# Poisson’s Ratio: Definition, Formula, Poisson’s Ratio of Steel

By Mukul Yadav|Updated : September 21st, 2022

Poisson's Ratio measures the strain ratio in the lateral direction to the linear direction. In this way, we can say that lateral direction strain is the direction along the diameter, and linear direction stain is the direction along the length. Poisson’s ratio defines the deformation in a lateral and linear direction in the form of a ratio. This is known as Poisson's ratio.

Poisson's ratio is the negative ratio of lateral strain to linear strain in some places because the material has properties for expansion and contraction. Still, when it shrinks, it shows a negative value. This ratio is very important in determining strain components by the applied load. We can design the structural member on their yield strength and apply a significant load.

## What is Poisson’s Ratio?

The negative ratio of transverse strain to lateral or axial strain is known as Poisson's ratio. It is identified by the Greek letter "nu" and is named after Siméon Poisson.

The Poisson’s ratio is represented as mew (μ) or 1/m. In the same context, different materials have different Poisson ratios. The maximum value of Poisson's ratio is 0.5, and the minimum value is 0. In exception, human tissue is (-1) Poisson's ratio. There is no unit of Poisson's Ratio. Different values of Poisson's ratio are listed below -

 Types of Material Poisson’s ratio Human Tissues -1 Cork 0 Concrete 0.10 - 0.20 Cast Iron 0.20 - 0.30 Mild Steel 0.25 - 0.33 Wrought iron 0.30 Aluminium 0.33 Brass 0.34 Copper 0.33 - 0.36 Rubber 0.45 - 0.50 Titanium 0.265 - 0.34 Clay 0.30 - 0.45 Platinum 0.39 Foam 0.10 - 0.50

## Poisson’s Ratio Formula

Poisson’s ratio is formulated as a ratio of change in diameter to the original diameter or lateral changes to the linear changes as a change in length to the original length. These changes in dimension are known as a strain. So basically, Poisson's ratio is the strain ratio in lateral to linear dimension.

Poisson’s Ratio = Lateral strain/Linear strain

Or

Poisson’s ratio (μ) = (Change in width, diameter, thickness/Original width, diameter, thickness)/(Change in length/Original length)

Or

Poisson’s ratio (μ) = (δd/d)/(δL/L)

Or

1/m = Lateral strain/Linear strain

Range of 1/m is 0 ≤ μ ≤ 0.5. Only in exceptional cases is this limit as the minimum value as -1.

## Poisson’s Ratio of Steel

The Poisson's ratio of material changes as per the type of material. Soft materials like rubber, copper, and brass have a higher Poisson's ratio, while hard materials like steel, wrought iron, and concrete have a low Poisson's ratio. In comparison to all, we need steel as mild steel, structural steel, and HYSD steel bars. The Poisson’s ratio of steel is given below.

 Steel Type Poisson’s ratio Mild steel 0.303 High Carbon steel 0.295 Structural steel 0.3 HYSD steel 0.28

## Poisson Ratio for Perfectly Incompressible Elastic Body

An incompressible body is a body that has no volume change with the effect of the application of load. Such types of bodies have constant density concerning load variation. An elastic material is a material that follows Hooke's law of elasticity.

The value of the Poisson's ratio varies from zero to 0.5, but in some cases, it will also be negative (e.g., Poisson ratio of human tissue=-1). And for Incompressible elastic body value of Poisson's ratio is 0.5

 Important Topics for Gate Exam Properties of Materials Resolution of Forces Riveted Joints Sampling Theorem Single Phase Transformer Soil Classification Soil Formation Strain Gauge Tension Members Test On Hardened Concrete

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## FAQs on Poisson’s Ratio

• The ratio of transverse strain to axial strain under the effect of the same force is known as Poisson's ratio. It has a fixed value and is a material property. It is the value of any material that we can adopt for our structural work based on its stability, durability, and serviceability.

• Poisson's ratio is affected by material properties within the elastic limit because different materials have different strain rates, but stress is unaffected by this. As a material, Poisson's ratio changes with material type hence Poisson's ratio gets affected by strain values.

• We know strain rate changes as increases by an increment of temperature, at high temperature, internal friction of material getting reduced and this reduction in friction resistance also decreases; by this the overall changes in strain is getting reduced gradually. Hence, a gradual decrement of the Poisson's ratio occurs by the temperature increment.

• Yes, in some exceptions, Poisson's ratio value for auxetic type materials, counterintuitive mechanical behavior material shows the negative value during the stretch when tensile force is applied over it. This is due to a reduction in cross-section also. For example, human tissue has Poisson's ratio as (-1).

• Zero Poisson's ratio means that material has a high chance to stop deformation like from compression or tension or minimum negligible deformation occurs. Like cork has zero Poisson's ratio, which is by it in the bottle as a stopper.

• We know the Poisson's ratio has a maximum value is 0.5 for elastic material or isotropic material. But for certain types of material that exceed the value of 0.5 also from 1, that type of material is known as an anisotropic material.

Example; Polyurethane foam.

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