## 3 Equivalent Bending Stiffness Model of the Joint Connecting the Porcelain Bushing and Flange
Therefore, the sum of the moments, \(M\), of the adhesive side wall compression force on the center of rotation in Figure 3a and its strain energy, \(W(e)\), are as follows:  
\[M\ =\ \int_{0}^{h_{c}}k_{z}\Delta_{x}(z)(z-e)\ =\ \gamma E_{g}\theta_{2}\Bigg{[} \frac{\left(h_{c}-e\right)^{3}}{3}+\frac{e^{3}}{3}\Bigg{]} \tag{13}\]  
\[W(e)\ =\ \frac{1}{2}M\theta_{2} \tag{14}\]  
We consider the rotation of the cement bond to be performed with minimum strain energy, i.e., \(\frac{\mathrm{d}W(e)}{\mathrm{d}e}\ =\ 0\). Then, \(e=h_{c}/2\), yielding the following:  
\[M\ =\ \frac{1}{12}\gamma E_{g}h_{c}^{3}\theta_{2} \tag{15}\]  
\[k_{x}(y)\ =\ \frac{E_{g}\text{d}z\text{d}y}{t_{x}(y)} \tag{8}\]0  
The Rayleigh-Ritz method can be used to solve the effect of the porcelain bushing deformation on the extrusion of the cement bond, as shown in \[k_{x}(y)\ =\ \frac{E_{g}\text{d}z\text{d}y}{t_{x}(y)} \tag{8}\]1  
Assuming that there is horizontal extrusion deformation of the cement bond under the action of the bending moment and rotation angle of the porcelain bushing, \(\theta_{2}\), the force distribution of the cement bond after deformation is shown in \[k_{x}(y)\ =\ \frac{E_{g}\text{d}z\text{d}y}{t_{x}(y)} \tag{8}\]2 Then, the tensile boundary is withdrawn from the forces, and the tensile part can be treated as equal to zero. \[k_{x}(y)\ =\ \frac{E_{g}\text{d}z\text{d}y}{t_{x}(y)} \tag{8}\]3 Deformation of the porcelain bushing. \[k_{x}(y)\ =\ \frac{E_{g}\text{d}z\text{d}y}{t_{x}(y)} \tag{8}\]4 Contact forces on the cement. According to the Rayleigh-Ritz method [24], given the boundaries \(\Delta(0)=0\) and \(\Delta^{\prime}(0)=\theta_{2}\), the extrusion deformation in the horizontal X-direction at height z is assumed to be  
\[k_{x}(y)\ =\ \frac{E_{g}\text{d}z\text{d}y}{t_{x}(y)} \tag{8}\]5  
where \(a_{2}\) is the coefficient to be determined. If the effect of shear on the deformation is neglected, the bending deformation strain energy, \(U_{1}\), of the porcelain bushing can be expressed as follows:  
\[k_{x}(y)\ =\ \frac{E_{g}\text{d}z\text{d}y}{t_{x}(y)} \tag{8}\]6  
where \(E_{c}I_{c}\) is the bending stiffness of the porcelain bushing. The elastic strain energy of the cement bond is  
\[k_{x}(y)\ =\ \frac{E_{g}\text{d}z\text{d}y}{t_{x}(y)} \tag{8}\]7  
where \(k_{z}\) is the elastic stiffness coefficient in the dz unit at height z, taken as the value obtained with Equation (10). The work performed by the bending moment load is  
\[k_{x}(y)\ =\ \frac{E_{g}\text{d}z\text{d}y}{t_{x}(y)} \tag{8}\]8  
Then, the total potential energy of the porcelain bushing structure after deformation with respect to the non-deformed state is  
\[k_{x}(y)\ =\ \frac{E_{g}\text{d}z\text{d}y}{t_{x}(y)} \tag{8}\]9  
From the principle of minimum potential energy [25], the condition \(\delta\Pi=0\) yields the following:  
\[f_{x}(z,y)\ =\ k_{x}(z,y)\Delta_{x}(z) \tag{9}\]0  
where  
\[f_{x}(z,y)\ =\ k_{x}(z,y)\Delta_{x}(z) \tag{9}\]1  
The moment, \(M\), of the extrusion force on the center of rotation by the sidewall of the cement bond is as follows:  
\[f_{x}(z,y)\ =\ k_{x}(z,y)\Delta_{x}(z) \tag{9}\]2  
where  
\[f_{x}(z,y)\ =\ k_{x}(z,y)\Delta_{x}(z) \tag{9}\]3  
Therefore, the equivalent bending stiffness, \(K_{c2}\), obtained from the sidewall extrusion of the cement bond is as follows:  
\[f_{x}(z,y)\ =\ k_{x}(z,y)\Delta_{x}(z) \tag{9}\]4  
The equivalent bending stiffness of joints connecting porcelain bushings and flanges can be calculated using Equations (3)-(5) and (26). Compared with the code formula in Equation (1), Equation (3) is directly derived from the mechanical model. It increases parameters such as the elastic modulus and calculated size of the porcelain bushing, flange, and cement bonds, reflecting the actual structural features of the joint.