Question

How much force is required to punch a 20 mm diameter hole in a plate that is 25 mm thick?

• A. 550 kN
• B. 1350 kN
• C. 1750 kN
• D. 175 kN

Hint:

For punching force: - Use F = π · d · t · τ . - Verify the shear strength (τ ) of the material for accurate results.

Answer 1

The Correct Option is A

The force required to punch a hole is calculated using the formula:
\[F = \pi \cdot d \cdot t \cdot \tau\]
where:
$d = 20 \, \text{mm} = 0.02 \, \text{m}$ (diameter of the hole),
$t = 25 \, \text{mm} = 0.025 \, \text{m}$ (thickness of the plate),
$\tau = 140 \, \text{MPa} = 140 \times 10^6 \, \text{N/m}^2$ (shear strength of the material).
Substitute the values:
\[F = \pi \cdot 0.02 \cdot 0.025 \cdot 140 \times 10^6 = 550 \, \text{kN}.\]