## 6 Conclusions  
In this research program, low-cycle fatigue experimental studies of welding material and steel welded joints in steel tubular truss structures were conducted under different loading conditions. The cyclic characteristics, variation of cyclic stress amplitude, and energy dissipation capacity were thoroughly discussed, with a focus on the law of damage accumulation of the welding material. Then, an evolution equation of damage accumulation for the welding material was obtained, and a hysteresismodel with damage accumulation was constructed. Based on this research of experiment and theory, the following conclusions can be drawn:  
1. The cumulative damage process of welding materials can be divided into three stages, which are presented as the stage of crack initiation, the stage of crack propagation, and the stage the specimenis fractured, and when the specimensare destroyed along the maximum main crack.
2. As the imposed displacement cycles increased, the cyclic softening behavior of the welding materials of the welded joints in a tubular truss structureis apparent, and the steel hardening behavior is shown. Furthermore, with the increase of cyclic cycles, the effect of damage accumulation on the welding materials is obvious, that is, the cyclic stress amplitude, unloadingstiffness, and energy dissipation capacity of the weldingmaterials degenerate gradually. Furthermore, the larger the controlled loading strain amplitude, the faster the rate of damage accumulation. The amplitude of the loading strain has a greater effect on the welding material of base metal Q235 than that of base metal Q345.
3. Based on the test results and Park-Ang model, an evolutionequation of damage accumulation for welding materials is established considering both energy and deformation comprehensively, in which the energy part is no longer confined to the perfect elastic-plastic condition. Then, the value of parameter \(\lambda\) is fitted by the test data.
4. It is revealed by the experimental research that the cyclic characteristic and constitutive behavior of the welding material is quite different from the base metal, and the constitutive model used for monotonic loading cannot simulate the damage degradation behavior of the welding materials under cyclic loading. Therefore, a hysteresismodel with damage accumulation of welding materials is constructed based on the Ramberg-Osgood model and the experimental results, which included the initial loading curve, cyclic stress-strain curve, and a model of the hysteretic curve. The model can reveal the effects of damage accumulation and the nonlinear constitutive relation of the plasticstage.
5. The damage parameters and model parameters \(\eta\), \(\xi\), \(g\), \(h\), \(K^{\prime}\) and \(n^{\prime}\) are fitted by the test results. The hysteretic curves calculated by the hysteretic model are compared with the test results, which show that the model has good applicability and the cumulative damage evolution law of the welding materials reflected by the model is basically consistent with the test results.  
[PERSON] designed the experiments. [PERSON] and [PERSON] performed the experiments. [PERSON] and [PERSON] analyzed the data and wrote the paper.  
This research was supported in part by The National Natural Science Foundation of China under Grant 51468054 and in part by the Funding Project of First-Class Discipline Construction of Universities in Ningxia (Domestic First-Class Discipline Construction) under Grant NXYDXK2017A03.  
The authors declare no conflict of interest.