---
title: "Define E, G, K and Poisson's ratio"
subject: "Strength of Materials"
chapter: 3
key: "semester_3/strength_of_materials:define-elastic-constants"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/define-elastic-constants
site: BCT Engineering
---

# Define E, G, K and Poisson's ratio

Strength of Materials · Chapter 3: Simple Stress and Strain

- Asked in: 2066 Jestha (old course), 4 marks
- Video: [Elastic Constants and their Relationship | Lec-5](https://www.youtube.com/watch?v=sZi0W3pr8Jg) — Unacademy GATE & ESE - Civil & ES
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/define-elastic-constants
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-3

## Question

Define the modulus of elasticity, modulus of rigidity, bulk modulus and Poisson's ratio.

## Short answer

Modulus of elasticity E = normal stress / linear strain. Modulus of rigidity G = shear stress / shear strain. Bulk modulus K = hydrostatic pressure / volumetric strain. Poisson’s ratio ν = |lateral strain| / longitudinal strain.

## Answer

#### Modulus of elasticity (Young's modulus, $E$)
The ratio of normal (tensile or compressive) stress to the corresponding linear strain, within the elastic limit:

$$
E = \frac{\text{normal stress}}{\text{linear strain}} = \frac{\sigma}{\varepsilon}
$$

For mild steel, $E \approx 2\times10^5\ \text{N/mm}^2$.

#### Modulus of rigidity (shear modulus, $G$)
The ratio of shear stress to shear strain within the elastic limit:

$$
G = \frac{\tau}{\phi}
$$

where $\phi$ is the shear strain (angular distortion in radians).

#### Bulk modulus ($K$)
The ratio of the uniform (hydrostatic) stress applied on all faces to the resulting volumetric strain, within the elastic limit:

$$
K = \frac{p}{\delta V/V}
$$

#### Poisson's ratio ($\nu$ or $1/m$)
The ratio of lateral strain to longitudinal (axial) strain within the elastic limit:

$$
\nu = \left|\frac{\text{lateral strain}}{\text{longitudinal strain}}\right|
$$

It is about 0.25 to 0.33 for most metals. The constants are related by $E = 2G(1+\nu) = 3K(1-2\nu)$.

## Check yourself

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

1. How is the modulus of elasticity defined?
   A. Ratio of shear stress to shear strain
   B. Ratio of lateral strain to axial strain
   C. Ratio of normal stress to linear strain within the elastic limit
   D. Ratio of hydrostatic pressure to volumetric strain
   Answer: C. E = sigma/epsilon within the elastic limit. (Key point: Young's modulus)

2. Which pair is correct?
   A. G = shear stress/shear strain; K = pressure/volumetric strain
   B. G = pressure/volumetric strain; K = shear stress/shear strain
   C. G = normal stress/linear strain; K = lateral/longitudinal strain
   D. G = lateral/longitudinal strain; K = shear stress/shear strain
   Answer: A. G relates shear stress to shear strain, K relates uniform pressure to volumetric strain. (Key point: Modulus of rigidity and bulk modulus)

3. Which statement about Poisson's ratio is correct?
   A. It is longitudinal over lateral strain, and E = G(1+nu)
   B. It is always above 1 for metals
   C. It is lateral strain over longitudinal strain, and E = 2G(1+nu) = 3K(1-2nu)
   D. It is stress over strain, and E = 3G(1-2nu)
   Answer: C. nu = |lateral/longitudinal| (about 0.25-0.33 for metals) and links E, G, K as stated. (Key point: Poisson's ratio and relations)

## Related in Strength of Materials

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