A simply supported beam of span L carries a couple M at distance a from the left support (b from the right). The shear force at the point of contraflexure is:

Asked in SSC JE 2012

Detailed Explanation

Contraflexure is not always a zero-shear point. Under a couple, the shear is the same everywhere, while the BM changes sign at the couple.

\[ R_A = \frac{M}{L},\quad R_B = -\frac{M}{L} \Rightarrow |V| = \frac{M}{L}\ \text{throughout} \]

Why “M/L” Is Correct

The BM changes sign at the couple (from −Ma/L to +Mb/L), but the shear there is still M/L — option (d).

Simply supported beam with a clockwise couple M at distance a from A. The reactions form an equal and opposite couple: M/L down at A, M/L up at B. So the SFD is a rectangle of height M/L over the whole span. The BMD is two straight lines: −Ma/L just left of the couple and +Mb/L just right of it, jumping by M at the couple and passing through zero there (point of contraflexure).

Why the Other Options Are Wrong

A. 0: Shear is zero where the BM is maximum — here it is never zero.
B. M/a: M/a would mean the reaction depends on the couple's position — it does not.
C. M/b: Same — the reactions depend only on the span L.

Key Point

Couple on SS beam: shear M/L everywhere, independent of where the couple acts.

Key Concepts for Students

Contraflexure means BM changes sign, not SF = 0.
Point of contraflexure here = point of application of the couple.
Max BM magnitudes: Ma/L and Mb/L.

Practice more: this is question 59 in Bending Moment and Shear Force MCQs – Part 4. Try the whole set and check every answer instantly.