---
title: "Explain indeterminacies; degrees of frame"
subject: "Theory of Structures II"
chapter: 1
key: "semester_5/theory_of_structures_ii:explain-indeterminacies-degrees-two-bay-frame"
source: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/explain-indeterminacies-degrees-two-bay-frame
site: BCT Engineering
---

# Explain indeterminacies; degrees of frame

Theory of Structures II · Chapter 1: Introduction

- Asked in: 2069 Asar, 2+2+2 marks
- Video: [Static Determinacy, Indeterminacy and Stability of a Plane Frame - Solved Examples](https://www.youtube.com/watch?v=gcPP8DCa2sw) — AF Math & 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/explain-indeterminacies-degrees-two-bay-frame
- Whole chapter: https://www.bctengineer.com/md/semester_5/theory_of_structures_ii/chapter-1

## Question

Explain static and kinematic indeterminacies of structures. Determine the degrees of static and kinematic indeterminacy of the structure shown in figure below. (Take all members are inextensible). [Figure: two-storey, two-bay frame; bases: fixed, hinged, roller as drawn.]

## Short answer

Static indeterminacy is 9 (external 3, internal 6). With inextensible members, kinematic indeterminacy is 11.

## Answer

#### Static indeterminacy
A structure is statically indeterminate when the equilibrium equations ($\Sigma F_x = 0,\ \Sigma F_y = 0,\ \Sigma M = 0$) are not enough to find all reactions and member forces. The excess number of unknowns is the degree of static indeterminacy $D_s$, the number of redundants. For plane frames $D_s = (3m + r) - (3j + c)$. It has an external part ($r - 3 - c$) and an internal part (from closed loops).

#### Kinematic indeterminacy
It is the number of independent joint displacements (rotations and translations) that are unknown. $D_k = 3j - r + c'$, and $D_k = 3j - r - m + c'$ if axial deformation is neglected. It decides the work of the displacement method.

#### Frame in the figure
Reading: two-storey, two-bay frame, bases fixed, hinged and roller, no internal hinge.

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

- $D_s = 3(10) + 6 - 3(9) = 9$ (external 3, internal $3 \times 2 = 6$)
- Members are inextensible: $D_k = 3(9) - 6 - 10 = 11$

**Answer: $D_s = 9$, $D_k = 11$.**

## Check yourself

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

1. A structure is statically indeterminate when:
   A. Equilibrium equations are insufficient to find all reactions and member forces
   B. It has hinges
   C. Joints can rotate
   D. It has more than one storey
   Answer: A. The excess of unknowns over equilibrium equations is Ds, the number of redundants. (Key point: Static indeterminacy meaning)

2. With no hinge, m=10, r=6, j=9: Ds =
   A. 8
   B. 9
   C. 10
   D. 6
   Answer: B. 30 + 6 - 27 = 9 (external 3, internal 6). (Key point: Ds of the frame)

3. Dk for inextensible members is 3j - r - m =
   A. 27 - 6 - 10 = 11
   B. 27 - 6 = 21
   C. 27 - 6 + 10 = 31
   D. 18 - 6 = 12
   Answer: A. No hinge so c' = 0; Dk = 11. (Key point: Dk inextensible)

## 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
- [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
- [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 and stability of frame and truss](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Aindeterminacy-stability-frame-and-truss-baishakh) — 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