Question
Calculate the force required to punch a hole 2cm square in a steel sheet 2mm thick whose shearing strength is 3.5 × 108Nm-2.
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Answer
The shearing stress is exerted on the rectangular surface (2.0cm × 2.0cm × 0.2cm) that is the boundary of the hole. The area of this surface is (see Fig).
A = 2.0 × 10-2 × 4 × 0.2 × 10-2m2
= 1.6 × 10-4m2
Since the minimum shearing stress to rupture the steel is:
$\Big(\frac{\text{F}}{\text{A}}\Big)_\text{min}=3.5\times10^8\text{Nm}^{-2}$
The force required is given by,
F = 3.5 × 108 × 1.6 × 10-4N = 5.6 × 104N
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