Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain Calculator

✖Hoop Stress on thick shell is the circumferential stress in a cylinder.ⓘ Hoop Stress on thick shell [σ_θ]			+10% -10%
✖Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.ⓘ Modulus of Elasticity Of Thick Shell [E]			+10% -10%
✖Tensile Strain is the ratio of change in length to original length.ⓘ Tensile Strain [ε_tensile]			+10% -10%
✖Radial Pressure is pressure towards or away from the central axis of a component.ⓘ Radial Pressure [P_v]			+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 for Thick Spherical Shell given Tensile Radial Strain [𝛎]

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Formula

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Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain

Formula

`"𝛎" = (1/(2*"σ"_{"θ"}))*((-"E"*"ε"_{"tensile"})-"P"_{"v"})`

Example

`"-393.5"=(1/(2*"0.002MPa"))*((-"2.6MPa"*"0.6")-"0.014MPa/m²")`

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Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain Solution

STEP 0: Pre-Calculation Summary

Formula Used

Poisson's Ratio = (1/(2*Hoop Stress on thick shell))*((-Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)
𝛎 = (1/(2*σ_θ))*((-E*ε_tensile)-P_v)
This formula uses 5 Variables

Variables Used

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.
Hoop Stress on thick shell - (Measured in Pascal) - Hoop Stress on thick shell is the circumferential stress in a cylinder.
Modulus of Elasticity Of Thick Shell - (Measured in Pascal) - Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.
Tensile Strain - Tensile Strain is the ratio of change in length to original length.
Radial Pressure - (Measured in Pascal per Square Meter) - Radial Pressure is pressure towards or away from the central axis of a component.

STEP 1: Convert Input(s) to Base Unit

Hoop Stress on thick shell: 0.002 Megapascal --> 2000 Pascal (Check conversion here)
Modulus of Elasticity Of Thick Shell: 2.6 Megapascal --> 2600000 Pascal (Check conversion here)
Tensile Strain: 0.6 --> No Conversion Required
Radial Pressure: 0.014 Megapascal per Square Meter --> 14000 Pascal per Square Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝛎 = (1/(2*σ_θ))*((-E*ε_tensile)-P_v) --> (1/(2*2000))*((-2600000*0.6)-14000)

Evaluating ... ...

𝛎 = -393.5

STEP 3: Convert Result to Output's Unit

-393.5 --> No Conversion Required

FINAL ANSWER

-393.5 <-- Poisson's Ratio

(Calculation completed in 00.004 seconds)

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< 24 Thick Spherical Shells Calculators

Hoop stress given tensile circumferential strain for thick spherical shell

Go Hoop Stress on thick shell = ((Circumferential strain*Modulus of Elasticity Of Thick Shell)-(Radial Pressure/Mass Of Shell))/((Mass Of Shell-1)/Mass Of Shell)

Radial pressure given tensile circumferential strain for thick spherical shell

Go Radial Pressure = ((Circumferential strain*Modulus of Elasticity Of Thick Shell)-Hoop Stress on thick shell*((Mass Of Shell-1)/Mass Of Shell))*Mass Of Shell

Modulus of elasticity given tensile circumferential strain for thick spherical shell

Go Adjusted design value = (Hoop Stress on thick shell*((Mass Of Shell-1)/Mass Of Shell)+(Radial Pressure/Mass Of Shell))/Circumferential strain

Tensile circumferential strain for thick spherical shell

Go Circumferential strain = (Hoop Stress on thick shell*((Mass Of Shell-1)/Mass Of Shell)+(Radial Pressure/Mass Of Shell))/Adjusted design value

Poisson's ratio for thick spherical shell given compressive radial strain

Go Poisson's Ratio = 1/((2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure))

Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain

Go Poisson's Ratio = (1/(2*Hoop Stress on thick shell))*((-Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)

Hoop stress on thick spherical shell given compressive radial strain and Poisson's ratio

Go Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)/(2*Poisson's Ratio)

Mass of thick spherical shell given compressive radial strain

Go Mass Of Shell = (2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)

Hoop stress on thick spherical shell given tensile radial strain and Poisson's ratio

Go Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)/(2*Poisson's Ratio)

Hoop stress on thick spherical shell given compressive radial strain

Go Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)*Mass Of Shell/2

Mass of thick spherical shell given tensile radial strain

Go Mass Of Shell = (2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)

Hoop stress on thick spherical shell given tensile radial strain

Go Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)*Mass Of Shell/2

Radial pressure on thick spherical shell given compressive radial strain and Poisson's ratio

Go Radial Pressure = (Adjusted design value*Compressive Strain)-(2*Hoop Stress on thick shell*Poisson's Ratio)

Compressive radial strain given Poisson's ratio for thick spherical shell

Go Compressive Strain = (Radial Pressure+(2*Hoop Stress on thick shell*Poisson's Ratio))/Adjusted design value

Modulus of elasticity given compressive radial strain and Poisson's ratio

Go Adjusted design value = (Radial Pressure+(2*Hoop Stress on thick shell*Poisson's Ratio))/Compressive Strain

Modulus of elasticity for thick spherical shell given compressive radial strain

Go Adjusted design value = (Radial Pressure+(2*Hoop Stress on thick shell/Mass Of Shell))/Compressive Strain

Radial pressure on thick spherical shell given compressive radial strain

Go Radial Pressure = (Adjusted design value*Compressive Strain)-(2*Hoop Stress on thick shell/Mass Of Shell)

Tensile radial strain given Poisson's ratio for thick spherical shell

Go Tensile Strain = ((Radial Pressure+(2*Hoop Stress on thick shell*Poisson's Ratio))/Adjusted design value)

Modulus of elasticity given tensile radial strain and Poisson's ratio

Go Adjusted design value = ((Radial Pressure+(2*Hoop Stress on thick shell*Poisson's Ratio))/Tensile Strain)

Compressive radial strain for thick spherical shells

Go Compressive Strain = (Radial Pressure+(2*Hoop Stress on thick shell/Mass Of Shell))/Adjusted design value

Radial pressure on thick spherical shell given tensile radial strain and Poisson's ratio

Go Radial Pressure = (Adjusted design value*Tensile Strain)-(2*Hoop Stress on thick shell*Poisson's Ratio)

Modulus of elasticity thick spherical shell given tensile radial strain

Go Adjusted design value = ((Radial Pressure+(2*Hoop Stress on thick shell/Mass Of Shell))/Tensile Strain)

Radial pressure on thick spherical shell given tensile radial strain

Go Radial Pressure = ((Adjusted design value*Tensile Strain)-(2*Hoop Stress on thick shell/Mass Of Shell))

Tensile radial strain for thick spherical shell

Go Tensile Strain = ((Radial Pressure+(2*Hoop Stress on thick shell/Mass Of Shell))/Adjusted design value)

Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain Formula

Poisson's Ratio = (1/(2*Hoop Stress on thick shell))*((-Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)
𝛎 = (1/(2*σ_θ))*((-E*ε_tensile)-P_v)

What is meant by hoop stress?

The hoop stress is the force over the area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall.

How to Calculate Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain?

Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain calculator uses Poisson's Ratio = (1/(2*Hoop Stress on thick shell))*((-Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure) to calculate the Poisson's Ratio, Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain formula is defined as the negative of the ratio of transverse strain to lateral or axial strain. Poisson's Ratio is denoted by 𝛎 symbol.

How to calculate Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain using this online calculator? To use this online calculator for Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain, enter Hoop Stress on thick shell (σ_θ), Modulus of Elasticity Of Thick Shell (E), Tensile Strain (ε_tensile) & Radial Pressure (P_v) and hit the calculate button. Here is how the Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain calculation can be explained with given input values -> -393.5 = (1/(2*2000))*((-2600000*0.6)-14000).

FAQ

What is Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain?

Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain formula is defined as the negative of the ratio of transverse strain to lateral or axial strain and is represented as 𝛎 = (1/(2*σ_θ))*((-E*ε_tensile)-P_v) or Poisson's Ratio = (1/(2*Hoop Stress on thick shell))*((-Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure). Hoop Stress on thick shell is the circumferential stress in a cylinder, Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it, Tensile Strain is the ratio of change in length to original length & Radial Pressure is pressure towards or away from the central axis of a component.

How to calculate Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain?

Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain formula is defined as the negative of the ratio of transverse strain to lateral or axial strain is calculated using Poisson's Ratio = (1/(2*Hoop Stress on thick shell))*((-Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure). To calculate Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain, you need Hoop Stress on thick shell (σ_θ), Modulus of Elasticity Of Thick Shell (E), Tensile Strain (ε_tensile) & Radial Pressure (P_v). With our tool, you need to enter the respective value for Hoop Stress on thick shell, Modulus of Elasticity Of Thick Shell, Tensile Strain & Radial Pressure 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 Poisson's Ratio?

In this formula, Poisson's Ratio uses Hoop Stress on thick shell, Modulus of Elasticity Of Thick Shell, Tensile Strain & Radial Pressure. We can use 1 other way(s) to calculate the same, which is/are as follows -

Poisson's Ratio = 1/((2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure))

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