Circumferential stress in solid disc given Outer radius Calculator

✖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%
✖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%
✖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%
✖The Radius of Element is the radius of the element considered in the disc at radius r from the centre.ⓘ Radius of Element [r]			+10% -10%

✖Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.ⓘ Circumferential stress in solid disc given Outer radius [σ_c]

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Circumferential stress in solid disc given Outer radius

Formula

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

Example

`"52.46457N/m²"=(("2kg/m³"*(("11.2rad/s")^2))*(((3+"0.3")*("900mm")^2)-(1+(3*"0.3")*("5mm")^2)))/8`

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Circumferential stress in solid disc given Outer radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
σ_c = ((ρ*(ω^2))*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*r^2)))/8
This formula uses 6 Variables

Variables Used

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.
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.
Outer Radius Disc - (Measured in Meter) - Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.
Radius of Element - (Measured in Meter) - The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

STEP 1: Convert Input(s) to Base Unit

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
Poisson's Ratio: 0.3 --> 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

σ_c = ((ρ*(ω^2))*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*r^2)))/8 --> ((2*(11.2^2))*(((3+0.3)*0.9^2)-(1+(3*0.3)*0.005^2)))/8

Evaluating ... ...

σ_c = 52.4645744

STEP 3: Convert Result to Output's Unit

52.4645744 Pascal -->52.4645744 Newton per Square Meter (Check conversion here)

FINAL ANSWER

52.4645744 ≈ 52.46457 Newton per Square Meter <-- Circumferential Stress

(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 » Circumferential stress in solid disc given Outer radius

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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

Maximum Radial Stress in solid disc

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

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

Circumferential stress in solid disc given Outer radius Formula

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 Circumferential stress in solid disc given Outer radius?

Circumferential stress in solid disc given Outer radius calculator uses 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 to calculate the Circumferential Stress, The Circumferential stress in solid disc given Outer radius formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction. Circumferential Stress is denoted by σ_c symbol.

How to calculate Circumferential stress in solid disc given Outer radius using this online calculator? To use this online calculator for Circumferential stress in solid disc given Outer radius, enter Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (r) and hit the calculate button. Here is how the Circumferential stress in solid disc given Outer radius calculation can be explained with given input values -> 52.46457 = ((2*(11.2^2))*(((3+0.3)*0.9^2)-(1+(3*0.3)*0.005^2)))/8.

FAQ

What is Circumferential stress in solid disc given Outer radius?

The Circumferential stress in solid disc given Outer radius formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction and is represented as σ_c = ((ρ*(ω^2))*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*r^2)))/8 or 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. 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, 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, Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary & The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

How to calculate Circumferential stress in solid disc given Outer radius?

The Circumferential stress in solid disc given Outer radius formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction is calculated using 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. To calculate Circumferential stress in solid disc given Outer radius, you need Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (r). With our tool, you need to enter the respective value for Density Of Disc, Angular Velocity, Poisson's Ratio, 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 Circumferential Stress?

In this formula, Circumferential Stress uses Density Of Disc, Angular Velocity, Poisson's Ratio, Outer Radius Disc & Radius of Element. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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