# Influence of Concrete Strength Class on the Long-Term Static and Dynamic Elastic Moduli of Concrete
## 3 Results and Discussions
### Dynamic Longitudinal Modulus of Elasticity  
The determination of the dynamic modulus of elasticity was based on the first resonant frequency of the cylindrical specimen, which was assessed by means of the Impact Echo Method. The free vibration response of all specimens, 15 for each of the mix proportions presented in Table 1, was recorded as shown in Figure 2. Fast Fourier Transform (FFT) was applied to the recorded signal so as to obtain the Fourier spectrum of the specimens from which the fundamental frequency of vibration was identified. For each cylindrical specimen at least four measurements were considered from which the fundamental frequency of vibration was calculated.  
Figure 2: _Cont._  
The part of the recorded signal considered for the assessment of the fundamental longitudinal frequency of vibration was selected after the initial response of the specimen to the impact load, akin to a transient part (Figure 2a,c,e) of the recorded response signal decay. This would ensure that any possible influence of reflected waves on the boundary of the specimen would be avoided and a cleaner signal would be recorded, similar to a steady-state response [20]. The influence of the initial, transient part on the response spectrum consisted of several peaks of comparable magnitude being identified. On the other hand, the steady state response resulted in a single dominant peak, as can be seen in Figure 2b,d,f.  
However, since the Fourier spectra showed a smaller peak around 6000 Hz, for all specimens belonging to each mix proportion additional measurements were taken to confirm the accuracy of the obtained results. Based on the processed data, it was concluded that the smaller peak near 6000 Hz was a combination of the peaks corresponding to the transversal and the torsional frequencies of vibration, as discussed in subsequent sections of this paper.  
By applying Equations (1) and (2) the dynamic modulus of elasticity was obtained for all specimens belonging to the considered mix proportions. The data are summarized in Table 3, where the presented values are the averages of all measurements.  
The low values of COV imply that the results are very closely spaced with respect to the median value. This means that the elastic properties of the cylinders from each of the three mixes are uniformly distributed throughout the specimens. This is proof that a good homogeneity of the mix was obtained during the mixing process.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Mix Designation**} & \multicolumn{2}{c}{**Dynamic Modulus**} & \multirow{2}{*}{**Standard Deviation**} & **Coefficient of** \\  & **of Elasticity, Ed** & & **Variation** \\ \cline{2-3}  & **[MPa]** & **[MPa]** & **[\%]** \\ \hline Mix 1 & 37,874 & 1071.14 & 2.83 \\ \hline Mix 2 & 37,900 & 1221.27 & 3.22 \\ \hline Mix 3 & 39,106 & 685.01 & 1.75 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Dynamic longitudinal modulus of elasticity.  
Figure 2: Measurements for the fundamental frequency of vibration: (**a**) sample of recorded signal for Mix 1; (**b**) FFT for Mix 1; (**c**) sample of recorded signal for Mix 2; (**d**) FFT for Mix 2; (**e**) sample of recorded signal for Mix 3; (**f**) FFT for Mix 3.