## 4 Analysis of Bending Stiffness Calculation Coefficients  
The cement bond primarily transmits the bending moment based on the distribution of tension and compression in the height direction, and cracks occur in some locations. Therefore, the cement bond should be involved in the calculation according to the secant modulus when it is in the elastic-plastic state. According to the stress-strain curve of concrete, the secant modulus at any moment can be expressed as the product of the initial elastic modulus and an elastic coefficient. Equation (26) is based on the initial modulus of elasticity of the cement bond, and the calculated result differs from the actual value by an elasticity factor, \(\mu\). Therefore, the equivalent bending stiffness of the flange joint becomes the following:  
\[\frac{1}{K_{c}}\ =\ \frac{1}{K_{c1}}+\frac{1}{\mu\times K_{c2}}+\frac{1}{K_{c3}} \tag{27}\]  
The outer diameter of the UHV electrical equipment ranges from 130 to 700 mm. To determine the value of the elasticity coefficient, \(\mu\), we selected nine representative UHV porcelain bushings [18; 22] as test specimens, as shown in Figure 6. Their basic parameters are listed in Table 1, where the thickness of the flange ring wall was assigned according to that of the conventional flange. In addition, a test loading device was designed in the literature [18; 22] to measure the bending stiffness of the joints connecting porcelain bushings and flanges. The device measured the relative rotation angle of the joints under the action of a specific bending moment, and the ratio of bending moment to angle characterizes the bending stiffness of the joints. Therefore, all nine specimens cited in this paper have corresponding experimental bending stiffness values. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline
**Specimen** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline Outside diameter, \(d_{c}\) & 130 & 130 & 140 & 160 & 205 & 245 & 275 & 375 & 500 \\ Inside diameter, \(\mathrm{d}_{b}\) & 80 & 80 & 80 & 105 & 125 & 145 & 175 & 275 & 420 \\ Bushing length & 1265 & 1275 & 1365 & 1385 & 1615 & 1615 & 1875 & 2500 & 2650 \\ Cement height, \(h_{c}\) & 60 & 55 & 60 & 65 & 85 & 100 & 110 & 170 & 230 \\ Cement thickness, \(t_{e}\) & 10 & 9 & 10 & 10 & 10 & 7.5 & 7.5 & 9 & 10 \\ Outside diameter, \(D_{f}\) & 192 & 190 & 202 & 224 & 252 & 304 & 348 & 456 & 580 \\ Inside diameter, \(d_{f}\) & 150 & 148 & 160 & 180 & 225 & 260 & 290 & 393 & 520 \\ \hline \end{tabular}
\end{table} 
Table 1: Specim size properties (Unitmm). Figure 6: Ultra-high voltage porcelain bushings. In the above specimens, the flange material of specimens 1-4 and 6 was cast aluminum, and the flange material of specimens 5 and 7-9 were cast iron. The modulus of elasticity, \(E_{g}\), of the cement bond; modulus of elasticity, \(E_{c}\), of porcelain bushing; modulus of elasticity of cast aluminum, and modulus of elasticity of cast iron were taken as 24 GPa, 90 GPa, 70 GPa, and 100 GPa, respectively. According to the above parameters, the bending stiffness of the porcelain bushing, \(K_{c1}\); the flange, \(K_{c3}\); and the cement bond, \(K_{c2}\), were calculated using Equations (4), (5), and (26), respectively. The equivalent bending stiffness value without considering the elasticity coefficient, \(\mu\), can be calculated using Equation (3). The literature [18,22] provides the experimental bending stiffness values for the nine specimens. The specific value of the elasticity coefficient, \(\mu\), in Equation (27) can be obtained by comparing the calculation results of Equation (3) with the experimental values, as summarized in Table 2.  
With an increase in the height of the cement bond in the flange, the bending stiffness of the joint connecting the porcelain bushing and flange gradually increases, and the load that can be borne will also gradually increase.