## 5 Design Method  
### Bearing Capacity Contributed by Bond and Head  
The basic form of the CHBC is steel bar splice which can be treated as the mutual anchorage of two steel bars. So, the bearing capacity of CHBC can be regarded as the anchorage capacity of single headed bar. In addition, it is known that the bearing capacity of CHBC consists of the bond behavior force and concrete compression-bearing force at head (Figure 37). Therefore, based on the superposition method, Equation (2) can be obtained:  
\[F_{u}=F_{h,u}+F_{b,u} \tag{2}\]  
where \(F_{u}\) is the bearing capacity of the CHBC; \(F_{h,u}\) is the contribution by concrete compression at head; \(F_{b,u}\) is the contribution by bond behavior. To determine the \(F_{h,u}\), the STM model as shown in Figure 38 is adopted. Figure 37: Capacity of CHBC (**a**) Sketch of the CHBC; (**b**) Head bearing and bond behavior. Figure 36: Stress contour at different level of height. Under the tension of headed bars, the heads are under compression. The heads are assumed to be a rigid body, then the heads can be considered as the load plate and support end in the beam. So, it can be regarded as the concrete beam with a small shear-span ratio subjected to shear force. Then, the force transmission mechanism at the lap zone concrete can be described as the trapezoidal truss. The \(AB\) component together with the \(CD\) component in the STM model is the diagonal concrete strut and the angle of the strut is the angle \(a\) mentioned above while the \(AD\) component represents the tension tie of stirrup. The forces are balanced at node \(A\) or node \(D\) and it can be regarded as the C-C-T node. Then, based on the trigonometric relation, the following Equation (3) can be determined:  
\[ \begin{array}{l}F_{AB}=F_{h}/\cos\alpha\\ F_{AD}=F_{h}\tan\alpha\end{array}  \tag{3}\]  
The capacity of the diagonal strut (\(AB\) component) is the multiplication of the strut cross-sectional area and concrete strength. The depth of the strut is equal to the side length of the square head [41] while the width of the strut can be determined according to [PERSON] and [PERSON]'s studies [51]. In addition, the concrete in CHBC is confined by the stirrup and therefore, the confined concrete strength should be adopted instead. The definition of the confined concrete strength is provided by the research work of [PERSON] [52]. It should be noted that the unconfined concrete strength is equal to the cubic concrete strength in the material test of this paper in order to verify the prediction accuracy while the design concrete strength can be adopted in design for safety. In addition, the yield strength of the stirrup is adopted to determine the capacity of the tension tie (\(AD\) component). The capacity of the diagonal strut and tension tie can be determined through Equation (4):  
\[ \begin{array}{l}F_{AB}=f_{cc}a_{h}l_{lap}\sin a\\ f_{cc}=f_{c}(-1.254+2.254\sqrt{1+\frac{7.94}{f_{c}}}-2\frac{f_{c}^{\prime}}{f_ {c}})\\ \tan a=s/l_{lap}\\ F_{AD}=n\times f_{y,p}\times A_{s,p}\end{array}  \tag{4}\]  
where \(n\) is the number of the stirrup rebars; \(f_{y,p}\) and \(A_{s,p}\) are the tensile strength and cross-sectional area of the stirrup rebar. Capacity of the C-C-T node is limited by the strength of concrete compression strut and stirrup tension tie. So, Equation (5) can be adopted to determine the C-C-T node strength as well as the \(F_{h,u}\):  
\[ \begin{array}{l}F_{h,u}=\min\left\{\begin{array}{l}F_{AB}\cos a\\ F_{AD}/\tan a\end{array}\right\}=\min\left\{\begin{array}{l}f_{cc}a_{h}l_{lap }\sin a\cos a\\ nf_{y,p}A_{s,p}/\tan a\end{array}\right\}\end{array}  \tag{5}\]  
Figure 38: Strut-and-tie model (**a**) Force at heads; (**b**) STM model; (**c**) C-C-T node. It is known that the bond stress is unevenly distributed along the anchorage length for steel bar. The uneven distribution relationship can be described by Equation (6) referring to [PERSON]'s study [53]:  
\[\tau(x)/\overline{\tau}=\left\{