A simply supported beam of span 4C carries loads W at C, 2W at 2C and W at 3C from the left support. The maximum shear force in the beam is:
Try it first: pick an option, then read the explanation.
Correct answer: C. 2W
Asked in SSC JE 03/03/2017 (Morning)
Detailed Explanation
Find the reactions; then step through the SFD. In a simply supported beam with point loads, the largest shear is next to a support.
\( R_A + R_B = W + 2W + W = 4W \); by symmetry \( R_A = R_B = 2W \).
Shear: \( 2W \) (A to C), \( W \) (C to 2C), \( -W \) (2C to 3C), \( -2W \) (3C to B).
Why “2W” Is Correct
The largest magnitude is 2W, in the end bays — option (c).
Why the Other Options Are Wrong
- A. 0: Shear is zero only at the change of sign at mid-span.
- B. W: W is the shear in the inner bays only.
- D. 4W: 4W is the total load, shared by two supports.
Key Point
Point loads on a SS beam: V_max = larger reaction.
Key Concepts for Students
- The SFD steps down by each load as you move right.
- Max BM where SF changes sign (here at mid-span, 3WC).
- Symmetry halves the work: R = total load / 2.
Practice more: this is question 48 in Bending Moment and Shear Force MCQs – Part 4. Try the whole set and check every answer instantly.