## 5 Calculation of Load Carrying Capacity  
### Comparison Calculations of Load Carrying Capacity  
There are two main methods for calculating the load carrying capacities of corroded members. One is that the corrosion only causes the reduction of the cross-section, and maintains the material property unchanged [9; 10; 11; 12; 13; 14]. The other is that the corrosion does not change the cross-section of member, but results in the degradation of material property [17; 18; 19]. Based on the above two ideas, the load carrying capacities of members can be calculated according to the relevant formulas in  
Figure 11: Relation between degradation of stiffness and corrosion ratio. Figure 10: Relation between degradation of load carrying capacity and corrosion ratio. GB50017-2017 [26], EN 1993-1-1 [27] and ANSI/AISC 360-16 [28], as shown in Equations (3)-(8). The calculation results are shown in Table 3, where \(N_{\rm cs}\) and \(N_{\rm cm}\) are the load carrying capacities of specimens calculated considering the section reduction and the material degradation, respectively. It can be seen that the calculation results of three specifications have a certain safety margin, and \(N_{\rm cs}\) is slightly larger than \(N_{\rm cm}\) in the results, which are basically the same. (1) GB50017-2017  
\[\frac{N}{\varphi Af_{y}}+\frac{\beta M}{\gamma_{m}W\Big{(}1-0.8N/N_{Ex}^{\prime }\Big{)}f_{y}}\leq 1.0 \tag{3}\]  
\[N_{Ex}^{\prime}=\pi^{2}EA/\Big{(}1.1\lambda_{x}^{2}\Big{)} \tag{4}\]  
where \(N\) is the required axial strength, N; \(N_{Ex}^{\prime}\) is the parameter according to Equation (4); \(\varphi\) is the stability reduction coefficient of concentrically loaded member; \(A\) is the gross cross-sectional area, mm\({}^{2}\); \(\beta\) is the equivalent moment factor; \(M\) is the required moment strength, N\(\cdot\)mm; \(\gamma_{m}\) is the plastic adaption coefficient; and \(W\) is the gross section modulus, mm\({}^{3}\). (2) EN 1993-1-1  
\[\frac{\frac{N_{Ed}}{\frac{\chi_{y}N_{Rk}}{\gamma_{\rm MI}}}+k_{yy}\frac{M_{y, Ed}+\Delta M_{y,Ed}}{\frac{M_{y,Rk}}{\gamma_{\rm MI}}}+k_{yz}\frac{M_{z, Ed}+\Delta M_{z,Ed}}{\frac{M_{z,Rk}}{\gamma_{\rm MI}}}\leq 1.0 \tag{5}\]  
\[\frac{\frac{N_{Ed}}{\frac{\chi_{z}N_{Rk}}{\gamma_{\rm MI}}}+k_{zy}\frac{M_{y, Ed}+\Delta M_{y,Ed}}{\frac{M_{y,Rk}}{\gamma_{\rm MI}}}+k_{zz}\frac{M_{z, Ed}+\Delta M_{z,Ed}}{\frac{M_{z,Rk}}{\gamma_{\rm MI}}}\leq 1.0 \tag{6}\]  
where \(N_{Ed}\), \(M_{y,Ed}\), and \(M_{z,Ed}\) are the design values of the compression force and the maximum moments about the y-y and z-z axis along the member, respectively; \(N_{Rk}\), \(M_{y,Rk}\), and \(M_{z,Rk}\) are the characteristic value of resistance to compression and the characteristic value of resistance to bending moments about the y-y and z-z axis along the member, respectively; \(\Delta M_{y,Ed}\) and \(\Delta M_{z,Ed}\) are the moments due to the shift of the centroidal axis; \(\chi_{y}\) and \(\chi_{z}\) are the reduction factors due to flexural buckling; \(\chi_{LT}\) is the reduction factor due to lateral torsional buckling; \(\gamma_{M1}\) is the partial factor, 1.0; and \(k_{yy}\), \(k_{yz}\), \(k_{zy}\), and \(k_{zz}\) are the interaction factors. (3) ANSI/AISC 360-16 When \(\frac{P_{r}}{P_{c}}\geq 0.2\)  
\[\frac{P_{r}}{P_{c}}+\frac{8}{9}\bigg{(}\frac{M_{rx}}{M_{cx}}+\frac{M_{yy}}{M_{ cy}}\bigg{)}\leq 1.0 \tag{7}\]  
When \(\frac{P_{r}}{P_{c}}<0.2\)  
\[\frac{P_{r}}{2P_{c}}+\bigg{(}\frac{M_{rx}}{M_{cx}}+\frac{M_{ry}}{M_{cy}}\bigg{)} \leq 1.0 \tag{8}\]  
where \(P_{r}\) is the required axial strength, kips (N); \(P_{c}\) is the design axial strength, \(P_{c}=\phi_{c}P_{n}\), kips (N); \(M_{r}\) is the required flexural strength, kip-in (N\(\cdot\)mm); \(M_{c}\) is the design flexural strength, \(M_{c}=\phi_{b}M_{n}\),kip-in (N\(\cdot\)mm); \(\phi_{c}\) is the resistance factor for compression, 0.9; \(\phi_{b}\) is the resistance factor for flexural, 0.9; \(x\) is the subscript relating symbol to major axis bending; and \(y\) is the subscript relating symbol to minor axis bending.