Having Trouble Finding G-Force of an Impact -- Details in post

[DontRememberMuch2015]

Hey guys first post on here for me. Graduated with a BS in Civil Engineering and working full time. Have a problem on my desk that myself and many coworkers are trying to figure out and would like some assistance as we haven't done anything like this in years. Not sure if we even have the capabilities with the given time frame to answer the problem (2 days). Here it goes (I will simplify the problem for here):

Picture a series of I beams with a steel plate welded on top and bottom. The dimensions of this big steel rectangle are 41' x 11'' and it has a weight of 125,570 lbs. Imagine it being suspended off the ground (by magic) at 1' height. It is sitting over a 4" reinforced concrete slab (Class A concrete where K=7.443 N/m and E=3,410,000). Suddenly the steel rectangle drops out of the air and falls onto the ground (currently trying to calculate both elastic and inelastic impact). I am trying to find the G-Force that the steel rectangle experiences. (In reality there is something on the steel rectangle and we need to make sure it didn't experience too high of a G-Force) ...really struggling with this one.

I will post some knowns as well as directions I took. If anyone knows where I made a mistake or what to do to find a G-Force I would appreciate it.

Impact Velocity: V=√2gh where g= 9.81m/s and h=0.3048m, therfore; v= 2.445 m/s
KE= 0.5mv^2 where m=56957.6kg and v=2.445 m/s, therfore; KE= 170,134.629J
F=ma where a=9.81 m/s^2, therfore; F=558,754 N

This is where things get hairy. I looked up some things online but the units just didn't make sense. I think I want to find the deflection of the concrete and the deflection of the steel from impact and somehow integrate them and use that to find the time where the velocity goes from 2.445 m/s to 0 then I can get the acceleration (or deceleration) of the acceleration which is the G-force. From my understanding the G-force is the 4th derivative of d... dx/dt, dv/dt, da/dt, then G-force... da'/dt.. if you will? I also thought I should look for Jerk force as well as relate the stiffness and deflection of the material but I am coming up empty. Anyone have leads? Can anyone walk me through the process or provide a step by step. This isn't homework its work related so I don't have a lot of time to go through this back and forth. Any suggestions will be MUCH appreciated.

Chose graduate because none of our engineers can figure it out. Might be high school knowledge, but we have lost it haha!

Edit: This was not measured with an accelerometer, we are trying to analyze an accident that happened so I am more concerned with the first initial impact G-force and trying to ignore the dampening effects.

 

[FactChecker]

G is a unit of acceleration. The acceleration of an object is the second derivative of position. Express that in units of G = 9.8m/s² = 32 ft/s². Jerk is the third derivative.

 

[DontRememberMuch2015]

G is a unit of acceleration. The acceleration of an object is the second derivative of position. Express that in units of G = 9.8m/s² = 32 ft/s². Jerk is the third derivative.

I'm not sure this adds much value to my problem. Although true, I need a way to figure out how to find out how many G's were experienced from this event which I am having trouble figuring out because I don't have the time it took to dissipate all the energy or a way to link the deflections of the materials.

 

[Nidum]

There is no realistic way of working this out which will give you definite values .

The only way to proceed is to estimate the impact force if the plate assembly is decelerated from arrival velocity to zero velocity in a distance which characterises the nature of the impact and which you judge to be credible .

Bear in mind that the steel assembly and the concrete slab are not flat and also that the steel assembly is very unlikely to land on the slab flat on - more likely on a corner or a bulge . So it touches down somewhere and then it both rotates about that initial contact point and flexes so as to touch down at progressively more and more points .

 

[A.T.]

I don't have the time it took to dissipate all the energy

Then you can't even get the average acceleration on impact, let alone the maximal acceleration.

 

[JRMichler]

Impact of anything more complex than elastic impact of a steel ball on a steel plate is almost impossible to calculate using hand methods. Calculating the system that you describe is a job for an experienced person using a high end FEA program. Even then, it would take more than two days to do it.

You might be able to geta rough estimate using hand methods. Take a close look at the steel and concrete and carefully note all signs of damage. Separately calculate the force to create each individual damage. Then attempt to combine those forces into an estimate of the acceleration to create those forces. Work upstream until you get to the object of interest.

This problem needs a person with extensive experience analyzing dynamic systems.

 

[FactChecker]

I'm not sure this adds much value to my problem. Although true, I need a way to figure out how to find out how many G's were experienced from this event which I am having trouble figuring out because I don't have the time it took to dissipate all the energy or a way to link the deflections of the materials.

Well, the first step in calculating something is to get its definition correct. You said it would be the 4'th derivative. That is wrong. I can assure you that the 4'th derivative would be gigantic.

Probably the best you can do without a great deal more information is to calculate the minimum acceleration that would stop the object in a certain distance. That would assume the gentlest possible deceleration. It would be a constant deceleration, but the jerk would be infinite.