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The effective length ratio for columns with both ends fixed is:
1. 1.2
2. 2.0
3. 0.5
4. 3.0

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Correct Answer - Option 3 : 0.5

Concept:

Euler buckling load for a column is given by,

\({{\rm{P}}_{\rm{E}}}{\rm{\;}} = {\rm{\;}}\frac{{{{\rm{\pi }}^2}{\rm{EI}}}}{{{\rm{L}}_{\rm{e}}^2}}\)

Where, Le is the effective length of the column that depends on the end support conditions, and EI is the flexural rigidity of the column.

Now, effective length (Le) for different end conditions in terms of actual length (L) are listed in the following table:

Support Conditions

Effective length (Le)

Both ends hinged/pinned

Le = L

One end hinged other end fixed

   Le = L/√2

Both ends fixed

 Le = L/2

One end fixed and the other end free

            Le = 2L

 

 

 ∴ For both ends fixed Effective length Le = 0.5 L

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