The Rankine's formula holds good for

Explanation:

For short or long columns Rankine’s Formula is used.

\(\frac{1}{P} = \frac{1}{{{P_C}}} + \frac{1}{{{P_E}}}\)

Where P is crippling load by Rankine formula; \({P_C}\;\) is crushing load; \({P_E}\;\) is crippling load by Euler’s formula.

For Short column: \({P_E}\;\) is very large so \(\frac{1}{{{P_E}}}\)  will be very small and negligible as compared to \(\frac{1}{{{P_C}}}.\) so

\(\frac{1}{P} = \frac{1}{{{P_C}}} \to P = {P_C}\)

For Long column: \({P_E}\;\) is small so \(\frac{1}{{{P_E}}}\) will be large as compared to. Hence the value of  \(\frac{1}{{{P_C}}}\;\) can be neglected. So

\(\frac{1}{P} = \frac{1}{{{P_E}}} \to P = {P_E}\)