Question

Calculate the smallest punch diameter that can be designed for piercing sheet metal strip with the following data. Crushing strength of the punch material is $1500$ MPa. Thickness of the sheet is $2$ mm, factor of safety is $3$, shear strength of the sheet material $500$ MPa s

• A. $2$ mm
• B. $6$ mm
• C. $8$ mm
• D. $24$ mm

Answer 1

The correct option is C $8$ mm

Punching force = $\pi dt\tau$
$=\pi \times d\times 2\times 500$ ....(i)
Considering crushing strength, we have
$Force=\frac{1500}{3}\times \frac{\pi d^2}{4}$ ....(ii)
Equating Eqs. (i) and (ii), we get
$1000\pi d=\frac{500}{4}\times \pi d^2,\text{or d}=8\text{mm}$