Circumferential stress in solid disc given Outer radius Calculator

✖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%
✖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 [𝛎]			+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%

✖Circumferential stress, also known as hoop stress, is a type of normal stress that acts tangentially to the circumference of a cylindrical or spherical object.ⓘ Circumferential stress in solid disc given Outer radius [σ_c]

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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, also known as hoop stress, is a type of normal stress that acts tangentially to the circumference of a cylindrical or spherical object.
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.
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.
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

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 00.020 seconds)

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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

Circumferential stress in solid disc given Outer radius Formula

LaTeX Go

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 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, 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, 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 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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