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GATE 2025 CE (CE1) – Question 29

Structural Analysis · Slope-deflection and moment distribution methods · 1 mark · Multiple select

Consider the frame shown in the figure under the loading of 100 kN.m couples at the joints B and G. Considering only the effects of flexural deformations, which of the following statements is/are true:

A frame with a beam B-C-G on top, 8 m from B to C and 8 m from C to G, with flexural rigidity 4EI. Three columns, 6 m high with 2EI, stand at B (fixed at A), C (fixed at D) and G (fixed at F). A 100 kN.m couple acts clockwise at B and a 100 kN.m couple acts anticlockwise at G.
  1. Axial force is zero in the member CD
  2. Shear force is zero in the member CD
  3. There is no rotation in the joint C
  4. The magnitude of bending moment developed in the member BC at the end C is more than 50 kN.m

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Correct answer: (B) Shear force is zero in the member CD; (C) There is no rotation in the joint C

Explanation

The frame is symmetrical about CD and the two couples are mirror images of each other (clockwise at B, anticlockwise at G), so the loading is symmetrical. By symmetry joint C neither rotates nor moves sideways, so C is true, and column CD, with a fixed base and no rotation or sway at the top, has no bending moment and no shear force, so B is true. At joint B, with C acting as if fixed against rotation, the stiffnesses are $\frac{4(4EI)}{8} = 2EI$ for BC and $\frac{4(2EI)}{6} = 1.33EI$ for BA, so BC takes $100 \times \frac{2}{3.33} = 60$ kN·m and carries over 30 kN·m to C, which is less than 50 kN·m, so D is false. The beams then send a vertical force of $\frac{60 + 30}{8} = 11.25$ kN into C from each side, so CD carries an axial force of 22.5 kN and A is false.