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Reactions at Column from an Impact Load

Reactions at Column from an Impact Load

Reactions at Column from an Impact Load

(OP)
Hey All,

Hoping someone can shed some light on this for me.

I have a project where an object, let's say weighting 200 lbs, is falling from approximately 20 stories (say 200 ft). The object is falling upon wood planking that is acting like roof projection, say 3x6 planks spanning 25' Planks are supported on a Steel beam supported by columns spanning 8ft o.c.

If the object falls right in the center of a single plank, and said plank is centered directly over a column (basically a simply supported beam), what reaction does my column see (Assuming plank can take impact load)

I understand terminal velocity may affect it as well as the shape of the object, but is there a simplified method that i can at least ballpark myself?

Thanks for any insight in advance,

RE: Reactions at Column from an Impact Load

I would design the column assuming the whole impact load that is happening to the plank, happens to the column as well, in case the falling object lands directly over the column and not in the middle of the plank. Conservative, yes, but can you guarantee the location of impact?

RE: Reactions at Column from an Impact Load

(OP)
Jayrod,

I completely agree with your assessment, but my question more lies in the value of the load itself. If a 200 lb object fell 200 ft directly onto the column, what load would you design the column for? It's not 200lbs, correct? I think it's more of a physics question. Mass, acceleration, headache...

RE: Reactions at Column from an Impact Load

Conservation of Energy and or momentum my friend. Potential at the top, kinetic right before impact.

RE: Reactions at Column from an Impact Load

Link Try this thread as a starting point

RE: Reactions at Column from an Impact Load

If you mean that the planks are directly above steel beams, that is, one plank above each beam, then you can probably reach a solution. If, on the other hand, you mean that planks are framing into a steel beam, which then frames into a column…you’ll never make it; you’d be off by orders of magnitude. The planks won’t even carry a 200# static load over 25’ on their own.

Here's one way to approach the problem:

Assume a deflected distance and use that to solve for the force by setting Work (F x d) equal to Energy (.5mv^2). Use the force to check the deflection in your system to see how close it comes to your assumption. Then iterate.

For example:

An object falling 200 feet falls for (2d/g)^.5 = (2*200/32.2)^.5 = 3.524537 seconds

Velocity at that point = gt = 32.2 x 3.524537 = 113.49 ft/sec

Mass = force/g = 200/32.2 = 6.211 pounds-mass or slugs or whatever they’re called

E = .5mv^2 = .5*6.211*(113.49^2) = 40,000 ft-lbs

F = E/d = 40,000/d

For d choose a starting point, say 3” = .25’…
…therefore F = 40,000/.25 = 160,000 pounds force...and your 3x6 plank ain’t gonna cut it.

Try a steel beam, say W24x55 (I=1,350 in^4), assuming sufficient lateral bracing:
Deflection = 3PL^3/48EI = 3x160x(25x12)^3 / (48x29,000x1350) = 6.90”

So…rerun the calculations with a d closer to 6.90” and iterate until your numbers converge to your satisfaction. When you’ve done that your reaction is half of the applied force and that gets applied to…whatever’s carrying your beam, be it a be it a girder or column.

Someone told me at one point that the above approach is not the correct one and if that’s the case then I suppose it’s time for a non-linear dynamic finite element modeling session…and someone else to do it. (But I do think that that approach is accepted by the barrier design people.)

Check my math, add a grain of salt and proceed with caution. And with all that said, if someone assigned you the task of designing something to stop a 200# object falling 200’ to be stopped with something spanning 25’ and you’re considering 3x6 planks to do the job…well…say, this isn’t a homework problem, by any chance, is it?

RE: Reactions at Column from an Impact Load

(OP)
haha....applause....Thanks Archie..This is a similar approach I took, and got a massive number as well....I was curious as to in reality terminal velocity would kick in and stop it from obtaining that large force...Originally, the plan was to include a net, which would be a completely different story as the deflection would be massive and the object would decelerate to zero, but i haven't much experience with dynamic loads so I wanted to get opinions.

Thanks for your help everyone,

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