Calculation Troubles!
Calculation Troubles!
(OP)
I am trying to work out induced compressive stress in a member from a dynamic load (a dropped member) using a formula taken from strength of materials, Case and Chilver second edition - 22.6 (rod struck by a moving mass). Has anyone ever worked through the example? Its part of an overall problem I have - controlling a potentially dropped (max 75mm high) steel girder onto timber cushions on top of a rigid steel frame. My theory is that the timber will compress enough to slow the girder to a stop and allow me to calculate and equivalent static load.






RE: Calculation Troubles!
F=ma
The mass is easy, but what's the deceleration? How long it takes to stop the falling load is going to depend of the stiffness of the wood. How much will it deflect from the energy of the falling load?
Good luck.
RE: Calculation Troubles!
If you’re wondering about your results post them here and we might be able to double-check them.
RE: Calculation Troubles!
I am essentially following your advice Archie by estimating a deflection within the timber but I am trying to justify that by showing induced compressive stress is in fact beyond yield in compression but also not ridiculously beyond that the timber cushions are ineffective. I have taken from the text an equation for induced compressive stress at impact but I am struggling with the units and not sure that my answer is correct:-
velocity,v = √(2*a*h) = √(2*9.81*0.075) = 1.21m/s
density,ρ = 350 kg/m3
Elastic modulus,E = 4600 N/mm2
induced compressive stress, v*√(ρ*E)
I work out the above to be 1.21*√(350*4600*10^-3) = 48.6N/mm2 which seems like a very big number.
Do I have the calculation correct?
RE: Calculation Troubles!
I would look at it as an energy equation 1/2mv^2 = 1/2kx^2
Model your frame with a 100n point load or so and find the deflection, you should be able to back K of your frame out of that.
Then solve for x from the above equation.
Once you have X, you can get the static load by F=kx.
Probably get you in the ballpark.
RE: Calculation Troubles!
Can you take a look at my induced compressive stress equation above, have I got my units correct for the result?
RE: Calculation Troubles!
Here's a 1 dof online shock calculator that may help.
Have Fun!
James A. Pike
www.xl4sim.com
www.erieztechnologies.com
RE: Calculation Troubles!
E=.5mv^2
W=Fd
d=F(l^3)/(48EI)
RE: Calculation Troubles!
I was ignoring the wood as well.
Seems like there are many ways to skin a cat.