Cantilever beam of length l carrying a uniformly distributed load w per unit length: Does the maximum bending moment occur at the middle of the span?

Introduction / Context:For a cantilever with UDL, locating the critical section is key to safe design. The support (fixed end) must resist the largest bending moment and shear.

Given Data / Assumptions:

• Cantilever of span l, fixed at one end and free at the other.
• Uniformly distributed load w along the entire span.
• Linear elastic behaviour; self-weight can be included in w.

Concept / Approach:Bending moment in a cantilever is largest where the lever arm of the resultant load to the support is greatest. For UDL, the resultant equals w * l acting at midspan, but the resisting moment is taken at the fixed end.

Step-by-Step Solution:

Verification / Alternative check:From differential relations, dM/dx = V; for UDL, V varies linearly and M is quadratic, peaking at the fixed boundary.

Why Other Options Are Wrong:Claiming the midspan is maximum ignores boundary conditions of a cantilever.Other conditional statements do not apply to this canonical case.

Common Pitfalls:Transferring simply supported intuition to cantilevers; forgetting that internal moments are highest at the restraint.

Final Answer:

False