GATE CE 2025 Set 1 — Question 41
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Structural Engineering → Stress, Strain & Beams → SFD & BMD
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Question
Consider the beam ACDEB given in the figure. Which of the following statements is/are correct:
Correct answer
(A) Bending moment is zero between the points A and C; (D) Bending moment is zero somewhere between the points D and E
Solution
1.Analysis of Segment CDEB (Right of the hinge C):
Let be the shear force at the hinge C (acting upward on the right segment). The loads on this segment are:- A concentrated clockwise couple at D: .
- A roller reaction at E.
- A downward point load of at B.
Vertical equilibrium for CDEB:
This means the right segment exerts a upward force on the hinge.
2.Equilibrium of Hinge C:
The hinge C is subjected to an external downward load of and an upward force of from the right segment. The net force on the hinge from these two is zero. Therefore, the force transmitted from the left segment AC to the hinge must be zero. Since and for segment AC, and there are no intermediate loads, the bending moment is zero throughout AC. Statement (A) is correct.3.Shear and Moment Diagrams:
- Segment CD: . varies from at C to at D (left).
- At Point D: The clockwise couple of causes a jump in bending moment: . There is no vertical point load at D, so there is no jump in shear force. Statement (B) is incorrect.
- Segment DE: . varies from at D to at E. Since the moment changes sign from to , it must be zero at some point between D and E. Statement (D) is correct.
- At Point E: The reaction causes a jump in shear force, not bending moment. Statement (C) is incorrect.
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