Force of a 2x4 2

[onlineeng]

In Florida, for the large missile impact test, a 2x4 (between 7' and 9' long), weighing between 9 lbs. and 9.5 lbs., is shot from a cannon and strikes the surface of a hurricane shutter. The distance from the end of the cannon to the hurricane shutter is 9' plus the length of the 2x4. The 2x4's speed at impact is 50 feet per second. What is the force with which the 2x4 strikes the hurricane shutter?

Using a 2x4 length of 9' and a weight of 9 lbs., I come up with 19.42 pounds of force, which does not seem correct.

Thanks!

 

[JStephen]

It seems to me the force would be dependent upon the deflection characteristics of the 2x4 and of the shutter at impact, and there would be no way to calculate it with the information given.

 

[Lion06]

JStephen is right. The force will be much higher if you're hitting a brick wall, than if you're hitting a pillow (just for extreme ends of the spectrum).

F=MA, you know the mass, but the acceleration is dependent upon the stiffness of whatever it's hitting.

 

[MiketheEngineer]

You have to assume some type of de-acceleration meaning you need to guess how much the shutter will deflect. That will give you the -A you need. Try 1'' then 3'' and then 6'' See what you get..

The actual answer can only be found through actual testing. Thats why Ford and Chevy and BMW wreck cars all the time....IF they could figure it out through computers or even hand calcs - they wouldn't be wrecking multi-thousand dollar cars.

 

[onlineeng]

JStephen, PAStructuralPE, MiketheEngineer:

Again -- thanks!

 

[rb1957]

your calc (of 2g) does look light.

as you say, you know the mass, and have a pretty good idea of the velocity at impact, but you need to estimate the duration of the impact which is influenced by the stiffness of the impact surface ... a window shutter sounds like it would deflect some (absorbing some of the impact energy) and increase the duration of the impact

 

[ash060]

I have checked for impact force before, and I usually pick a very small impluse interval so that the force seems reasonable like a tenth or twentieth of a second. Also, I just assume that the final velocity is zero (just hits the wall and drops, not accurate but gotta use something maybe if it is a hard wall I would give it a backwards velocity but it would still be just a guess)

I usually get around 250 lbs and than I double it because it is an impact load (so I can use it with a static analysis).

 

[racookpe1978]

Well, unless this is some professor's idea of a (useless without approximations and assumptions!) exam question, the real answer has to come from testing.

But a useable velocity doesn't need to come from a cannon: A 2x4 dropped vertically should reach terminal velocity that in about 80 - 100 feet. You'd need a clear span and a safely restricted area below to prevent injuries. Then test a few - back-derive the assumptions (stiffness, movement/deflection/times you need to make the real calc's with the legally-required numbers.

 

[abusementpark]

You going to need calculus. Of course, you still remember how to do integration by parts, right?

 

[paddingtongreen]

It is going to be different depending on whether it hits at a support or in the most flexible spot.
For the most flexible spot, calculate the "spring rate". The energy equals the spring rate by the deflection squared divided by 2. The maximum force equals the spring rate by the deflection.

For the most rigid point, it may well be the crushing strength of the 2x4.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[JLNJ]

ash060

250 pounds equiv static load seems very very low to me.

I imagine that an equivalent static load is several hundred psi over the 2x4 surface area.

 

[ash060]

I usually double the static load I get for impact, so I would use 500 lbs.

Again it is just an estimate, but something is better than nothing and I used some numbers to get to an answer.

 

[WARose]

Using conservation of momentum and assuming the time it takes for the 2x4 to come to a complete stop = 0.1 sec, I came out with a force of 148 lbs. Since it is a dynamic force, a Dynamic Load Factor would have to be applied [and that could be as high as 2.0].

 

[IceNine]

The problem is determining the time it takes to stop. Where did you get 0.1 sec? If it takes 0.05 seconds, which seems just as arbitrary, your force is much greater.

Seem like a test is the sure fire way to get an answer.

 

[WARose]

Quite true IceNine. My guess comes from previous experience with impact....but it may not be applicable here. In fact I have seen delta t as low as 0.0001 sec. So you are right: testing is the way to go. I just wanted to respond and make note that 19.42 lbs does seem way off (as the OP suggests).

 

[ash060]

I have yet to encounter a client that will pay for such a test.

 

[IceNine]

I imagine some of the manufacturers of these hurricane shutters have done tests. I know several years back when I did curtain wall calculations we used several metal panel systems that had been tested.

Check out the BIA videos below:

http://www.youtube.com/brickindustry#p/search/1/obuzLZ6ZBJI

http://www.youtube.com/brickindustry#p/search/3/Uk7cwI3Z5ag

 

[a2mfk]

If it was only 20lbs you wouldn't need shudders...

Someone said IMPULSE, which is the key term for impact forces. I am too rusty at my mechanics but like others have said you would need to know the exact time of the deceleration. I would think from watching Myth Busters you would need a high speed camera with a timer on it, then you could determine the time from initial impact to the point the 2x4 stops moving forward. Then you could plug this time into your impulse formula to determine the force.

I think

 

[rb1957]

'cept the time of the impact is affected by the stiffness of the support (ie the shutter).

if you're trying to pass a design, then testing would do it (and be some fun as well).

I imagine your code says something like "the shutter has to withstand the impact of a 10lbs 2x4 with a velocity of ?? ft/sec", a bit like our birdstrike requirements.

 

[cvg]

50 fps sounds a bit low, that is not even close to hurricane force winds. Even a Cat 1 has sustained wind speeds up to 95 mph. I would expect something over 100 fps.