A long steel column of uniform cross section is subjected to a crippling load of $10\text{ kN}$ as per the Euler designed condition. If the length of the column is reduced to half, then what would be the maximum Euler's crippling load?
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Because the column length term is squared in the denominator of Euler's formula, any change in length impacts the buckling load inversely by the square of that change:
- Double the length $\rightarrow$ Critical load drops to $\frac{1}{4}$th.
- Halve the length $\rightarrow$ Critical load increases by $4$ times.