Outer radius of disc given max circumferential stress in solid disc Calculator

✖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 [σ_c]			+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%
✖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 of disc given max circumferential stress in solid disc [r_outer]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Strength of Materials Formula PDF PDF Image

Outer radius of disc given max circumferential stress in solid disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))
r_outer = sqrt((8*σ_c)/(ρ*(ω^2)*(3+𝛎)))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Outer Radius Disc - (Measured in Meter) - Outer radius disc is the distance from the center of the disc to its outer edge or boundary.
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.

STEP 1: Convert Input(s) to Base Unit

Circumferential Stress: 100 Newton per Square Meter --> 100 Pascal (Check conversion here)
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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_outer = sqrt((8*σ_c)/(ρ*(ω^2)*(3+𝛎))) --> sqrt((8*100)/(2*(11.2^2)*(3+0.3)))

Evaluating ... ...

r_outer = 0.983003361719965

STEP 3: Convert Result to Output's Unit

0.983003361719965 Meter -->983.003361719965 Millimeter (Check conversion here)

FINAL ANSWER

983.003361719965 ≈ 983.0034 Millimeter <-- Outer Radius Disc

(Calculation completed in 00.105 seconds)

You are here -

Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Solid Disc » Mechanical » Radius of Disc » Outer radius of disc given max circumferential stress in solid disc

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

Payal Priya has verified this Calculator and 1900+ more calculators!

< Radius of Disc Calculators

Outer radius of disc given Circumferential stress

LaTeX Go Outer Radius Disc = sqrt(((8*Circumferential Stress)/((Density Of Disc*(Angular Velocity^2))*((1+(3*Poisson's Ratio)*Radius of Element^2))))/(3+Poisson's Ratio))

Disc outer radius given Radial stress in solid disc

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

Outer radius of disc given Constant at boundary condition for circular disc

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

Outer radius of disc given max circumferential stress in solid disc

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

Outer radius of disc given max circumferential stress in solid disc Formula

LaTeX Go

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

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 Outer radius of disc given max circumferential stress in solid disc?

Outer radius of disc given max circumferential stress in solid disc calculator uses Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio))) to calculate the Outer Radius Disc, The Outer radius of disc given max circumferential stress in solid disc formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface. Outer Radius Disc is denoted by r_outer symbol.

How to calculate Outer radius of disc given max circumferential stress in solid disc using this online calculator? To use this online calculator for Outer radius of disc given max circumferential stress in solid disc, enter Circumferential Stress (σ_c), Density Of Disc (ρ), Angular Velocity (ω) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Outer radius of disc given max circumferential stress in solid disc calculation can be explained with given input values -> 983003.4 = sqrt((8*100)/(2*(11.2^2)*(3+0.3))).

FAQ

What is Outer radius of disc given max circumferential stress in solid disc?

The Outer radius of disc given max circumferential stress in solid disc formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface and is represented as r_outer = sqrt((8*σ_c)/(ρ*(ω^2)*(3+𝛎))) or Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio))). 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 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.

How to calculate Outer radius of disc given max circumferential stress in solid disc?

The Outer radius of disc given max circumferential stress in solid disc formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface is calculated using Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio))). To calculate Outer radius of disc given max circumferential stress in solid disc, you need Circumferential Stress (σ_c), Density Of Disc (ρ), Angular Velocity (ω) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Circumferential Stress, Density Of Disc, Angular Velocity & 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 Outer Radius Disc?

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

Outer Radius Disc = sqrt(((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))+(Radius of Element^2))
Outer Radius Disc = sqrt(((8*Circumferential Stress)/((Density Of Disc*(Angular Velocity^2))*((1+(3*Poisson's Ratio)*Radius of Element^2))))/(3+Poisson's Ratio))
Outer Radius Disc = sqrt((8*Constant at Boundary Condition)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))

Home

FREE PDFs

🔍 Search