Quantification of residual activity is an important issue for high-power accelerator facilities like the Facility for Antiprotons and Ion Research (FAIR). While beam losses of 1 W/m are at present accepted for proton machines as a tolerable level for ensuring "hands-on" maintenance, the beam-loss tolerances for high-energy heavy-ion accelerators have not yet been quantified. The Monte Carlo particle transport codes FLUKA and SHIELD were used to simulate the irradiation of copper and stainless steel by different ions (1H, 4He, 12C, 20Ne, 40Ar, 84Kr, 132Xe, 197Au, and 238U) with energies typical for FAIR machines. Copper and stainless steel were chosen as common materials for accelerator structures. The isotope inventory contributing >90% to the total residual activity does not depend on the projectile species; it depends only on the target material and projectile energy. The activity per watt induced by a 1 GeV/u heavy ion is lower than the activity per watt induced by a 1-GeV proton. A tolerable beam-loss level for a 1 GeV/u 238U beam was found to be [approximately]5 W/m.