A simply supported beam of span L carries two point loads, each P, at the one-third points of the span. Which statement about the BMD is correct?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 14/11/2022
Detailed Explanation
Where the shear force is zero over a length, the bending moment does not change there (dM/dx = V). Symmetric two-point loading produces exactly that between the loads.
\( R_A = R_B = P \)
\( M_C = P \cdot \dfrac{L}{3} = \dfrac{PL}{3} \), \( M_D = P\cdot\dfrac{2L}{3} - P\cdot\dfrac{L}{3} = \dfrac{PL}{3} \)
Shear on CD: \( V = P - P = 0 \Rightarrow M = \) constant.
Why “Bending moment is constant in the middle one-third part” Is Correct
The bending moment is constant (PL/3) in the middle one-third — option (a). This zone is in pure bending, which is why the two-point (third-point) loading test is used for flexural strength of concrete.
Why the Other Options Are Wrong
- B. Bending moment increases linearly to mid-span and then decreases in the middle third: That describes a single central load; here the middle third has zero shear.
- C. Bending moment is constant in the left one-third part: In the end thirds the shear is ±P, so the moment changes linearly.
- D. Bending moment is zero at the mid-span section: Mid-span lies in the constant zone, where M = PL/3.
Key Point
Two equal loads at third points: M = PL/3 constant between loads (pure bending).
Key Concepts for Students
- The end zones (constant shear P) are the shear spans.
- Flexure test of concrete (IS 516) uses two-point loading.
- Zero shear over a length ⇒ constant moment over that length.
Practice more: this is question 19 in Bending Moment and Shear Force MCQs – Part 2. Try the whole set and check every answer instantly.