The maximum deflection due to a load W at the free end of a cantilever of length L and having flexural rigidity E$$I$$, is A. $$\frac{{{\text{W}}{{\text{L}}^2}}}{{2{\text{E}}I}}$$ B. $$\frac{{{\text{W}}{{\text{L}}^2}}}{{3{\text{E}}I}}$$ C. $$\frac{{{\text{W}}{{\text{L}}^3}}}{{2{\text{E}}I}}$$ D. $$\frac{{{\text{W}}{{\text{L}}^3}}}{{3{\text{E}}I}}$$

The correct answer is $\frac{{{\text{W}}{{\text{L}}^3}}}{{3{\text{E}}I}}$.

The maximum deflection due to a load $W$ at the free end of a cantilever of length $L$ and having flexural rigidity $EI$ is given by the following equation:

$$\delta = \frac{{{\text{W}}{{\text{L}}^3}}}{{3{\text{E}}I}}$$

where:

• $\delta$ is the maximum deflection,
• $W$ is the load,
• $L$ is the length of the cantilever,
• $E$ is the Young’s modulus, and
• $I$ is the moment of inertia.

The equation can be derived using the following steps:

1. Assume that the cantilever is a uniform beam with a constant cross-section.
2. Apply the principle of superposition to find
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