## 4 Results and Discussions  
The vertical displacement at the loading point was controlled up to 25 mm. The corresponding vertical reactions were monitored during simulations. Figure 6a shows cracking at loading stages 0.1, 0.2, 0.5, and 1.0. At stages 0.1 and 0.2, flexural cracks were dominant and spread because of the bottom reinforcement. As loading increased, diagonal cracks developed in the shear span and spread perpendicularly to form three major shear cracks. Figure 6b shows the rebar stresses in the bottom and top reinforcements and the stirrups. The maximum longitudinal stress in the bottom reinforcement was elastic as the shear cracks developed. Figure 6c shows the damage to three sections of the shear span. The tensile damage was higher in the section of the loading plane; the diagonal tensile cracks were more severe than the other cracks. Figure 6d shows the blunt crack patterns yielded by Vector2/MCFT analyses. These patterns were similar to patterns derived using ABAQUS (Figure 6a). Figure 4: Compression and tension behaviors of SFRC. (**a**) Compressive softening. (**b**) Tension softening. (**c**) The P-CMOD for a single-notched SFRC beam. Figure 5: MCFT: Fiber-induced stress at a cracked surface and the associated shear force. Figure 6: Failure patterns of the SFRC T-beam under the three-point bending test. **(a)** Crack patterns of ABAQUS. **(b)** von-Mises stress in the reinforcements. **(c)** Tensile damage. **(d)** Crack patterns of Vector2. Three windows of 360 \(\times\) 360 mm in the shear span: (1) flexure-dominant, (2) primary shear-critical, and (3) secondary shear-critical (Figure 7a) were selected for the sake of the modified compression field theory. Figure 7b plots the deformations of all windows at a displacement factor = 0.9 (10-fold magnification). The shear deformations of windows 2 and 3 are the deformations of web elements under bi-axial stress. Figure 7c,d depicts migration (expansion/shrinkage) during stretching and softening. The angle of inclination of the principal axis tended to fall because the transverse strain \(\varepsilon_{t}\) gradually increased as the shear cracks spread; this was followed by abrupt failure in the middle of the shear span. Figure 7e,f shows the rotations of the principal axis according to the load-induced stress variations in the web elements. Figures 8 and 9 show the changes in the inclination angle of the web-shear crack according to the web shear force reinforcement. As shown in Figure 9, the longitudinal average tensile strain \(\varepsilon_{t,avg}\) decreased while the transverse strain \(\varepsilon_{t}\) gradually increased. Web elements in a biaxial stress state rotate the crack angle as the averaged tensile strain of the bottom rebar increases, and the strain is released when the SFRC beam failed abruptly. As the inclined cracks of the web elements disperse and increase, the transverse strain also increases, accelerating the rotation of the crack angle. These series of immigration processes are well represented in Figure 7d-f by load level in Mohr circle. In the case of Vector2/MCFT, which is based on strain, the progressive failure of web elements is well depicted in the biaxial strain relationship, as shown in Figure 7d. Conversely, Abaqus result shows better failure trace of web elements under their biaxial stress state in a stress-based Mohr circle as shown in Figure 7e. MCFT, which analyzes changes in macro web elements based on average strain and average stress, can be interpreted as more suitable for SFRC structures than relatively local nodal or element-based analysis. Figure 7: _Cont._  
Figure 8: Variations in the angle of inclination of the web-shear crack according to the load factor. (**a**) ABAQUS. (**b**) Vector2. Figure 7: Variations in the angle of inclination of the web-shear crack according to the web shear force reinforcements. (**a**) Three windows in the web. (**b**) Shear distortions in web elements (10-fold magnification).