Question

Determine the diameter of the largest circular hole which can be punched into a sheet of polystyrene 6mm thick, knowing that the force exerted by the punch is 45KN and that a 55MPa average shearing stress is required to cause the material to fail.

Answer 1

$$D=\frac{F}{\pi\tau t}=\frac{45000}{3.142\cdot55\cdot10^6\cdot 0.006}=0.0434\text{ m}$$

The shearing streets will emerge along the circumference with diameter D in the material.