We present extensive computations of photoabsorption and photoionization cross sections across the K-edge of Ne, Mg, Si, S, Ar, and Ca ions with less than 11 electrons. The calculations are performed using the Breit-Pauli R-matrix method and include the effects of radiative and Auger damping by means of an optical potential. The wave functions are constructed from single-electron orbital bases obtained using a Thomas-Fermi-Dirac statistical model potential. Configuration interaction is considered among all fine-structure levels within the n = 2 complex. The damping processes affect the resonances converging to the K thresholds causing them to display symmetric profiles of constant width that smear the otherwise sharp edge at the photoionization thresholds.