Interpreting shear force diagram (SFD): If the SFD between two points is a parabolic curve, what type of loading exists between those points?

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:

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