Radius of disc given stresses on disc Calculator

✖Increase in radius is the increase in inner radius of outer cylinder of compound cylinder.ⓘ Increase in radius [R_i]			+10% -10%
✖Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.ⓘ Circumferential Stress [σ_c]			+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%
✖Radial Stress induced by a bending moment in a member of constant cross section.ⓘ Radial Stress [σ_r]			+10% -10%
✖Modulus Of Elasticity Of Disc is a quantity that measures disc's resistance to being deformed elastically when a stress is applied to it.ⓘ Modulus Of Elasticity Of Disc [E]			+10% -10%

✖Disc Radius is a radial line from the focus to any point of a curve.ⓘ Radius of disc given stresses on disc [r_disc]

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Formula

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Radius of disc given stresses on disc

Formula

`"r"_{"disc"} = "R"_{"i"}/(("σ"_{"c"}-("𝛎"*"σ"_{"r"}))/"E")`

Example

`"1.04mm"="6.5mm"/(("80N/m²"-("0.3"*"100N/m²"))/"8N/m²")`

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Radius of disc given stresses on disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Disc Radius = Increase in radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc)
r_disc = R_i/((σ_c-(𝛎*σ_r))/E)
This formula uses 6 Variables

Variables Used

Disc Radius - (Measured in Meter) - Disc Radius is a radial line from the focus to any point of a curve.
Increase in radius - (Measured in Meter) - Increase in radius is the increase in inner radius of outer cylinder of compound cylinder.
Circumferential Stress - (Measured in Pascal) - Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.
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.
Radial Stress - (Measured in Pascal) - Radial Stress induced by a bending moment in a member of constant cross section.
Modulus Of Elasticity Of Disc - (Measured in Pascal) - Modulus Of Elasticity Of Disc is a quantity that measures disc's resistance to being deformed elastically when a stress is applied to it.

STEP 1: Convert Input(s) to Base Unit

Increase in radius: 6.5 Millimeter --> 0.0065 Meter (Check conversion here)
Circumferential Stress: 80 Newton per Square Meter --> 80 Pascal (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required
Radial Stress: 100 Newton per Square Meter --> 100 Pascal (Check conversion here)
Modulus Of Elasticity Of Disc: 8 Newton per Square Meter --> 8 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_disc = R_i/((σ_c-(𝛎*σ_r))/E) --> 0.0065/((80-(0.3*100))/8)

Evaluating ... ...

r_disc = 0.00104

STEP 3: Convert Result to Output's Unit

0.00104 Meter -->1.04 Millimeter (Check conversion here)

FINAL ANSWER

1.04 Millimeter <-- Disc Radius

(Calculation completed in 00.020 seconds)

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Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Rotating Thin Disc » Radius of disc given stresses on disc

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< 21 Expression for Stresses in Rotating Thin Disc Calculators

Poisson's ratio given initial radial width of disc

Go Poisson's Ratio = (Radial Stress-((Increase in Radial Width/Initial Radial Width)*Modulus Of Elasticity Of Disc))/(Circumferential Stress)

Modulus of elasticity given initial radial width of disc

Go Modulus Of Elasticity Of Disc = (Radial Stress-(Poisson's Ratio*Circumferential Stress))/(Increase in Radial Width/Initial Radial Width)

Modulus of elasticity given radius of disc

Go Modulus Of Elasticity Of Disc = ((Circumferential Stress-(Poisson's Ratio*Radial Stress))/(Increase in radius/Disc Radius))

Increase in radius of disc given stresses

Go Increase in radius = ((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc)*Disc Radius

Radius of disc given stresses on disc

Go Disc Radius = Increase in radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc)

Poisson's ratio given radius of disc

Go Poisson's Ratio = (Circumferential Stress-((Increase in radius/Disc Radius)*Modulus Of Elasticity Of Disc))/Radial Stress

Poisson's ratio given circumferential strain on disc

Go Poisson's Ratio = (Circumferential Stress-(Circumferential strain*Modulus Of Elasticity Of Disc))/(Radial Stress)

Modulus of elasticity given circumferential strain on disc

Go Modulus Of Elasticity Of Disc = (Circumferential Stress-(Poisson's Ratio*Radial Stress))/Circumferential strain

Poisson's ratio given radial strain on disc

Go Poisson's Ratio = (Radial Stress-(Radial strain*Modulus Of Elasticity Of Disc))/(Circumferential Stress)

Modulus of elasticity given radial strain on disc

Go Modulus Of Elasticity Of Disc = (Radial Stress-(Poisson's Ratio*Circumferential Stress))/Radial strain

Angular speed of rotation for thin cylinder given hoop stress in thin cylinder

Go Angular Velocity = Hoop Stress in Disc/(Density Of Disc*Disc Radius)

Density of cylinder material given hoop stress (for thin cylinder)

Go Density Of Disc = Hoop Stress in Disc/(Angular Velocity*Disc Radius)

Mean radius of cylinder given hoop stress in thin cylinder

Go Disc Radius = Hoop Stress in Disc/(Density Of Disc*Angular Velocity)

Hoop stress in thin cylinder

Go Hoop Stress in Disc = Density Of Disc*Angular Velocity*Disc Radius

Initial circumference given circumferential strain for rotating thin disc

Go Initial circumference = Final Circumference/(Circumferential strain+1)

Final circumference given circumferential strain for rotating thin disc

Go Final Circumference = (Circumferential strain+1)*Initial circumference

Tangential velocity of cylinder given hoop stress in thin cylinder

Go Tangential Velocity = Hoop Stress in Disc/(Density Of Disc)

Density of material of cylinder given hoop stress and tangential velocity

Go Density Of Disc = Hoop Stress in Disc/Tangential Velocity

Hoop stress in thin cylinder given tangential velocity of cylinder

Go Hoop Stress in Disc = Tangential Velocity*Density Of Disc

Increase in radius given circumferential strain for rotating thin disc

Go Increase in radius = Circumferential strain*Disc Radius

Radius of disc given circumferential strain for rotating thin disc

Go Disc Radius = Increase in radius/Circumferential strain

Radius of disc given stresses on disc Formula

Disc Radius = Increase in radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc)
r_disc = R_i/((σ_c-(𝛎*σ_r))/E)

What is compression stress force?

Compression stress force is the stress that squeezes something. It is the stress component perpendicular to a given surface, such as a fault plane, that results from forces applied perpendicular to the surface or from remote forces transmitted through the surrounding rock.

How to Calculate Radius of disc given stresses on disc?

Radius of disc given stresses on disc calculator uses Disc Radius = Increase in radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc) to calculate the Disc Radius, The Radius of disc given stresses on disc formula is defined as line segment extending from the center of a circle or sphere to the circumference or bounding surface. Disc Radius is denoted by r_disc symbol.

How to calculate Radius of disc given stresses on disc using this online calculator? To use this online calculator for Radius of disc given stresses on disc, enter Increase in radius (R_i), Circumferential Stress (σ_c), Poisson's Ratio (𝛎), Radial Stress (σ_r) & Modulus Of Elasticity Of Disc (E) and hit the calculate button. Here is how the Radius of disc given stresses on disc calculation can be explained with given input values -> 1040 = 0.0065/((80-(0.3*100))/8).

FAQ

What is Radius of disc given stresses on disc?

The Radius of disc given stresses on disc formula is defined as line segment extending from the center of a circle or sphere to the circumference or bounding surface and is represented as r_disc = R_i/((σ_c-(𝛎*σ_r))/E) or Disc Radius = Increase in radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc). Increase in radius is the increase in inner radius of outer cylinder of compound cylinder, Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius, 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, Radial Stress induced by a bending moment in a member of constant cross section & Modulus Of Elasticity Of Disc is a quantity that measures disc's resistance to being deformed elastically when a stress is applied to it.

How to calculate Radius of disc given stresses on disc?

The Radius of disc given stresses on disc formula is defined as line segment extending from the center of a circle or sphere to the circumference or bounding surface is calculated using Disc Radius = Increase in radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc). To calculate Radius of disc given stresses on disc, you need Increase in radius (R_i), Circumferential Stress (σ_c), Poisson's Ratio (𝛎), Radial Stress (σ_r) & Modulus Of Elasticity Of Disc (E). With our tool, you need to enter the respective value for Increase in radius, Circumferential Stress, Poisson's Ratio, Radial Stress & Modulus Of Elasticity Of 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 Disc Radius?

In this formula, Disc Radius uses Increase in radius, Circumferential Stress, Poisson's Ratio, Radial Stress & Modulus Of Elasticity Of Disc. We can use 2 other way(s) to calculate the same, which is/are as follows -

Disc Radius = Hoop Stress in Disc/(Density Of Disc*Angular Velocity)
Disc Radius = Increase in radius/Circumferential strain

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