## 2 Shear Critical Failure Test of an R/FRC T-Beam  
[PERSON] et al. [27] compared experimental results with the data of a blind analysis competition featuring three-point loading of concrete beams reinforced with short steel fibers. Blind analysis using the flexural performance and material constants of SFRC (disclosed in advance) predicted the maximum shear strength and strain of the lower rebar of the load action point using various models (smeared crack, discrete crack, and continuum-damage). The compressive strength of SFRC used in both the experiments and the analyses was 67 MPa, the water-cement ratio was 0.4, and the SF per unit volume was 60 kg. The volume fraction of steel fiber was 0.76%. Residual flexural stresses were provided in advance via SFRC three-point bending tests. The T-shaped beam in that work has the cross-section and specifications as shown in Figure 1a. The shear critical span ratio (a/d) was approximately 3.0 (2.955) and the beam was slender. The bottom reinforcement was three singly arranged \(\upphi\)25 rebar; the left side of the asymmetric three-point loading area without shear reinforcement. It is important to explore whether SFs can be used to resist shear in the absence of conventional reinforcement. SFs are presumed to enhance strength and ductility (despite sagging), while increasing resistance to extreme loads. An SF draws on the surface near a shear crack; the direction of drawing is thus important. Shear transfer strength via aggregate interlocking greatly contributes to the total shear resistance. As shown in Figure 1b, the beam finally underwent shear failure. Three inclined cracks developed and expanded at speeds proportional to the loads, such that longitudinal cracks occurred along the bottom rebar; a large, inclined crack then developed in the middle and destroyed the beam. [PERSON] et al. (2013) found that the shear crack angle depended on the shear-span-to-depth (a/d) ratio; it was smaller between \(\alpha\) and \(\theta\), where \(\alpha\) is the angle of the shortest distance between the inner points of the support platen, and the loading point and \(\theta\) is the angle of the inclined crack (Figure 1b). The angles of the three major inclined cracks increased with the level of loading ((1)\(\rightarrow\)(2)\(\rightarrow\)(3)\(\rightarrow\)(4)); \(\theta_{1},\ \theta_{2},\ \text{and}\ \theta_{3}\) were \(32^{\circ}\), \(35^{\circ}\), and \(50^{\circ}\) (by inspection); \(\alpha\) was \(21^{\circ}\). The shear crack angle thus depends on the minimum angle (here, \(21^{\circ}\)).  
Because the angle of inclination rotates under different loading/unloading conditions, the angle was developed vertically (under flexure); it was then extended and rotated toward both the loading point and the support. Figure 2 illustrates the shear force V and its relationship with the inclined angle \(\theta\); this relationship is affected by the nature of web reinforcement.  
Figure 1: Specim layout and crack pattern. (**a**) Cross-section, geometry, and reinforcements of the SFRC beam. (**b**) Failure pattern of the SFRC T-beam during the three-point bending test (kN).  
Figure 2: Variation in the angle of inclination of a web-shear crack according to the chosen web reinforcement, against the shear force.  
The angle of inclination of the web strut varied with the applied loading (Figure 3). During early loading, when the web-induced diagonal tensile stress attained the concrete tensile strength, a diagonal crack commenced; as the shear force increased, cracks gradually spread, eventually reducing the strain inclination angle of the strut (after some oscillating variations). The web fibers yielded when the shear force increased further; the diagonal crack was then stabilized. The longitudinal, transverse, and compressive strut strains in a web element are shown in Figure 3a. The transverse strain \(\varepsilon_{t}\) increases when the angle of inclination is reduced, as shown by the Mohr circle of Figure 3b.