Question

Calculate the force required to punch a hole 30 mm diameter in a sheet of 3mm thickness given that the shear stress is 60 X 107 N/m. (Hint the area to be cut is the circumference of the hole X thickness).​

Answer 1

Answer:

stress = F/A

f=stressxA

f=60x107x 2xpiex.015x.003

Answer 2

Answer:

The force required to punch a hole is 170kN.

Explanation:

The shear stress is given as,

$S=\frac{F}{A}$      (1)

Where,

S=shear stress

F=force required to punch

A=area along the force

From the question we have,

diameter of hole=30mm=30×10⁻³m

The thickness of the sheet=3mm=3×10⁻³m

S=60× 10⁷N/m

The area along the force is given as,

$A=\frac{2\pi\times 3\times 10^-^3\times 30\times 10^-^3}{2} =282.6\times 10^-^6=2.826\times 10^-^4m^2$     (2)

By substituting the value of A and S in equation (1) we get;

$60\times 10^7=\frac{F}{2.826\times 10^-^4}$

$F=60\times 10^7\times 2.826\times 10^-^4=169.56\times 10^3\approx170kN$

Hence, the force required to punch a hole is 170kN.