# Seismic Behavior of Steel Plate-Concrete Shear Walls with Holes
## 4 Theoretical Calculation
### Ono Reduction Rate Calculation  
[PERSON], a Japanese scholar, proposed the calculation method of Ono reduction rate through a series of experiments wherein the influences of hole positions are considered [27] (Figure 15). \[r_{u}=\sqrt{\sum A_{ei}/hl}, \tag{3}\]  
when \(0.1\leq\gamma\leq 0.53\),  
\[r_{e}=(\frac{0.025}{0.0303^{\gamma}})\times\alpha\beta+(\frac{0.6}{0.55^{ \gamma}})/(\frac{1.55}{\gamma^{2}})^{k}, \tag{4}\]  
when \(0.53\leq\gamma\leq 1.00\),  
\[r_{e}=(\frac{5.24}{717.24^{\gamma}})\times\alpha\beta+(\frac{0.6}{0.55^{ \gamma}})/(\frac{1.55}{\gamma^{2}})^{k}, \tag{5}\]  
where \(A_{ei}\) is the area of shadow part, \(h\) is the floor height, and \(l\) is the center distance of frame columns. \(\alpha\beta=2 bD/tl^{\prime}\); where \(bD\) is the sectional area of columns, \(t\) is the wall thickness, and \(l^{\prime}\) is the net span. \(\gamma=2l_{w}/l^{\prime}\); and where \(l_{w}\) is the length of the wall after the hole is removed. \(\kappa=h_{0}/h^{\prime}\), where \(h_{0}\) is the height of the hole and \(h^{\prime}\) is the net height of the wall. In this study, the horizontal ultimate bearing capacity of SPSW members with holes can be obtained by multiplying the reduction rate by that of the corresponding members without holes. The  
Figure 15: Effective supporting area in the Ono reduction rate calculation method. lateral stiffness of SPSW members with holes can be obtained with the same method. Change of the concrete compression zone is considered in the method of Ono reduction rates. The reduction rates are different in different directions for the specimen with biased holes. Table 8 displays the comparison between the test results of horizontal ultimate loads and the calculated results based on strength reduction rate. Table 9 compares the test results of lateral stiffness and calculated results based on the stiffness reduction rate. This test has no effective lateral stiffness of I-shaped SPSW structures without holes, and only the comparisons between the calculated and test results of SCW-4 and SCW-6 are presented. According to the average ratio, the calculated value of the Ono formula is closer to the experimental value than that of the code formula. Table 9 shows that the calculated results of AIJ codes are relatively safe. Moreover, the difference of bearing capacity along different loading directions under eccentric holes is neglected, thus resulting in the low accuracy. The Ono calculation formula considers the influences of loading direction and reflects the effects of hole position on horizontal bearing capacity along different loading directions. The calculation accuracy of the Ono calculation formula is thus higher than that of AIJ codes with respect to specimens with small holes (SCW-4 and SCW-6) and with large holes (SCW-8 and SCW-9). With respect to stiffness, the bottom slippage of the wall can influence the test results to a certain extent, resulting in the difference in stiffness along the two loading directions. Therefore, the calculation method may differ. In summary, the calculation formulas of AIJ codes and Ono are feasible in determining the influences of holes on the horizontal bearing capacity of SPSW structures. Compared with the calculation results of AIJ codes, those of the Ono formula are closer to the actual test results, indicating its high calculation accuracy. Due to the bottom slippage of walls, the rigidity in the negative direction is lower than the calculated values. In the positive direction, the calculated values are lower than the test results, which is due to the fact that the AIJ code and Ono formula are used for structure design and the result are relatively safer. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Specimen** & \begin{tabular}{c} **Stress** \\ **State** \\ \end{tabular}  & \(Q_{test}\) /\(\mathbf{k}\)N & \(Q_{code}\)/\(\mathbf{k}\)N & \(Q_{cold}\)/\(Q_{test}\) & \(Q_{ano}\)/\(\mathbf{k}\)N & \(Q_{ano}\)/\(Q_{test}\) & \begin{tabular}{c} **Axial** \\ **Compression/\(\mathbf{k}\)N** \\ \end{tabular}  &