### Research Significance  
The steps of Method A and Method B are described in detail. They make it possible to obtain the exact interaction formulae. Three interaction formulae for the calculation of the plastic resistance of cross sections under the bending moment about the strong axis, \(M_{y,\text{Ed}}\), the bending moment about the weak axis, \(M_{z,\text{Ed}}\), and the bimoment, \(B_{\text{Ed}}\), are compared for the beams with the I- and H-sections. The proposal is presented in Section 3. **2. Calculation of Exact Interaction Curves**  
**Method A is applied to obtain the interaction curves with parameter \(M_{\text{z,Ed}}\)**  
**Step 1. ** Calculation of \(M_{\text{pl,z,Rd}}\) for the given \(N_{\text{Ed}}=0.0\), \(M_{y,\text{Ed}}=0.0\) and \(B_{\text{Ed}}=0.0\). Considering constraints by Equations (17)-(20):  
\[-f_{y}\leq\sigma_{i}\leq f_{y} \tag{17}\]  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{18}\]  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}z_{i}=M_{y,Ed}=0.0 \tag{19}\]  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}y_{i}z_{i}=B_{Ed}=0.0 \tag{20}\]  
Calculation of maximum \(M_{\text{z,Ed}}\):  
\[M_{pl,z,Rd}=\max(M_{z,Ed})=\max(\sum_{i=1}^{n}\sigma_{i}A_{i}y_{i}) \tag{21}\]  
**Step 2. ** Calculation of \(B_{\text{Ed,\gamma}}\) to achieve plastic resistance for the given \(N_{\text{Ed}}=0.0\), \(M_{y,\text{Ed}}=0.0\), \(M_{z,\text{Ed}}=\gamma\cdot M_{\text{pl,z,Rd}}\); \(\gamma\) [0,1]  
Constraints Equations (22)-(25):  
\[-f_{y}\leq\sigma_{i}\leq f_{y} \tag{22}\]  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{23}\]  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}z_{i}=M_{y,Ed}=0.0 \tag{24}\]  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}y_{i}=M_{z,Ed}=\gamma\cdot M_{pl,z,Rd} \tag{25}\]  
Calculation of maximum \(B_{\text{pl,Rd,\gamma}}\):  
\[B_{pl,Rd,f_{\gamma}}(M_{z,Ed})=\max(\sum_{i=1}^{n}\sigma_{i}A_{i}y_{i}z_{i}) \tag{26}\]  
**Step 3. ** Calculation of \(M_{y,\text{Ed,\gamma,\eta}}\) to achieve the plastic resistance for the given \(N_{\text{Ed}}=0.0\), \(B_{\text{Ed}}=\eta B_{\text{pl,Rd,\gamma}}\), \(M_{z,\text{Ed}}=\gamma\cdot M_{\text{pl,z,Rd}}\); \(\gamma\) [0,1] and \(\eta\) [0,1]. Considering constraints by Equations (27)-(30):  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{18}\]0\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{18}\]1  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{18}\]2  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{18}\]3  
Calculation of maximum \(M_{y,Ed\gamma,\eta}\):  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{18}\]4  
**Application of Method B:**  
Dividing the section into three parts (top flange, bottom flange, and web):  
The axial force that leads to the plastic behavior of the top flange:  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{18}\]5  
The axial force that leads to the plastic behavior of the bottom flange:  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{18}\]6  
If the axial force equals zero (\(N_{\text{Ed}}=0\)), the axial force at the web will be as follows:  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{18}\]7  
The bending moment that leads to the plastic behavior at the web:  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{18}\]8  
The resultant bending moment \(M_{y,\text{Ed}}\) is then:  
\[\sum_{i=1}^{n}\sigma_{i}A_{i}=N_{Ed}=0.0 \tag{18}\]9  
**3. Proposal for Improved Interaction Formulae (Variant No. 4)**  
The original formulae of variants Nos. 1, 2, and 3, presented in Table 1[1], are improved by variant No. 4. In variant No. 4, the definitions of the parameters \(\alpha\), \(\beta\), and \(\delta\) are different. The improved formulae of variant No. 4 with the changed parameters (Equations in (37)) provide results that agree well with the exact results obtained by linear programming (Figures 1 and 2). \[ \begin{array}{c}\hline\hline 0\leq\frac{M_{\pi,\mu,\delta}}{M_{\pi,\mu,\delta}}< \delta\leq\frac{M_{\pi,\mu,\delta}}{M_{\pi,\mu,\delta}}\leq 1.0\\ \hline\frac{\frac{\delta_{\pi,\mu,\delta}}{M_{\pi,\mu,\delta}}}{1-\frac{M_{\pi, \mu,\delta}}{M_{\pi,\mu,\delta}}}\leq 1.0\\ \hline\hline\end{array} \]  
where  
\[