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

# Structure analysis and its basic approaches

Theory of Structures I · Chapter 1: Introduction

- Asked in: 2075 Bhadra, 1+3 marks
- 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/structure-analysis-approaches
- Whole chapter: https://www.bctengineer.com/md/semester_4/theory_of_structures_i/chapter-1

## Question

What is structure analysis? Explain the basic approaches of structural analysis.

## Short answer

Structural analysis determines reactions, internal forces, stresses and displacements so structures can be designed safely and economically. Every method satisfies equilibrium, compatibility and force-displacement relations. The force method uses redundant forces and compatibility; the displacement method uses joint displacements and equilibrium. Force method suits few redundants; displacement method suits few degrees of freedom and computer implementation.

## Answer

**Structural analysis** is the process of determining the reactions, internal forces (axial force, shear force, bending moment, torsion), stresses and displacements of a structure under given loads, so that it can be designed safely and economically.

#### Basic approaches
Every method of analysis must satisfy three conditions: equilibrium, compatibility (continuity of displacements) and the force-displacement (constitutive) relation. Depending on the unknown chosen, two approaches exist.

**1. Force (flexibility) method**
- Unknowns: redundant forces.
- Remove redundants to get a statically determinate (released) structure, then apply compatibility equations.
- Examples: method of consistent deformation, three-moment theorem.

**2. Displacement (stiffness) method**
- Unknowns: joint displacements (rotations and translations).
- Write joint equilibrium equations using stiffness coefficients.
- Examples: slope-deflection, moment distribution, matrix stiffness method.

The force method suits structures with few redundants; the displacement method suits structures with few degrees of freedom and is used in computer programs.

## Check yourself

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

1. Structural analysis is the process of:
   A. Selecting the cheapest material
   B. Drawing architectural plans
   C. Estimating construction cost
   D. Determining reactions, internal forces, stresses and displacements under given loads
   Answer: D. Analysis finds the response of the structure to loads. (Key point: Definition)

2. Every method of analysis must satisfy:
   A. Equilibrium, compatibility and force-displacement relation
   B. Equilibrium and cost only
   C. Compatibility and buckling only
   D. Strength and aesthetics
   Answer: A. These three conditions are always required. (Key point: Three conditions)

3. In the force method, after removing redundants we apply:
   A. Joint equilibrium equations in displacements
   B. Compatibility equations
   C. Only the Hooke's law
   D. Moment distribution factors
   Answer: B. The released structure must satisfy compatibility at the removed points. (Key point: Force method)

4. Which method is used in computer programs and suits few degrees of freedom?
   A. Force method
   B. Three-moment theorem
   C. Displacement (stiffness) method
   D. Consistent deformation
   Answer: C. Stiffness method is easy to programme. (Key point: Choice)

## Related in Theory of Structures I

- [Two basic approaches of structural analysis](https://www.bctengineer.com/question.md?key=semester_4%2Ftheory_of_structures_i%3Atwo-basic-approaches) — Theory of Structures I, chapter 1, asked 3×
- [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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