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(OP)
Hello,
Assume the end of a cantilever beam is impacted with a quick shock load of 100 lbf and deflects x inches. If this load was very gradually applied at the same location with the same impact area would the deflection be the same if the very slowly rising gradual load reached 100 lbf as well?

Does the "speed" of the load application affect the deflection of the beam if the measured force and force area remain constant?

Thanks!

makes sense to me that an impact load would have a larger displacement

another day in paradise, or is paradise one day closer ?

#### Quote:

Assume the end of a cantilever beam is impacted with a quick shock load of 100 lbf and deflects x inches. If this load was very gradually applied at the same location with the same impact area would the deflection be the same if the very slowly rising gradual load reached 100 lbf as well?

No.

#### Quote:

Does the "speed" of the load application affect the deflection of the beam if the measured force and force area remain constant?

Yes.

Rephrasing the question: If the WEIGHT were applied at gradual vs. impact there would be a difference because you would have the resulting force from the mass decelerating being much higher than the static WEIGHT of the entity being supported by the cantilever.

If the resulting FORCE from F=ma were applied as impact, the force is just the force, whether static or not.
At least that's my first thought on this. Force simply produces deflection "x" whether it is from a larger static WEIGHT or a smaller weight creating a same FORCE through deceleration.

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Actually, it depends. On the scale you are talking about it makes no difference whether its applied quickly or slowly. But for extremely large loads, such as a blast, it does make a difference due to the effects of strain hardening. The load is applied and removed before the beam has a chance to deflect (over a period of milliseconds).

You are talking apples and oranges here.

A gradual or static load would be just the 100 pounds force sitting politely on the end of the cantilever, whereas the impact load implies the added Kinetic Energy of 100 pounds force stopping over a certain finite distance.

JAE has it right.

Mike McCann, PE, SE (WA)

It is possible to have longer-term deflections due to creep in concrete, in steel at high temperatures, etc., and these are not included in typical deflection calcs.
With the quick shock load, part of the resistance to the load is from elasticity of the beam, part of it is due to inertia of the beam, so the deflection in the dynamic case could be considerably lower for a given force.

See the discussion in Chapter 14.4 of Hibbeler, Mechanics of Materials (8e). This section derives an impact factor based on height of drop, but that should still answer your question conceptually.

The usual horrible example given is for an undamped single degree of freedom system. A force that causes a staitic deflection x will cause a dynamic deflection of 2x if applied 'suddenly'. The maths is trivial. People seem happy to design using this, but for a real system it is neither accurate nor conservative.

Cheers

Greg Locock

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