I've transcribed just about all the CSRs of Arkansas troops, and have found that it's hard in a great many cases to pin down a CSR to a specific ancestor, because Arkansas records are so fragmentary. I haven't looked at many Alabama records, but I hear from other researchers that the CSRs of Alabama soldiers -- especially those who served in the Army of Northern Virginia -- are in far better shape.
One rule of thumb you can use in researching a Confederate ancestor is that most Southern boys generally tended to enlist in companies being organized in or near their home counties. In the case of Hiram Beam, the 48th Alabama seems to fit. Next, you can compare a roster of his company to the 1860 census of Cherokee County. If you see the names of brothers, cousins or neighbors, then you can be pretty sure that it's your Hiram Beam on that roster. Sometimes you get lucky and the CSR will include some identifying information, such as date and place of birth. That's the part that's so lacking in many Arkansas records.
Good luck with your research, and if there's anything we on this message board can do to help, just ask. There's a lot of good talent on this board.