# Laboratory Evaluation of Tensile Creep Behavior of Concrete at Early Ages
## 3 Tensile Creep Tests
### Procedures  
Uniaxial tensile creep tests were conducted with standard concrete cylinders (100 \(\times\) 200 mm) at the ages of 2.7, 4.3, 6.8, and 13.3 days using a servo-controlled MTS testing machine. One sample per age was used to verify the modeling approach. Immediately after casting, the concrete cylinders were moved to a moisture curing room with a controlled temperature and humidity at 25 \({}^{\circ}\)C and 100%. The cylinder specimens were moved to the testing room (25 \({}^{\circ}\)C and 40% RH) for instrumentation at 24 h before the respective ages of testing. A pair of steel connections for direct tensioning of the test specimen was epoxy-bonded at each end of the cylinder. In order to provide a surface for epoxy bonding, both ends of the concrete cylinder were ground by approximately 5 mm in depth. The epoxy work was performed with a specially prepared concentric jig as shown in Figure 2. After the epoxy work, the specimens were kept in the testing room until the time of testing in order for the epoxy to develop its full bond strength. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **Unit Content (kg/m\({}^{3}\))** & & & \\ \hline
**Cement** & **Fly Ash** & **Fine Aggregate** & **Coarse Aggregate** & **Water** & **w/c** \\ \hline
200.5 & 66.4 & 800.3 & 1037.1 & 143.5 & 0.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Concrete mixture proportions. Figure 2: Alignment of test specimen and the end fixtures. A designated level of tensile load was introduced to the specimen within 0.1 s, and subsequent changes in displacement as a function of time was monitored up to 20,000 s (5.5 h), while keeping the load constant. The level of load was controlled with a 4.5 kN capacity load cell. The load level ranged from 1 to 2 kN depending on the ages of the specimens. Displacement data were traced by the two LVDTs installed on the mid-surface of the cylinder specimens with 100 mm gage lengths. Figure 3 shows the test set-up. The level of test load was determined to be 15% of the tensile strength of the concrete at the respective ages of testing. Tensile strength was assumed to be 1/8 of the compressive strength at all ages of testing. Development of the compressive strength of the concrete was estimated by the ACI equation [18] shown in Equation (11). The average 28-day compressive strength of the test concrete was 15.51 MPa, found by separate strength tests. Table 2 summarizes the determination of the test load for the respective ages of testing. \[f_{c}(t)=f_{c}\prime\frac{t}{4+0.85\,t} \tag{11}\]  
where \(f_{c}(t)=\) compressive strength at time \(t\), and \(f_{c}\prime\) = reference compressive strength at the age of 28 days. Earlier studies on the creep of aged concrete suggested that the principle of superposition would be valid within the service range of stresses (up to 1% of the strength) under a monotonically increasing strain condition [29; 34]. Recent studies found that early-age concrete also shows proportional creep responses to the stress level below 50% of static strength, regardless of mixture characteristics [25; 35; 36]. Based on these previous observations, no additional linearity check was conducted in this study. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Age at Test** **(Day)** & \(f_{c}\)**(\(t\)) by ACI** & \(f_{c}\)**(\(t\)) by ACI** & \multicolumn{2}{c}{**Test Load**} & \(\sigma_{t}\)**(\(t\))**(\(t\))** \\ \cline{3-6}
**F\({}_{\text{f}}\) (kN)** & \(\sigma_{t}\)**(MPa)** & \(\sigma_{t}\)**(MPa)** & \(\sigma_{t}\)**(MPa)** & \(\sigma_{t}\)**(\(t\))**(\(t\))** \\ \hline
2.7 & 6.65 & 0.83 & 1.0 & 0.127 & 15.3 \\ \hline
4.3 & 8.71 & 1.09 & 1.3 & 0.166 & 15.2 \\ \hline
6.8 & 10.78 & 1.35 & 1.6 & 0.204 & 15.1 \\ \hline
13.3 & 13.48 & 1.68 & 1.9 & 0.242 & 14.4 \\ \hline \hline \end{tabular} \(f_{c}(t)\): compressive strength at age \(t\), \(f_{c}(t)\): tensile strength at age \(t\), 1/8 of \(f_{c}(t)\), \(F_{t}\), and \(\sigma_{t}\): test load determined in terms of tensile force and stress, respectively.  
\end{table}