The correct answer is: C. One end is fixed and other end is free.
Euler’s crippling load is the maximum load that a column can support without buckling. The equation for Euler’s crippling load is:
$$P = \frac{{4{\pi ^2}{\text{E}}I}}{{{{\text{L}}^2}}}$$
where:
- $P$ is the Euler’s crippling load
- $E$ is the Young’s modulus of the material
- $I$ is the moment of inertia of the cross-section of the column
- $L$ is the length of the column
For a column with one end fixed and the other end free, the moment of inertia is given by:
$$I = \frac{1}{3}bh^3$$
where:
- $b$ is the width of the column
- $h$ is the height of the column
Substituting this into the equation for Euler’s crippling load gives:
$$P = \frac{{4{\pi ^2}{\text{E}} \left( \frac{1}{3}bh^3 \right)}}{{{{\text{L}}^2}}}$$
$$P = \frac{{16{\pi ^2}{\text{E}}bh^2}}{{9{{\text{L}}^2}}}$$
Therefore, the equation for Euler’s crippling load for a column with one end fixed and the other end free is:
$$P = \frac{{16{\pi ^2}{\text{E}}bh^2}}{{9{{\text{L}}^2}}}$$
The other options are incorrect because they do not give the correct equation for Euler’s crippling load for a column with one end fixed and the other end free.