What is the degree of kinematic indeterminacy of the truss as shown in figure? [3-bay plane truss with 8 joints, double diagonals in each bay, hinged at bottom-left joint and roller at bottom-right joint]
- A10
- B11
- C12
- D13Correct
Solution
Concept
In a plane truss each joint has 2 translational degrees of freedom (DOF). Subtract the number of support restraints to get the kinematic indeterminacy.
Formula
Dk = 2j - r
Step-by-step solution
1. Number of joints: j = 8. 2. Total DOF = 2 × 8 = 16. 3. Hinge support gives 2 restraints and roller support gives 1 restraint, so r = 3. 4. Dk = 16 - 3 = 13. 5. The answer is option D.
Explanation
Each joint of a plane truss can move in x and y directions, so it has 2 DOF. With 8 joints there are 16 DOF. The hinge stops 2 movements and the roller stops 1, so Dk = 13.
Why the other options are wrong
A (10), B (11) and C (12) come from wrong joint counts or wrong support restraint counts. The number of members (or double diagonals) does not change Dk of a truss.
Shortcut
For a plane truss, Dk = 2j - r = 2(8) - 3 = 13.
Common mistake
Using members or diagonals in the count, or taking the roller as 2 restraints.
Correct answer: D) 13