Question

For columns (square cross section having side 100 mm) resists a buckling load of P. Now, the columns glued together to act as a single column. The percentage increase in buckling load is

• A. 300

Answer 1

The correct option is A 300
When four columns were acting indepnedently, buckling load
$P=P_{cr}=4\times \frac{{\pi }^{2}EI}{l_{eff}^2}=\frac{4\times {\pi }^{2}E\times (100{)}^4}{l_{eff}^2\times 12}....\left(1\right)$
Now, when the four columns are glued, buckling load
$P_{cr}^{\prime }=\frac{{\pi }^{2}E}{l_{eff}^2}\left(\frac{{200}^4}{12}\right).....\left(2\right)$
% increase $=\left(\frac{P_{cr}^{\prime }-P_{cr}}{P_{cr}}\right)\times 100$
$=[\frac{1}{4}\times {\left(\frac{200}{100}\right)}^4-1]\times 100$
$=300\%$