# Improved Shear Strength Equation for Concrete Wide Beams
## 5 Proposal Equation for Capacity  
### Consideration of Transverse Spacing  
In this study, an experimental data of 27 specimens was composed to develop the shear strength equation for concrete wide beam. Tables 4 and 5 show the details of experiment performed by [PERSON] et al. [4] and [PERSON] [5]. Two considerations were taken into account for the effect of transverse reinforcement spacing on the shear capacity. First, ACI 318-14 code assumes that the effects of shear reinforcement are equally distributed over the longitudinal reinforcement spacing, and does not consider shear capacities distributed in transverse reinforcement spacing. Therefore, the distribution of the shear reinforcement capacity in the transverse direction should be considered. Based on test results, the distribution ratio was determined by evaluating the effective depth (\(d\)) to transverse reinforcement spacing (\(s_{w}\)) ratio. The distribution ratio was defined in the longitudinal direction as \(\Phi_{1}\) and in the transverse direction as \(\Phi_{2}\). The shear strength contribution to the longitudinal direction decreased as the transverse reinforcement spacing increased. The summation of the shear capacity distribution ratios in the transverse and longitudinal directions cannot exceed 1. Therefore, when \(\phi_{1}\) is determined, \(\phi_{2}\) is dependent on that value. The equations for calculating the distribution are described by Equations (11) and (12). Equation (11) is proposed as shown in Figure 8.  
\[\Phi_{1}=-0.1\bigg{(}\frac{s_{w}}{d}\bigg{)}+1 \tag{11}\]  
\[\Phi_{1}+\Phi_{2}=1 \tag{12}\] \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No**} & \multirow{2}{*}{**Name**} & \(\dot{f}_{c}\) & \(f_{yy}\) & \(d\) & \(A_{v}\) & \(s_{L}\) & \(s_{w}\) & \(s_{w}\)/\(d\) & \(c_{x}\) & \(c_{y}\) & \(b_{w}\) & \(\kappa\) & \(V_{n,ACI}\) \\  & & [MPa] & [MPa] & [mm] & [mm\({}^{2}\)] & [mm\({}^{2}\)] & \(n\) & [mm] & [mm] & \(s_{w}\)/\(d\) & [mm] & [mm] & [mm] & \(\kappa\) & [kN] \\ \hline
1 & AW4 & 39.9 & - & 506 & - & - & 300 & - & - & 305 & 305 & 1168 & 0.26 & 619.66 \\ \hline
2 & AW8 & 39.4 & - & 507 & - & - & 300 & - & - & 152 & 1169 & 1169 & 1.00 & 620.16 \\ \hline
3 & AX8 & 41 & - & 289 & - & - & 175 & - & - & 152 & 152 & 705 & 0.22 & 217.46 \\ \hline
4 & AX6 & 41 & - & 288 & - & - & 175 & - & - & 152 & 703 & 703 & 1.00 & 216.03 \\ \hline
5 & AW5 & 34.8 & 458 & 511 & 272 & 4 & 300 & 375 & 0.73 & 305 & 305 & 1170 & 0.26 & 802.50 \\ \hline
6 & AW7 & 35.8 & 458 & 512 & 272 & 4 & 300 & 370 & 0.72 & 152 & 1170 & 1170 & 1.00 & 807.52 \\ \hline
7 & AW2 & 39.3 & 452 & 507 & 400 & 2 & 300 & 1080 & 2.13 & 305 & 305 & 1172 & 0.26 & 929.55 \\ \hline
8 & AW6 & 43.7 & 452 & 509 & 400 & 2 & 300 & 1080 & 2.12 & 152 & 1170 & 1169 & 1.00 & 966.67 \\ \hline
9 & AW3 & 37.2 & 452 & 509 & 400 & 2 & 300 & 800 & 1.57 & 305 & 305 & 1165 & 0.26 & 909.54 \\ \hline
10 & AX1 & 42 & 458 & 289 & 136 & 2 & 175 & 625 & 2.16 & 152 & 703 & 703 & 1.00 & 322.31 \\ \hline
11 & AX2 & 42 & 600 & 286 & 103.2 & 2 & 175 & 625 & 2.79 & 152 & 703 & 703 & 1.00 & 318.36 \\ \hline
12 & AX3 & 42 & 613 & 285 & 116.1 & 3 & 175 & 350 & 1.23 & 152 & 707 & 707 & 1.00 & 333.54 \\ \hline
13 & AX4 & 42 & 625 & 285 & 103.2 & 4 & 175 & 235 & 0.82 & 152 & 698 & 698 & 1.00 & 319.91 \\ \hline
14 & AX5 & 41 & 458 & 283 & 136 & 2 & 175 & 470 & 1.66 & 152 & 697 & 697 & 1.00 & 311.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Details of [PERSON]’s specimens.