Question

A steel punch can be worked to a compressive stress of 800 N/mm². Find the least diameter of hole 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 hole in mm 

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

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

= 350 × 10πd = 3500πd (N) 

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

Compressive stress on the punch 

σ_C = 3500πd/{(π/4)d²} = 14000/d 

But σ_C is limited to 800 N/mm² and therefore 

800 = 14000/d 

d = 17.5mm