A cantilever of span length l and flexural rigidity EI under span-wide UDL w/unit length develops a maximum deflection of_________________?
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Answer: C. wl4/8EI
Explanation
Integrating the differential equation of the elastic curve twice gives the exact cantilever deflection profile. Applying boundary conditions at the fixed support determines integration constants for maximum deflection calculations. Evaluating the resulting equation at the free end yields the maximum deflection value of wl4 over eight EI. A cantilever beam is rigidly fixed at one end and completely free at the other end. Flexural rigidity represents the product of elastic modulus and area moment of inertia resisting bending. Uniformly distributed loads apply continuous pressure along the entire horizontal length of the cantilever.
Balconies extending outward from building facades are often analyzed as cantilever beams carrying uniform loads. Checking maximum deflection ensures that cantilever structures do not experience serviceability failures over time. Cantilever retaining walls use these deflection principles to control structural movement under soil pressure. Option A uses an incorrect denominator of three EI and wrong power for length calculations. Option B fails standard integration steps required for uniform load cantilever deflection equations. Option D underestimates deflection by utilizing an incorrect denominator coefficient in the denominator term.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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