The strength and deformation capacities of the structural elements are affected by the cumulative damage of that component. For this purpose the loading protocols used for investigating the performance of the connections should give an accurate estimation of the structural components capacities and yield appropriate simulation of the reality. It is essential to investigate the differences and features of the loading protocols. On the other hand, regarding the widespread use of the moment connections of I-shaped beam sections in the box-section columns, investigating the seismic performance of these moment connections is of vital importance. Meanwhile, the majority of code details for accepting moment connections are presented for H-shaped columns. For this purpose 12 types of RBS and WUF-W moment connections with box-section columns were designed and examined as analytical models in the study. The seismic behavior and difference in performance of these two types of moment connections were investigated and compared at the level of the relative displacement acceptance in the codes and also the collapse threshold under SAC and ATC-24 loading protocols. In continuation, while investigating the demand and applied energy, and the features and differences between the loading protocols, the conditions for strength loss at the collapse threshold of moment connections in the special moment resisting frame are also proposed.