The mechanical response of fibre-reinforced brittle-matrix structural elements subjected to bending is discussed in the framework of fracture mechanics. By means of numerical simulations based on the bridged crack model, the flexural behaviour of steel fibre-reinforced concrete (FRC) beams has been investigated, taking into account pull-out or yielding bridging mechanism of the secondary phase. In both cases, the numerical results predict a transition of the global structural behaviour, which can range from ductile to catastrophic. This behaviour is governed by a dimensionless parameter, the brittleness number, N P , in which the effects of the structural size and the fibre volume fraction are included. An experimental campaign is carried out on FRC beams subjected to three-point bending tests, considering three different beam sizes and four different fibre contents. A comparison between experimental tests and numerical simulations shows that the bridging mechanism is due to the fibre slippage into the matrix, rather than the fibre plastic flow. The expected ductileto-brittle transition is found for each beam scale, as predicted by N P. As a consequence, the minimum fibre volume fraction can be defined according to this model, providing an effective structural bearing capacity of FRC structural members.

The scale effects on the global structural response of fibre-reinforced concrete (FRC) beams subjected to bending are discussed in the framework of Fracture Mechanics by means of the Updated Bridged Crack Model (UBCM). This model predicts different post-cracking regimes depending on two dimensionless numbers: the reinforcement brittleness number, NP, which is related to the fibre volume fraction, Vf; and the pull-out brittleness number, Nw, which is related to the fibre embedment length, wc. Both these dimensionless numbers depend on the beam depth, h, which, keeping the other variables to be constant, drives a ductile-to-brittle transition in the post-cracking regime of the composite. The critical value of the reinforcement brittleness number, NPC, allows for prediction of the minimum (critical) specimen size, hmin, which, analogously to the minimum fibre volume fraction, Vf,min, is required to achieve a stable post-cracking response. Numerical simulations are compared to experimental results reported in the scientific literature, in which FRC specimens, characterized by the same fibre volume fraction but different sizes, are tested in bending.

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