---
title: "Define kinematic indeterminacy"
subject: "Theory of Structures II"
chapter: 1
key: "semester_5/theory_of_structures_ii:define-kinematic-indeterminacy"
source: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/define-kinematic-indeterminacy
site: BCT Engineering
---

# Define kinematic indeterminacy

Theory of Structures II · Chapter 1: Introduction

- Asked in: 2073 Shrawan, 1 marks
- Video: [Kinematic Indeterminacy - Introductory Concepts - Advanced Structural Analysis](https://www.youtube.com/watch?v=Od8HXeVvkeM) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/define-kinematic-indeterminacy
- Whole chapter: https://www.bctengineer.com/md/semester_5/theory_of_structures_ii/chapter-1

## Question

Define and explain the term kinematic indeterminacy.

## Short answer

Kinematic indeterminacy (degree of freedom) is the number of independent joint displacements (translations and rotations) needed to describe the deformed shape. For a plane frame Dk=3j-r (extensible) or 3j-r-m (inextensible); for a truss Dk=2j-r. Example: a fixed-based portal frame has Dk=3.

## Answer

**Kinematic indeterminacy** (degree of freedom) is the number of independent joint displacements, translations and rotations, that are unknown and must be determined to describe completely the deformed shape of a structure under load.

It is the number of unknowns in the displacement (stiffness) method. For a plane frame, $D_k = 3j - r + c'$ when axial deformation is allowed, and $D_k = 3j - r - m + c'$ when members are axially rigid. For a plane truss, $D_k = 2j - r$.

**Example:** A fixed-based portal frame ($j = 4,\ r = 6,\ m = 3$) has $D_k = 12 - 6 - 3 = 3$ for inextensible members: the rotations of the two top joints and one sway. A propped cantilever has $D_k = 1$, the rotation at the roller end.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Kinematic indeterminacy is the number of:
   A. Redundant forces
   B. Independent unknown joint displacements
   C. Supports
   D. Equilibrium equations
   Answer: B. It is the number of independent unknown joint translations and rotations, also called degrees of freedom. (Key point: Definition)

2. For a plane frame with axially rigid members and no hinges, Dk =
   A. 3j - r
   B. 2j - r
   C. 3j - r - m
   D. 3j + r - m
   Answer: C. Each axially rigid member removes one unknown: Dk = 3j - r - m. (Key point: Axially rigid frame)

3. Fixed-based portal (j=4, r=6, m=3), inextensible: Dk = 3. These are:
   A. Two base rotations and a sway
   B. Rotations of the two top joints and one sway
   C. Three vertical settlements
   D. Three top rotations
   Answer: B. Two top-joint rotations and one sway; fixed bases do not move. (Key point: Fixed portal)

## Related in Theory of Structures II

- [External/internal static and kinematic indeterminacy of frame](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Adegrees-indeterminacy-frame-asar-2070) — Theory of Structures II, chapter 1
- [Static and kinematic indeterminacy with examples](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Aindeterminacy-define-examples) — Theory of Structures II, chapter 1, asked 5×
- [Static and kinematic indeterminacy of frame](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Adegrees-indeterminacy-frame-bhadra) — Theory of Structures II, chapter 1
- [Static and kinematic indeterminacy of frame](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Adegrees-indeterminacy-frame-old-2070) — Theory of Structures II, chapter 1
- [Degrees of indeterminacy of frame with hinges](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Adegrees-indeterminacy-frame-hinges-1) — Theory of Structures II, chapter 1
- [Indeterminacy of frame with internal hinges](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Adegrees-indeterminacy-trapezoid-frame) — Theory of Structures II, chapter 1