## 4 Results and Discussions
Mohr’s circles showing (**c**) the ABAQUS strain, (**d**) the Vector2 strain, (**e**) the ABAQUS stress, and (**f**) the Vector2 stress. The inclination angle \(\theta\) decreased continuously until approximately 21\({}^{\circ}\) in the strain and 14-28\({}^{\circ}\) in the stress Mohr circles. If web reinforcements were present, the compressive strain limit of concrete was attained at \(\varepsilon_{c}=0.0033\) (i.e., the concrete crush strain), at \(\varepsilon_{t}\sim 0.001\) for the bottom reinforcement (the tensile strain) and at \(\varepsilon_{t}\sim 0.0025\) for the web element (the transverse strain when the rebar is fully yielded; Figure 7). Then, the inclination angle \(\theta\) decreased to approximately 21\({}^{\circ}\) at shear failure during loading. Because we did not apply any web reinforcement, the SFs were lodged in plain concrete. The vertical (transverse) strains at various longitudinal locations were monitored as shown in Figure 10. Six locations were chosen at 0, 250, 330, 640, 940, and 1200 mm distant from the loading point (Figure 10a). The transverse strain increased with increasing shear strain. In the flexure-dominant monitoring line at 0 mm, the transverse strain increased to 0.001, whereas the transverse strains of the shear-dominant lines at 640 and 940 mm increased to 0.0025-0.0029 (Figure 10b). The longitudinal strains decreased as the transverse strains increased at the shear-dominant lines (Figure 10c). Figure 10d,e shows the longitudinal and transverse strains associated with deflections under the loading points. Figure 10: _Cont._  
Figure 9: Variations in the angle of inclination of the web-shear crack according to the average tensile strain of the bottom reinforcement. (**a**) ABAQUS. (**b**) Vector2. The shear stress-strain curves at the various monitoring lines exhibited shear stress maxima of 1.4-2.1 MPa as the shear strains failed at approximately 0.003, with the exception of the flexure-dominant line at 0 mm (Figure 11a). The average tensile damage was 0.1-0.26 in shear-dominant web elements but 0.42 in the flexure-dominant element (Figure 11b). Figure 6c shows a graphical representation of tensile damage across the various cross-sections. [PERSON] et al. [16; 17] defined a critical loading zone under the loading plate, which creates the tip of the shear crack. This was viewed as a rigid block; the \"whole truss analogy\" was used to model the bottom longitudinal reinforcements and several radial compression struts (Figure 12a). Axial deformation of the bottom longitudinal reinforcements causes a radial rigid strut to rotate around the loading platten, widens the inclined crack, and triggers slippage on the crack surface. The two kinematic compatibility conditions are the vertical displacement \(\Delta_{c}\) under the loading platten and the average strain \(\epsilon_{t,\mu\text{erg}}\) of the bottom longitudinal reinforcements (i.e., the displacement field between the two overall shears). The first term represents the behavior of elastic-fixed dowels subjected to a relative transverse support displacement \(\Delta_{c}\). The second term reflects the formation of plastic hinges at the ends of the dowels; the moment capacities of the hinges are reduced by the tension force T acting on the bars. The variable \(l_{t}\) is the length of the bottom reinforcement within the cracked part of the shear span, as illustrated in the free-body diagram of Figure 12a. Figure 11: (**a**) Shear stress–strain plots, and (**b**) Tensile damage index-deflection plots at the various monitoring lines (0, 250, 330, 640, 940, and 1200 mm). Figure 5:0 Strains. (**a**) Monitoring locations. (**b**) Shear strain-transverse strain plots. (**c**) Longitudinal strain-transverse strain plots. (**d**) Longitudinal strain-deflection plots. (**e**) Transverse strain-deflection plots. The shear resistance of SFRC in a beam without shear reinforcement is given by Equation (1).