# A Review of the T-Stub Components for the Analysis of Bolted Moment Joints
## 4 Numerical Models
This research was also focused on the prediction of more T-stub geometries. Therefore, after the calibration, a parametric studied was performed, see Figure 26c. In 2007, [PERSON] [67] investigated the effects of backing plates (BP) used to reinforce beam to column connections. The T-stub, which is the main component in bolted joint in bending, was analysed in the non-reinforcement stage to calibrate the FEM, see Figure 27a,b. This calibration was done in two types of FE models: (1) a 2D model (2) a 3D model, which were both compared to define the limits of the 2D model. After the calibration, a parametric study was conducted to examine the prying forces' relevance and the evolution of the contact areas under the T-stub. Afterwards, the study was focused on investigating the effects of the BP thickness and the bolts preloaded. On the one hand, the results of the 2D simulations showed that this type of model is suitable to analyse the T-stub without backing plates, see Figure 27c, and gave satisfactory results for short T-stubs, see Figure 27d,e, with backing plate. However, the resistance is a little underestimated. On the other hand, a long T-stub, see Figure 27f, is more suitable for being analysed by 3D FEM. They concluded that the T-stub resistance and the initial stiffness increase with the thickness of the backing plate, according to 3D models. EC3 prediction of the T-stubs with backing-plates gives satisfactory results for the resistance compared to numerical results. In 2010, [PERSON] et al. [15] investigated T-stub connections with blind bolt Hollo bolts. This research investigated the effects of this type of bolts on the initial stiffness, strength and ductility. Thus, two 3D numerical models were developed, see Figure 28. The first was the T-stub connection model with Hollo bolt, which was reckoned for studying the clamping effect, the force transfer mechanisms, stiffness, strength and deformation capacity of the connection, and the other was developed for studying the standard bolt. The models were calibrated with experimental data (Hollo bolt T-stub model [68]) before the results of both models were compared to understand the behaviour changes. Afterwards, a parametric study was performed, and the parameters that were taken into account are the following: angle of the flaring sleeve (\(\beta\)), bolt shank diameter (d\({}_{\text{sh}}\)) and flange thickness (t\({}_{\text{f}}\)). The main conclusions of the investigation are that the T-stub connections made with the blind-bolt results in less initial stiffness than those with standard bolts. According to the parametric study results, the flange thickness most influences the strength and stiffness of the blind-bolted connection compared to the flaring sleeve angle and the bolt shank diameter. Figure 26: (**a**) FEM of the rolled T-stub; (**b**) bolt discretization; (**c**) FEM of the parametric study of the filled welded T-stub; (**d**) Force-displacement curve of the fillet welded T-stub [66]. Figure 27: Finite element models of the T-stub: (**a**) Non-reinforcement 2D T-stub; (**b**) Non-reinforcement 3D T-stub; (**c**) Quarter of non-reinforcement 2D T-stub; (**d**) Quarter of Reinforcement 3D short T-stub; (**e**) Quarter of Reinforcement 2D short T-stub; (**f**) Quarter of Reinforcement 3D long T-stub [67]. “Reproduced with permission from [PERSON], [PERSON], Journal of Constructional Steel Research; published by Elsevier, 2007”. Figure 28: 3D finite element mesh: (**a**) Blind-bolted T-stub; (**b**) Standard bolted T-stub [15]. “Reproduced with permission from [PERSON], [PERSON], [PERSON], Engineering Structures; published by Elsevier, 2010”. In 2010, [PERSON] et al. [69] developed two different FEM models to determine important variables of the T-stub, which were used to propose an analytical model that took into account compatibility requirements and prying forces. The first model was calibrated with the experimental result of Faella (TS11) and was discretised using eight-nodes brick elements.