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

# Static and kinematic indeterminacy of frame

Theory of Structures II · Chapter 1: Introduction

- Asked in: 2070 Chaitra (old course), 6 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-old-2070
- Whole chapter: https://www.bctengineer.com/md/semester_5/theory_of_structures_ii/chapter-1

## Question

Determine degrees of static and kinematic indeterminacies for the frame shown below. [Figure: two-storey, two-bay frame with an internal hinge at the top-left; supports: fixed at the left, hinged in the middle (with a fixed base), roller/hinge at the right as drawn.]

## Short answer

Static indeterminacy = 8. Kinematic indeterminacy = 22, or 12 if members are axially inextensible.

## Answer

Reading of the figure: two-storey, two-bay frame with three column lines, a hinge at the top-left joint, and supports fixed (left), hinged (middle) and roller (right).

$j = 9,\ m = 10\ (6\ \text{columns} + 4\ \text{beams}),\ r = 3 + 2 + 1 = 6,\ c = 1$

#### Static indeterminacy
$D_s = 3m + r - 3j - c = 30 + 6 - 27 - 1 = 8$

#### Kinematic indeterminacy
- Axial deformation considered: $D_k = 3j - r + c' = 27 - 6 + 1 = 22$
- Axial deformation neglected: $D_k = 22 - m = 22 - 10 = 12$

**Answer: $D_s = 8$; $D_k = 22$ (12 for inextensible members).**

## Check yourself

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

1. Which data is used: j, m, r, c?
   A. j=9, m=10, r=6, c=1
   B. j=6, m=10, r=9, c=1
   C. j=9, m=6, r=10, c=0
   D. j=10, m=9, r=6, c=1
   Answer: A. Nine joints, 6 columns + 4 beams = 10 members, r = 3+2+1 = 6, one hinge. (Key point: Joint and member count)

2. In Ds = 3m + r - 3j - c, the hinge enters as:
   A. An added redundant
   B. A subtracted equation of condition
   C. A reaction
   D. Nothing
   Answer: B. A hinge gives an extra equation of condition, reducing Ds by one. (Key point: Role of c)

3. Ds is:
   A. 9
   B. 7
   C. 10
   D. 8
   Answer: D. 30 + 6 - 27 - 1 = 8. (Key point: Ds result)

4. Dk with axial deformation (3j - r + c') and without are:
   A. 22 and 12
   B. 21 and 11
   C. 20 and 10
   D. 22 and 17
   Answer: A. 27 - 6 + 1 = 22; subtract m = 10 for 12. (Key point: Dk result)

## 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
- [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
- [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: 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
- [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

## 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
- [Frame SFD, BMD (100 kN, 20 kN/m, hinge)](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aframe-sfd-bmd-100kn-hinge-60deg) — Strength of Materials, chapter 1
- [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
- [AFD, SFD, BMD for frame with internal hinge](https://www.bctengineer.com/question.md?key=semester_1%2Fapplied_mechanics%3Aframe-afd-sfd-internal-hinge-5kn-per-m) — Applied Mechanics, chapter 6