Experimental and formula deduction on the mechanical performance of Fang in Dou-Gong of Song dynasty

In Song dynasty, Dou-Gong construction techniques, Tou-Xin-Zao and Ji-Xin-Zao, varied by the number of Fang connecting to the exterior. This study examines the impact of Fang connections on the mechanical characteristics of Dou-Gong. Six full-scale models were constructed and subjected to quasi-static loading tests in the horizontal Beam and Fang directions under vertical load. The hysteresis behavior, deformation, and stiffness variations were obtained and analyzed. The test results revealed the hysteresis curve of Dou-Gong developed into a flat shape, with good deformation recovery ability and seismic performance. Beam-direction loading led to brittle failure, with Dou-Gong having fewer Fang experiencing bearing capacity loss and those with more Fang succumbing to overturning. Beam-direction stiffness rose by approximately 29% as the number of connecting Fang increased. Fang-direction loading induced ductile failure, predominantly characterized by overturning. Notably, Fang-direction stiffness remained largely unchanged by the varying number of connecting Fang. Dou-Gong slip deformation ratio decreased by 5 -10% as the number of Fang increased. Furthermore, Fang-direction exhibited about 10% greater slip deformation capacity than the Beam-direction. Based on the force transfer mechanism of Dou-Gong components, a stiffness formula for the elastic stage of Dou-Gong in the Beam-direction and Fang-direction was established and validated against experimental data.