The equivalent length of a column of length L, having both the ends hinged, is A. 2L B. L C. $$\frac{{\text{L}}}{2}$$ D. $$\frac{{\text{L}}}{{\sqrt 2 }}$$

The correct answer is $\frac{{\text{L}}}{{\sqrt 2 }}$.

A column is a structural element that is designed to support loads primarily by compression. The equivalent length of a column is the length of a pinned-pinned column that would have the same buckling load as the actual column.

A pinned-pinned column is a column that is supported at both ends by pins, which allow the column to rotate freely about its ends. The buckling load of a pinned-pinned column is given by the following equation:

$P_b = \frac{\pi^2}{EI} \frac{L^2}{12}$

where:

• $P_b$ is the buckling load
• $E$ is the Young’s modulus of the material
• $I$ is the moment of inertia of the cross-section
• $L$ is the length of the column

For a column with both ends hinged, the equivalent length is given by the following equation:

$L_e = \frac{L}{\sqrt{2}}$

Therefore, the equivalent length of a column of length $L$, having both the ends hinged, is $\frac{{\text{L}}}{{\sqrt 2 }}$.

The other options are incorrect because they do not represent the equivalent length of a column with both ends hinged.