Question

In a simply supported beam, bending moment at the end

• A. Is always zero if it does not carry couple at the end
• B. Is zero if the beam has uniformly distributed load only
• C. Is zero if the beam has concentrated loads only
• D. May or may not be zero

Hint:

For a simply supported beam, bending moment at supports is {zero} because the supports cannot resist a moment. Only an externally applied end couple can make the end moment non-zero.

Answer 1

The Correct Option is A

Step 1: Recall the boundary condition of a simply supported beam.
In a simply supported beam, the supports are usually a pin support and a roller support.
These supports provide reactions (vertical and/or horizontal), but they do not resist a moment (i.e., they cannot provide a fixing moment).
So, the bending moment at the supports is zero unless an external couple (moment) is applied exactly at that end.
Step 2: Apply the concept to the given statement.
At the end (support) of a simply supported beam:
- If no couple is applied at the end, the support cannot develop a resisting moment.
- Hence, the bending moment at that end must be zero.
Step 3: Analyze each option.
(A) Is always zero if it does not carry couple at the end: Correct, because supports of a simply supported beam cannot resist bending moment unless a couple is applied externally.
(B) Is zero if the beam has uniformly distributed load only: Incorrect reasoning, because the bending moment at the supports is zero for any loading type (UDL, point load, etc.) as long as no end couple is applied.
(C) Is zero if the beam has concentrated loads only: Incorrect for the same reason as (B). The type of load does not change the end moment condition.
(D) May or may not be zero: Incorrect for a simply supported beam, because it is zero unless an end couple is applied (which is exactly covered in option A).
Step 4: Conclusion.
Therefore, the correct statement is (A) Is always zero if it does not carry couple at the end.