Disc outer radius given Radial stress in solid disc Calculator

✖Radial Stress induced by a bending moment in a member of constant cross section.ⓘ Radial Stress [σ_r]			+10% -10%
✖Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.ⓘ Density Of Disc [ρ]			+10% -10%
✖The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.ⓘ Angular Velocity [ω]			+10% -10%
✖Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5.ⓘ Poisson's Ratio [𝛎]			+10% -10%
✖The Radius of Element is the radius of the element considered in the disc at radius r from the centre.ⓘ Radius of Element [r]			+10% -10%

✖Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.ⓘ Disc outer radius given Radial stress in solid disc [r_outer]

⎘ Copy

👎

Formula

✖

Disc outer radius given Radial stress in solid disc

Formula

`"r"_{"outer"} = sqrt(((8*"σ"_{"r"})/("ρ"*("ω"^2)*(3+"𝛎")))+("r"^2))`

Example

`"983.0161mm"=sqrt(((8*"100N/m²")/("2kg/m³"*(("11.2rad/s")^2)*(3+"0.3")))+(("5mm")^2))`

Calculator

LaTeX

Reset

👍

Download Strength of Materials Formula PDF

Disc outer radius given Radial stress in solid disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Outer Radius Disc = sqrt(((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))+(Radius of Element^2))
r_outer = sqrt(((8*σ_r)/(ρ*(ω^2)*(3+𝛎)))+(r^2))
This formula uses 1 Functions, 6 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 radius of the larger of the two concentric circles that form its boundary.
Radial Stress - (Measured in Pascal) - Radial Stress induced by a bending moment in a member of constant cross section.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.
Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Poisson's Ratio - Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5.
Radius of Element - (Measured in Meter) - The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

STEP 1: Convert Input(s) to Base Unit

Radial 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
Radius of Element: 5 Millimeter --> 0.005 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_outer = sqrt(((8*σ_r)/(ρ*(ω^2)*(3+𝛎)))+(r^2)) --> sqrt(((8*100)/(2*(11.2^2)*(3+0.3)))+(0.005^2))

Evaluating ... ...

r_outer = 0.983016077769205

STEP 3: Convert Result to Output's Unit

0.983016077769205 Meter -->983.016077769205 Millimeter (Check conversion here)

FINAL ANSWER

983.016077769205 ≈ 983.0161 Millimeter <-- Outer Radius Disc

(Calculation completed in 00.020 seconds)

You are here -

Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Solid Disc » Radius of Disc » Disc outer radius given Radial 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!

< 9 Radius of Disc Calculators

Outer radius of disc given Circumferential stress

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))

Radius of disc given Circumferential stress in solid disc

Go Disc Radius = sqrt((((Constant at boundary condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*((3*Poisson's Ratio)+1)))

Radius of Circular disc given Radial stress in solid disc

Go Disc Radius = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))

Disc outer radius given Radial stress in solid disc

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

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 Circumferential stress at center of solid disc

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

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

Outer radius of disc given Radial stress at center of solid disc

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

Outer radius of disc given Maximum radial stress in solid disc

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

Disc outer radius given Radial stress in solid disc Formula

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

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 Disc outer radius given Radial stress in solid disc?

Disc outer radius given Radial stress in solid disc calculator uses Outer Radius Disc = sqrt(((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))+(Radius of Element^2)) to calculate the Outer Radius Disc, The Disc outer radius given Radial 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 Disc outer radius given Radial stress in solid disc using this online calculator? To use this online calculator for Disc outer radius given Radial stress in solid disc, enter Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Radius of Element (r) and hit the calculate button. Here is how the Disc outer radius given Radial stress in solid disc calculation can be explained with given input values -> 983016.1 = sqrt(((8*100)/(2*(11.2^2)*(3+0.3)))+(0.005^2)).

FAQ

What is Disc outer radius given Radial stress in solid disc?

The Disc outer radius given Radial 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_r)/(ρ*(ω^2)*(3+𝛎)))+(r^2)) or Outer Radius Disc = sqrt(((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))+(Radius of Element^2)). Radial Stress induced by a bending moment in a member of constant cross section, Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc, The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time, Poisson's Ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.1 and 0.5 & The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

How to calculate Disc outer radius given Radial stress in solid disc?

The Disc outer radius given Radial 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*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))+(Radius of Element^2)). To calculate Disc outer radius given Radial stress in solid disc, you need Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Radius of Element (r). With our tool, you need to enter the respective value for Radial Stress, Density Of Disc, Angular Velocity, Poisson's Ratio & 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 Outer Radius Disc?

In this formula, Outer Radius Disc uses Radial Stress, Density Of Disc, Angular Velocity, Poisson's Ratio & Radius of Element. We can use 6 other way(s) to calculate the same, which is/are as follows -

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

Home

FREE PDFs

🔍 Search