Shear force diagram interpretation: If the SFD between two points is an inclined straight line, what does it indicate about the loading between those points?
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AYes, it indicates a uniformly varying load (constant w).
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BNo, it indicates a point load only.
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CIt indicates zero loading.
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DIt indicates a linearly varying distributed load.
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EIt indicates a constant bending moment only.
Answer
Correct Answer: Yes, it indicates a uniformly varying load (constant w).
Explanation
Introduction / Context:The relationships among load, shear force, and bending moment are foundational: load intensity is the derivative of shear, and shear is the derivative of bending moment. Recognizing diagram shapes lets you infer the type of loading.
Given Data / Assumptions:
- Euler–Bernoulli beam assumptions.
- Load intensity w(x) distributed along the span.
- Sign conventions standard.
Concept / Approach:Fundamental relations:dV/dx = −w(x)dM/dx = V(x)Thus, if V varies linearly (inclined straight line), its derivative is constant, which means the load w is uniform (constant in magnitude).
Step-by-Step Solution:
Observe SFD: straight, inclined line → V(x) = a + b x.Compute derivative: dV/dx = b (constant).Hence w(x) = −b is constant → uniformly distributed load.Verification / Alternative check:For a span with constant w, integrate once to get V as a straight line; integrate again to get M as a quadratic (parabola). This matches textbook diagram shapes.
Why Other Options Are Wrong:Point load generates a jump in V, not a linear segment.Zero loading would give constant V (horizontal line), not inclined.Linearly varying distributed load gives a curved (parabolic) SFD, not straight.Constant bending moment implies zero shear (horizontal SFD).
Common Pitfalls:Mixing up the relationships between w, V, and M; misreading jumps (point loads) as slopes; sign convention errors.
Final Answer:
Yes, it indicates a uniformly varying load (constant w).