GATE 2024 CE (CE1) – Question 33

Structural Analysis · Stiffness matrix method · 1 mark · Numerical answer

The plane frame shown in the figure has fixed support at joint A, hinge support at joint F, and roller support at joint I. In the figure, A to I indicate joints of the frame.

If the axial deformations are neglected, the degree of kinematic indeterminacy is ________ (in integer).

a plane frame with the joints A to I. A column A-B-C on the left (A fixed), a beam C-D with an overhang D-G, a column D-E-F with F on a hinge support, and a lower right part E-H-I with H-I vertical and I on a roller. The bracing members B-D, C-E, B-F, B-E, F-H and F-I are also present.

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Correct answer: 7

Explanation

With the axial deformations neglected, every member keeps its length, so the translations of all joints are fixed by the supports and the braced triangles: the supports fix A and F and the vertical movement of I, and the rigid members and the diagonals (such as B-D, C-E and B-F) lock the joints B, C, D, E, H in place. What remains are the joint rotations. The joints B, C, D, E and H can rotate (5), the hinge F can rotate (1) and the roller I can rotate (1), while the fixed support A cannot. That makes $5 + 1 + 1 = 7$ degrees of freedom. The free overhang end G is statically determinate and is not counted.