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The effective stiffness of a cantilever beam of length L and flexural rigidity EI subjected to a transverse tip load W is

1. 3EI/L³
2. 2EI/L³
3. L³/2EI
4. L³/3EI

Correct answer: 3EI/L³

Solution

The effective stiffness of a cantilever beam under a transverse load is derived from its deflection characteristics, where the stiffness is defined as the load divided by the deflection at the tip. For a cantilever beam, the relationship shows that the effective stiffness is three times the flexural rigidity divided by the cube of the length, hence 3EI/L³.

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