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RE: loader surcharge at top of retaining wall

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Timoshenko's Mechanics of Materials has an example which shows that a statically applied sudden load corresponds to a impact factor equal to 2. Imagine you have a simply supported beam with a mass M held at midspan, so it just touches the beam, without imparting any load. If you suddenly release the load (no dropping height or initial velocity), you get a deflection in the beam that is double that of the deflection from a statically (infinitely slowly) applied load. Thus an impact factor of 2 without any incoming kinetic energy. The above assumes no energy losses, elastic behaviour, etc., etc.

Gunnar Hafsteinn Isleifsson

-----Original Message-----
From: Sherman, William [mailto:ShermanWC(--nospam--at)]
Sent: Tuesday, November 14, 2000 19:42
To: 'seaint(--nospam--at)'
Subject: RE: loader surcharge at top of retaining wall

Christopher Wright wrote:

> 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.

Your first statement is a valid statement - but I'm not sure why you say it 
doesn't account for any kinetic energy. Isn't kinetic energy accounted for 
in the formula F=Ma?

At 10 MPH, the speed equates to 14.7 feet per second. Using my assumed 
deceleration rate of 0.25 seconds, my equivalent force formula is as

F = Mass x acceleration = (weight/32.2 ft/sec^2) x (14.7/0.25 sec) = 1.83 W

But I must admit that if the deceleration rate is, for example, 0.10
the force increases to F = 4.6 W. Thus the force is very dependent upon the 
rate of deceleration. I'm sure a detailed dynamic equation can be written to

determine a more accurate deceleration rate based on the wall stiffness
a moving object impacting on a spring), although the wall stiffness requires

some additional assumptions regarding materials properties (instantaneous 
modulus of elasticity, cracked section properties, base fixity, etc).
the best one can do is get an "estimate" of the magnitude of load.