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RE: loader surcharge at top of retaining wall

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>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 

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)        | this distance"   (last words of Gen.
___________________________| John Sedgwick, Spotsylvania 1864)