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In the article, the semi-permanent aluminum alloy portal frame is used as the research background, beam-column joints are used as the research object, and experimental and numerical analyses are carried out. The influence of different bolt diameters and arch angles on the mechanical properties of beam-column joints under vertical load was analyzed using five sets of experiments. The experimental results show that the load–displacement curves of different bolt diameters in the elastic stage are basically consistent. After entering the plastic stage, the ultimate load first increases and then decreases, and the ultimate displacement is basically consistent. According to the experiment, there is no significant difference in the load–displacement curve when the arch angle increases from 90 degrees to 108 degrees. When the arch angle increases to 126 degrees, the stiffness and ultimate bearing capacity of the node under vertical load significantly increase. Then, a numerical analysis model was established to analyze the mechanical performance of beam-column joints under horizontal loads. The numerical analysis results indicate that under horizontal load, as the diameter of the bolt increases, the yield load, yield displacement, ultimate load, and ultimate displacement of the beam-column node exhibit no significant changes, and the change amplitude is minimal. When the beam-column node is subjected to horizontal loads, as the arch angle increases, the yield and ultimate displacement increase by 2.14 times and 2.78 times, respectively, and the yield and ultimate load decrease by 58% and 48%, respectively. Finally, a simplified design method for beam-column joints was proposed based on experiments and numerical analysis.