A steel punch can be stressed to maximum compressive stress of 800 MN/m². If the ultimate shear strength is 300 MN/m², the least diameter of the hole that can be punched through a steel plate of 14 mm thickness will be
- A41 mm
- B31 mm
- C21 mmCorrect
- D11 mm
Solution
Concept
Equate the punching force to the compressive capacity of the punch
Formula
τ π d t = σ π d² / 4 ⇒ d = 4 τ t / σ
Step-by-step solution
1. Shear resistance of the plate = τ × (π d t). 2. Compressive capacity of the punch = σ × π d² / 4. 3. d = 4 τ t / σ = 4 × 300 × 14 / 800 = 21 mm.
Explanation
The punch can make a hole only if the force needed to shear the plate does not exceed what the punch can carry in compression. The smallest hole results when the two are equal.
Why the other options are wrong
41, 31 and 11 mm do not satisfy 4τt/σ.
Shortcut
d = 4 τ t / σ.
Common mistake
Using the radius instead of the diameter.
Correct answer: C) 21 mm