## 2 Experimental Program
### Methods
#### 2.2.2 Beam Specimen Details  
In this study, 12 mini-scale UHPC rectangular beams were prepared for the experimental investigation. The size of beam test specimens was 150 mm \(\times\) 150 mm \(\times\) 600 mm. Figure 2 shows the geometry and reinforcement properties. It is noteworthy that the bottom \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**PC**} & \multirow{2}{*}{**SF**} & \multirow{2}{*}{**FA**} & \multirow{2}{*}{**WS**} & \multirow{2}{*}{**RS**} & \multirow{2}{*}{**Water**} & \multirow{2}{*}{**SP**} & \multicolumn{2}{c}{**Fiber**} \\ \cline{5-6}  & & & & & & & **A** & **B** & **C** \\ \hline
1123.1 & 239.1 & 66.1 & 481.2 & 160.9 & 212.7 & 39.7 & 151.8 & 43.0 & 7.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mix proportions of the developed UHPC (in kg/m\({}^{3}\)). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & & **Length** & **Diameter** & **Unit Weight** & **Tensile Strength** \\  & & **(mm)** & **(\(\mu\)m)** & **(kg/m\({}^{3}\))** & **(MPa)** \\ \hline A & \(\mathbf{t}\cdot\mathbf{0}\) & \(\mathbf{1}\mathbf{m}\) & \(\mathbf{2}\) & \(\mathbf{1}\mathbf{3}\) & \(\mathbf{2}\mathbf{0}\) & \(\mathbf{7}\mathbf{8}\mathbf{0}\) & \(\mathbf{2}\mathbf{6}\mathbf{0}\) \\ \cline{5-6} B & \(\mathbf{t}\cdot\mathbf{0}\) & \(\mathbf{1}\mathbf{m}\) & \(\mathbf{2}\) & \(\mathbf{2}\mathbf{0}\) & & \\ \cline{5-6} C & \(\mathbf{t}\cdot\mathbf{0}\) & \(\mathbf{1}\mathbf{m}\) & \(\mathbf{2}\) & \(\mathbf{3}\mathbf{0}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Physicochemical properties of microsteel fibers. and side cover of bars were 20 mm. Moreover, a set of prefabricated concrete spacers (20 \(\times\) 20 \(\times\) 20 mm) was used to fix the single-layer reinforcing bars. Table 5 lists the details of the beam's bars and their percentages of reinforcement. In the current investigation, the key variable between the various beam sets was the percentage of the tensile reinforcement. The maximum employed percentage of reinforcement was designed to be less than the balance threshold (\(\rho_{b}\)), which was calculated by following Equation (1), which has been recently proposed by [PERSON] et al. (2019) for singly reinforced beams. It is noteworthy that the balance failure is a state of simultaneous concrete compressive and steel tensile strains approaching the crushing and yielding thresholds, respectively. \[\rho_{b}=\frac{2\mu[\lambda_{cu}(\alpha-1)+\alpha-\psi]+\alpha\gamma\psi(2 \lambda_{cu}-\omega)-\alpha}{2n\psi(\lambda_{cu}+\psi)}. \tag{1}\]  
where, \begin{tabular}{l l l} \(\mu\) & : & \(\sigma_{p}/\sigma_{cr}\) (a normalized residual tensile strength of the UHPC); \\ \(\lambda_{cu}\) & : & UHPC's peak compressive strain; \\ \(\alpha\) & : & \(d/h\); \\ \(\psi\) & : & \(\varepsilon_{sy}/\varepsilon_{cr}\) (a normalized yielding strain of steel); \\ \(\gamma\) & : & \(E_{c}/E\) (UHPC's normalized compressive modulus); \\ \(\omega\) & : & \(\varepsilon_{cy}/\varepsilon_{cr}\) (UHPC's normalized compressive yielding strain); \\ \(n\) & : & \(E_{s}/E\) (modular ratio); \\ \(\sigma_{p}\) & : & residual tensile strength of UHPC; \\ \(\sigma_{cr}\) & : & UHPC's cracking stress; \\ \(\varepsilon_{sy}\) & : & yielding strain of steel; \\ \(\varepsilon_{cr}\) & : & UHPC's cracking strain; \\ \(E_{s}\) & : & steel Young's modulus; \\ \(E_{c}\) & : & UHPC's Young's modulus of concrete unr compression; \\ \(E\) & : & UHPC's Young's modulus of concrete under tension; \\ \(d\) & : & beam's effective depth; and \\ \(h\) & : & beam's overall depth. \\ \end{tabular}   
In the preliminary design of the UHPC beams, the material properties presented in ([PERSON] et al., 2019) (with elasticity modulus and compressive and tensile strengths of 46.4 GPa, 194 MPa, and 30.6 MPa, respectively) were selected due to their proximity to the current investigation.