---
title: "Two basic approaches of structural analysis"
subject: "Theory of Structures I"
chapter: 1
key: "semester_4/theory_of_structures_i:two-basic-approaches"
source: https://www.bctengineer.com/q/semester_4/theory_of_structures_i/two-basic-approaches
site: BCT Engineering
---

# Two basic approaches of structural analysis

Theory of Structures I · Chapter 1: Introduction

- Asked in: 2079 Chaitra, 2 marks; 2077 Chaitra, 2 marks; 2070 Bhadra, 3 marks (asked 3 times)
- Video: [Lec 1 | Basics of structural analysis | Introduction to structural analysis | Civil tutor](https://www.youtube.com/watch?v=Gv7t_OVxf-Q) — Civil Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/theory_of_structures_i/two-basic-approaches
- Whole chapter: https://www.bctengineer.com/md/semester_4/theory_of_structures_i/chapter-1

## Question

What are the two basic approaches of structural analysis? Explain them briefly.

## Short answer

The force/flexibility method takes redundant forces as unknowns and solves compatibility equations; it suits structures with few redundants. The displacement/stiffness method takes joint displacements as unknowns and solves joint equilibrium equations; it suits structures with few kinematic degrees of freedom and is the basis of computer programs. Examples include consistent deformation/three-moment and slope-deflection/moment distribution.

## Answer

Structural analysis is carried out by one of two basic approaches, depending on which quantity is taken as the unknown. Both satisfy equilibrium, compatibility and force-displacement relations.

#### 1. Force method (flexibility method)
- The unknowns are **redundant forces** (reactions or internal forces).
- The structure is made statically determinate by removing redundants, and **compatibility** conditions at the removed points are written in terms of flexibility coefficients.
- Used mainly for structures with a low degree of static indeterminacy.
- Examples: consistent deformation, three-moment equation, Castigliano's second theorem.

#### 2. Displacement method (stiffness method)
- The unknowns are **joint displacements** (rotations and translations).
- **Equilibrium** equations of joints are written in terms of stiffness coefficients and solved for displacements, then member forces are found.
- Used when the degree of kinematic indeterminacy is small, and it is easy to programme.
- Examples: slope-deflection method, moment distribution, matrix stiffness method.

| Point | Force method | Displacement method |
|---|---|---|
| Unknowns | Redundant forces | Joint displacements |
| Conditions written | Compatibility | Equilibrium |
| Coefficients | Flexibility | Stiffness |
| Suitable for | Few redundants | Few degrees of freedom |

## Check yourself

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

1. In the force (flexibility) method the unknowns are:
   A. Redundant forces
   B. Joint displacements
   C. Joint rotations only
   D. Stiffness coefficients
   Answer: A. Redundants are removed and found from compatibility. (Key point: Force method unknowns)

2. The displacement (stiffness) method writes which conditions for solving the unknowns?
   A. Compatibility using flexibility coefficients
   B. Equilibrium of joints using stiffness coefficients
   C. Only the force-displacement relation
   D. Energy conservation of the whole structure
   Answer: B. Joint equilibrium gives equations in displacements. (Key point: Displacement method condition)

3. Which is an example of the displacement method?
   A. Three-moment equation
   B. Consistent deformation
   C. Slope-deflection method
   D. Castigliano's second theorem
   Answer: C. Slope-deflection, moment distribution and matrix stiffness are displacement methods. (Key point: Examples)

## Related in Theory of Structures I

- [Structure analysis and its basic approaches](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Astructure-analysis-approaches) — Theory of Structures I, chapter 1
- [Use of computers in structural analysis](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Ause-of-computers-analysis) — Theory of Structures I, chapter 1, asked 2×
- [Non-linearity in structural analysis](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Anonlinearity-structural-analysis) — Theory of Structures I, chapter 1
- [Characteristics of structural mechanics](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Astructural-mechanics-characteristics) — Theory of Structures I, chapter 1

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