How Is Shearing Modulus Used to Calculate Force in Punching a Hole in Steel?

[Myung]

Homework Statement

How much force is required to punch a hole ½ in. in diameter from a 1/8 in. thick steel sheet of shearing strength 4x10^4 psi.

Homework Equations

Shearing Modulus = Shearing Stress / Shearing Strain

Shearing Stress = F/A
Shearing Strain = S/L

S = Length Sheared
L = Length to be sheared

The Attempt at a Solution

FIND: FORCE IN lb-f

Shearing Modulus = Shearing Stress / Shearing Strain

thus:

shearing modulus ( shearing strain ) = Shearing Stress

4x10^4 PSI * ( S/L ) = F/A

A = ∏/4 (1/2)^2

(∏/4 (1/2inch)^2)*(4x10^4 PSI)*(S)
------------------------------------- = Force
1/2 inch
I don't know what S to use because the length sheared(S) is not given.

Can i still solve the equation without the length sheared(S)?

 

[JaWiB]

http://en.wikipedia.org/wiki/Shear_strength

 

[Myung]

http://en.wikipedia.org/wiki/Shear_strength

Can you atleast explain to me the relationship of Shearing Strength to this equation and how I can use the value of the Strength of the object to get the force?