Poisson's Ratio given max circumferential stress in solid disc Calculator

✖Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.ⓘ Circumferential Stress [σ_c]			+10% -10%
✖Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.ⓘ Density Of Disc [ρ]			+10% -10%
✖The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.ⓘ Angular Velocity [ω]			+10% -10%
✖Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.ⓘ Outer Radius Disc [r_outer]			+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 given max circumferential stress in solid disc [𝛎]

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Poisson's Ratio given max circumferential stress in solid disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
𝛎 = ((8*σ_c)/(ρ*(ω^2)*(r_outer^2)))-3
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.
Circumferential Stress - (Measured in Pascal) - Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.
Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Outer Radius Disc - (Measured in Meter) - Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.

STEP 1: Convert Input(s) to Base Unit

Circumferential 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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

𝛎 = 0.936759889140842

STEP 3: Convert Result to Output's Unit

0.936759889140842 --> No Conversion Required

FINAL ANSWER

0.936759889140842 ≈ 0.93676 <-- Poisson's Ratio

(Calculation completed in 00.004 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 max circumferential stress in solid disc

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National Institute Of Technology (NIT), Hamirpur

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< Stresses in Disc Calculators

Circumferential stress in solid disc

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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 max circumferential stress in solid disc Formula

LaTeX Go

Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
𝛎 = ((8*σ_c)/(ρ*(ω^2)*(r_outer^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 max circumferential stress in solid disc?

Poisson's Ratio given max circumferential stress in solid disc calculator uses Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3 to calculate the Poisson's Ratio, The Poisson's Ratio given max circumferential stress in solid disc 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 max circumferential stress in solid disc using this online calculator? To use this online calculator for Poisson's Ratio given max circumferential stress in solid disc, enter Circumferential Stress (σ_c), Density Of Disc (ρ), Angular Velocity (ω) & Outer Radius Disc (r_outer) and hit the calculate button. Here is how the Poisson's Ratio given max circumferential stress in solid disc calculation can be explained with given input values -> 0.93676 = ((8*100)/(2*(11.2^2)*(0.9^2)))-3.

FAQ

What is Poisson's Ratio given max circumferential stress in solid disc?

The Poisson's Ratio given max circumferential stress in solid disc 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_c)/(ρ*(ω^2)*(r_outer^2)))-3 or Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3. Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius, Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc, The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time & Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.

How to calculate Poisson's Ratio given max circumferential stress in solid disc?

The Poisson's Ratio given max circumferential stress in solid disc 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*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3. To calculate Poisson's Ratio given max circumferential stress in solid disc, you need Circumferential Stress (σ_c), Density Of Disc (ρ), Angular Velocity (ω) & Outer Radius Disc (r_outer). With our tool, you need to enter the respective value for Circumferential Stress, Density Of Disc, Angular Velocity & Outer Radius Disc 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 Circumferential Stress, Density Of Disc, Angular Velocity & Outer Radius Disc. 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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