Question

A steel punch can be worked to a compressive stress of 800 N/mm2. Find the least diameter of **** which can be punched through a steel plate 10 mm thick if its ultimate shear strength is 350 N/mm2.

Answer 1

Let d be the diameter of **** in mm

Area being sheared = π.d.t = πd × 10 = 10πd mm2

Force required to punch the **** = Ultimate shear strength x area sheared

= 350 × 10πd = 3500πd (N)

Cross sectional area of the **** = (π/4)d2 mm2

Compressive stress on the punch

σC = 3500πd/{(π/4)d2} = 14000/d

But σC is limited to 800 N/mm2 and therefore

800 = 14000/d

d = 17.5mm