---
title: "Characteristics of structural mechanics"
subject: "Theory of Structures I"
chapter: 1
key: "semester_4/theory_of_structures_i:structural-mechanics-characteristics"
source: https://www.bctengineer.com/q/semester_4/theory_of_structures_i/structural-mechanics-characteristics
site: BCT Engineering
---

# Characteristics of structural mechanics

Theory of Structures I · Chapter 1: Introduction

- Asked in: 2071 Bhadra, 6 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/structural-mechanics-characteristics
- Whole chapter: https://www.bctengineer.com/md/semester_4/theory_of_structures_i/chapter-1

## Question

Explain the characteristics of structural mechanics and describe, with suitable examples, the two basic approaches of structural analysis.

## Short answer

Structural mechanics studies forces, stresses, strains and displacements using equilibrium, compatibility and constitutive relations. It idealises structures into members, supports and loads, and assumes linear elasticity, small displacements and superposition. The force method uses redundant forces and compatibility, e.g. prop reaction RB=3wL/8 in a propped cantilever; the displacement method uses joint displacements and equilibrium, e.g. slope-deflection.

## Answer

**Structural mechanics** is the branch of mechanics that studies how structures respond to loads, i.e. the forces, stresses, strains and displacements produced in them.

#### Characteristics of structural mechanics
1. It is based on **three fundamental conditions**: equilibrium of forces, compatibility of displacements, and the material's force-displacement relation (Hooke's law).
2. It idealises real structures into simple models: members as lines (beams, columns, bars), supports as hinges, rollers or fixed supports, and loads as point, line or distributed loads.
3. It assumes materials are homogeneous, isotropic and linearly elastic, and that displacements are small.
4. It uses the **principle of superposition** for linear structures.
5. It divides structures into **statically determinate** (solved by equilibrium alone) and **indeterminate** (needing compatibility as well).
6. It supplies the data (forces and displacements) needed for the **design** of members and for checking serviceability.

#### Two basic approaches of structural analysis
**Force (flexibility) method:** The unknowns are redundant forces. Example: a propped cantilever carrying a UDL is made determinate by removing the prop at B. The upward deflection at B caused by the prop reaction, $\dfrac{R_BL^3}{3EI}$, is set equal to the downward deflection of the cantilever under the UDL, $\dfrac{wL^4}{8EI}$, since the net deflection at the prop is zero. This gives the prop reaction:

$$
R_B = \frac{3wL}{8}
$$

**Displacement (stiffness) method:** The unknowns are joint displacements. Example: in a continuous beam, the support rotation $\theta_B$ is taken as the unknown and found from joint moment equilibrium, $\sum M_B = 0$ (slope-deflection method); the member end moments are found afterwards.

| Point | Force method | Displacement method |
|---|---|---|
| Unknown | Redundant forces | Joint displacements |
| Condition solved | Compatibility | Equilibrium |
| Best for | Few redundants | Few displacement unknowns, computers |

## Check yourself

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

1. Structural mechanics is based on:
   A. Only equilibrium
   B. Only compatibility
   C. Plasticity and creep
   D. Equilibrium, compatibility and Hooke's law relation
   Answer: D. These are the three fundamental conditions. (Key point: Fundamental conditions)

2. Which assumption is made in structural mechanics?
   A. Materials are homogeneous, isotropic, linearly elastic with small displacements
   B. Materials are anisotropic and plastic
   C. Displacements are always large
   D. Loads change the support type
   Answer: A. These allow superposition. (Key point: Assumptions)

3. For a propped cantilever with UDL by the force method, the prop is removed and then:
   A. Moment at the fixed end is set zero
   B. Cantilever deflection at the prop point is equated to the prop deflection
   C. Prop reaction is set equal to wL
   D. Rotation at the prop is taken as unknown
   Answer: B. Compatibility at the prop gives R = 3wL/8. (Key point: Propped cantilever)

4. In a continuous beam by slope-deflection, the unknowns are:
   A. Redundant reactions
   B. Prop deflections
   C. Support rotations found from joint moment equilibrium
   D. Flexibility coefficients
   Answer: C. Joint rotations are solved from sum of M = 0. (Key point: Displacement method example)

## 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×
- [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

## Related in other subjects

- [Basic theorems of limit analysis](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Alimit-analysis-two-theorems) — Theory of Structures II, chapter 5, asked 2×