Sudden Loading. In engineering, this refers to the application of a given load suddenly, as the term implies, such that the member bearing the load
goes from unloaded to fully loaded in a very short period of time (effectively instantaneously).
This specifically excludes the effects of impulsive contribution due to collision. In the context of a column supporting a load, sudden loading
refers to bringing the load into contact with the column, which is initially unloaded, then releasing the load suddenly as opposed to gradually
applying the load in a quasi-static fashion.
Being an engineering term alien to physics, I didn't know this until Tony Szamboti explained it to me - the missing link being the fact that the load
is first brought into contact. It made no sense that dynamic loading ALWAYS produced twice the peak of the same load statically when impact is
involved. Clearly, intuition indicates that, the greater the impact velocity, the greater the impulse delivered, all other things equal.
In NIST's FAQs, they describe a situation in which floors (or stories of an upper block? There's a difference, and it's never made clear...) from
above drop onto a floor below, and say the dynamic load amplification factor is two. This is false, and for more than simply the reason that there is
a non-zero impact velocity, though this is obviously also true. A dynamic amplification factor of 2 relies on contact and release only and excludes
impact, but it also very subtly involves a usually unspoken assumption of linear response in the support.
First, the non-impulsive nature of sudden loading.
From
The practical design of plate girder bridges,
where the context is a train rolling onto a bridge:
Also it should be noticed that the load comes on the structuree suddenly, and if the span is only a short one, the full live load effect is
induced in a fraction of a second.
...
Then, as regards sudden loading, it can be shown theoretically that if a load is suddenly applied to a piece of material, the strain produced will be
just twice that produced by the same load gradually applied, and, therefore, the equivalent stress will be twice that produced by the same load
gradually applied, as calculated in the usual way.
"In the usual way." This phraseology belies its origins in everyday engineering statics. Bridge builders when designing cannot exclusively do
calculations the 'usual way' for engineering, which is primarily static analysis. There are dynamic considerations when a train rolls onto the bridge
- it is suddenly loaded - where a moment ago it was fully unloaded with respect to live load.
The support
gives in response to the applied load; that is, it deforms. In so doing, the load is allowed to drop ever so slightly beyond the
equilibrium (unloaded) position, thus losing potential energy. Where does this energy go? Until the support displaces far enough to counter the
static load, it will not even resist the downward acceleration of the load. That occurs when the displacement is equal to the loaded static
equilibrium displacement. So the lost potential energy goes into kinetic, and the load accelerates downward.
Until that displacement of static equilibrium is achieved. At that point, the force is equal and further deformation increases the resistive force.
Then the load will decelerate. Assuming the support doesn't fail, there will come a point where the downward momentum of the load is reduced to zero
and the object is momentarily at rest. For materials with
linear response, this happens to be twice the deflection of the static equilibrium
position and twice the associated strain.
Of course, the restoring force at maximum deflection is also twice the static load, so the load now begins to accelerate upwards as the support
rebounds. The force will reduce as the load moves up, being equal to the static load at the midpoint of travel and zero at the top. At the top, the
original position is restored, velocity is zero, and all the kinetic energy has gone back into potential. The dynamics of simple harmonic oscillator
with a mass at one end under the external force of gravity.
In the real world, response is (usually highly) damped, and the oscillation rapidly reduces in magnitude to zero. But, in the real world, response is
not usually linear, and is never linear over a sufficiently large deflection.
Bridge builders, while having to account for dynamic sudden loading, do not have to account for trains
dropping onto bridges. Likewise,
structural engineers do not generally need to consider non-linear response, because they stay within elastic range by design.
Continued...
edit on 5-2-2012 by IrishWristwatch because: (no reason given)