GATE CE 2023 Set 1 — Question 49
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Structural Engineering → Stress, Strain & Beams → SFD & BMD
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Question
Consider the beam shown in the figure (not to scale), on a hinge support at end A and a roller support at end B. The beam has a constant flexural rigidity, and is subjected to the external moments of magnitude at one-third spans, as shown in the figure. Which of the following statements is/are TRUE?
Correct answer
(A) Support reactions are zero; (B) Shear force is zero everywhere
Solution
1.Support Reactions: Let and be the vertical reactions at A and B. Taking moments about A:
From vertical equilibrium: . Thus, support reactions are zero. Statement (A) is true.2.Shear Force: Since there are no vertical loads and the support reactions are zero, the shear force is zero throughout the entire span of the beam. Statement (B) is true.
3.Bending Moment:
- For :
- For :
- For :
4.Deflection: In the middle span (), the bending moment is non-zero (). According to the Euler-Bernoulli beam theory, . Since , there is curvature, and consequently, the beam will deflect. Statement (D) is false.
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