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# RE: loader surcharge at top of retaining wall

• To: "SEAOC Newsletter" <seaint(--nospam--at)seaint.org>
• Subject: RE: loader surcharge at top of retaining wall
• From: Christopher Wright <chrisw(--nospam--at)skypoint.com>
• Date: Tue, 14 Nov 00 11:06:41 -0600

```>This may be a stupid question, but I have always had
>trouble with the deceleration rate
Not a stupid question at all. The 1/4 second estimate sounds like a
hipshot that provided stresses that made someone feel good. Your impact
factor of 2 is probably a little low--it implies a statically applied
sudden load without any incoming kinetic energy or energy loss in the
collision. Probably there is enough energy lost in friction so that
you're not too far off, but you're not all that conservative unless you
can live with some damage.

Depending on the objects involved real impacts can be much shorter or
longer. The deceleration rate depends on the energy transfer at the point
of collision. The incoming kinetic energy has to be shared or dissipated
so that both objects end up conserving momentum and all the energy is
accounted for. Deceleration obtains from the forces that develop and the
laws of motion. For example a rock dropped onto a beam will act like a
single DOF system while the two are in contact so the motion is
sinusoidal, determined by the impacting mass and the equivalent spring
rate.

Everyone's first strength of materials course shows a very conservative
approach which assumes that all of the incoming kinetic energy is
absorbed by elastic deformation of the impacted structure. Since a lot of
energy turns to heat or is absorbed by inelastic behavior you can
including damping (usually a guessed critical damping ratio) as the
dissipation mechanism. For metal structures you can assume that most of
the impact is used up in plastic deformation (true for severe
collisions). You come up with a limit impact load which remains constant
during the collision by assuming elastic/perfectly plastic behavior. The
kinetic energy equals the limit load times the local deformation, and the
deceleration equals the limit load divided by the impacting mass.

All the above are pretty simple minded. Entire careers have been devoted
to very elaborate solutions, that really aren't all that precise. A very
good reference is _Structural Dynamics for the Practising Engineer_ by H.
M. Irvine. Best practical book on dynamics I've ever seen. Sound theory,
good examples and a real world perspective.

And that concludes this morning's lecture on impact dynamics. Read
Chapter 2 in Irvine. Test on Friday.

Christopher Wright P.E.    |"They couldn't hit an elephant from
chrisw(--nospam--at)skypoint.com        | this distance"   (last words of Gen.
___________________________| John Sedgwick, Spotsylvania 1864)
http://www.skypoint.com/~chrisw

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