The equivalent length of a column of length L having one end fixed and the other end free, 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 a measure of its stiffness, and it is used in the design of columns to ensure that they are not overloaded.

The equivalent length of a column with one end fixed and the other end free is $\frac{{\text{L}}}{{\sqrt 2 }}$. This is because the fixed end of the column provides no support against lateral movement, so the column is effectively twice as long as it actually is.

The other options are incorrect because they do not take into account the fact that the fixed end of the column provides no support against lateral movement.