GATE CE 2014 Set 1 — Question 21
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Structural Engineering → Indeterminate Analysis & Influence Lines → Indeterminate Structures
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Question
The degree of static indeterminacy of a rigid jointed frame PQR supported as shown in the figure is
Correct answer
(A) zero
Solution
The degree of static indeterminacy for a 2D frame is given by:
Where:
Alternatively, considering the frame PQR as a single rigid body (since Q is rigid), it has 3 degrees of freedom. The roller at P removes 1 DOF. The cable RS (acting as a link) removes 1 DOF at R. This leaves 1 DOF, but the geometry prevents motion, making it statically determinate ().
Where:
- = number of members = 3 (PQ, QR, and cable RS)
- = number of external reactions = 1 (at P) + 3 (at S) = 4
- = number of joints = 4 (P, Q, R, S)
- = number of internal releases. Since the cable RS is a link, it is pinned at R and S. This provides 2 releases (one at each end of the cable).
Alternatively, considering the frame PQR as a single rigid body (since Q is rigid), it has 3 degrees of freedom. The roller at P removes 1 DOF. The cable RS (acting as a link) removes 1 DOF at R. This leaves 1 DOF, but the geometry prevents motion, making it statically determinate ().
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