# Experimental Study on Mechanical Behavior of Shear Connectors of Square Concrete Filled Steel Tube
## 4 Calculation of the Ultimate Bearing Capacity  
The test results show that the specimens fail because of the shear failure of the concrete and the stress state is shown in Figure 10. 'Recommendations for Design and Construction of Concrete Filled Steel Tubular Structures' [15] gives the Equation (4) to calculate the ultimate bearing capacity.  
\[P_{u}=\sqrt{A_{c}\cdot A_{b}}\cdot f_{c}^{\prime} \tag{4}\]  
In Equation (4), the width-to-thickness ratio (\(B/t\)) is not taken into consideration because in reference 15, rather than steel plates, the diaphragms are adopted as the shear connectors. When using diaphragms, the confinement caused by the diaphragms is very strong, so that the \(B/t\) effect can be omitted. However, when using steel plates as the shear connectors, the \(B/t\) effect should not be omitted. Hence, considering the \(B/t\) effect, the coefficient \(\alpha\) corresponding to the \(B/t\) ratio has been proposed, and the following Equation (5) can be obtained.  
\[P_{u}=\alpha\cdot P_{c1}=\alpha\cdot A_{b}\cdot\sqrt{A_{c}/A_{b}}\cdot f_{c}^{ \prime}=\alpha\cdot\sqrt{A_{c}\cdot A_{b}}\cdot f_{c}^{\prime} \tag{5}\]  
Figure 9: Strain characteristics of specimen P8-8-0-120. (**a**) Load-strain curves; (**b**) Strain distribution.  
Equation (6) has been developed for calculating the ultimate bearing capacity of double-layer shear connectors.  
\[P_{u}=\alpha\cdot\beta\cdot P_{c1}=\alpha\cdot\beta\cdot\sqrt{A_{c}\cdot A_{b}} \cdot f_{c}^{\prime} \tag{6}\]  
where \(P_{u}\) is the ultimate bearing capacity; \(A_{c}\) is the cross-sectional area of the core concrete; \(A_{b}\) is the projection area of the steel plate as shown in Figure 10; and \(f_{c}^{\prime}\) is the concrete strength. \(\alpha\) is the influential factor for the width to thickness ratio of the steel tube, as given by Figure 11; In Figure 11, the black dots are the test data; the solid curve is the fitting curve; \(\beta\) is the influential factor for the _s/n_ ratio of steel plates, as given in Equation (3) and Figure 8.  
The comparison of the calculated ultimate bearing capacities and the test data is shown in Table 5. It can be seen that the calculated capacities are in good agreement with the test datas. The average test data to calculated values ratio is 1.068. For some specimens, the value of \(P_{u,exp}/P_{u,cal}\) is relative higher, especially for specimens P12-8-150-120 and P8-8-150-150, the values are 15.3% and 22.3%. For specimen P12-8-150-120, the steel plate is thicker, and for specimen P8-8-150-150, the steel plate is longer. Hence, for both specimens, the confinement caused by the steel plate is stronger than other specimens. According to reference [15], the confinement to the concrete is not considered in the calculation, hence, the calculation will slightly underestimate the experimental results. In other words, the values of \(P_{u,exp}/P_{u,cal}\) becomes higher. However, these calculated capacities are in conservative side, therefore, the developed formula for calculating the ultimate bearing capacity can be used in engineering design.  
Figure 11: Influence factor \(\alpha\) of width to thickness ratio.  
Figure 10: Stress state of shear connector.