Young's Modulus using Poisson's Ratio Calculator

✖The Tensile Stress is the external force per unit area of the material resulting in the stretch of the material.ⓘ Tensile Stress [σ_t]			+10% -10%
✖Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5.ⓘ Poisson's Ratio [𝛎]			+10% -10%
✖The Volumetric Strain is the ratio of change in volume to original volume.ⓘ Volumetric Strain [ε_v]			+10% -10%

✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus using Poisson's Ratio [E]

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Formula

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Young's Modulus using Poisson's Ratio

Formula

`"E" = (3*"σ"_{"t"}*(1-2*"𝛎"))/"ε"_{"v"}`

Example

`"199200MPa"=(3*"16.6MPa"*(1-2*"0.3"))/"0.0001"`

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Young's Modulus using Poisson's Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Young's Modulus = (3*Tensile Stress*(1-2*Poisson's Ratio))/Volumetric Strain
E = (3*σ_t*(1-2*𝛎))/ε_v
This formula uses 4 Variables

Variables Used

Young's Modulus - (Measured in Pascal) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Tensile Stress - (Measured in Pascal) - The Tensile Stress is the external force per unit area of the material resulting in the stretch of the material.
Poisson's Ratio - Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5.
Volumetric Strain - The Volumetric Strain is the ratio of change in volume to original volume.

STEP 1: Convert Input(s) to Base Unit

Tensile Stress: 16.6 Megapascal --> 16600000 Pascal (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required
Volumetric Strain: 0.0001 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E = (3*σ_t*(1-2*𝛎))/ε_v --> (3*16600000*(1-2*0.3))/0.0001

Evaluating ... ...

E = 199200000000

STEP 3: Convert Result to Output's Unit

199200000000 Pascal -->199200 Megapascal (Check conversion here)

FINAL ANSWER

199200 Megapascal <-- Young's Modulus

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Stress and Strain » Elastic Constants » Volumetric Strain » Young's Modulus using Poisson's Ratio

Credits

Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

Vaibhav Malani has created this Calculator and 600+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Calculator and 2500+ more calculators!

< 17 Volumetric Strain Calculators

Volumetric Strain given Change in Length, Breadth and Width

Go Volumetric Strain = Change in Length/Length of Section+Change in Breadth/Breadth of Bar+Change in Depth/Depth of Bar

Volumetric Strain given Change in Length

Go Volumetric Strain = (Change in Length/Length of Section)*(1-2*Poisson's Ratio)

Volumetric Strain using Young's Modulus and Poisson's Ratio

Go Volumetric Strain = (3*Tensile Stress*(1-2*Poisson's Ratio))/Young's Modulus

Young's Modulus using Poisson's Ratio

Go Young's Modulus = (3*Tensile Stress*(1-2*Poisson's Ratio))/Volumetric Strain

Poisson's Ratio using Bulk Modulus and Young's Modulus

Go Poisson's Ratio = (3*Bulk Modulus-Young's Modulus)/(6*Bulk Modulus)

Poisson's Ratio given Volumetric Strain and Longitudinal Strain

Go Poisson's Ratio = 1/2*(1-Volumetric Strain/Longitudinal Strain)

Longitudinal Strain given Volumetric Strain and Poisson's Ratio

Go Longitudinal Strain = Volumetric Strain/(1-2*Poisson's Ratio)

Volumetric Strain of Cylindrical Rod using Poisson's Ratio

Go Volumetric Strain = Longitudinal Strain*(1-2*Poisson's Ratio)

Lateral Strain given Volumetric and Longitudinal Strain

Go Lateral Strain = -(Longitudinal Strain-Volumetric Strain)/2

Longitudinal Strain given Volumetric and Lateral Strain

Go Longitudinal Strain = Volumetric Strain-(2*Lateral Strain)

Volumetric Strain of Cylindrical Rod

Go Volumetric Strain = Longitudinal Strain-2*(Lateral Strain)

Volumetric Strain given Longitudinal and Lateral Strain

Go Volumetric Strain = Longitudinal Strain+2*Lateral Strain

Bulk Modulus using Young's Modulus

Go Bulk Modulus = Young's Modulus/(3*(1-2*Poisson's Ratio))

Young's Modulus using Bulk Modulus

Go Young's Modulus = 3*Bulk Modulus*(1-2*Poisson's Ratio)

Direct Stress for given Bulk Modulus and Volumetric Strain

Go Direct Stress = Bulk Modulus*Volumetric Strain

Volumetric Strain given Bulk Modulus

Go Volumetric Strain = Direct Stress/Bulk Modulus

Bulk Modulus given Direct Stress

Go Bulk Modulus = Direct Stress/Volumetric Strain

< 5 Modulus of Elasticity Calculators

Young's Modulus of Elasticity as per ACI 318 Building Code Requirements for Reinforced Concrete

Go Young's Modulus = (Weight of Concrete^1.5)*0.043*sqrt(28 Day Compressive Strength of Concrete)

Young's Modulus using Poisson's Ratio

Go Young's Modulus = (3*Tensile Stress*(1-2*Poisson's Ratio))/Volumetric Strain

Modulus of Elasticity of Normal Weight and Density Concrete in USCS Units

Go Modulus of Elasticity of Concrete = 57000*sqrt(28 Day Compressive Strength of Concrete)

Young's Modulus of Concrete

Go Modulus of Elasticity of Concrete = 5000*(sqrt(Characteristic Compressive Strength))

Young's Modulus using Bulk Modulus

Go Young's Modulus = 3*Bulk Modulus*(1-2*Poisson's Ratio)

< 17 Volumetric Strain Calculators

Volumetric Strain given Change in Length, Breadth and Width

Go Volumetric Strain = Change in Length/Length of Section+Change in Breadth/Breadth of Bar+Change in Depth/Depth of Bar

Volumetric Strain given Change in Length

Go Volumetric Strain = (Change in Length/Length of Section)*(1-2*Poisson's Ratio)

Volumetric Strain using Young's Modulus and Poisson's Ratio

Go Volumetric Strain = (3*Tensile Stress*(1-2*Poisson's Ratio))/Young's Modulus

Young's Modulus using Poisson's Ratio

Go Young's Modulus = (3*Tensile Stress*(1-2*Poisson's Ratio))/Volumetric Strain

Poisson's Ratio using Bulk Modulus and Young's Modulus

Go Poisson's Ratio = (3*Bulk Modulus-Young's Modulus)/(6*Bulk Modulus)

Poisson's Ratio given Volumetric Strain and Longitudinal Strain

Go Poisson's Ratio = 1/2*(1-Volumetric Strain/Longitudinal Strain)

Longitudinal Strain given Volumetric Strain and Poisson's Ratio

Go Longitudinal Strain = Volumetric Strain/(1-2*Poisson's Ratio)

Volumetric Strain of Cylindrical Rod using Poisson's Ratio

Go Volumetric Strain = Longitudinal Strain*(1-2*Poisson's Ratio)

Lateral Strain given Volumetric and Longitudinal Strain

Go Lateral Strain = -(Longitudinal Strain-Volumetric Strain)/2

Longitudinal Strain given Volumetric and Lateral Strain

Go Longitudinal Strain = Volumetric Strain-(2*Lateral Strain)

Volumetric Strain of Cylindrical Rod

Go Volumetric Strain = Longitudinal Strain-2*(Lateral Strain)

Volumetric Strain given Longitudinal and Lateral Strain

Go Volumetric Strain = Longitudinal Strain+2*Lateral Strain

Bulk Modulus using Young's Modulus

Go Bulk Modulus = Young's Modulus/(3*(1-2*Poisson's Ratio))

Young's Modulus using Bulk Modulus

Go Young's Modulus = 3*Bulk Modulus*(1-2*Poisson's Ratio)

Direct Stress for given Bulk Modulus and Volumetric Strain

Go Direct Stress = Bulk Modulus*Volumetric Strain

Volumetric Strain given Bulk Modulus

Go Volumetric Strain = Direct Stress/Bulk Modulus

Bulk Modulus given Direct Stress

Go Bulk Modulus = Direct Stress/Volumetric Strain

Young's Modulus using Poisson's Ratio Formula

Young's Modulus = (3*Tensile Stress*(1-2*Poisson's Ratio))/Volumetric Strain
E = (3*σ_t*(1-2*𝛎))/ε_v

What is Young's Modulus?

Stress is proportional to strain within elastic limits. The constant of proportionality is called young's modulus. It is the ratio of stress to strain.

How to Calculate Young's Modulus using Poisson's Ratio?

Young's Modulus using Poisson's Ratio calculator uses Young's Modulus = (3*Tensile Stress*(1-2*Poisson's Ratio))/Volumetric Strain to calculate the Young's Modulus, The Young's Modulus using Poisson's Ratio formula is defined as three times the ratio of tensile stress to volumetric strain multiplier by the term one minus twice of Poisson's ratio. Young's Modulus is denoted by E symbol.

How to calculate Young's Modulus using Poisson's Ratio using this online calculator? To use this online calculator for Young's Modulus using Poisson's Ratio, enter Tensile Stress (σ_t), Poisson's Ratio (𝛎) & Volumetric Strain (ε_v) and hit the calculate button. Here is how the Young's Modulus using Poisson's Ratio calculation can be explained with given input values -> 0.1992 = (3*16600000*(1-2*0.3))/0.0001.

FAQ

What is Young's Modulus using Poisson's Ratio?

The Young's Modulus using Poisson's Ratio formula is defined as three times the ratio of tensile stress to volumetric strain multiplier by the term one minus twice of Poisson's ratio and is represented as E = (3*σ_t*(1-2*𝛎))/ε_v or Young's Modulus = (3*Tensile Stress*(1-2*Poisson's Ratio))/Volumetric Strain. The Tensile Stress is the external force per unit area of the material resulting in the stretch of the material, Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5 & The Volumetric Strain is the ratio of change in volume to original volume.

How to calculate Young's Modulus using Poisson's Ratio?

The Young's Modulus using Poisson's Ratio formula is defined as three times the ratio of tensile stress to volumetric strain multiplier by the term one minus twice of Poisson's ratio is calculated using Young's Modulus = (3*Tensile Stress*(1-2*Poisson's Ratio))/Volumetric Strain. To calculate Young's Modulus using Poisson's Ratio, you need Tensile Stress (σ_t), Poisson's Ratio (𝛎) & Volumetric Strain (ε_v). With our tool, you need to enter the respective value for Tensile Stress, Poisson's Ratio & Volumetric Strain and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Young's Modulus?

In this formula, Young's Modulus uses Tensile Stress, Poisson's Ratio & Volumetric Strain. We can use 4 other way(s) to calculate the same, which is/are as follows -

Young's Modulus = 3*Bulk Modulus*(1-2*Poisson's Ratio)
Young's Modulus = (Weight of Concrete^1.5)*0.043*sqrt(28 Day Compressive Strength of Concrete)
Young's Modulus = 3*Bulk Modulus*(1-2*Poisson's Ratio)
Young's Modulus = 3*Bulk Modulus*(1-2*Poisson's Ratio)

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