Question

Calculate the force required to punch a 15 mm diameter hole into a plate 20mm thick, if the shear strength is 300 MN/m.

Answer 1

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.

1. **Calculate the radius of the hole:**
The diameter of the hole is 15 mm, so the radius \( r \) is:

\[
r = \frac{15 \text{ mm}}{2} = 7.5 \text{ mm} = 0.0075 \text{ m}
\]

2. **Calculate the area of the hole:**
The area \( A \) of a circle is given by:

\[
A = \pi r^2
\]

Substituting the radius:

\[
A = \pi (0.0075 \text{ m})^2 \approx \pi (5.625 \times 10^{-5} \text{ m}^2) \approx 1.769 \times 10^{-4} \text{ m}^2
\]

3. **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**.