## 4 Torsional Shear Deformation Characteristics of Segment Joints
### Bolt Stress Response  
A node on each bolt where the stress first reaches 900 MPa is selected as the characteristic point for the bolt stress. The stress variation at this characteristic point is then extracted for quantitative analysis. Figure 13 illustrates the relationship between bolt stress and the rotational angle, with Figure 13a,b corresponding to the cases with and without the mortise and tenon at the segmental joint (C1-C5 and C6-C10, respectively). As observed in the figure, the relationship between bolt stress and rotation angle remains generally consistent across different joint configurations and axial forces. This suggests that, during torsional-shear deformation of the segmental joint, the bolt stress is predominantly governed by the rotation angle of the segment. The variation in bolt stress with respect to the rotation angle can be categorized into three distinct stages. In the rotational angel in a range from 0\({}^{\circ}\) to 0.03\({}^{\circ}\), the bolt stress increases gradually, with the bolt primarily undergoing bending deformation. During this stage, the bolt does not make contact with the segmental bolt hole wall, and the rotation of the segment induces bending deformation in the bolt. In the rotational angel in a range from 0.03\({}^{\circ}\) to 0.045\({}^{\circ}\), the bolt stress increases more rapidly, with the bolt predominantly experiencing shear deformation. Here, the bolt comes into contact with the segmental bolt hole wall, which causes the bolt to undergo shear deformation. Once the rotational angle exceeds 0.045\({}^{\circ}\), the bolt stress reaches the yield strength, and the bolt is locally compressed by the segment's bolt hole wall. This leads to the yielding and potential failure of the bolt at the segment joint. To prevent shear failure of the bolts, it is recommended that the segment's rotation angle be maintained at less than 0.045\({}^{\circ}\) in practical engineering applications. Figure 14a shows the bolt stress distribution under different rotational angles (\(N=4000\) kN). As observed, the stress distribution across the bolts remains generally consistent across different joint configurations. With an increase in the rotation angle,  
Figure 13: Relationship between the bolt stress and rotational angle. (**a**) NMT; (**b**) MT. the bolt stress gradually rises. When \(\theta<0.03^{\circ}\), the bolt stress distribution is relatively uniform, and the stress levels are low. However, when \(\theta>0.045^{\circ}\), localized stress concentrations begin to occur in the bolts, with the maximum stress primarily concentrated at the joint. As the rotation angle exceeds \(\theta>0.09^{\circ}\), the stress at the contact section of the bolt reaches the yield strength, and the range in yielding progressively expands with further increases in rotation. Figure 14b shows the bolt stress distribution under different axial forces (\(\theta=0.135^{\circ}\)). It can be observed that, once the rotation angle reaches \(0.135^{\circ}\) and the stress level approaches 900 MPa, the bolts have already yielded under all conditions. Notably, the stress distribution remains consistent across varying axial force conditions, indicating that the rotation angle is the dominant factor influencing the stress behavior, rather than the axial load. Additionally, the presence or absence of the mortise and tenon has a minimal impact on the overall stress distribution. Instead, the primary factor driving the stress is the interaction between the bolts and the bolt holes. This interaction induces shear deformation as the bolts come into direct contact with the bolt holes during torsional loading, resulting in concentrated stress at the contact points. The observed high stress levels, regardless of the joint configuration, underscore the risk of shear failure in the bolts under torsional deformation. Although the mortise and tenon may provide additional stability, it does not significantly reduce the shear stress on the bolts.