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Relation between shear force and bending moment: extremum condition For a loaded beam, use V = dM/dx. State the value/nature of bending moment at a point where the shear force is zero.

Difficulty: Easy

Zero
Minimum
Maximum
Infinite

Correct Answer: Maximum

Explanation:

Concept/Derivative relationShear force V = dM/dx. When V = 0, the slope of the bending-moment diagram is zero; therefore, M has an extremum (maximum or minimum) at that location.

Engineering usageIn most practical positive-moment regions of simply supported beams, the zero-shear point corresponds to the maximum bending moment.

Common pitfallRemember it is an extremum in general. With usual loading on simply supported beams, that extremum is the maximum sagging moment.

Final AnswerMaximum.

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