## 5 Conclusions and Perspectives  
The intertwining of the three types of fibers has enabled an enhanced pullout mechanism in a cementitious matrix with low water content. Based on the fact that fibers with shorter aspects become more numerous than longer fibers under the same proportion, shorter microfibers are more likely to be unidirectional and compactly distributed in the axial axis of the highly compacted and flowable cementitious matrix under the concrete pouring direction. Accordingly, short microfibers become more effective in controlling the initiation and propagation of microcracks while the longer fibers control the macroracks. As a result, this ternary combination would prevent micro- and macro-crack growth in the generated cementitious matrix. The concept of high packing density and highly distributed microfibers due to the selected additives with optimal proportions is validated through the performance-based approach relied on post-cracking strength and toughness. In the current research, the experimental mechanical response (load-deflection and moment-curvature curves, ductility, crack response, and failure patterns) to the four-point loading condition of UHPC beams was accordingly discussed. Furthermore, analytical prediction formulas for the calculation of the UHPC beam's moment capacity were presented. Based on this study, the following conclusions were drawn:  
* The inclusion of the fibrous system of fibers in the UHPC concrete increased its compressive and flexural strengths by 31.5% and 237.8%, which indicated the significance of fibers in promoting the tensile and flexural properties of UHPC. * The investigation of the load-deflection curves of beams revealed that the UHPC beams with low \(\rho\) failed by a sudden brittle flexural failure; however, the beams with medium to high \(\rho\) altered this failure behavior to semi-ductile to ductile ones. This conclusion implies that better safety could be achieved by optimizing the tensile reinforcement for a UHPC beam. Additionally, the entire load-deflection behavior was enhanced by the introduction of more bar reinforcement (especially after yielding the bar reinforcement). * The analysis of the moment-curvature curves demonstrated that most of the UHPC beams were prospective under reinforcement (tension-controlled). Additionally, the slope of the pre- and post-steel yielding was almost typical for all beams. This was due to the efficient hybrid fibrous system in the UHPC that controls the post-cracking curvatures of beams. In the current study, \(\mu_{D}\) and \(\mu\) were calculated to investigate the ductility behavior of UHPC beams with different \(\rho\) The percentage differences of these ductility parameters for the duplicate samples were 1.95-11.12% and 30.44-76.21%, respectively. The relatively high percentage difference for \(\mu\) was likely due to the bilinearization hypothesis of the \(M-\varnothing\) curve. Moreover, it was concluded that as \(\rho\) increases, the \(\mu_{D}\) exponentially increases; however, the relation between \(\rho\) and \(\mu\) showed a robust third-order polynomial trend. According to this analysis, B3 and B4 had inferior curvature ductility with respect to B1, which was attributed to the compressive failure of their concrete at the top surface or tensile failure of bars prior to achieving high ductility. The cracking response of the UHPC beams demonstrated that increasing \(\rho\) notably decreased the crack opening width of the UHPC beams at the same service loading. Moreover, increasing the bar reinforcement ratio contributed to stabilizing the crack propagation. The cracking pattern beams showed that increasing the bar reinforcement percentages notably enhanced their initial stiffness and deformability. The existence of bar reinforcement helped to enhance the failure pattern, as more flexure shear cracks were observed as its existence increased. These flexural cracks were the main cause of failure for all beams; however, flexure shear cracks were observed in moderately reinforced beams.