## 4 Axial Load-Bearing Capacity of Concrete-Filled Steel Tubes
### Circular Composite Sections  
For the circular composite section, the area for the concrete core can be computed from  
\[\text{A}_{\text{c}}=\frac{\pi(\text{D}-2t)^{2}}{4} \tag{10}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Ref. ** & **L (mm)** & **B (mm)** & \(\mathbf{t_{f}}\) (mm)** & **H (mm)** & \(\mathbf{t_{w}}\) (mm) & \(\mathbf{f_{y}}\) (MPa) & \(\mathbf{f_{c}}\) (MPa) & \(\mathbf{P_{exp}}\) (kN) & \(\mathbf{P_{pred}}\) (kN) & \(\mathbf{P_{pred}}\)/\(\mathbf{P_{exp}}\) \\ \hline \multirow{10}{*}{[19]} & 1318.3 & 329.9 & 4.47 & 329.9 & 4.47 & 370.3 & 31.6 & 4363.3 & 4864.3 & 1.11 \\  & 1328.4 & 331.0 & 4.47 & 331.0 & 4.47 & 370.3 & 27.4 & 4411.7 & 4510.8 & 1.02 \\  & 1320.8 & 331.0 & 4.50 & 331.0 & 4.50 & 370.3 & 27.4 & 4656.8 & 4520.3 & 0.97 \\  & 1318.3 & 331.0 & 4.50 & 331.0 & 4.50 & 370.3 & 31.6 & 4411.7 & 4901.2 & 1.11 \\  & 1318.3 & 333.0 & 6.38 & 333.0 & 6.38 & 444.7 & 31.6 & 5862.8 & 6207.0 & 1.06 \\  & 1318.3 & 331.0 & 6.30 & 331.0 & 6.30 & 444.7 & 31.6 & 5843.2 & 6113.8 & 1.05 \\  & 1318.3 & 331.0 & 6.32 & 331.0 & 6.32 & 444.7 & 27.4 & 5833.4 & 5742.2 & 0.98 \\  & 1320.8 & 331.0 & 6.32 & 331.0 & 6.32 & 444.7 & 27.4 & 5637.2 & 5742.5 & 1.02 \\ \hline \multirow{10}{*}{[20]} & 800.0 & 150.0 & 1.40 & 150.0 & 1.40 & 247.3 & 22.5 & 711.5 & 655.5 & 0.92 \\  & 800.0 & 150.0 & 2.10 & 150.0 & 2.10 & 248.5 & 22.5 & 792.8 & 710.2 & 0.90 \\  & 800.0 & 200.0 & 1.40 & 150.0 & 1.40 & 247.0 & 22.5 & 881.0 & 868.3 & 0.99 \\  & 800.0 & 200.0 & 2.10 & 150.0 & 2.10 & 248.3 & 22.5 & 843.8 & 914.3 & 1.08 \\  & 800.0 & 150.0 & 1.40 & 150.0 & 1.40 & 247.3 & 35.3 & 973.1 & 911.1 & 0.94 \\  & 480.0 & 200.0 & 1.40 & 150.0 & 1.40 & 247.0 & 33.7 & 1191.7 & 1167.4 & 0.98 \\  & 800.0 & 200.0 & 2.10 & 150.0 & 2.10 & 248.3 & 35.3 & 1288.4 & 1231.2 & 0.96 \\ \hline \multirow{10}{*}{[21]} & 485.1 & 323.1 & 4.37 & 323.1 & 4.37 & 261.3 & 25.4 & 3365.5 & 3465.6 & 1.03 \\  & 485.1 & 323.1 & 4.37 & 323.1 & 4.37 & 261.3 & 41.0 & 4949.1 & 4720.8 & 0.95 \\  & 485.1 & 323.1 & 4.37 & 323.1 & 4.37 & 261.3 & 41.0 & 4828.5 & 4720.8 & 0.98 \\  & 485.1 & 323.6 & 4.37 & 323.6 & 4.37 &and the area for the steel tube is given by  
\[\text{A}_{\text{s}}=\frac{\pi\text{D}^{2}}{4}-\frac{\pi(\text{D}-2t)^{2}}{4} \tag{11}\]  
The strict contribution of the concrete core to the maximum axial load can be found by  
\[P_{c}=\text{A}_{c}\text{f}_{c}=\bigg{[}\frac{\pi(\text{D}-2t)^{2}}{4}\bigg{]} \text{f}_{c} \tag{12}\]  
while the corresponding contribution of steel tube is given by  
\[P_{\text{s}}=\text{A}_{\text{s}}\text{f}_{y}=\bigg{[}\frac{\pi\text{D}^{2}}{4}- \frac{\pi(\text{D}-2t)^{2}}{4}\bigg{]}\text{f}_{y} \tag{13}\]  
To quantify the composite action for the aforementioned contribution of the discrete materials, the following empirical expressions can be expressed for the concrete core  
\[{P^{\prime}}_{c}=a_{c}P_{c}=\bigg{[}a_{1}+a_{2}\bigg{(}\frac{D}{t}\bigg{)}+a_{ 3}\bigg{(}\frac{f_{y}}{f_{c}}\bigg{)}\bigg{]}P_{c} \tag{14}\]  
where \(a_{c}\) and \(a_{1}\)-\(a_{3}\) are parameters that are presented in Table 3. Similarly, the effective axial force for the steel tube is given by  
\[{P^{\prime}}_{s}=b_{s}P_{s}=\bigg{(}\text{b}_{1}+\text{b}_{2}\bigg{(}\frac{D}{ t}\bigg{)}+\text{b}_{3}\bigg{(}\frac{f_{y}}{f_{c}}\bigg{)}\bigg{)}P_{s} \tag{15}\]  
where \(\text{b}_{s}\) and \(\text{b}_{1}\)-\(\text{b}_{3}\) are parameters that are presented in Table 3. It should be mentioned that D is the circular section's diameter and t is the steel tube section thickness.