Solving Steel Shear Stress Problems

[psycovic23]

I have a problem that I'm not sure how to approach. "If the shear stress in steel exceeds about 4.00 x 10^8 N/m^2, the steel ruptures. Determine the shearing force necessary to (a) shear a steel bolt 1.00 cm in diameter and (b) punch a 1.00 cm diameter hole in a steel plate .500 cm thick.

I think I got A right (3.14x10^4, right?), but I'm stuck on B. I'm trying to use

$$\frac{F}{A} = S \frac{\Delta x}{h}$$

but I don't know what to use for h. So far, I'm solving for F, A=pi*.005^2, S = 8.4x10^10, delta x = .500 cm, but I don't know what H is. Any ideas?

 

[mathmike]

wouldnt h be the thickness of theplate you are punching through?

 

[psycovic23]

But aren't I still missing one piece of information?

 

[quark]

Shear force is always perpendicular to the plane of the plate(or in simple terms, it acts in the plane of thickness) I am not sure about the basis of your equation. Calculate the lateral area of sheared material. Once you get the area, what relation holds stress to force?

Clue to your second question : What is left when you shear a bolt in the plate?