## 3 Finite Element Models  
Two principal, constitutive, SFRC finite element models were used for nonlinear analysis; the first analysis was conducted using the continuum-damaged plasticity model of ABAQUS [28]. The compressive strength, initial elastic modulus, and Poisson's ratio were set to \(f_{c}^{\prime}=67.1\) MPa, \(E_{ci}=21,500[f_{cm}/10]^{1/3}=40,552\) MPa, and \(\upsilon=0.2\), respectively. A nonlinear material model to consider material damage in both compression and tension was used. The dilation angle, eccentricity, the ratio of the equi-biaxial compressive yield stress to the uniaxial initial yield stress, and the ratio of the second stress invariants on the tensile meridian to the second stress invariants on the compressive meridian were \(52^{\circ}\), \(0.1\), \(1.16\), and \(2/3\), respectively. The damaged plasticity model for concrete in ABAQUS is based on the models proposed by [PERSON] et al. [29] and by [PERSON] [30]. The Modified Drucker-Prager yield criterion is used with consideration of Lubliner Model ([PERSON], 1989) and damaged plasticity model ([PERSON], 1998) for concrete and other quasi-brittle materials. This concrete damaged plasticity model has been widely used for RC and FRC application in both static and dynamic situation [31; 32; 33; 34]. The volume fraction of SF was set to \(0.76\%\) (\(l_{f}=33\) mm, \(d_{f}=0.55\) mm). A linear-hardening model to manage the rebar and stirrups was used. The yield and ultimate strengths of the rebars and stirrups in compression/tension were \(538/696\) for \(10\) mm rebar, \(557/678\) for \(25\) mm rebar, and \(527/700\) MPa for \(6\) mm stirrups, respectively. The elastic modulus of the rebar/stirrups was \(E_{s}=\)210 GPa; \(\upsilon\) was \(0.3\) when employing a three-dimensional (3D) continuum element for concrete and a 3D truss element for the rebars. When running ABAQUS, 9910 elements (T3D) were used for rebars, and 3432 (C3D20) and 90,321 (C3D8) elements were used for the SFRC T-beam. Nonlinear steel was assumed to be perfectly plastic. Figure 4a,b show the compressive and tensile strength of SFRC in terms of the inelastic strain. To build a tension-stiffening model of SFRC, Figure 4c was calibrated using the Load-CMOD data of a flexural tensile test ([PERSON] et al. [27]).  
Figure 3: Strains in the web element. (**a**) Longitudinal, transverse, and compressive strut strains. (**b**) The transverse strain increased when the angle of inclination was reduced (Mohr circle).  
In the 2D models, 829 truss elements for the rebars and 1240 rectangular elements for the SFRC T-beam were used when running the Vector2 [35], Modified Kent-Park, and Vecchio (1992) models. A Hognestad parabola was used to examine compression post-peak behavior and softening. A modified [PERSON] model (2003) and a nonlinear Hordijk model were employed to manage tension stiffening and softening, respectively. The simplified diverse embedment model (2013) was combined with the post-crack FRC tension model. The Eligehausen model [36] was used to manage concrete bonding. The Distributed Stress Field model combined with modified compression field theory (MCFT, [4]) was employed to calculate crack stress (Figure 5).