Question

In shear cutting operation, a sheet of $5$ mm thickness is cut along a length of $200$ mm. The cutting blade is $400$ mm long (see figure) and zero-shear $S=0$ is provided on the edge. The ultimate shear strength of the sheet is $100$ MPa and penetration to thickness ratio is $0.2$. Neglect friction



Assuming force vs displacement curve to be rectangular, the work done (in J) is

• A. $100$
• B. $200$
• C. $250$
• D. $300$

Answer 1

The correct option is A $100$

Maximum force: $F=L\left(t\right).\tau$
L = Perimeter of cut, t = Thickness of cut, P = Penetration

$F=200\times \left(5\right)\times 100=100kN$
$\text{Work done}=F\times Kt$
$=100\times {10}^3\times 5\times {10}^{-3}\times 0.2$
$=100Nm=100J$