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A prismatic, straight, elastic cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L, Young’s modulus E, and area moment of inertia I, the magnitude of the maximum deflection is

1. qL⁴/15EI
2. qL⁴/30EI
3. qL⁴/10EI
4. qL⁴/60EI

Correct answer: qL⁴/30EI

Solution

The maximum deflection of a cantilever beam under a linearly distributed load can be derived using beam theory, specifically the formula for deflection due to such loading conditions. The correct option, qL⁴/30EI, accurately represents the relationship between the load intensity, beam length, material properties, and geometric properties, confirming it as the appropriate solution.

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