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The ratio of equivalent length of a column having both ends fixed, to its length is:

  • A.2
  • B.\(\sqrt{2}\)
  • C.\(\frac{1}{2}\)
  • D.\(\frac{1}{\sqrt{2}}\)

Answer: C

For both ends fixed the ratio is \(\frac{1}{2}\).

Effective length is the length of an equivalent pin-ended column that buckles at the same load. With both ends fixed, the column bends between two points of contraflexure a quarter length from each end, so the effective length is \(L/2\).

A ratio of 2 belongs to a column fixed at one end and free at the other, \(1/\sqrt{2}\) to one fixed at one end and hinged at the other, and \(\sqrt{2}\) is not a standard case.

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