## 3 Experimental Results
### Distributive Relationship of Headed Bar Force
#### 3.5.2 Effects of Head Size  
The distributive relationship of bond behavior and head bearing among specimens with different head sizes is shown in Figure 21. Additionally, the plateau region of the curves represents the yielding of headed bars. For the head size increases from 3\(A_{s}\) (specimen M3-D12-7.5d) to 4\(A_{s}\) (specimen M4-D12-7.5d), both the head-bearing stiffness at an early stage and the head-bearing force at the yielding of headed bars increase. For the head size increases from 4\(A_{s}\) (specimen M4-D12-7.5d) to 6\(A_{s}\) (specimen M6-D12-7.5d), a slight decrease can be observed in the stiffness of the head bearing at an early stage with a small increase in the head-bearing force at the yielding of the headed bars. For the head size increases from 6\(A_{s}\) (specimen M6-D12-7.5d) to 8\(A_{s}\) (specimen M8-D12-7.5d), both the stiffness and head-bearing force change little. Figure 19: Comparison of head bearing among specimens with different lap length. Figure 20: Bond behavior with different lap length (**a**) Bond force; (**b**) Average bond stress. The \(F_{b}/F_{h}\) values for the yielding of headed bars are shown in Figure 22. In general, the \(F_{b}/F_{h}\) values decrease with the increase in the head size, indicating the increase in head size improves the contribution by head bearing. In general, the head-bearing force and the stiffness improve with the increase in head size. Additionally, when the head size is increased by 100% (increasing from \(4A_{s}\) to \(8A_{s}\)), the \(F_{b}/F_{h}\) value is decreased by 20.8% and the change in the \(F_{b}/F_{h}\) value induced by the change of head size is considerably smaller than that of the lap length. In addition, specimen M3-D12-7.5d shows a remarkable difference compared to other specimens. Similar situations can be seen in Figure 23 in which both the head-bearing response and bond behavior of specimen M3-D12-7.5d are distinct from the other specimens which show a similar response. Figure 21: Distribution of headed bar force among specimens with different head size (**a**) Specimen M3-D12-7.5d; (**b**) Specimen M4-D12-7.5d; (**c**) Specimen M6-D12-7.5d; (**d**) Specimen M8-D12-7.5d. Figure 22: Relationship between \(F_{b}/F_{h}\) and head size. Although the change in head size can induce the change in head-bearing response, the reasons for the enormous difference for specimen M3-D12-7.5d may be caused by the specimen's manufacture. Perforated plug welding (Figure 24) is adopted in the connection of head and headed bar, while welding fillet on the head-bearing surface is inevitable. Such a welding fillet effect can reduce the bearing surface area of the head and therefore, the head-bearing capacity is diminished. For specimen M3-D12-7.5d, the difference between the head and steel bar in dimension is relatively small. The side length of the square head is equal to 18 mm while the diameter of the headed bar is equal to 12 mm for specimen M3-D12-7.5d. So, the welding fillet effect is strong and it can greatly reduce the bearing surface area of the head, which changes the contribution by head bearing to a great extent. The average bond stress before yielding of headed bar is shown in Figure 25. When the head size is increased by 100% (increasing from 4\(A_{s}\) to 8\(A_{s}\)), the value of \(F_{b}\) is decreased by 15.0% and the average bond stress is decreased by 16.8%. In addition, the average bond stress and bond stiffness of specimen M3-D12-7.5d is significantly higher than the other specimens which show a similar bond stress development, due to the welding fillet effect mentioned above. Additionally, the average bond stress of specimen M3-D12-7.5d is larger than the peak bond stress specified in Chinese code GB/T 50010-2020 [37] which is equal to three times the concrete tensile strength. It should be noted that the peak bond stress is related to the concrete cover thickness and stirrup ratio and the required concrete cover thickness specified in Chinese code GB/T 50010-2020 [37] is two times larger than the steel bar diameter.