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I am planning on getting "wood crates" to be the legs of a lofted bed.

Each box measures 18" x 12". For thickness, the long sides are strips of 1/4" pine and the short sides are solid 3/4" pine:

enter image description here

I want to make the legs 54" (18*3) tall in front, and stacking four crates with some 2x4s at the top (to fill in the gap to reach 54".

enter image description here

Starting in the bottom left corner and going clockwise: I plan on cutting out slots for two 2x4s in the crates for stability. Then, along the back left, there is a 1' 2x4 for support (and will probably add another one in the middle). Along the back bottom is a 1x2. Inside the front bottom is a 2' 1x2. Last, the top frame is made of 2x4s.

Will this design be strong enough to support a sheet of plywood under a mattress? Is there a good rule of thumb related to figure this out?

Edit

The wood crates are pine and they are all the same dimensions. They are fastened together with staples as seen in the picture. (These are commonly available at home improvement stores.) My qualm is how these are marketed as decorative boxes.

  • the brads used to attach the slats to the ends are nowhere near strong enough to support a long-occupied bed. The crates are likely also a softwood, which will deform with vibration and lateraral force to the point that the brads loosen. – dandavis Aug 31 at 20:53
  • Thank you for the input. It is pine. I am working on redesigning it with vertical 2x4s... – adamaero Aug 31 at 21:05
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    you could line the inside wall with a snug 1x8x17.something to keep the same aesthetic yet transfer the load to a wood compression instead of staples. I guess that only applies to the right-side stack in the illustration, the back is actually likely ok as shown (didn't realize the asymmetry initially). – dandavis Aug 31 at 21:10
  • Try replacing the 1/4” pine slats with 1/4” aluminum slats :). In fact replace only half of them, but have them be continuous the whole 54”... – Harper - Reinstate Monica Aug 31 at 22:44
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That's impossible to say because not all such boxes are built to the same specifications. Wood species and size, fastener type and schedule, and other factors vary widely. If forced to answer it would be no out of an abundance of concern for safety.

I would follow your plan, but lay 1x4 posts alongside the boxes where appropriate and aesthetically pleasing. Fasten the boxes to the posts and to the bed frame. Make sure it all has enough diagonal bracing, which is the most likely failure concern. That gets into design a fair bit, which isn't really on topic here.

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quarter inch pine nailed to 3/4" seems too flimsy to me.

Each time you halve the thickness wood losses three quarters of its stiffness.

If a 2x4 is stiff enough to be a leg for the bed 4 1x4 would work instead or 16 1/2x4 or 64 1/4x4 So at 1/4" thick you need 256" of width to get the equivalent stiffness of a 2x4
your crates have only about 20" so they'll be about 13 times worse.

I'd use solid 3/4" thick wood panels 3/4" (lumber, MDF, or plywood) to construct shelving units to be the legs, if securely fastened together they will be strong enough.

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