What is the expected shape of a cantilever under a uniformly distributed load?

• A. Straight line
• B. Parabolic
• C. Hyperbolic
• D. Elliptical

Answer: (B)

The expected shape of a cantilever under a uniformly distributed load is parabolic. This is due to the way the load is applied across the length of the cantilever and how the material responds to that load. When a cantilever beam is subjected to a uniform load, the deflection of the beam is not constant along its length. The maximum deflection occurs at the free end of the cantilever, and the curvature of the beam progresses along its length, forming a parabolic curve.

The mathematics of beam deflection shows that under a uniformly distributed load, the equation governing the deflection of the beam results in a parabolic shape. This shape allows for the most efficient distribution of stress and strain in the material, ensuring that the structure can support the load without leading to failure.

This understanding is fundamental in structural engineering and helps engineers design safe and effective cantilever structures. The parabolic shape indicates how the bending moment varies along the length of the cantilever, which is important for both analysis and design purposes.