Tracy writes:

> (There have been no documented instances of this)
>  1) You're claiming proof of a negative, which can't be done.
>  2) There ARE documented cases of bridges failing when harmonic vibration
>  gets out of hand.

In the case of soldiers' in-synch cadence affecting the load-bearing
structure of a bridge, it isn't resonance that is the concern. It's that
during that moment that everyone lifts themselves up, they weigh more than
they do standing still [i.e. (<- notice the use of a Latin phrase that the
Roman soldiers would have readily understood), the force applied against the
bridge is F = mass of all soldiers * (gravity + upward acceleration)].

If the bridge was near its load bearing strength under the static weight of
the column, soldiers marching in step could potentially collapse it because
they might weigh 1.2 to 1.5 times as much on their uplift and downtread as
they do when they are standing still.

A great number of physical processes depend on a statistical distribution of
users (Jon Broz's commode/water pressure example is one, but so are your
ISP's modem count and the number of switches the telephone company installs
at its central offices). If the soldiers broke step and marched randomly, the
average load presented to the bridge would only be slightly higher than a
static column would present.

Wirt Atmar