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when deriving the above formula we considered a case in which both the joints are pinned at ends. rather than deriving the formula for all other cases. we took some most used cases and generalized the formula using effective length. there is no formal definition for effective length but can be defined as.

The length of an imaginary section of the column which is equivalent to a pinned-pinned column with same cross-section and material property. this is better explained in the picture itself.

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