Increase in radius of disc given stresses Calculator

✖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.ⓘ Disc Radius [r_disc]			+10% -10%

✖Increase in radius is the increase in inner radius of outer cylinder of compound cylinder.ⓘ Increase in radius of disc given stresses [R_i]

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Formula

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Increase in radius of disc given stresses

Formula

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

Example

`"6250mm"=(("80N/m²"-("0.3"*"100N/m²"))/"8N/m²")*"1000mm"`

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Increase in radius of disc given stresses Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
Disc Radius - (Measured in Meter) - Disc Radius is a radial line from the focus to any point of a curve.

STEP 1: Convert Input(s) to Base Unit

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)
Disc Radius: 1000 Millimeter --> 1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_i = ((σ_c-(𝛎*σ_r))/E)*r_disc --> ((80-(0.3*100))/8)*1

Evaluating ... ...

R_i = 6.25

STEP 3: Convert Result to Output's Unit

6.25 Meter -->6250 Millimeter (Check conversion here)

FINAL ANSWER

6250 Millimeter <-- Increase in radius

(Calculation completed in 00.004 seconds)

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

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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

Increase in radius of disc given stresses Formula

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

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 Increase in radius of disc given stresses?

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

How to calculate Increase in radius of disc given stresses using this online calculator? To use this online calculator for Increase in radius of disc given stresses, enter Circumferential Stress (σ_c), Poisson's Ratio (𝛎), Radial Stress (σ_r), Modulus Of Elasticity Of Disc (E) & Disc Radius (r_disc) and hit the calculate button. Here is how the Increase in radius of disc given stresses calculation can be explained with given input values -> 6.3E+6 = ((80-(0.3*100))/8)*1.

FAQ

What is Increase in radius of disc given stresses?

The Increase in radius of disc given stresses formula is defined as increase in length of line segment extending from the center of a circle or sphere to the circumference or bounding surface and is represented as R_i = ((σ_c-(𝛎*σ_r))/E)*r_disc or Increase in radius = ((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc)*Disc Radius. 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 & Disc Radius is a radial line from the focus to any point of a curve.

How to calculate Increase in radius of disc given stresses?

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

In this formula, Increase in radius uses Circumferential Stress, Poisson's Ratio, Radial Stress, Modulus Of Elasticity Of Disc & Disc Radius. We can use 1 other way(s) to calculate the same, which is/are as follows -

Increase in radius = Circumferential strain*Disc Radius

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