I'm about to assemble a few Ikea cabinet frames and was wondering if strengthening the backboards would help with anything or would it just be adding work and cost for nothing of practical benefit.
Let's assume there is a single freestanding frame with its back to the wall.
Ikea themselves in the assembly manuals notes some potential issues with the frames such as going out of square or bowing.
From what I understand the part of the frame whose job is to prevent that from happening is the thin, typically supplied folded in half piece of backboard made of laminated particle board. Once assembled the frame is then anchored to the wall (those backboard cutouts near the top in the picture above are where either the wall screws or brackets for attaching to a special rail would go).
That board is either lowered into the recess created at the back of the frame then nailed in place, or slid into the slot in the four frame walls, or a combination of the two (I think this might be the intermediate version before the slotted design was introduced removing the need for using nails).
In the first scenario the flimsy board can be easily replaced by something chunkier that fits within the recess. In the second this won't work as the size of the slot determines the maximum thickness of the replacement board. What one could do is to slide the original backing board in place to form a recess and then put another chunkier board on top, maybe glue them together with melamine wood glue and then nail both to the frame, though nailing may be a little risky since the nails would have to go in at an angle now and there is nothing much to nail to due to the frame material having been removed to make the slot.
Anyway, the point is it's a lot of work, especially with the latest design of the frame. What would reinforcing of the backboard help with?

