Poisson's ratio given Radial stress in solid disc and outer radius Calculator

✖Radial stress refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis.ⓘ Radial Stress [σ_r]			+10% -10%
✖Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc.ⓘ Density Of Disc [ρ]			+10% -10%
✖Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time.ⓘ Angular Velocity [ω]			+10% -10%
✖Outer radius disc is the distance from the center of the disc to its outer edge or boundary.ⓘ Outer Radius Disc [r_outer]			+10% -10%
✖Radius of element often referred to as the atomic radius, is a measure of the size of an atom, typically defined as the distance from the center of the nucleus to the outermost shell of electrons.ⓘ Radius of Element [R]			+10% -10%

✖Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.ⓘ Poisson's ratio given Radial stress in solid disc and outer radius [𝛎]

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Poisson's ratio given Radial stress in solid disc and outer radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3
𝛎 = ((8*σ_r)/(ρ*(ω^2)*((r_outer^2)-(R^2))))-3
This formula uses 6 Variables

Variables Used

Poisson's Ratio - Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.
Radial Stress - (Measured in Pascal) - Radial stress refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc.
Angular Velocity - (Measured in Radian per Second) - Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time.
Outer Radius Disc - (Measured in Meter) - Outer radius disc is the distance from the center of the disc to its outer edge or boundary.
Radius of Element - (Measured in Meter) - Radius of element often referred to as the atomic radius, is a measure of the size of an atom, typically defined as the distance from the center of the nucleus to the outermost shell of electrons.

STEP 1: Convert Input(s) to Base Unit

Radial Stress: 100 Newton per Square Meter --> 100 Pascal (Check conversion here)
Density Of Disc: 2 Kilogram per Cubic Meter --> 2 Kilogram per Cubic Meter No Conversion Required
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required
Outer Radius Disc: 900 Millimeter --> 0.9 Meter (Check conversion here)
Radius of Element: 5 Millimeter --> 0.005 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝛎 = ((8*σ_r)/(ρ*(ω^2)*((r_outer^2)-(R^2))))-3 --> ((8*100)/(2*(11.2^2)*((0.9^2)-(0.005^2))))-3

Evaluating ... ...

𝛎 = 0.93688139782596

STEP 3: Convert Result to Output's Unit

0.93688139782596 --> No Conversion Required

FINAL ANSWER

0.93688139782596 ≈ 0.936881 <-- Poisson's Ratio

(Calculation completed in 00.007 seconds)

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Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Solid Disc » Mechanical » Stresses in Disc » Poisson's ratio given Radial stress in solid disc and outer radius

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< Stresses in Disc Calculators

Circumferential stress in solid disc

Go Circumferential Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8)

Constant at boundary condition given Radial stress in solid disc

Go Constant at Boundary Condition = 2*(Radial Stress+((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8))

Radial stress in solid disc

Go Radial Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8)

Poisson's ratio given Radial stress in solid disc

Go Poisson's Ratio = ((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-3

Poisson's ratio given Radial stress in solid disc and outer radius Formula

Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3
𝛎 = ((8*σ_r)/(ρ*(ω^2)*((r_outer^2)-(R^2))))-3

What is radial and tangential stress?

The “Hoop Stress” or “Tangential Stress” acts on a line perpendicular to the “longitudinal “and the “radial stress;” this stress attempts to separate the pipe wall in the circumferential direction. This stress is caused by internal pressure.

How to Calculate Poisson's ratio given Radial stress in solid disc and outer radius?

Poisson's ratio given Radial stress in solid disc and outer radius calculator uses Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3 to calculate the Poisson's Ratio, The Poisson's ratio given Radial stress in solid disc and outer radius formula is defined as a measure of the Poisson effect, the phenomenon in which a material tends to expand in directions perpendicular to the direction of compression. Poisson's Ratio is denoted by 𝛎 symbol.

How to calculate Poisson's ratio given Radial stress in solid disc and outer radius using this online calculator? To use this online calculator for Poisson's ratio given Radial stress in solid disc and outer radius, enter Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω), Outer Radius Disc (r_outer) & Radius of Element (R) and hit the calculate button. Here is how the Poisson's ratio given Radial stress in solid disc and outer radius calculation can be explained with given input values -> 0.936881 = ((8*100)/(2*(11.2^2)*((0.9^2)-(0.005^2))))-3.

FAQ

What is Poisson's ratio given Radial stress in solid disc and outer radius?

The Poisson's ratio given Radial stress in solid disc and outer radius formula is defined as a measure of the Poisson effect, the phenomenon in which a material tends to expand in directions perpendicular to the direction of compression and is represented as 𝛎 = ((8*σ_r)/(ρ*(ω^2)*((r_outer^2)-(R^2))))-3 or Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3. Radial stress refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis, Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc, Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time, Outer radius disc is the distance from the center of the disc to its outer edge or boundary & Radius of element often referred to as the atomic radius, is a measure of the size of an atom, typically defined as the distance from the center of the nucleus to the outermost shell of electrons.

How to calculate Poisson's ratio given Radial stress in solid disc and outer radius?

The Poisson's ratio given Radial stress in solid disc and outer radius formula is defined as a measure of the Poisson effect, the phenomenon in which a material tends to expand in directions perpendicular to the direction of compression is calculated using Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3. To calculate Poisson's ratio given Radial stress in solid disc and outer radius, you need Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω), Outer Radius Disc (r_outer) & Radius of Element (R). With our tool, you need to enter the respective value for Radial Stress, Density Of Disc, Angular Velocity, Outer Radius Disc & Radius of Element 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 Radial Stress, Density Of Disc, Angular Velocity, Outer Radius Disc & Radius of Element. We can use 3 other way(s) to calculate the same, which is/are as follows -

Poisson's Ratio = ((((Constant at Boundary/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-3
Poisson's Ratio = (((((Constant at Boundary Condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-1)/3
Poisson's Ratio = ((8*Constant at Boundary Condition)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3

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