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Costs and weight I'd say. Somebody who understands material science better than me will likely correct me, but a rectangular cross section (with the long edge vertical) will be stiffer than a square cross section of similar cross sectional area. So I'd rather use a 2x4 in that fashion than a 3x3 for the same/similar volume/weight of timber.
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Same reason as ovalised seat stays.
Wide timbers will resist movement in a direction that is not relevant to a bed.
Your challenge will be the strength of any mattress support whether that is slats or a sheet of plywood.
stevo_com
Grumpy_Git
@CYOA
Toying with making a bed (starting another project that'll never be completed like the kitchen / wardrobes etc).
Was amused by this quote for walnut cut to size: £1225735699.36 + VAT
https://www.timbersource.co.uk/
On that note, is there a reason the two long side panels of most bed designs are vertical 2x4 style beams instead of 4x4 other than keeping costs lower? I want something I can basically jump on and a square seems stronger in my head than a rectangle but physics isn't my first language.