# Study on New Bolted T-Stub Connection with Inserted Plates under Axial and Cyclic Loads
## 2 Mechanical Model  
To establish the mechanical model of the T-stub connection with inserted plates, predictions of both the initial stiffness and load bearing capacity are required. Firstly, the stiffness of the T-stub connection is determined by following the approach of an equivalent cantilever model in [25]. Secondly, the tensile bearing capacity of the T-stub connection with inserted plates is assumed to be similar to that of a conventional T-stub connection without inserted plates, so the mechanical model tension can be directly drawn upon traditional T-stub connections from previous studies [26; 27]. Hence, this paper is primarily concerned with the compressive bearing capacity of the mechanical model. Based on speculations of two different failure modes, two calculation methods of compressive bearing capacity are deduced.  
The type of compression failure mechanism used in the new connection is subject to the relative strength between the T-stub flange and the two bolts. The Type 1 failure mode is characterized by the formation of four plastic hinges in the T-stub flanges, two of which are on the sections over the inner edge of the inserted plates, while the other two are located at the sections corresponding to the flange-to-web connections, as shown in Figure 2a. This occurs when the strength of the T-stub is weaker and the strength of two bolts is stronger, which is partially similar to the Type 1 failure mode of traditional T-stub connections under tension [27; 28]. By contrast, when the T-stub strength is greater than that of two bolts, the Type 2 failure mode appears, which is represented by the formation of two plastic hinges located at the sections corresponding to the flange-to-web connection, as well as the two bolts (see Figure 2b).  
Figure 1: Configuration of new T-stub connections with inserted plates.  
According to the formation of the two plastic hinges on the flange sections corresponding to the flange-to-web connections in Figure 2a, an equilibrium equation is developed as follows:  
\[(0.5F_{c1,Rd}+B)\ m_{1}-B\ (m_{1}+n_{1})=M_{f,Rd} \tag{1}\]  
where \(F_{c1,Rd}\) and \(F_{c2,Rd}\) indicate the compressive bearing capacity of failure Type 1 and Type 2, respectively; \(B\) is the prying force of high-strength bolts; \(M_{f,Rd}\) represents the bending capacity of the T-stub flange; \(m_{1}\) is the distance from the inside of the inserted plate to the flange-to-web connection of T-stub; and \(e_{1}\) and \(n_{1}\) are the distance from the center line of the bolt to the outside and inside of the inserted plate, respectively.  
Moreover, based on the two plastic hinges on the flange sections at the inner edge of inserted plates, another equation can be set up:  
\[B^{*}n_{1}=M_{f,Rd} \tag{2}\]  
Therefore the final equation corresponding to the compressive resistance of failure Type 1 can be derived by taking Equation (2) to Equation (1) as follows:  
\[F_{c1,Rd}=4M_{f,Rd}/m_{1} \tag{3}\]  
Similarly, another equilibrium equation can be formed according to the position of plastic hinges following on the basis of Figure 2b,  
\[M_{f,Rd}+B_{Rd}\ ^{*}n_{1}=0.5F_{c2,Rd}\ ^{*}m_{1} \tag{4}\]  
Correspondingly, the final equation for compressive resistance of failure Type 2 can be described by  
\[F_{c2,Rd}=2(M_{f,Rd}+B_{Rd}\ ^{*}n_{1})/m_{1} \tag{5}\]