## 3 Study on the Main Bending Form of Hangers
### Experimental Study on the Ultimate Tensile Strength of the Seven-Wire Strands under Lateral Bending  
A tensile test of the seven-wire strands under lateral bending was implemented to confirm the accuracy of the results of the finite element analysis. In this test, the lateral bending angle was set for the seven-wire strands by setting the places for the anchorage opening on the anchor plates at both ends. Normally, the anchorage openings on the anchor plates at opposite ends of the seven-wire strand share one axis, which can help the anchored seven-wire strands to remain straight under tension. When the anchorage openings on the anchor plates at opposite ends of the seven-wire strand have different axes, the seven-wire strand will bend (as shown in Figure 16). Thus, four pairs of anchorage openings (as shown in Figure 17a) were set on two anchor plates (due to the limitations of the area of the anchor plate, four anchorage openings at most can be set on an anchor plate). When the seven-wire strand is anchored through different pairs of anchorage openings, the lateral bending angle is set at different values (as shown in Figure 18). In order to maintain consistency with the finite element analysis in the previous section, the lateral bending angles are set, as follows: 0 mrad, 10 mrad, 20 mrad, and 30 mrad. The anchor plate is then attached to the reaction frame, and a single strand is tensioned on the reaction frame each time. The length of tested seven-wire strands is 1.14 m and the length of tested strands cannot reach to the length of real hangers due to the limitation on the size of the reaction frame, so the tests here are scale model tests and the effect that is caused by the scale of components is not considered [34]. According to [35; 36], the order of applying loads to cables does not influence the finally stress state of cables so we can set the angles for seven-wire strands before applying tensile stress in the test.  
The tensile tests were repeated three times at each lateral bending angle. The seven-wire strands were tensioned to break (shown in Figure 17b), and Table 2 records the breaking forces.  
strength of the seven-wire strands at different lateral bending angles, as obtained by the finite element analysis, is chosen to conduct further studies, since the production lot decides the performance of each seven-wire strand in the test at random. The fitting curve (as shown in Figure 19b) of the ultimate tensile strength of the seven-wire strands at different lateral bending angles is  
\[y=-14.03x+1800 \tag{18}\]  
where \(y\) is the ultimate tensile strength \(\sigma_{u}\) of the seven-wire strands under lateral bending, and the unit is \(\text{MPa}\); \(x\) is the lateral bending angle \(\theta\) of the seven-wire strands, and unit is \(\text{mrad}\).  
It can be calculated using formula (18) that the ultimate tensile strength of the seven-wire strands in the hangers decreases by 23.3% when the lateral bending angle is 30 mrad. Such a drastic reduction of strength in the seven-wire strands indicates that the adverse influence of lateral bending cannot be ignored and it necessitates a method for assessing the safety of seven-wire strands in hangers under lateral bending.