By means of two dimensional contact dynamics simulations, we analyzed the effect of the particle size distribution (PSD) on the shear strength of granular materials composed of unbreakable disks. We modelled PSDs with a normalized beta function, which allows for building S-shaped gradation curves, such as those that typically occur in soils. We systematically controlled and varied the size span and the shape of the PSD, and found that the shear strength is independent both characteristics. This implies that PSD modification procedures such as material scalping (i.e., removing the smallest and/or largest particles in the sample) should not affect significantly the shear strength of the material composed of unbreakable discs. In order to explore the origins of the invariance of the shear strength with PSD, we analyzed the connectivity, force transmission, and friction mobilization in terms of anisotropies, finding that the constant shear strength is due to a subtle compensation of anisotropies.