---
title: "Static and kinematic indeterminacy of frame"
subject: "Theory of Structures II"
chapter: 1
key: "semester_5/theory_of_structures_ii:degrees-indeterminacy-frame-bhadra"
source: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/degrees-indeterminacy-frame-bhadra
site: BCT Engineering
---

# Static and kinematic indeterminacy of frame

Theory of Structures II · Chapter 1: Introduction

- Asked in: 2078 Bhadra, 4 marks
- Video: [Degree of Static and Kinematic Indeterminacy of Frame - Problem 1 & 2 - Structural Analysis 2](https://www.youtube.com/watch?v=MOkptdjC5bc) — 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/degrees-indeterminacy-frame-bhadra
- Whole chapter: https://www.bctengineer.com/md/semester_5/theory_of_structures_ii/chapter-1

## Question

Determine degrees of static and kinematic indeterminacies of the frame shown in the figure below. [Figure: single-storey frame with three columns (left hinged, middle fixed, right roller).]

## Short answer

Static indeterminacy = 3. Kinematic indeterminacy = 12 (7 if members are axially inextensible).

## Answer

The frame is a single-storey frame with three columns: left hinged, middle fixed, right on a roller. A continuous girder joins the column tops.

$j = 6,\ m = 5\ (3\ \text{columns} + 2\ \text{beams}),\ r = 2 + 3 + 1 = 6,\ c = 0$

#### Static indeterminacy
$D_s = 3m + r - 3j - c = 15 + 6 - 18 = 3$

External $= r - 3 = 3$; internal $= 0$ (no closed loop).

#### Kinematic indeterminacy
- Axial deformation considered: $D_k = 3j - r = 18 - 6 = 12$
- Axial deformation neglected: $D_k = 3j - r - m = 18 - 6 - 5 = 7$

The 7 are: rotations of the three top joints (3), rotation of the hinged base (1), rotation of the roller base (1), horizontal movement of the roller base (1) and sway of the girder (1).

**Answer: $D_s = 3$; $D_k = 12$ (7 for inextensible members).**

## Check yourself

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

1. Left hinged, middle fixed, right roller: r equals:
   A. 5
   B. 7
   C. 6
   D. 8
   Answer: C. 2 + 3 + 1 = 6. (Key point: Reaction count)

2. With m = 5, j = 6, r = 6, c = 0, Ds = 3m + r - 3j - c is:
   A. 3
   B. 6
   C. 0
   D. 9
   Answer: A. 15 + 6 - 18 = 3. (Key point: Static indeterminacy)

3. Dk with axial deformation considered is:
   A. 7
   B. 18
   C. 12
   D. 6
   Answer: C. Dk = 3j - r = 18 - 6 = 12. (Key point: Kinematic with axial deformation)

4. Neglecting axial deformation, the Dk becomes:
   A. 12 - 5 = 7
   B. 12 + 5 = 17
   C. 12 - 6 = 6
   D. 12 - 3 = 9
   Answer: A. Each axially rigid member removes one unknown: 12 - m = 7. (Key point: Inextensible members)

## Related in Theory of Structures II

- [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
- [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
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- [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
- [Indeterminacy: frame with hinge and truss](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Adegrees-indeterminacy-frame-and-truss) — Theory of Structures II, chapter 1

## Related in other subjects

- [Frame: horizontal displacement and rotation at roller](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Aframe-horizontal-rotation-roller-2079) — Theory of Structures I, chapter 3
- [Frame: roller displacement and hinge rotation](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Aframe-roller-hinge-rotation-2071b) — Theory of Structures I, chapter 3