Interpreting shear force diagram (SFD): If the SFD between two points is a parabolic curve, what type of loading exists between those points?
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APoint load at the two points only
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BNo loading between the points
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CUniformly distributed load (constant w) between the points
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DUniformly varying load (linearly varying w) between the points
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EPure bending with zero shear between the points
Answer
Correct Answer: Uniformly varying load (linearly varying w) between the points
Explanation
Introduction / Context:The shapes of SFD and BMD reveal the underlying load distribution. Knowing the differential relationships allows rapid diagnosis from diagrams: dV/dx = w and dM/dx = V.
Given Data / Assumptions:
- SFD is parabolic between two points.
- Beam theory relations apply in the elastic range.
- Loading is vertical and statically determinate in the region evaluated.
Concept / Approach:If dV/dx = w, then the curvature of V(x) reflects the variation of w. A parabolic V(x) implies that its derivative w(x) is linear—i.e., a uniformly varying load. Conversely, constant w → linear V; zero w → constant V; point loads cause jumps (discontinuities) in V.
Step-by-Step Solution:
Given V(x) is parabolic → second derivative of M is nonzero but first derivative V is curved.Compute w(x) = dV/dx → linear function.Therefore, loading is a uniformly varying load between the points.Verification / Alternative check:Classic example: triangular (linearly varying) load on a span produces a parabolic SFD and cubic BMD, consistent with the relationships.
Why Other Options Are Wrong:UDL gives linear SFD, not parabolic. Point loads create step changes, not smooth parabolas. “No loading” gives constant V (horizontal line).
Common Pitfalls:Confusing the shapes: UDL → linear V; UVL → parabolic V; no load → constant V.
Final Answer:Uniformly varying load (linearly varying w) between the points