Shear force diagram (SFD): identifying load types by diagram jumps When there is a sudden increase or decrease (a vertical jump) in the SFD at a section between two adjacent points along a beam, it indicates the presence of what kind of loading at that section?

Difficulty: Easy

Correct Answer: A concentrated (point) load acting at that section

Explanation:


Introduction / Context:
Engineers diagnose the type and location of loads on a beam by interpreting the shear force diagram (SFD) and bending moment diagram (BMD). A key signature is how the SFD changes from point to point: vertical jumps, straight sloping lines, or curves each correspond to different loading conditions.


Given Data / Assumptions:

  • Prismatic beam under transverse loading.
  • Small deflection theory and linear elasticity.
  • Standard sign conventions for shear and moment.


Concept / Approach:
Differential relations link load intensity w(x), shear V(x), and bending moment M(x): dV/dx = -w(x) and dM/dx = V(x). A concentrated point load is mathematically represented by an impulse (Dirac delta) in w(x), which produces a finite jump in V but leaves M continuous (unless a couple is applied).


Step-by-Step Solution:
If w(x) = 0 over an interval, then dV/dx = 0 ⇒ V is constant (a horizontal segment in SFD).If w(x) = constant ≠ 0 (UDL), then V varies linearly (a straight sloped line in SFD).If w(x) varies linearly (UVL), then V is quadratic (a curve in SFD).If a point load P acts at x = a, V has a sudden jump of magnitude P at x = a, while M remains continuous there.Therefore, a vertical jump between two adjacent plotted points of the SFD indicates a point load at that section.


Verification / Alternative check:
Integrate w(x) over an infinitesimal interval around the suspected section: ∫ w dx = P produces ΔV = -P (sign per convention). That finite ΔV confirms a point load.


Why Other Options Are Wrong:
No loading gives a flat SFD segment, not a jump. UDL gives linear variation, not a sudden jump. UVL gives a curved SFD. A pure couple (moment) causes a jump in the BMD, not in the SFD.


Common Pitfalls:
Confusing the jump in SFD (point load) with the jump in BMD (applied couple); misreading plotted points spaced too far apart and missing the exact load location.


Final Answer:
A concentrated (point) load acting at that section

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion