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GATE 2025 CE (CE1) – Question 41

Solid Mechanics · Bending moment and shear force in statically determinate beams · 2 marks · Multiple select

Consider the beam ACDEB given in the figure. Which of the following statements is/are correct:

A beam ACDEB with a fixed support at A and an internal hinge at C. A is 5 m from C, then C to D, D to E and E to B are 2 m each. A 3 kN downward load acts at C. At D a 4 kN horizontal force acts to the right on a bracket 1 m above the beam axis and a 4 kN horizontal force acts to the left 1 m below it. A roller support is at E and a 2 kN downward load acts at B.
  1. Bending moment is zero between the points A and C
  2. There is a sudden jump in shear force at the point D
  3. There is a sudden jump in bending moment at the point E
  4. Bending moment is zero somewhere between the points D and E

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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

Explanation

The two 4 kN forces at D form a clockwise couple of $4 \times 2 = 8$ kN·m and no net force. Take part CDEB, supported by the hinge at C and the roller at E. Moments about C give $4R_E - 2 \times 6 - 8 = 0$, so $R_E = 5$ kN, and then the hinge force on CB is $2 - 5 = -3$ kN, that is 3 kN downward. The pin at C carries the 3 kN load downward and CB pulls it back upward with 3 kN, so no force passes into AC. AC has no shear and no bending, so A is true. The bending moment is $-3x$ from C, which is $-6$ kN·m just before D. The couple raises it by 8 kN·m to $+2$ kN·m, and it falls to $-4$ kN·m at E, so it is zero between D and E (at $x = 8/3$ m), and D is true. There is no vertical load at D, so the shear force does not jump there, and B is false. E is a roller with no couple, so the shear force jumps at E but the bending moment does not, and C is false.