In this paper, the quasi-static reciprocating loading test was carried out for the T-stub steel middle column joints with blind-bolt connections. As the thickness of the T-stub steel increased, the damage failure modes were different. The load–displacement curve, cumulative energy dissipation, equivalent viscous damping coefficient, damage index and other characteristics of the joints were analysed. When T-stub steel was used as a connector, its thickness affected the damage development mode. As the thickness of T-stub steel increased, the bearing capacity and plastic displacement were improved, the energy dissipation capacity was significantly increased, and the rotational stiffness retention ability of the joint was improved, but the damage index value was not significantly increased. Finally, the damage index and the rotational stiffness degradation coefficient under each loading level were numerically fitted, and the polynomial and exponential rotational stiffness models were established, taking into account the damage index. These two models took into account the reduction in rotational stiffness caused by damage under each level of load, and the rotational stiffness under each loading level could be obtained from the damage index and the initial rotational stiffness.