What is the equivalent length of a column which has one of its ends fixed and the other end free, according to Euler's column theory? The actual length of the column is 10 m.
DSSSB JE - 2023,
Answer: D
In Euler's column theory the equivalent (effective) length of a column depends on its end conditions. A column fixed at one end and free at the other behaves like half of a column of twice the length which is pinned at both ends, so its effective length is \(2L\):
\[ L_e = 2 \times 10 = 20\ \text{m} \]An effective length equal to L (10 m) applies to a column hinged at both ends, L/2 (5 m) to a column fixed at both ends, and \(L/\sqrt{2}\) (about 7.07 m) to a column fixed at one end and hinged at the other. These are the other options.
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