GATE CE 2023 Set 2 — Question 26
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Structural Engineering → Indeterminate Analysis & Influence Lines → Analysis of Frames
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Question
In the frame shown in the figure (not to scale), all four members (AB, BC, CD, and AD) have the same length and same constant flexural rigidity. All the joints A, B, C, and D are rigid joints. The midpoints of AB, BC, CD, and AD, are denoted by E, F, G, and H, respectively. The frame is in unstable equilibrium under the shown forces of magnitude acting at E and G. Which of the following statements is/are TRUE?
Correct answer
(A) Shear forces at H and F are zero; (B) Horizontal displacements at H and F are zero; (D) Slopes at E, F, G, and H are zero
Solution
The frame and the loading are symmetric about both the horizontal axis (passing through E and G) and the vertical axis (passing through H and F).
1.Shear Force: Due to symmetry about the vertical axis, the shear force at the midpoints of the horizontal members (H and F) must be zero. Statement (A) is true.
2.Horizontal Displacement: Due to symmetry about the vertical axis, points on that axis (H and F) cannot move horizontally. Statement (B) is true.
3.Vertical Displacement: The inward forces at E and G will cause the frame to bulge out at H and F. Thus, there will be vertical displacement at H and F. Statement (C) is false.
4.Slopes: Due to symmetry of the structure and the loading, the tangent to the elastic curve at the midpoints of the members (E, F, G, and H) remains horizontal or vertical (no rotation). Thus, the slopes are zero. Statement (D) is true.
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