We provide quantum Monte Carlo calculations of a two-component Fermi system interacting with an attractive interaction confined in harmonic traps. We investigate the role of the interaction’s scattering length and effective range and show their important role in modifying shell effects in the structure of these systems. We show that in the strongly interacting regime, where the scattering length is large, the dominant contribution to shell effects is due to the effective range. These conclusions are very relevant for nuclear physics, in particular for neutron-rich systems, and open the way to perform new atomic experiments that can help to explain the disappearance of shell effects in nuclei.