A cantilever ABCD is fixed at A and carries 300 N at B (0.5 m from A), 500 N at C (0.7 m from B) and 800 N at the free end D (0.8 m from C). Identify the INCORRECT statement.

Asked in SSC JE 06/11/2024 (9 am–11 am)

Detailed Explanation

Draw (or picture) the SFD and BMD from the free end. Each load adds to the shear as you move towards the fixed end, and the bending moment grows steadily.

Shear: \( V_{CD} = 800\ \text{N},\ V_{BC} = 800 + 500 = 1300\ \text{N},\ V_{AB} = 1300 + 300 = 1600\ \text{N} \)

Moment: \( M_D = 0,\ M_C = 800(0.8) = 640,\ M_B = 800(1.5) + 500(0.7) = 1550,\ M_A = 800(2) + 500(1.2) + 300(0.5) = 2350\ \text{N·m} \)

Why “Shear force at point C is greater than that at point B.” Is Correct

Moving from C to B the shear rises (800/1300 N at C, 1300/1600 N at B), so the shear at C is less, not greater, than at B. Statement (c) is the incorrect one.

Cantilever ABCD fixed at A with 300 N at B (0.5 m), 500 N at C (1.2 m) and 800 N at the free end D (2 m). Shear: 800 N on CD, 1300 N on BC, 1600 N on AB. Bending moment (hogging): 0 at D, 640 N·m at C, 1550 N·m at B, 2350 N·m at A.

Why the Other Options Are Wrong

A. Bending moment at point C is greater than that at point D.: True: 640 N·m at C is more than 0 at the free end D.
B. Shear force at point D is less than that at point B.: True: 800 N at D is less than the 1300–1600 N at B.
D. Bending moment at point C is less than that at point B.: True: 640 N·m at C is less than 1550 N·m at B.

Key Point

In a cantilever with downward loads, both V and M increase towards the fixed end.

Key Concepts for Students

Shear jumps by the load value at each point load.
The BMD between point loads is a straight line.
The fixed-end moment equals Σ load × distance from the support.

Practice more: this is question 14 in Bending Moment and Shear Force MCQs – Part 1. Try the whole set and check every answer instantly.