Question

Calculate the force F needed to punch a 1.46 cm diameter **** in a steel plate 1.27 cm thick. The ultimate shear stress of steel is 3.45 x 108 Nm-2. Fig

Answer 1

In punching, shear elasticity, (i.e., modulus of rigidity) is involved.

The **** will be punched, if

(F/A) ≥ ultimate shear stress

or, (F) ≥ ( Shear stress) x A

where A is = 2π rd

Hence, F = (3.45 x 108) x 2πrd

= (3.45 x 108) x (2 x 22/7 x 0.73 x 10-2 x 1.27 x 10-2)

≈ 2 x 105 N