---
title: "Define force method and primary structure"
subject: "Theory of Structures II"
chapter: 2
key: "semester_5/theory_of_structures_ii:define-force-method-primary-structure"
source: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/define-force-method-primary-structure
site: BCT Engineering
---

# Define force method and primary structure

Theory of Structures II · Chapter 2: Force method

- Asked in: 2070 Asar, 4 marks
- Video: [Force Method for Indeterminate Structures - Intro to Structural Analysis](https://www.youtube.com/watch?v=kwjt1H3Ycjw) — Structures with Prof. H
- 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-force-method-primary-structure
- Whole chapter: https://www.bctengineer.com/md/semester_5/theory_of_structures_ii/chapter-2

## Question

Define force method and primary structure.

## Short answer

Force method analyzes indeterminate structures by releasing redundants to form a primary structure, then applying compatibility equations to find redundant forces. Primary structure is the statically determinate stable structure obtained by removing redundants; it is not unique but must remain stable.

## Answer

#### Force method
The **force method** (flexibility or compatibility method) is a method of analysing statically indeterminate structures in which the **redundant forces** are taken as the unknowns. The redundants are removed to get a determinate structure, the loads and the unit redundants are applied to it, and the redundants are found from compatibility equations that restore the real displacement conditions at the releases:

$$
\Delta_{i0} + \sum_j f_{ij}X_j = \delta_i
$$

Here $\Delta_{i0}$ is the displacement due to the loads, $f_{ij}$ the flexibility coefficient and $\delta_i$ the actual displacement of the support (usually zero). After finding the $X_j$, the final forces follow by superposition, $M = M_0 + \sum X_jm_j$. The number of unknowns equals the degree of static indeterminacy $D_s$.

#### Primary structure
The **primary structure** is the statically determinate, stable structure obtained by removing the redundants (supports, members or moment restraints) from the indeterminate structure. It is not unique, but it must stay stable.

Example: a propped cantilever (fixed at A, roller at B) has $D_s = 1$. If the roller reaction $R_B$ is removed, the primary structure is a cantilever; if the fixed-end moment $M_A$ is released, it is a simply supported beam.

## Check yourself

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

1. In the force method the unknowns are:
   A. Joint displacements
   B. Redundant forces, equal in number to D_s
   C. Member stiffnesses
   D. Support settlements
   Answer: B. Redundant forces are the unknowns; their number equals the degree of static indeterminacy. (Key point: Force method unknowns)

2. The primary structure is:
   A. Any indeterminate structure
   B. The structure with extra loads
   C. A mechanism
   D. A statically determinate, stable structure obtained by removing the redundants
   Answer: D. It must be determinate and stable, and is not unique. (Key point: Primary structure)

3. After finding the redundants, final bending moments follow from:
   A. M = M0 + ΣXj mj
   B. M = M0 - ΣΔ
   C. M = ΣXj only
   D. M = M0 × ΣXj
   Answer: A. Superposition of the primary-structure effect and the redundant effects. (Key point: Final forces)

## Related in Theory of Structures II

- [Define primary structure](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Adefine-primary-structure) — Theory of Structures II, chapter 2
- [Force method: frame with 120 k load](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Aforce-method-frame-120k-sfd-bmd) — Theory of Structures II, chapter 2

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