## 3 Experimental Results
### Distributive Relationship of Headed Bar Force
#### 3.5.1 Effects of Lap Length  
The distributive relationship between bond behavior and head bearing among specimens with different lap lengths is given in Figure 17. The plateau region of the curves represents the yielding of headed bars. It can be concluded that the increase in lap length reduces the contribution by head bearing with the increased contribution by bond behavior. Details can be seen in the following.  
Figure 16: Stirrup skeleton after the test.  
Figure 17: Distribution of headed bar force among specimens with different lap length (**a**) Specim M4-D12-6d; (**b**) Specim M4-D12-7.5d; (**c**) Specim M4-D12-9d.  
At the early stage of loading, for the specimens with a smaller lap length (specimen M4-D12-6d), the headed bar tensile force is mainly carried by concrete compression at the head; for the specimens with a lap length equal to 7.5 times the headed bar diameter (specimen M4-D12-7.5d), these two force components are close to each other; for the specimens with a larger lap length (specimen M4-D12-9d), the force carried by the concrete compression at the head is smaller than that sustained by the bond behavior. In terms of stiffness, the stiffness of CHBC is the superposition of the concrete compression stiffness at the head and the stiffness of the bond behavior. At the early stage of loading, for the specimens with a smaller lap length (specimen M4-D12-6d), the stiffness of the head bearing is significantly larger than that of the bond; for the specimens with a lap length equal to 7.5 times the headed bar diameter (specimen M4-D12-7.5d), these two stiffness components are close to each other but with increase in the tensile load, the stiffness of the head bearing tends to be greater than that of the bond; for the specimens with a larger lap length (specimen M4-D12-9d), the stiffness of the head bearing is lower than that of the bond but similar to specimen M4-D12-7.5d, the stiffness of the head bearing tends to be greater than that of the bond as the load increases. The \(F_{b}\)/\(F_{h}\) values for the yielding of headed bars are given in Figure 18. Approximately, the \(F_{b}\)/\(F_{h}\) values increase linearly with the lap length, and the larger value of \(F_{b}\)/\(F_{h}\) indicates the lower contribution of the head bearing with more contributed by bond behavior. When the lap length of six times the headed bar diameter is increased by 25% and 50%, the \(F_{b}\)/\(F_{h}\) value is increased by 160.9% and 310.0%, respectively. In summary, in terms of the load-bearing contribution and stiffness, the increase in lap length decreases the contribution by head bearing.  
In the comparison of head bearing among specimens with a different lap length, similarity in stiffness of head bearing can be found as highlighted in Figure 19. The reason for the trend is that the head bearing functions as the concrete at the head is under compression, then the stiffness of the head bearing is actually related to the concrete compression elastic modulus. Since the same concrete and head geometry are adopted among these three types of specimens, similarity is thus found for their stiffness of head bearing.  
Figure 18: Relationship between \(F_{b}\)/\(F_{h}\) and lap length.  
The bond force and average bond stress before the yielding of the headed bar are shown in Figure 20. The average bond stress is determined by \(\overline{\tau}=F_{b}/(\tau dl_{lap})\). When the lap length of six times of the headed bar diameter is increased by 25% and 50%, the value of \(F_{b}\) is increased by 103.0% and 163.8%, respectively, while the average bond stress is increased by 62.1% and 71.9%, respectively. Additionally, the development of average bond stress for specimen M4-D12-7.5d and specimen M4-D12-9d is similar. In addition, for specimens with a different lap length, the average bond stress is approximately linearly increased with the applied tension load.