There are two bed frame problems for which strengthening can be appropriate. You can stabilize a wobbly bed frame with cross braces, and you can shore up a sagging frame with under-mattress material. Other kinds of weak bed frames usually are best replaced rather than repaired as the risks of catastrophic failure outweigh the benefits of saving money with a do-it-yourself repair.
Cut four wooden strips to either 6 or 12 inches long. Use the shorter measurement for standard bed frames, and the longer measurement for loft beds and bunk beds.
Set one wooden strip at an angle in one corner formed by the support leg and mattress frame, overlapping onto each of those pieces of the structure. Together, they should form a right triangle. Screw the strip in place using two wood screws at each point of connection.
Repeat step 2 three more times, adding a stabilizing brace to each of the three remaining open corners of the bed frame.
Measure the distance between the support rails of your bed frame. Measure both the length and width of the frame.
Cut your plywood to match the measurements you took in step one. For queen and king beds, you may need to cut two pieces of plywood, each to half the size of your mattress frame.
Slide the plywood sheets into the mattress frame, hanging on the rails like the bottom of your mattress.
Put your mattress on top of the plywood. This will not only support the mattress, but it will distribute the weight more evenly along the frame.