To calculate the force required to punch a hole in the plate, we first need to find the area of the hole that is being punched and then multiply that by the shear strength of the material.
-
Calculate the radius of the hole:
The diameter of the hole is 15 mm, so the radius \( r \) is:\[ r = \frac{15 \text{ mm}}{2} = 7.5 \text{ mm} = 0.0075 \text{ m} \]
-
Calculate the area of the hole:
The area \( A \) of a circle is given by:\[ A = \pi r^2 \]
Substituting the radius:
\[ A = \pi (0.0075 \text{ m})^2 \approx \pi (5.625 \times 10^{-5} \text{ m}^2) \approx 1.769 \times 10^{-4} \text{ m}^2 \]
-
Calculate the force required to punch the hole:
The force \( F \) required can be calculated using the formula:\[ F = \text{Shear Strength} \times \text{Area} \]
The shear strength is given as 300 MN/m², which is \( 300 \times 10^6 \text{ N/m}^2 \).
Substituting the values we have:
\[ F = 300 \times 10^6 \text{ N/m}^2 \times 1.769 \times 10^{-4} \text{ m}^2 \]
\[ F \approx 300 \times 10^6 \times 1.769 \times 10^{-4} \text{ N} \]
\[ F \approx 53,070 \text{ N} \]
So, the force required to punch a 15 mm diameter hole in a 20 mm thick plate, with a shear strength of 300 MN/m², is approximately 53,070 N.