Question

A cantilever beam of length L is subjected to a uniformly distributed load of w kN/m over half of length from the free end. The variation of bending moment in the left half of length is

• A. No variation
• B. Linear
• C. Parabola
• D. Cubic parabola

Hint:

Remember the graphical relationship between load, shear, and moment:
The shape of the BMD is always one order higher than the SFD, which is one order higher than the load diagram.
- No Load (0 order) $\rightarrow$ Constant Shear (0 order) $\rightarrow$ Linear Moment (1st order).
- UDL (0 order) $\rightarrow$ Linear Shear (1st order) $\rightarrow$ Parabolic Moment (2nd order).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Cantilever with UDL on outer half. BMD shape in unloaded inner half?

Step 2: Key Relationship (Alternate):
dM/dx=V. Where no load, V=constant, so M=linear. Under UDL, V=linear, M=parabolic.

Step 3: Detailed Explanation:
In unloaded left half (near support), total UDL load to right is constant → shear V constant → dM/dx constant → M linear. In loaded right half, shear varies linearly → M parabolic. If question meant loaded half, answer is parabola.

Step 4: Final Answer:
For the unloaded half, BMD is linear. For the loaded half, BMD is parabolic.