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# RE: loader surcharge at top of retaining wall

• To: "SeaInt Listserver (E-mail)" <seaint(--nospam--at)seaint.org>
• Subject: RE: loader surcharge at top of retaining wall
• From: "Sherman, William" <ShermanWC(--nospam--at)cdm.com>
• Date: Wed, 15 Nov 2000 19:22:10 -0500

```James Lutz wrote:

> The force transmitted to the wall is equal to the momentum of the vehicle
> (mass times velocity) divided by the time it takes to stop.

I agree, this is why F = ma does take into account momentum: since "velocity

divided by the time it takes to stop" is equal to the "deceleration", this
resolves to the same equation: F = mv/t = ma. The key point here is that
velocity becomes zero at the point of maximum deflection of the structure,
thus there is no remaining kinetic energy at that point.

Design of Welded Structures by Blodgett has a very good chapter on Designing
for
Impact Loads. It states that the impact force is F = ma = Wa/g. It also
states
that "the member will deflect slightly and allow a certain time for the
moving
body to come to rest, thereby reducing the impact force. Since the time
interval
is usually unknown, the formula cannot be used directly to find the force.
However,
it is usually possible to solve for this force by finding the amount of
kinetic
energy or potential energy that must be absorbed by the member."

Thus F = ma is still valid "if" the time interval is known. The energy
method is
simply another means of obtaining the same result, which of course requires
a more
detailed analysis of member and material properties. It is certainly more
accurate
than "guessing" the time interval, but it does not negate the validity of F
= ma.

```