# Prediction of Post-Yield Performance of Hybrid Precast Beams Based on Strength Degradation
## 2 Materials and Methods
### Material Properties  
Table 2 [5,7,21,22,23,24,25,26] presents material properties of Specimens #1 to #3 [24] and of Specimens #4 to #7 [21,22,25,26]. For Specimens #4 to #7, the cross-sections of the composite beams were reinforced with a 4-D25 mm top reinforcement, a 2-D25 mm bottom reinforcement, a 2-D13 mm reinforcement in the middle, and a D10 mm dowel bar. The compressive strength of the concrete (f'c) was 38.8 MPa, and the yield stress (\(f_{y}\)) of the top and bottom reinforcement was 548.9 MPa. The yield stress (\(f_{y}\)) of the D13 mm bar and dowel bar was 400 MPa. Tension bars were used for reinforcement in the middle prior to the placement \begin{table}
\begin{tabular}{c c c} \hline \hline
**Specimen** & \multicolumn{3}{c}{**Material Properties**} \\ \hline CS1 \#1 & \(A_{top}\ =\ 1548.4\) mm\({}^{2}\)\(A_{bottom}\ =\ 253.4\) mm\({}^{2}\) T \(-150\times 150\times 6.5\times 9\) \\ CS2 \#2 & \(f_{ck}\ =\ 27\) MPa \(f_{y}\ =\ 400\) MPa \(f_{y}\ =\ 330\) MPa \\ CP \#3 & & \\ S-PS \#4 & \(A_{top}^{conter}\ =\ 2026.8\) mm\({}^{2}\) & \(A_{top}^{end}\ =\ 2026.8\) mm\({}^{2}\) \\ S-PS \#5 & \(A_{bottom}^{conter}\ =\ 1013.4\) mm\({}^{2}\) & \(A_{bottom}^{end}\ =\ 1013.4\) mm\({}^{2}\) \\ S-PS \#6 & \(f_{ck}\ =\ 40.1\) 38.8 MPa, \(f_{y}\ =\ 548.9\) MPa & T \(-200\times 200\times 8\times 12\) \\  & \(F_{y}\ =\ 325\) MPa & \(f_{ck}\ =\ 40.1\) 38.8 MPa \\  & \(X-\text{Strand}\ =\ 4\phi 15.2\) mm \(=\ 1860\) MPa & \(f_{y}\ =\ 548.9\) MPa \\  & & \(X-\text{Strand}\ =\ 3\phi 15.2\) mm \(=\ 1860\) MPa \\  & & \(A_{top}^{end}\) = 2533.5 mm\({}^{2}\); \(A_{bottom}^{end}\ =\ 397.2\) mm\({}^{2}\) \\ F-PS \#8 & \(f_{ck}\ =\ 40.1\) 38.5 MPa, \(f_{y}\ =\ 435\) MPa & \(f_{ck}\ =\ 40.1\) 38.5 MPa, \(f_{y}\ =\ 435\) MPa \\  & \(F_{y}\ =\ 325\) MPa & \(F_{y}\ =\ 325\) MPa (SM490) \\  & \(\text{Strand}\ =\ 2\phi 15.2\) mm \(=\ 1860\) MPa & Strand \(=\ 2\phi 15.2\) mm \(=\ 1860\) MPa \\ F-SRC \#9 & \(A_{top}^{conter}\ =\ 1013.4\) mm\({}^{2}\); \(A_{bottom}^{conter}\ =\ 253.4\) mm\({}^{2}\) & \(A_{top}^{end}\) = 2533.5 mm\({}^{2}\); \(A_{bottom}^{end}\ =\ 397.2\) mm\({}^{2}\) \\  & \(F_{y}\ =\ 325\) MPa & \(F_{y}\ =\ 435\) MPa \\  & & \(F_{y}\ =\ 325\) MPa & \(A_{top}^{end}\) = 2539.5 mm\({}^{2}\) \\  & & & \(F_{y}\ =\ 435\) MPa \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \end{tabular} For MHS \#10, MHS \#12 : \(A_{top}\ =\ 2322.6\) mm\({}^{2}\), \(A_{bottom}^{end}\ =\ 774.2\) mm\({}^{2}\) \\  & & & & & \\  & & & For MHS \#11, MHS \#13 : \(A_{top}\ =\ 1548.4\) mm\({}^{2}\), \(A_{bottom}^{end}\ =\ 1935.5\) mm\({}^{2}\) \\ MHS \#10 to \#13 & & & For MHS \#10, MHS \#12 : \(\mathrm{H}-340\times 250\times 9\times 14\) \\  & & & For MHS \#11, MHS \#13 : \(\mathrm{H}-440\times 300\times 11\times 18\) \\  & & & \(f_{ck}\ =\ 27\)MPa for concrete, \(f_{y}\ =\ 400\) MPa for rebar \\  & & & For steel : \(F_{y}\ =\ 240\) MPa (SS400) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties of specimens for estimation of post-yield deflection [5,7,21,22,23,24,25,26]. Figure 1: Specim details. (**a**) Cantilever Specimens #1, #2, and #3 (non-pre-stressed, CS1, CS2, and CP) [24]. (**b-1**) Specimens #4, #5 (pre-stressed); cross-sections of the test specimens with pinned joints [21,22]. (**b-2**) Specimens #6, #7 (pre-stressed); side views of the test specimens with pinned joints [21,22]. (**c-1**) Specim #8 (pre-stressed); end and mid-section of a pre-stressed composite beam with fixed ends [7]. (**c-2**) Specim #9 (non-pre-stressed); end and mid-section of a non-pre-stressed composite beam with fixed ends [7]. (**d**) Specimens #10 to #13; Steel-concrete composite beams with fixed ends (yield strength of concrete: 27 MPa, yield strength of rebar: 400 MPa; yield strength of steel: 240 MPa) [5]. of the concrete for the slab. A 2026.8 mm\({}^{2}\) area of top steel reinforcement was placed at the ends, while four pre-stressed strands were installed at mid-span with a smaller steel area (1013.4 mm\({}^{2}\)), as shown in Figure 1b [21; 22; 25; 26].