There's no way to answer that unfortunately. It would help to know what body you're thinking of, as manufacturers quote anticipated shutter life in their specs. It's the shutter which is likely to fail first due to the fact that DSLRs have a focal plane shutter which basically suffers far more than other type from wear in repeated use.
Bottom end starter bodies tend to have a quoted life of 50,000 shutter cycles, mid range ones around 100,000 cycles, while top end cameras have claimed lives of 200,000 or even 300,000 shutter cycles.
These are only guesstimates of what actuations they should achieve before failure though, many will fail before that, and some will well exceed it. :shrug:
Shutters can be replaced so it isn't a death sentence for the camera anyway. I wouldn't say 20K actuations is excessive even for a starter body, but you have to accept it may fail before or after the anticipated number of shots.