Problem # p024

Shear and Axial Stress , Hole Puncher

The production of coins starts with punching holes into a sheet of metal and saving the punched out disk to be processed further.
In the figure to the left the punch of diameter d is pushed through a metal sheet of thickness t by a force P to create a disk of diameter d and thickness t.

How big must the force P be if
  • the ultimate shear stress the material of the metal sheet is 250 MPa
  • ,
  • the diameter of the disk d = 15 mm
  • the thickness of the metal sheet t = 2 mm
At the same value of P, how big is the axial stress in the punch ?