# Hybrid Fibres as Shear Reinforcement in High-Performance Concrete Beams with and without Openings
## 1 Introduction
[PERSON] [44] developed a simple model for predicting the shear capacity of FRC beams without stirrups under transversal load taking into account the abilities of steel fibres to bridge tensile stress across crack as well as to contain shear crack slips. The ability of fibre for mitigating the shear size effect was taken into account by the geometrical characteristics of fibres. Although a number of experimental studies have been carried out so far to assess the shear strength of steel FRC beams, there is little research on the shear strength of steel fibre-reinforced high-strength concrete members [35; 37; 40; 45]. Therefore, further experiments are needed to evaluate the behaviour of fibre-reinforced beams made of high-strength concrete. The use of steel fibres in such concrete is particularly attractive as high-strength concrete brittleness may be limited by the fibre addition [46; 47]. Despite the significant increase in the cost of a HPC mix, the application of this steel fibre combined with another fibre type, e.g., polypropylene fibre, may be interesting to provide a structural alternative to traditional shear reinforcement. The typical volume percent of polypropylene fibres ranges from 0.1% to 0.3% [48], but even the lower percentage of polypropylene fibres can improve crack control in the early age of curing and early stages as well as increase fire resistance. The influence of steel fibres in increasing the shear strength of RC structural members has been recognized in the MC2010 [49] and is defined as shear strength extension recommended in Eurocode 2 [50] by introducing a modified longitudinal reinforcement ratio. Researchers have developed empirical equations for predicting the ultimate average shear stress [24; 33; 35; 39]. The empirical models of shear strength calculation are a function of several factors such as specimen shape and size, shear span to depth ratio, longitudinal reinforcement ratio, fibre aspect ratio, fibre volume content and the strength of the concrete and reinforcing steel. The first group of models predicts shear resistance by establishing a separate contribution of concrete and fibres, while the second group is based on global improvement of FRC shear strength [31]. An altered method based on the strain approach was suggested in [51]. With respect to the analytical response of plain or FRC beams under the impact of flexure and shear, some models have also been also developed, whose main purpose was to determine the moment-curvature diagrams [52]. These models are based on the finite element method within the hypothesis of the plane section theory or of approximate models, taking into account the compressive and tensile behaviour of FRC. [PERSON] et al. [53] reported the effectiveness of nonlinear finite element method to predict the structural behaviour of RC beams with steel fibres as well as beams with stirrups and steel fibres as transverse reinforcement. The experimental and numerical results highlighted that the transverse reinforcement provided by stirrups and steel fibres is an optimum solution in terms of the costs and structural performance. However, there is not a large number of test results to evaluate the existing design procedures for estimating shear strength. This study reports mainly experimental investigations of the implications of using steel and polypropylene fibres as shear reinforcement in RC flexural beams. The tests described in this paper were carried out on six beams, with openings in the shear regions and without openings, made of HPC with/without stirrups under a four-point bending configuration. All the beams were reinforced with compressive and tensile longitudinal steel deformed rebars, while conventional RC beams were also prepared with transversal stirrups.