## 4 Numerical Tests on Mechanical Performance Following Secondary Pre-Tightening of Supports
### Simulation and Analysis of U29 Steel Supports
#### 4.2.3 Results Analysis
300 N-m, the support bearing capacity increased from 612 kN to 687 kN and 716 kN, and the rates of change in the secondary pre-tightening bearing capacity were 12% and 17%, respectively. It was observed that when the secondary pre-tightening torque was less than the initial torque, this had no obvious enhancing effect on the support bearing capacity; the higher the secondary pre-tightening torque, the more significant was the enhancement of the support bearing capacity. In terms of the support joint yield pressure, under conditions of an initial pre-tightening torque of 200 N-m, after applying secondary pre-tightening torques of 100 N-m and 150 N-m, the support joint yield pressure decreased from 365 mm to 360 mm and 355 mm, and the rates of change in the secondary pre-tightening joint yield pressure amounted to only 1.7% and 2.7%, respectively. When the secondary torque was increased to 200 N-m and 300 N-m, the support joint yield pressure decreased from 365 mm to 330 mm and 315 mm, and the rates of change in the secondary pre-tightening bearing capacity were 9.6% and 13.7%, respectively. Thus, it can be seen that when the secondary pre-tightening torque is less than the initial torque, this has no obvious influence on the yield-pressure performance of the support joint; the higher the secondary pre-tightening torque, the more significant is its the influence on the slippage performance of the support joint. Analysis of the Influence of the Timing of Secondary Pre-tightening  
Under conditions where both the initial pre-tightening torque and the secondary pre-tightening torque were 200 N-m, comparison of the influence of different timings of secondary pre-tightening on the support bearing capacity is shown in Figure (a)a, and comparison of the influences on the support joint yield pressure is shown in Figure (b)b. Regarding the support bearing capacity, it can be seen from Figure (a)a,b that when the secondary pre-tightening torque was applied at 30% and 40% of the ultimate yield pressure of the joint, the support bearing capacity increased from 612 kN to 635 kN and 642 kN, and the rates of change in the secondary pre-tightening bearing capacity were only 3.8% and 4.9%, respectively. When the secondary pre-tightening torque was applied at 50% and 70% of the ultimate yield pressure of the joint, the support bearing capacity increased to 687 kN and 706 kN, and the rates of change in the secondary pre-tightening bearing capacity were 12.3% and 15.4%, respectively. Thus, it was observed that when the secondary pre-tightening torque was applied before the joint underwent sufficient slippage, the enhancing effect on the support bearing capacity was limited; meanwhile, when the secondary pre-tightening torque was applied after the joint had slipped by more than 50% of the ultimate yield pressure, the enhancing effect on the support bearing capacity was significant. Figure 11: Analysis of the impact of secondary pre-tightening of brackets. Regarding the support joint yield pressure, when the secondary pre-tightening torque was applied at 30% and 40% of the ultimate yield pressure of the joint, the support joint yield pressure decreased from 365 mm to 355 mm and 350 mm, and the rates of change in the secondary pre-tightening joint yield pressure were only 2.7% and 4.1%, respectively. When the secondary pre-tightening torque was applied at 50% and 70% of the joint's ultimate yield pressure, the yield pressure on the joint decreased from 365 mm to 330 mm and 310 mm, and the rates of change in the secondary pre-tightening joint yield pressure were only 12.3% and 15.1%, respectively. It was observed that when the secondary pre-tightening torque was applied before the joint had slipped sufficiently, the degree of influence degree on the yield-pressure performance of the support was low; when the secondary pre-tightening torque was applied after the joint had slipped by more than 50% of the ultimate yield pressure, the influence on the support's yield pressure performance was significant.