David Scheidt wrote:

I think you under estimate the problem.  A modern MBT (an M1, T80, t72, that
sort of thing) has a ground pressure of about 12 or 14 psi.

Also, ignoring ground pressure for the moment, a vehicle using a 'running' stride will of necessity have periods during the stride where the ground load is well in excess of total weight (200-300%), and periods where the ground load is zero. Thus, a 10 ton mech running across a bridge will be applying forces ranging from none to 20-30T, making collapsing the bridge far more likely than it is with rolling vehicles. The situation is less problematic when walking, but walking pace just isn't very fast, a 20' mech might walk at 8 mph or so.
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