## 4 Analysis of the Bearing Capacity and Crack Width of SCGCs
### Crack Width  
Structural components must not only meet the relevant requirements for bearing capacity but also control cracks and deformations during their service life. According to the JGJ12-2006 [41], the calculation formula for the maximum crack width (\(\omega_{\mathrm{max}}\)) of rectangular columns under combined compression and bending is as follows:  
\[\omega_{\mathrm{max}}=\alpha_{\mathrm{cr}}\psi\frac{\sigma_{\mathrm{s}}}{E_{ \mathrm{s}}}\bigg{(}1.9C+0.04\frac{d_{\mathrm{eq}}}{\rho_{\mathrm{te}}}\bigg{)} \tag{17}\]where \(\alpha_{\rm cr}\) is the structural characteristic coefficient; \(\psi\) is the non-uniformity coefficient, \(\psi=1.1-0.65f_{\rm t}/\rho_{\rm te}\sigma_{\rm s}\); \(\sigma_{\rm s}\) is the tensile stress of the SSR, in MPa; \(E_{\rm s}\) is the elastic modulus of the steel, in GPa; \(C\) is the concrete cover thickness, in mm; \(\rho_{\rm te}\) is the ratio of the SSR cross-sectional area \(A_{\rm f}\) to the effective tensile area of the concrete \(A_{\rm te}\), \(\rho_{\rm te}=A_{\rm f}/A_{\rm te}\), where \(A_{\rm te}=0.5 bh\), \(h\) and \(b\) are the height and width of the cross-section, respectively; and \(d_{\rm eq}\) is the equivalent diameter of the longitudinal tensile reinforcement, in mm, \(d_{\rm eq}=\sum_{i}{\rm{d}}_{i}{\rm{d}}^{2}/\sum_{i}{\rm{v}}_{i}{\rm{d}}_{i}\), where \(d_{i}\), \(n_{i}\), and \(v_{i}\) are the nominal diameter (mm), number of bars, and relative bond characteristic coefficient of the \(i\)-th type of longitudinal tensile reinforcement, respectively. As shown in Figure 28 (taking SCGC1, SCGC3, SCGC4, and SCGC7 for examples), the calculation formulas proposed by the aforementioned three standards fail to accurately describe the \(N/f_{\rm c}bh\)-crack width curve. Considering the following factors: (i) the bond performance between the CAGC and SSR differs from that between OPC and carbon steel bars, so the \(\psi\) calculation formula has been revised as shown in Equation (18); (ii) under a small eccentric load, the tensile SSR strain \(\varepsilon_{\rm s}=\varepsilon_{\rm cu}(h_{0}/x_{\rm c}-1)\), while under a large eccentric load, the tensile SSR strain \(\varepsilon_{\rm s}=\varepsilon_{\rm y}\). In summary, the revised crack width calculation formula is shown below. \[\left\{ \begin{array}{l}\omega_{\rm max}=\alpha_{\rm cr}\psi e_{\rm s}\bigg{(} 1.9C+0.04\frac{d_{\rm eq}}{\rho_{\rm te}}\bigg{)}\\ \psi=1.65-0.975f_{\rm t}/\rho_{\rm te}\sigma_{\rm s}\end{array} \right. \tag{18}\]  
Columns, which in actual engineering practice, are typically subjected to standard combination and quasi-permanent combination loads according to the GB50068-2018 [42]. The load factor \(\gamma\) is 1.367 for the standard combination. The relationship between the axial force \(N_{\rm k}\) under the standard combination and the axial force design value  
Figure 28: Comparison of test and predicted \(N/f_{\rm c}bh\)–crack width curves. is \(N_{\rm k}=N/1.367=0.7N\). Similarly, the load factor \(\gamma\) is 1.64 for the quasi-permanent combination. The relationship between \(N_{\rm k}\) under the quasi-permanent combination and \(N\) is \(N_{\rm k}=N/1.64=0.6N\). Therefore, the standard combination and quasi-permanent combination loads correspond to 70% and 60% of the ultimate load, respectively. As shown in Figure 28, Equation (18) not only accurately predicts the crack width under standard combination (70% \(N_{\rm u}\)) and quasi-permanent combination (60% \(N_{\rm u}\)) loads but also effectively captures the overall trend of the \(N/f_{\rm c}bh\)--crack width curve. This paper proposes a column structure using a novel material--SCGC--that demonstrates the potential for practical application in island and marine buildings. The use of coral aggregates reduces material transportation costs and carbon emissions, while SSRs can help the structure face the durability challenges posed by the marine environmental context and extend the service life of marine structures. Therefore, this paper suggests the use of SCGC in the marine area with more coral waste.