2x4s may very well be holding the roof above your head. They're pretty strong when done right. What are you planning to keep on the shelves?

More than 2x4 strength, looking at your design I'd be concerned about balance. If putting heavy things on the forward edge of that middle shelf, you'd need to be certain that the vertical pieces are attached very firmly to the bottom. Probably a half-lap, possibly a half-dovetailed one, and I'd consider a diagonal brace from the forward edge of the base up to about the middle shelf as well.

But as you say "work area", if just being used as a desk or similar, with normal desky things on the shelves (even books or files), 2x4s are more than adequate. Way more than adequate.