Lots of physics, lots of trial and error, and sometimes even a bit of common sense. Many of the guidelines that engineers use are determined “empirically”, meaning that they were literally tested to compliance instead of just derived from the physics – sometimes it’s just quicker/cheaper to build a scale model.
One of the primary purposes of a bolt is to hold two objects together. Once you hold them together tight enough, they don’t slide anymore and the bolt itself is only held in tension, no longer subjected to shear – this is desirable since most cheap bolts aren’t strong in shear force, but quite strong in tension.
We know from physics how much force a bolt can handle, so we know how much torque to apply before possibly causing the bolt to stretch and fail.
We also know from physics how much force is needed to prevent slipping, so once we’ve got that and the bolt “strength” we can either add more bolts till there’s enough to prevent slipping, or we go up a size in bolt diameter!
For highly specialised applications, we don’t generally like bolts, though, since torque alone isn’t a very reliable way to know if it’s good enough… Rivets, welds, assembly adhesives and interlocking shapes all work significantly better.
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