Question

A cast iron column has internal diameter of 200 mm. What sholud be the minimum external diameter so that it may carry a load of 1.6 MN without the stress exceeding 90 N//mm^(2)?

Answer 1

The minimum diameter is 249.8 mm

Explanation:

Given :

Force $F = 1.6 \times 10^{6}$ N

Stress = $90 \times 10^{6}$ $\frac{N}{m^{2} }$

internal diameter $d_{1} = 200 \times 10^{-3}$ m

from the equation of stress,

   $\frac{F}{A} = stress$

   $A = \frac{1.6 \times 10^{6} }{90 \times 10^{6} }$

Since area of column is,

   $A = \pi \frac{d_{2}^{2} - d_{1} ^{2} }{4}$

$0.022 = d_{2} ^{2} - d_{1} ^{2}$

$d_{2} ^{2} = 0.04 +0.022$

$d_{2} = \sqrt{0.062} = 0.249$

$d_{2} = 249.8$ mm