Impact Formula

[Quence]

If a heavy objects fall down directly at center of a beam. What is the formula to determine if the beam would crack (and nature) given the weight of the object and the size of the beam and other properties like concrete strength, reinforcement ratio, etc?

 

[3DDave]

If (kinect energy - ability to elastically deform enough to absorb) >= 0, then breakage.

 

[BAretired]

This may help a little:

http://hyperphysics.phy-astr.gsu.edu/hbase/flobi.html

BA

 

[Quence]

3ddave.. I wasnt talking about long term loading but sudden impact. For example when a refrigerator falls over any beam. Its sudden impact that can cause localized damage to the beam that can chip off a part of it. Imagine a bullet hitting a beam...you dont use elastic analysis.. likewise for a falling heavy object. So how does one model sudden impact?

 

[BAretired]

You can calculate the force of impact if you can determine how far the beam deflects. See my previous post.

BA

 

[BAretired]

There have been several threads on this topic on eng-tips:

https://www.eng-tips.com/search.cfm...bject&t=&h=&searchSite=1&searchArea=1&d=1&s=1

BA

 

[3DDave]

It is still an elastic analysis. Long term loading is a matter of time scale. Elastic deflection is elastic deflection.

Sonic behavior impact, which was not in your original request, would also include the localized inertial effects of the items, but fracture only happens when the elastic properties are exceeded. It is also critical to understand elasticity as that limits the speed of propagation for any shock-wave behavior.

At this point the typical solution to the described bullet-hitting-a-beam problem will run into the millions of equations necessary to describe the components in sufficient detail. There is not room or time to do so here. There are specialized FEA programs, but in the US most of those will be ITAR controlled as they are used in the evaluation of ballistic armor.

In most cases investigators simply create laboratory experiments.

 

[ThomasH]

Quence,
If you have an object falling down on a beam or a bullit hitting the beam, the appoach is not that different.

When the object hits the beam it will either stop att that location, continue to move with the beam or bounce back. My quess is that it will move with the beam so the velocity will decrease. Now the kinetic energy should be transforemed to elastic or elasto-plastic effects.

If you look att BAretireds link you see that the force depends on the distance travelled. Basically, drive into a mountain wall and the force from impact will be huge, drive into cotton and it will be something completely different.

As for the formaula you ask for. I don't think there is one. You have to find a balance between the kinetic energy of the falling object and the beams force-deformation properties. That can be done "by hand" in some cases and requires FEM-software in other situations.

If the problem actually is an object falling on a beam I have done that type of calculation. And it was "by hand" using the principles described. My analysis was a steel beam so concrete will probably complicate it.

Good Luck

Thomas

 

[UcfSE]

Chapter 14 of Mechanics of Materials, 8e by Hibbeler deals with impact loading using conservation of energy. The author derives an equation for the impact factor n.

 

[WARose]

[blue](Quence)[/blue]

If a heavy objects fall down directly at center of a beam. What is the formula to determine if the beam would crack (and nature) given the weight of the object and the size of the beam and other properties like concrete strength, reinforcement ratio, etc?

.........

3ddave.. I wasnt talking about long term loading but sudden impact. For example when a refrigerator falls over any beam. Its sudden impact that can cause localized damage to the beam that can chip off a part of it. Imagine a bullet hitting a beam...you dont use elastic analysis.. likewise for a falling heavy object. So how does one model sudden impact?

The questions you are asking are so broad....it's hard to give a single, concise answer. As far as cracking goes....that goes to shear strength. As far as "chips" coming off a beam....that's getting into contact stresses. And that is a whole different class of problem.

Bottom line: you've got to have a more specific problem to get a specific answer. I've handled a lot of impact problems in my career.....and it's a different set of worries from case to case.