---
title: "External/internal static and kinematic indeterminacy of frame"
subject: "Theory of Structures II"
chapter: 1
key: "semester_5/theory_of_structures_ii:degrees-indeterminacy-frame-asar-2070"
source: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/degrees-indeterminacy-frame-asar-2070
site: BCT Engineering
---

# External/internal static and kinematic indeterminacy of frame

Theory of Structures II · Chapter 1: Introduction

- Asked in: 2070 Asar, 3+3 marks
- Video: [External and Internal Static Indeterminacy of Frames](https://www.youtube.com/watch?v=XgUywwSsQsE) — Master Civil Engineering
- 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-asar-2070
- Whole chapter: https://www.bctengineer.com/md/semester_5/theory_of_structures_ii/chapter-1

## Question

Determine the external and internal degrees of static indeterminacy of the structure shown in figure below. Also determine the kinematic indeterminacy. [Figure: two-storey frame with an internal hinge at top-left; left base fixed, middle base hinged, right top end on a roller.]

## Short answer

External static indeterminacy is 3, internal is 5 (total 8). Kinematic indeterminacy is 22 with extensible members, or 12 if axial deformation is neglected.

## Answer

Reading of the figure: two-storey, two-bay frame with a hinge at the top-left joint, fixed left base, hinged middle base, and a roller at the right-hand support.

$j = 9,\ m = 10,\ r = 3 + 2 + 1 = 6,\ c = 1$

#### Static indeterminacy
- External: $r - 3 = 6 - 3 = 3$
- Internal: $3 \times (\text{closed loops}) - c = 3 \times 2 - 1 = 5$ (the two upper panels are closed loops; the lower panels are open at the base)
- Total: $D_s = 3 + 5 = 8$. Check: $3m + r - 3j - c = 30 + 6 - 27 - 1 = 8$.

#### Kinematic indeterminacy
- With axial deformation: $D_k = 3j - r + 1 = 27 - 6 + 1 = 22$
- Without axial deformation: $D_k = 22 - 10 = 12$

**Answer: external 3, internal 5 (total 8); kinematic 22 (12 if inextensible).**

## Check yourself

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

1. External static indeterminacy equals:
   A. r - 3 = 3
   B. 3m - r
   C. 3j - r
   D. c + 3
   Answer: A. With r = 6 reactions, external = 6 - 3 = 3. (Key point: External indeterminacy)

2. Internal indeterminacy is 3 x loops - c = 5 because:
   A. There are 2 closed loops and 1 hinge
   B. There are 3 loops and 4 hinges
   C. There is 1 loop and no hinge
   D. The roller releases it
   Answer: A. Two closed upper panels give 6, minus 1 for the hinge = 5. (Key point: Internal indeterminacy)

3. Total Ds can be cross-checked as:
   A. 3m + r - 3j - c = 8
   B. m + r - 2j = 8
   C. 3j - r = 8
   D. r + c = 8
   Answer: A. 30 + 6 - 27 - 1 = 8 = 3 + 5. (Key point: Total check)

4. Dk without axial deformation is:
   A. 22
   B. 10
   C. 12
   D. 32
   Answer: C. 22 - 10 = 12. (Key point: Kinematic)

## 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
- [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
- [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
- [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: 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
- [Explain indeterminacies; degrees of frame](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Aexplain-indeterminacies-degrees-two-bay-frame) — Theory of Structures II, chapter 1

## Related in other subjects

- [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
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