A detailed study of the influence of space charge on the crossing of second-order resonances is presented and associated with the space-charge limit of high-intensity rings. Two-dimensional simulation studies are compared with envelope models, which agree in the finding of an increased intensity limit due to the coherent frequency shift. This result is also found for realistic bunched beams with multiturn injection painting. Characteristic features such as the influence of tune splitting, structure resonances, and the role of envelope instabilities are discussed in detail. The theoretical limits are found to be in good agreement with the performance of high-intensity proton machines.