As others have said, the vast majority of people I've spoken with at the gym (myself included) experience the same pain when doing any sort of straight-bar curl. I personally stopped doing them years ago, as I generally notice the same benefit when substituting dumbbells and/or a curl bar. I may attempt them every so often just for variety, but it doesn't happen all that much.
In the end, if something hurts, don't do it. Stop, re-evaluate your form to be sure it's correct, and if so (and it still hurts), find something else to do. Everyone's physiological mechanics are a bit different, so some exercises will hurt you when others can do them without pain, and vice-versa. Ultimately, it's not worth risking potential injury, as there are generally always substitutes that you can plug in instead.