Difficulty: Easy
Correct Answer: parabola
Explanation:
Introduction / Context:
Recognizing the qualitative shape of shear force (S.F.) and bending moment (B.M.) diagrams is a fundamental skill in structural analysis. It enables quick checks and hand calculations before detailed numerical analysis.
Given Data / Assumptions:
Concept / Approach:
For a cantilever under UDL, the shear force at a distance x from the free end is V(x) = w x (taking zero at the free end), which varies linearly with x. The bending moment is the integral of shear, M(x) = ∫ V dx = w x^2/2 (with sign per convention), hence a second-degree curve (parabola) that is zero at the free end and maximum in magnitude at the fixed end.
Step-by-Step Solution:
Verification / Alternative check:
Different sign conventions invert the diagram vertically but do not change its parabolic shape. The curvature of the elastic line is proportional to moment; a parabolic M(x) produces cubic deflection, consistent with classical beam theory results.
Why Other Options Are Wrong:
Common Pitfalls:
Final Answer:
parabola.
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