Circumferential stress at center of solid disc 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%

✖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 at center of solid disc [σ_c]

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Circumferential stress at center of solid disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8
σ_c = (ρ*(ω^2)*(3+𝛎)*(r_outer^2))/8
This formula uses 5 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.

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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

σ_c = 83.82528

STEP 3: Convert Result to Output's Unit

83.82528 Pascal -->83.82528 Newton per Square Meter (Check conversion here)

FINAL ANSWER

83.82528 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 » Mechanical » Stresses in Disc » Circumferential stress at center of 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

Circumferential stress at center of solid disc Formula

LaTeX Go

Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8
σ_c = (ρ*(ω^2)*(3+𝛎)*(r_outer^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 Circumferential stress at center of solid disc?

Circumferential stress at center of solid disc calculator uses Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8 to calculate the Circumferential Stress, The Circumferential stress at center of solid disc 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 at center of solid disc using this online calculator? To use this online calculator for Circumferential stress at center of solid disc, enter Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Outer Radius Disc (r_outer) and hit the calculate button. Here is how the Circumferential stress at center of solid disc calculation can be explained with given input values -> 83.82528 = (2*(11.2^2)*(3+0.3)*(0.9^2))/8.

FAQ

What is Circumferential stress at center of solid disc?

The Circumferential stress at center of solid disc 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))/8 or Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^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.

How to calculate Circumferential stress at center of solid disc?

The Circumferential stress at center of solid disc 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))/8. To calculate Circumferential stress at center of solid disc, you need Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Outer Radius Disc (r_outer). With our tool, you need to enter the respective value for Density Of Disc, Angular Velocity, Poisson's Ratio & 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 Circumferential Stress?

In this formula, Circumferential Stress uses Density Of Disc, Angular Velocity, Poisson's Ratio & Outer Radius Disc. 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)-(1+(3*Poisson's Ratio)*Radius of Element^2)))/8
Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8

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