A few modifications can prevent back pain with dumbbell curls.
Done incorrectly, any exercise can cause pain or injury in one or more parts of your body. Sometimes the pain may develop in an area that seems totally unrelated to the move, such as lower-back pain from dumbbell curls that work the biceps at the front of your upper arm. Fortunately, your back pain isn't likely to require you to pass on biceps curls altogether. Some modification or strengthening exercises for other areas should do the trick.
Why it Hurts
If you're experiencing back pain after a standing biceps workout, chances are your back is arching sometime during, or even throughout, the lifting phase. Proper form requires your head, back and pelvis to be aligned throughout the movement. Knowing when your back arches can provide a clue as to the remedy. Stand sideways in front of a mirror while performing your curls and carefully monitor your form.
A major cause of back strain in connection with any standing exercise is locking your knees. In fact, standing with locked knees can strain your back just in the course of everyday life. Make sure your knees remain "soft" throughout the exercise. That is, don't significantly bend them but don't lock them either. Next, try to align your pelvis so you have a natural curve in your lumbar region.
The Core of the Problem
If you're standing with soft knees but still have difficulty aligning your pelvis, it could be due to weak core muscles. Until you strengthen those muscles, you should do your curls either seated or standing with your back pressed against a wall. In the meantime, add core stabilizing exercises, such as abdominal hollowing, planks and curls, to your workout session. While you should leave a day between working other muscles, you can work your core on consecutive days, so if it's very weak, consider adding an extra workout day just for core muscles. Also, practice standing on an inflatable dome. You'll work your core muscles as you stabilize yourself for balance.
Too Much of a Good Thing
The proper weight is one with which you can do a certain number of repetitions -- usually eight to 12 for two sets or 15 for one set -- in proper form. If you start out in proper alignment, but your back starts to arch about halfway through the curl, your back is compensating for what your arms can't lift. If you can do the minimum number of reps in good form, stop when your back starts to arch. If you can't get to the minimum number without your back arching, the weight is too heavy. Keep dropping the dumbbell weight until you can do the minimum number properly.
Some people have lordosis, commonly known as swayback, which is simply too much curve in the lumbar area. Stand against a wall with your feet a couple of inches out. When pressing your back against the wall, you should be able to just slide your flat hand between the wall and your back. If it's too easy, you may have excessive lordosis. In this case you may never be able to comfortably do standing dumbbell curls. Seated curls, curling with your back pressed against a wall or using a preacher bench should help, but check with your physician first.