# Experimental Study on the Torsional Behaviour of Prestressed HSC Hollow Beams
## 2 Experimental Program
### Materials Properties  
The average value of the compressive concrete strength used in each tested beam was obtained from 5 cube specimens, casted and tested at the same time of the corresponding beam. The equivalent cylindrical values were computed by following the indications from Eurocode 2 [16]. Table 2 presents the concrete mix design used to produce the concrete.  
Table 1 also presents, for each tested beam, the average values for the tensile concrete strength (\(f_{ctm}\)) and for the concrete Young's Modulus (\(E_{c}\)). These two parameters were computed from \(f_{c}\) also following the indications from Eurocode 2 [16].  
As example, Figure 3 illustrates a stress (\(\alpha\))-strain (\(\varepsilon\)) curve recorded during the test of one of the concrete samples. The initial part of the graph shows the influence of the adjustment due to the existent gap between the loading plates of the test machine and the concrete specimen.  
\begin{table}
\begin{tabular}{c c} \hline
**Components** & **Dosage** \\ \hline Thin sand & 164 kg \\ Thick sand & 908 kg \\ Crushed Granit 5–11 mm & 734 kg \\ Normal Portland Cement (C): Type & 375 kg \\ I/42.5R & 4.8 \(\ell\) \\ Admixture—Rheobuild 1000 & 41 kg \\ Silica Fume (Sikacrete HD) & 41 kg \\ Water (A) & 145 \(\ell\) \\ A/(C + Additions) & 0.35 \\ \hline \end{tabular}
\end{table}
Table 2: Concrete mix design (contents per m\({}^{3}\)).  
Figure 3: Uniaxial \(\sigma\)–\(\varepsilon\) curve for concrete.  
The ordinary reinforcement used in the beams consisted of hot rolled ribbed steel bars (with 10 and 16 mm diameters) sold commercially as Class A500. In order to know the average values of the yield stress and corresponding strain of the bars (\(f_{y}\) and \(\varepsilon_{y}\), respectively), tensile tests on steel samples were carried out (6 samples of each of the diameters that were used in the beams). The following average values were obtained--\(f_{y}=686\) MPa and \(\varepsilon_{y}=3.43\times 10^{-3}\). For the steel Young's Modulus, the typical value set in codes of practice was assumed, \(E_{s}=200\) GPa [16].  
As example, Figure 3(a) illustrates some \(\sigma\)-\(\varepsilon\) curves recorded during the tensile tests of steel specimens (ordinary reinforcement).  
The prestress reinforcement used in Beams D-1.79 and D-3.08 consisted of four 0.6\({}^{\prime\prime}\) wires (0.6 inches or 1.52 cm diameter) belonging to Class S1670/1860. Tests on 6 prestress wire specimens were also carried out and the average values of the 0.1% limit proportional stress (\(f_{p0.1\%}\)) and the ultimate stress (\(f_{pu}\)) of the wires were obtained--\(f_{p0.1\%}=1670.5\) MPa and \(f_{pu}=1867.1\) MPa, respectively. The corresponding strain at 0.1% was computed by assuming a linear relationship between strains and stresses, which led to \(\varepsilon_{p0.1\%}=8.567\times 10^{-3}\). The Young's Modulus was assumed to be the one indicated by the supplier, \(E_{p}=195\) GPa.  
As example, Figure 3(b) illustrates \(\sigma\)-\(\varepsilon\) curves recorded during the tensile test of two prestress steel specimens (with \(4\times 0.6\) inches wires each).  
It should be referred that some slip was observed between the steel specimens and the claws of the test machine. This explains the apparent different initial stiffness between the curves for 10  
Figure 4: Uniaxial \(\sigma\)–\(\varepsilon\) curves for reinforcement: (**a**) ordinary and (**b**) prestress.  
and 16 mm bars in Figure 4a and also the initial part of the curves in Figure 4b. This problem had no implication to the previously presented strain values at the end of the elastic stage. The strains were computed from [PERSON]'s law by knowing the stresses and assuming the Young's Modulus.