the various intersecting curves. As the key role of joints in energy dissipation and seismic resistance, the weld is easy to damage, as a result the constitutive behavior of the weld is different from that of the base metal. In order to define the cumulative damage characteristic and study the constitutive behavior of welded metal with the influence of damage accumulation, low-cycle fatigue tests were carried out to evaluate overall response characteristics and to quantify variation of cyclic stress amplitude, unloading stiffness and energy dissipation capacity. The results show that the cyclic softening behavior of welding materials is apparent, however, the steel shows hardening behavior with the increase of cyclic cycles, while the cyclic stress amplitude, unloading stiffness, and energy dissipation capacity of the welding materials degenerate gradually. Based on the Ramberg–Osgood model and introducing the damage variable D, a hysteretic model of welding material with the effect of damage accumulation was established, including an initial loading curve, cyclic stress-strain curve, and hysteretic curve model. Further, the evolution equation of D was also built. The parameters reflecting the damage degradation were fitted by the test data, and the simulation results of the model were proved to be in good agreement with the test results.