Question

With a punch for which the maximum crushing stress is 4 times the maximum shearing stress of the plate, the biggest hole that can be punched in the plate would be of diameter equal to

1.

¼ × Thickness of plate

2.

½ × Thickness of plate

3.

Plate thickness 

4. 2 × Plate thickness

Answer 1

Correct Answer - Option 3 :

Plate thickness 

Concept:

For finding the maximum diameter in punching, punching pressure = strength of the punch.

As punch fails by crushing, so punching pressure = σc

Calculation:

\(\tau = \frac{1}{4}{\sigma _c}\)

\(\pi dt\tau = {\sigma _c} \times \frac{\pi }{4}{d^2}\)

\(\Rightarrow t\tau = {\sigma _c} \times \frac{d}{4} \Rightarrow t \times \frac{{{\sigma _c}}}{4} = {\sigma _c} \times \frac{d}{4} \Rightarrow t = d\)