they’d either be very stocky or all break their ankles.

Suppose there were giants on Earth. As in things that were built basically like humans, but ten times taller so that they could look over small trees. They’d all have broken bones all the time.

First, a caveat. I am not trained in either physiology nor civil engineering; the derivations below are for illustrative purposes only.

Bones act like both columns and beams. The physics of each is different, but the end result is the same.

The stress placed on a beam is determined by

width × load × length

8 I

where I is the area moment of inertia, a function of the shape of the cross-section of the beam and generally proportional to the square of its cross-sectional surface area. Plugging in 10× size, we get

10 × 1000 × 10

10000

= 10× overall stress, meaning that it takes one tenth as much relative load to snap a giant’s bone.

Columns buckle when the load on them exceeds a factor proportional to

I

length2

. This increases 100×, but load increases 1000× so the net result is the same as with beams: it takes one tenth as much relative load to buckle a giant’s bone.

So, what if we make the giant’s stockier? Increasing width but not height by a factor of w increases load by w² and area moment of inertia by w⁴, so the stress on a beam changes by

w × w2

w4

=

1

w

. To compensate for the 10× weaker bones, we’d need a 10× increase in girth; our giants would be wider than they are tall.

The above assumes we increase all width (that’s what made the load increase so quickly). If we only increased the girth of the bones, not anything else, we’d still have stocky giants and ones that look like skeletons to boot. If total body mass is M and skeleton mass is sM then the change in load from a w-increase in bone width is

w × (1 − s + sw2)

w4

A shallow web searchthat is, I did not look up the original sources of the various hits suggests bones comprise 10-30% of body mass. At the 10% level bone width would need to increase by 2.5×; at the 30% level bone width would need to increase by 3.5×. To spread the same amount of muscle around three-times as much bone circumference means the muscle depth, skin thickness, etc, would shrink to a third its normal width, meaning these giants would basically look like thin translucent red paste spread over really fat bones.

Of course, they might be wider than they are tall and thus incapable of moving, or they might suffer chronic broken bones. but if you see a giant that looks like anything other than a stocky skeleton, fear not: they’ll snap their bones just walking.