32 tonne mass dropped from 1.5m

[glenbo_m]

I am an engineer working on the design of a concrete ground floor slab.

the slab in question could be subject to the impact loading of a 32 metric tonne mass falling from a heigh of 1.5m. i am trying to convert this into a point load in kN.

could some kind soul please review my calculations below:

velocity = square root of 2gh = 5.4222 m/s

kinetic energy = 0.5mv^2 = 0.5 x 32000 x 5.4222^2 = 470400 joules...

as joules is a work force it converts to kNm. can it be converted to a kN point load??

 

[Bloodthunder]

Since energy would more or less be conserved, you could have just calculated PE = mgh = KE instead of going a whole loop.

Also, do floors not take into account the pressure (as well as the maximum weight) that it can hold, instead of the force?

 

[rock.freak667]

You can see the formula for impact stress here.

You will need to know how much it will deflect the concrete though in either case.

 

[glenbo_m]

but i can't work out deflection of floor slab until i derive a load in kN.

 

[glenbo_m]

can anybody help me convert a 32 tonne load, into a point load when dropped from a height of 1.5m?

 

[sophiecentaur]

It looks, at first, as if you need to know both the force and the distance moved, before you work out either of the quantities. But there are ways round this problem.

If you were to assume that the floor is like a spring (with a spring constant that could be found out) then you could equate the energy stored in this 'spring' when it is fully deflected to the energy at the start..
E =kx²/2 would be the same as the initial Gravitational Potential energy of the mass (mgh) at 1.5m (k is the spring constant). So you can write an equation with the Strain energy on one side and the gravitational potential energy on the other.

That would tell you how far a spring would deflect but it wouldn't include the effect of energy loss (which must be there or the mass would bounce back up again). At least this could give you a maximum deflection and a value for the force at this deflection.

The link (above) does something like this but with more complexity and considers a mass landing on the end of a metal bar. This, simpler, calculation can be done on the proverbial fag packet - as long as you know a value for the effective k of the spring. (I am really just putting what that link says in simpler terms).

As for the problem of finding a value for k, I know there are tables of stress / strain values for beams of various types and dimensions so I should imagine they would also exist for slabs as well. That would give you a ballpark value for k.