Question

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

Answer 1

43.41 mm

Step-by-step explanation:

Given:

thickness of sheet, t = 6 mm

Force exerted by punch, F = 45 KN

Average shearing stress, T = 55 MPa

From average shearing stress T = Force F / Area A

Hence area = force/stress =45000/ 55 =
`818.18 mm^2`

From area = pi*diameter*thickness

diameter = area/(pi* thickness)

= 818.18/(3.142*6)

= 43.41 mm