Calculate the force F needed to punch a 1.46 cm diameter hole in a ste

1.	Calculate the force F needed to punch a 1.46 cm diameter hole in a steel plate 1.27 cm thick. The ultimate shear stress of steel is 3.45 x 108 Nm-2. Fig
Answer» In punching, shear elasticity, (i.e., modulus of rigidity) is involved. The hole 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

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

Answer»

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

The hole 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