# A Review of the T-Stub Components for the Analysis of Bolted Moment Joints
## 4 Numerical Models
This model was used to characterise the deformation response and the distance between the plastic hinges in the T-stub flange. Thus, the results showed that the \(m\) parameter was quite similar to the EC3. The second was a FEM plate model of half T-stub geometry, which was validated with the experimental results of Faella (TS22, TS11). After the calibration of the model, a parametric study was performed to determine the effective length. In 2011, [PERSON] et al. [70] started an investigation with the objective of developing computationally efficient and accurate finite element models for bolted joints under impact loading. Therefore, a 3D detailed FEM model of the T-stubs was developed to analyse the T-stub behaviour without considering the computational cost. The element type C3D8R of the detailed model was chosen due to the large strain and large deflection capabilities. Additionally, the element allowed the reduced integration for computational effectiveness. The reduced integration does not create stiffness in some deformation modes and the hour glassing effect may occur. Afterwards, simplified models were developed to reduce the computational cost. Therefore, (i) the full model with shell plate were analysed (the same considerations for the bolt, but the flange was discretized using shell elements), (ii) rigid shank with coupling constrains (shell elements for the flange, the bolt shaft was considered rigid and coupling constrains were assigned to simulate the effect of bolt head and nut), (iii) deformable shell bolt (shell elements for modelling the nut and bolt assembly), (iv) rigid shell bolt (the same of iii, but the nut-bolt assembly is modelled with rigid shell), (v) Timoshenko beam with coupling constraints (the bolt shaft is modelled with a Timoshenko beam 3D node quadratic element), (vi) Timoshenko beam with coupling constraints without a hole (the flange did not have bolt hole, the other elements are the same of v and the coupling constrain was assigned), (vii) tie constraint with hole (the force transfer between the frame and the plate was achieved through a tie constraint defined between the inner surfaces of the sheets in the region compressed by the washers), (viii) tie constraint without a hole (the tie constraint was used to model the clamping effect of the bolt-nut assembly), (ix) cross-coupling constraint (a kinematic coupling constraint is used to simulate the force transmission between the sheets), (x) connector beams along the perimeter of the hole (beam type elements were defined in the perimeter of the hole), (xi) connector beams along the perimeter of the hole and the washer's outer profile (similar to x, but beam elements were assigned to the edge of the washer's profile), (xii) cross connector beams (12 connector beam-type elements that joined the midpoint of the line between the centres of the holes and nodes at the perimeters). Finally, all the models were tested with the same mesh density and that showed that only the simplified model (i) did not save computational time. Moreover, the simplified model (iii) was the most accurate to predict the T-stub behaviour for different loading cases and mesh densities. In 2014, [PERSON], [PERSON] and [PERSON] [71] investigated the relevance of influence of the bolt bending on the behaviour of T-stubs. Therefore, a 3D numerical model was developed in the software Cast3m and validated with experimental results found in the literature. These FE models were used to predict the behaviour of T-stub connections, quantify the axial and bending loads in the bolts. The numerical models took into account the non-linearity due to the plastic behaviour of the material and the evolution of the contact area between the two flanges. A parametric study was performed to evaluate the influence of the bolt bending moment on the behaviour of the T-stub by varying the flange thickness and the bolt diameter. Afterwards, an analytical model was proposed, which considered the bending of the bolt and the axial force.