Question

Calculate the force ${}^{\prime }{F}^{\prime }$ needed to punch a $1.46cm$ diameter hole in a steel plate $1.27cm$ thick. The ultimate shear strength of steel is $345MN/m^2$ (Approx).

• A. $300KN$
• B. $400KN$
• C. $200KN$
• D. $100KN$

Answer 1

The correct option is C $200KN$

$\begin{array}{c}\text{Given, a hole of diameter}=1.46cm\\ \text{height}=1.27cm\\ \text{shear strength of steel}=345\times {10}^6\frac{N}{m^2}\\ \text{Shear strength}=\frac{F}{A_{\text{along the force}}}\end{array}$

$\begin{array}{cc}345\times {10}^6& =\frac{F}{2\pi (\frac{1.46\times {10}^{-2})(1.27\times {10}^{-2})}{2}\times {10}^{-2}}\\ \Rightarrow F=& 200\times {10}^{3}N\\ =& 200KN\\ \text{Option}C\text{is the correct option.}& \end{array}$