# Analytical Study of Reinforced Concrete Beams Tested under Quasi-Static and Impact Loadings
## Materials and Methods
### Impact Loading  
A drop weight impact machine with a capacity of 14.5 kJ was used, as shown in Figure 3. A mass of 591 kg (including the striking top) can be dropped from as high as 2.5 m. During a test, the hammer is raised to a certain height above the specimen using a hoist and chain system. At this position, air brakes are applied on the steel guide rails to release the chain from the hammer. By releasing the breaks, the hammer falls and strikes the specimen. Instrumented anvil supports were used to record the bending loads during the impact [22; 23; 24].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Beam’s Designation**} & \multirow{2}{*}{**Stirrups?**} & **Sprayed GFRP** & \multirow{2}{*}{**Width of Sprayed GFRP**} & \multirow{2}{*}{**Thickness of Sprayed GFRP**} \\  & & **on Two Sides** & & **Sprayed GFRP** \\  & & **or Three?** & **on the Sides** & **(mm)** & **(mm)** \\ \hline C-NS & No & N/A & N/A & N/A \\ B2-NS & No & 2 & 100 & 4 & N/A \\ B2-4B-NS-3 & No & 2 & 100 & 4 & 4 \\ B2-6B-NS-1 & No & 2 & 100 & 3.5 & 6 \\ C-S-2 & Yes & N/A & N/A & N/A & N/A \\ B2-5-1 & Yes & 2 & 150 & 3.5 & N/A \\ B2-4B-S-1 & Yes & 2 & 150 & 3.5 & 4 \\ B2-6B-S-1 & Yes & 2 & 150 & 4 & 6 \\ B3-S-2 & Yes & 3 & 150 & 4 & N/A \\ \hline \hline \end{tabular}
\end{table}
Table 4: Designations of RC beams tested under quasi-static loading as shown in Figures 1 and 2.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Value** & **Unit** \\ \hline Ultimate tensile strength & 1517 & MPa \\ Tensile modulus & 72.4 & GPa \\ Ultimate tensile strength per unit width & 0.536 & KN/mm/ply \\ Tensile modulus per unit width & 25.6 & KN/mm/ply \\ Ultimate rupture strain & 2.1 & \% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Fabric GFRP properties.  
Figure 3: Impact machine.  
Figure 2: Bold configuration of RC beams with sprayed GFRP: (**a**) four bolts; (**b**) six bolts; (**c**) cross-sections with no stirrups; (**d**) cross-sections with stirrups [(22)].  
Dimensions and reinforcement details of the beams tested under impact loading are shown in Figure 4. Enough stirrups were provided to make sure that the beam would fail under bending. Two beams (BS and BS-GFRP) were tested under quasi-static loading and the rest under impact loading with various impact velocities ranging from 2.80 to 6.26 m/s (see Table 5). It is worth mentioning that BS-GFRP and BI-600-GFRP are identical beams strengthened by fabric GFRP. One layer of unidirectional GFRP fabric with a total thickness of about 1.2 mm, length of 750 mm, and width of 150 mm was applied longitudinally on the tension (bottom) side of the beam for flexural strengthening. An extra layer with fibers perpendicular to the fiber direction of the first layer was applied on three sides (two sides and the tension side) for shear strengthening. It is important to note that while the control RC beam (beam \"BS\") failed in flexure, the strengthened RC beam failed in shear, indicating that shear strengthening was not as effective as flexural strengthening and perhaps more layers of GFRP were needed to overcome the deficiency of shear strength in these beams. Beam displacement was measured via an accelerometer affixed to the bottom face of the beam in impact experiments (refer to Figure 4).  
Figure 4: Elevation and cross-section of RC beams tested under impact loading; (**a**) elevation; (**b**) cross-section [22].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Beam’s Designation** & **Quasi-Static or Impact?** & **Drop Height (mm)** & **Impact Velocity (m/s)** \\ \hline BS & Quasi-static (control) & NA & NA \\ BI-400 & Impact & 400 & 2.8 \\ BI-500 & Impact & 500 & 3.13 \\ BI-600 & Impact & 600 & 3.43 \\ BI-1000 & Impact & 1000 & 4.43 \\ BI-2000 & Impact & 2000 & 6.26 \\ BS-GFRP & Quasi-static (control) & NA & NA \\ BI-600-GFRP & Impact & 600 & 3.43 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Designations and details of RC beams tested under impact loading as shown in Figure 4.