A plane frame has a kinematic indeterminacy of 4. What does this indicate?
- AThere are 4 internal force redundancies
- BThere are 4 independent joint displacement parametersCorrect
- CThe structure can undergo 4 virtual work displacements
- DThe stiffness matrix will be of order more than 4 × 4
Solution
Concept
Independent joint displacements in structural frames
Formula
Dk = Total independent unconstrained nodal DOF
Step-by-step solution
1. Kinematic indeterminacy (Dk), or degrees of freedom, defines the number of independent coordinates required to define joint positions. 2. Unlike static indeterminacy which counts force redundancies, kinematic indeterminacy counts displacement unknowns. 3. A plane frame with Dk = 4 indicates exactly 4 independent unconstrained joint translations and rotations. 4. Hence, option B correctly expresses the meaning of kinematic indeterminacy. Answer: B
Explanation
Kinematic indeterminacy represents the number of unconstrained, independent joint displacement components (rotations and translations) necessary to completely describe the deformed geometry of a structure under load. A value of 4 means there are 4 independent joint displacement parameters.
Why the other options are wrong
A) Internal force redundancies define static indeterminacy, not kinematic. C) Virtual displacements can be arbitrary and are not limited to 4. D) The primary stiffness matrix matches the kinematic indeterminacy order (4x4), not greater.
Shortcut
Static indeterminacy = Redundant forces; Kinematic indeterminacy = Unknown joint displacements.
Common mistake
Confusing kinematic indeterminacy (displacement degrees of freedom) with static indeterminacy (internal force redundancies).
Correct answer: B) There are 4 independent joint displacement parameters