This work is intended to be a simple contribution to building a model able to implement theoretical results related to the random oriented fiber reinforced concrete in a procedure that could be used in structures analysis and design involving fiber reinforced elements. Here follows a short outline: In the introduction chapter the problem is presented together the work done. Section 2 develops some ancillary concepts of this material and its mechanical properties, while in Section 3, following the path of other researchers, the assumptions made to solve the problem are presented, together with the most relevant results related to presence of 3D randomly oriented fiber. In the following section a review of the mechanical process of fiber pull-out is done, and the results, mostly due to Victor Li researches, of a 3D randomly oriented synthetic fiber stress vs crack opening in a pull-out process from a cement matrix. In Section 5 the author, after making some assumptions about the configuration of the strain and crack geometry in the cross section where failure is assume to occur under flexural bending moment, the resultant stress is integrated to find the resultant internal moment vs increasing strain and crack width. In this analysis, the crack bridging law for synthetic fiber in FRC presented in the previous section is taken into account. In Section 6, a procedure to find a cross section configuration in equilibrium under external bending moment has been built. Under the assumption of a perfectly plastic collapse mechanism a numerical simulation is conducted on a specimen that undergoes a four-point bending test. A comparison with the trend of a similar test on a synthetic FRC sample has been done. The work is completed by the conclusions that could be inferred from this work.
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