# Hybrid Fibres as Shear Reinforcement in High-Performance Concrete Beams with and without Openings
## 1 Introduction  
In cases where the major tensile stresses in the shear region of a RC beam exceed the concrete tensile strength, diagonal cracks finally cause failure. Several experimental and theoretical studies have confirmed that the key parameters affecting the response of RC beams are the type and direction of external loads, the shape and dimensions of the specimen, the strength of the concrete and steel reinforcement, the shear span to depth ratio and the reinforcement arrangement [1; 2; 3; 4; 5; 6; 7; 8]. Depending on the factors, the ultimate loads and failure modes can change. In the most favourable case, ductile flexural failure follows, and in the worst case sudden shear failure occurs a short time after the first diagonal crack forms due to the brittle concrete properties. Research emphasizes that the strength and ductility of RC beams are increased by using fibres as an additive to plain concrete [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. This is thanks to the greater resistance to cracking of fibre-reinforced concrete (FRC). This post-cracking tensile strength also tends to reduce crack sizes and spacing [20]. Generally, FRC contains a single type of fibre. The use of at least two types of fibres in a suitable combination can potentially not only improve the concrete properties, but also result in performance synergy. The combination of fibres is often referred to as hybrid fibres [21; 22]. Positive interaction between different fibres in hybrid FRC exceeds the sum of the single fibre properties. The first type of fibre is smaller and thereforebridges microcracks as well as controls their growth, which results in a higher tensile strength of the composite. The second type of fibre is larger and arrests the propagation of macro cracks, thus leading to a significant improvement in fracture toughness [21]. Furthermore, it has been revealed that it is possible to replace conventional shear reinforcement by steel fibres and achieve similar ductility and strength [18; 23; 24; 25; 26; 27; 28; 29; 30; 31]. Numerous tests have also been carried out to select the type of fibre and optimum volume percentage, as well as to ensure the shear strength of RC beams without brittle failure [18; 19; 20; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42]. Nevertheless, the increase in shear strength depends not only on the fibre volume fraction, but also on the aspect ratio as well as the fibre anchorage conditions. From the workability point of view, the use of smooth and stocky fibres is effective. However, hook-ended or crimped steel fibres are most commonly used in proportions of 0.5 to 1.5 vol % as they effectively bridge cracks due to their high pull-out resistance and consequently FRC has higher tensile deformations than plain concrete. In addition, owing to the increased tensile strength of FRC, there are large tensile strains in the longitudinal rebars, which result in high ductility of the beams. The increase in shear strength varies considerably depending on the beam geometry and material properties (from 12% to >100%) [33]. The ultimate shear strength of FRC beams diminishes as the shear span to depth ratio increases and rises with an increasing flexural reinforcement ratio and concrete compressive strength. The other tests suggested a scale effect linked to the height of the steel fibre RC beam without stirrups. For higher beams, wider cracks at failure were observed [43]. [PERSON] et al. [30] presented a model to estimate the shear strength of hook-ended steel FRC beams without stirrup reinforcement on the basis of large-scale beams experiments. They assumed that shear stress carried in the compression zone and tension transferred across diagonal cracks by steel fibres. The reduced diagonal crack spacing and width increase the aggregate interlock effect. Additionally, the presence of steel fibres indicates that the usage of fibre reinforcement could potentially lead to a reduction of the size effect in shear beams without stirrups within the beam depths range from 455 to 685 mm.