Circumferential stress in solid disc Calculator

✖Constant at boundary condition is a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain.ⓘ Constant at Boundary Condition [C₁]			+10% -10%
✖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%
✖Disc radius is the distance from the center of the disc to any point on its circumference.ⓘ Disc Radius [r_disc]			+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%

✖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 [σ_c]

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Circumferential stress in solid disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Circumferential Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8)
σ_c = (C₁/2)-((ρ*(ω^2)*(r_disc^2)*((3*𝛎)+1))/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.
Constant at Boundary Condition - Constant at boundary condition is a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain.
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.
Disc Radius - (Measured in Meter) - Disc radius is the distance from the center of the disc to any point on its circumference.
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.

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
Disc Radius: 1000 Millimeter --> 1 Meter (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_c = (C₁/2)-((ρ*(ω^2)*(r_disc^2)*((3*𝛎)+1))/8) --> (300/2)-((2*(11.2^2)*(1^2)*((3*0.3)+1))/8)

Evaluating ... ...

σ_c = 90.416

STEP 3: Convert Result to Output's Unit

90.416 Pascal -->90.416 Newton per Square Meter (Check conversion here)

FINAL ANSWER

90.416 Newton per Square Meter <-- Circumferential Stress

(Calculation completed in 00.012 seconds)

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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 in solid disc Formula

LaTeX Go

Circumferential Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8)
σ_c = (C₁/2)-((ρ*(ω^2)*(r_disc^2)*((3*𝛎)+1))/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 in solid disc?

Circumferential stress in solid disc calculator uses Circumferential Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8) to calculate the Circumferential Stress, The Circumferential stress in 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 in solid disc using this online calculator? To use this online calculator for Circumferential stress in solid disc, enter Constant at Boundary Condition (C₁), Density Of Disc (ρ), Angular Velocity (ω), Disc Radius (r_disc) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Circumferential stress in solid disc calculation can be explained with given input values -> 90.416 = (300/2)-((2*(11.2^2)*(1^2)*((3*0.3)+1))/8).

FAQ

What is Circumferential stress in solid disc?

The Circumferential stress in solid disc formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction and is represented as σ_c = (C₁/2)-((ρ*(ω^2)*(r_disc^2)*((3*𝛎)+1))/8) or 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 is a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain, 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, Disc radius is the distance from the center of the disc to any point on its circumference & 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.

How to calculate Circumferential stress in solid disc?

The Circumferential stress in solid disc formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction is calculated using Circumferential Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8). To calculate Circumferential stress in solid disc, you need Constant at Boundary Condition (C₁), Density Of Disc (ρ), Angular Velocity (ω), Disc Radius (r_disc) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Constant at Boundary Condition, Density Of Disc, Angular Velocity, Disc Radius & Poisson's Ratio 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 Constant at Boundary Condition, Density Of Disc, Angular Velocity, Disc Radius & Poisson's Ratio. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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