Radial 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%

✖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 in solid disc given Outer radius [σ_r]

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Radial stress in solid disc given Outer radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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_r = (ρ*(ω^2)*(3+𝛎)*((r_outer^2)-(R^2)))/8 --> (2*(11.2^2)*(3+0.3)*((0.9^2)-(0.005^2)))/8

Evaluating ... ...

σ_r = 83.8226928

STEP 3: Convert Result to Output's Unit

83.8226928 Pascal -->83.8226928 Newton per Square Meter (Check conversion here)

FINAL ANSWER

83.8226928 ≈ 83.82269 Newton per Square Meter <-- Radial 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 » Mechanical » Stresses in Disc » Radial stress in solid disc given Outer radius

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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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

Radial stress in solid disc given Outer radius Formula

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

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 Radial stress in solid disc given Outer radius?

Radial stress in solid disc given Outer radius calculator uses Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))/8 to calculate the Radial Stress, The Radial stress in solid disc given Outer radius formula is defined as stress towards or away from the central axis of a component. Radial Stress is denoted by σ_r symbol.

How to calculate Radial stress in solid disc given Outer radius using this online calculator? To use this online calculator for Radial 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 Radial stress in solid disc given Outer radius calculation can be explained with given input values -> 83.82269 = (2*(11.2^2)*(3+0.3)*((0.9^2)-(0.005^2)))/8.

FAQ

What is Radial stress in solid disc given Outer radius?

The Radial stress in solid disc given Outer radius formula is defined as stress towards or away from the central axis of a component and is represented as σ_r = (ρ*(ω^2)*(3+𝛎)*((r_outer^2)-(R^2)))/8 or Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(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 Radial stress in solid disc given Outer radius?

The Radial stress in solid disc given Outer radius formula is defined as stress towards or away from the central axis of a component is calculated using Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))/8. To calculate Radial 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 Radial Stress?

In this formula, Radial 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 -

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

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