Aluminum alloy gusset (AAG) joints have been applied extensively in single-layer latticed shells. This paper investigates the resistance of the aluminum alloy bar (AL bar) in AAG joints under monotonic tensile loading. The main failure mode is the fracture of the I-shaped AL bar, accompanied by local buckling of the web. The fracture modes of the flanges differ: block tensile–shear fracture in the small plate (SP) group, whereas net-section fracture in the big plate (BP) group. Compared with traditional simulation, the simulation which considers the fracture can yield a load-elongation curve with a declining stage so that the ultimate resistance can be obtained straightforward. This simulation is based on the modified Mohr–Coulomb (MMC) fracture criterion with damage-induced softening, which is achieved by VUHARD and VUSDFLD subroutines implemented into ABAQUS/Explicit. The parameters in this criterion are calibrated on smooth plate specimen tests. The results from the finite element models are in excellent agreement with the experimental results in terms of the web buckling, fracture path, and ultimate resistance governed by the crack initiation and succeeding propagation. This simulation, particularly the fracture model and its detailed calibration procedures, have a broad prospect of applications for evaluating the resistance of aluminum components that are governed by various ductile fracture modes under monotonic loadings, such as the rupture of bolt connections and block tearing of AAG joint plates.