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

Simply supported beams rest on a pin support and a roller support, both of which can only supply force reactions, never a moment reaction.

1. Zero unless a couple acts at the end: Since the supports physically cannot resist rotation, the bending moment there has nothing to balance against unless an external couple is applied right at that point, so it must be zero in the absence of one, no matter what other loads act along the span.
2. Zero only for UDL: Wrongly singles out one load type when the zero-moment condition is a property of the support type, not the loading pattern.
3. Zero only for point loads: Same flaw as above.
4. May or may not be zero: Understates how definite this condition actually is for this type of support.

Answer 2

Another way to see this is to draw a free body of an infinitesimal slice right at the support and ask what could possibly balance a nonzero moment there.

1. Zero unless a couple acts at the end: At the very end of the beam, there is no beam material beyond that point to provide an internal resisting moment, and the support itself (pin or roller) offers no moment reaction, so the only way a nonzero moment could exist at that exact point is if an external couple were applied directly there.
2. Zero only for UDL: The free-body argument at the end doesn't care what loading exists elsewhere along the span, so restricting the rule to UDL loading is unjustified.
3. Zero only for point loads: Same issue, the conclusion doesn't depend on the type of loading present, only on whether a couple acts right at the end.
4. May or may not be zero: The free-body argument shows this is not actually ambiguous, it's zero by default unless a couple is applied there.

Therefore, the correct answer is is always zero if it does not carry a couple at the end.