Impact loading for a lowered object

[Bucko1]

hi,

Trying to look at the impact loads on an object when it is lowered by a crane. Assuming a constant crane lowering speed and a known stiffness of the item onto which the object is lowered. ie a mass being lowered onto a beam at a constant speed. I've looked at the classic impact equation for the dropping of objects onto beams , but not sure how to adjust them for lowering of a suspended mass. Any help will be much appreciated.

Cheers

 

[Dr.D]

A lot depends upon the shape of the two surfaces where they will come in contact. What did you have in mind?

 

[jack action]

A very crude approximation would be the conservation of energy:
$$E_k = E_s$$
$$\frac{1}{2}mv^2 = \frac{1}{2}kx^2$$
$$x = v\sqrt{\frac{m}{k}}$$
Where:

• $m$ is the mass of the object;
• $v$ is the speed of the object;
• $k$ is the vertical stiffness of the beam;
• $x$ is the vertical displacement of the beam.

The impact load is then $F_i = kx = kv\sqrt{\frac{m}{k}}= v\sqrt{km}$.