## 5 Conclusions  
This paper presented the characterization of fiber-reinforced concrete mechanical properties by three-point bending tests of fiber-reinforced concrete prisms and compressive tests of plain and fiber-reinforced concrete cubes. The focus of interest of this study was on the post-cracking behavior and the computational simulation of this behavior. Two computational procedures for the structural analysis (load-displacement calculations) of fiber-reinforced concrete elements were presented. The first computational procedure, a nonlinear semi-numeric procedure, was based on the moment-curvature relation, plastic hinge approach, and virtual work method. Two calculations were performed with the nonlinear semi-numeric computational procedure: one with back-calculated (by an inverse analysis based on the moment-curvature relation) tensile strength properties, and one with tensile strength properties calculated with simplified expressions from the _fib Model Code for Concrete Structures 2010_[17]. The second computational procedure was a nonlinear finite element analysis considering the Menetrey-Willam material model. The experimental and computational results were compared. The following conclusions could be drawn from the present research: \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \begin{tabular}{c} **Average** \\ **Experimental** \\ **Load** \\ \end{tabular} & \begin{tabular}{c} **Corresponding** \\ **Experimental** \\ **Displacement** \\ \end{tabular} & \begin{tabular}{c} **M-\(\kappa\)** \\ **Calculated** \\ **Load** \\ \end{tabular} & \begin{tabular}{c} **M-\(\kappa\)** \\ **Calculated** \\ **Displacement** \\ \end{tabular} & \begin{tabular}{c} **M-\(\kappa\) (fib)** \\ **Calculated** \\ **Displacement** \\ \end{tabular} & \
\begin{tabular}{c} **M-\(\kappa\) (fib)** \\ **Calculated** \\ **Load** \\ \end{tabular} &
\begin{tabular}{c} **FEA** \\ **Displacement** \\ \end{tabular} \\ \hline  & [kN] & [mm] & [kN] & [mm] & [kN] & [mm] & [km] & [km] & [mm] \\ \hline Max. load & 14.14 & 0.053 \({}^{*}\) & 14.14 & 0.051 & 14.33 & 0.051 & 14.09 & 0.067 \\ CMOD = 0.5 mm & 6.54 & 0.465 & 0.473 & 8.29 & 0.480 & 7.15 & 0.452 \\ CMOD = 2.5 mm & 8.42 & 2.165 & 8.42 & 2.216 & 8.41 & 2.220 & 6.98 & 2.117 \\ \hline \hline \end{tabular} \({}^{*}\) Average value of displacements at maximum loads of all fiber-reinforced prisms.  
\end{table} 
Table 11: Comparison of measured and calculated load values at certain displacements. * All fiber-reinforced prisms showed the same failure mode: a crack occurred at the notched cross-section. The fiber-reinforced prisms showed softening behavior (the residual load-bearing capacity was less than the load at (or shortly after) crack formation). However, the load started to increase again for larger displacements. This behavior can be described as post-crack hardening behavior. * The compressive strength of the fiber-reinforced concrete cubes was slightly lower than the compressive strength of the plain concrete cubes. This can be attributed to the relatively high fiber dosage. * The nonlinear semi-numeric computational procedure based on the moment-curvature relation with back-calculated tensile strength properties agreed with the averaged experimental results. The result matching was especially good at the maximum load and CMOD values of 0.5 mm and 2.5 mm. The calculated load-displacement curve matched (accurate to around 0.05 mm) the averaged experimental results at the maximum load and at CMOD values of 0.5 mm and 2.5 mm. This agreement can be attributed to the fact that the tensile strength properties for the calculation were determined by an inverse analysis, where the maximum load and loads at presumed CMOD values of 0.5 mm and 2.5 mm were matched with the experimental results. The load-displacement calculation proves that the back-calculated (by inverse analysis) mechanical properties (tensile strength and residual tensile strengths at CMOD values of 0.5 mm and 2.5 mm) are correct.