Poisson's ratio given constant at boundary condition for circular disc Calculator

✖Constant at boundary condition is value obtained for stress in solid disc.ⓘ Constant at boundary condition [C₁]			+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 constant at boundary condition for circular disc [𝛎]

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Formula

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Poisson's ratio given constant at boundary condition for circular disc

Formula

`"𝛎" = ((8*"C"_{"1"})/("ρ"*("ω"^2)*("r"_{"outer"}^2)))-3`

Example

`"8.81028"=((8*"300")/("2kg/m³"*(("11.2rad/s")^2)*(("900mm")^2)))-3`

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Poisson's ratio given constant at boundary condition for circular disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Poisson's Ratio = ((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
𝛎 = ((8*C₁)/(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.
Constant at boundary condition - Constant at boundary condition is value obtained for stress in solid disc.
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

Constant at boundary condition: 300 --> No Conversion Required
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*C₁)/(ρ*(ω^2)*(r_outer^2)))-3 --> ((8*300)/(2*(11.2^2)*(0.9^2)))-3

Evaluating ... ...

𝛎 = 8.81027966742253

STEP 3: Convert Result to Output's Unit

8.81027966742253 --> No Conversion Required

FINAL ANSWER

8.81027966742253 ≈ 8.81028 <-- Poisson's Ratio

(Calculation completed in 00.004 seconds)

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< 19 Expression for Stresses in Solid Disc Calculators

Circumferential stress in solid disc given Outer radius

Go Circumferential Stress = ((Density Of Disc*(Angular Velocity^2))*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2)))/8

Poisson's ratio given Circumferential stress in solid disc

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

Constant at boundary condition given Circumferential stress in solid disc

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

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 and outer radius

Go Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3

Radial stress in solid disc given Outer radius

Go Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))/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 constant at boundary condition for circular disc

Go Poisson's Ratio = ((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3

Constant at boundary condition for circular disc

Go Constant at boundary condition = (Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))/8

Poisson's ratio given Circumferential stress at center of solid disc

Go Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3

Poisson's Ratio given max circumferential stress in solid disc

Go Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3

Circumferential stress at center of solid disc

Go Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8

Maximum circumferential stress in solid disc

Go Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8

Poisson's ratio given Radial stress at center of solid disc

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

Poisson's ratio given maximum radial stress in solid disc

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

Radial stress at center of solid disc

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

Maximum Radial Stress in solid disc

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

Poisson's ratio given constant at boundary condition for circular disc Formula

Poisson's Ratio = ((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
𝛎 = ((8*C₁)/(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 constant at boundary condition for circular disc?

Poisson's ratio given constant at boundary condition for circular disc calculator uses Poisson's Ratio = ((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3 to calculate the Poisson's Ratio, The Poisson's ratio given constant at boundary condition for circular 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 constant at boundary condition for circular disc using this online calculator? To use this online calculator for Poisson's ratio given constant at boundary condition for circular disc, enter Constant at boundary condition (C₁), 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 constant at boundary condition for circular disc calculation can be explained with given input values -> 8.81028 = ((8*300)/(2*(11.2^2)*(0.9^2)))-3.

FAQ

What is Poisson's ratio given constant at boundary condition for circular disc?

The Poisson's ratio given constant at boundary condition for circular 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*C₁)/(ρ*(ω^2)*(r_outer^2)))-3 or Poisson's Ratio = ((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3. Constant at boundary condition is value obtained for stress in solid disc, 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 constant at boundary condition for circular disc?

The Poisson's ratio given constant at boundary condition for circular 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*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3. To calculate Poisson's ratio given constant at boundary condition for circular disc, you need Constant at boundary condition (C₁), Density Of Disc (ρ), Angular Velocity (ω) & Outer Radius Disc (r_outer). With our tool, you need to enter the respective value for Constant at boundary condition, 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 Constant at boundary condition, Density Of Disc, Angular Velocity & Outer Radius Disc. We can use 7 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*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3
Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3

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