Beef can be brined. Most food people--when they write about it--assume that since most people cook beef to a lower internal than the measts we usually associte with brining, brining will be of no benefit. Brining also discolors the meat making, say, a roast cooked to medium-rare look unappealing grey throughout.
Obviously, the color issue isn't an issue when cooking beef to high internals and there are those that brine beef for barbecue. That said, I find that a marinade-brine (a marinade with an increased salt level) tends to work better, imo, as the finish texture is less affected.
If you want to try a brine, I suggest upping the salt and reducing the time in the brine. Smoke immediately after brining.