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Circumferential stress in solid disc given Outer radius Formula

GoCircumferential stress in solid disc Formula

GoCircumferential stress at center of solid disc Formula

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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. Check FAQs

σ c = \frac{(ρ \cdot (ω^{2})) \cdot (((3 + 𝛎) \cdot {r outer}^{2}) - (1 + (3 \cdot 𝛎) \cdot R^{2}))}{8}

σ_c - Circumferential Stress?ρ - Density Of Disc?ω - Angular Velocity?𝛎 - Poisson's Ratio?r_outer - Outer Radius Disc?R - Radius of Element?

Circumferential stress in solid disc given Outer radius Example

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Here is how the Circumferential stress in solid disc given Outer radius equation looks like with Values.

Here is how the Circumferential stress in solid disc given Outer radius equation looks like with Units.

Here is how the Circumferential stress in solid disc given Outer radius equation looks like.

52.4646 = \frac{(2 \cdot ({11.2}^{2})) \cdot (((3 + 0.3) \cdot 900^{2}) - (1 + (3 \cdot 0.3) \cdot 5^{2}))}{8}

52.4646N/m² = \frac{(2kg/m³ \cdot ({11.2rad/s}^{2})) \cdot (((3 + 0.3) \cdot {900mm}^{2}) - (1 + (3 \cdot 0.3) \cdot {5mm}^{2}))}{8}

52.4646 = \frac{(2 \cdot ({11.2}^{2})) \cdot (((3 + 0.3) \cdot 900^{2}) - (1 + (3 \cdot 0.3) \cdot 5^{2}))}{8}

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Circumferential stress in solid disc given Outer radius Solution

Follow our step by step solution on how to calculate Circumferential stress in solid disc given Outer radius?

FIRST Step Consider the formula

σ c = \frac{(ρ \cdot (ω^{2})) \cdot (((3 + 𝛎) \cdot {r outer}^{2}) - (1 + (3 \cdot 𝛎) \cdot R^{2}))}{8}

Next Step Substitute values of Variables

∴

σ c = \frac{(2kg/m³ \cdot ({11.2rad/s}^{2})) \cdot (((3 + 0.3) \cdot {900mm}^{2}) - (1 + (3 \cdot 0.3) \cdot {5mm}^{2}))}{8}

Next Step Convert Units

∴

σ c = \frac{(2kg/m³ \cdot ({11.2rad/s}^{2})) \cdot (((3 + 0.3) \cdot {0.9m}^{2}) - (1 + (3 \cdot 0.3) \cdot {0.005m}^{2}))}{8}

Next Step Prepare to Evaluate

∴

σ c = \frac{(2 \cdot ({11.2}^{2})) \cdot (((3 + 0.3) \cdot {0.9}^{2}) - (1 + (3 \cdot 0.3) \cdot {0.005}^{2}))}{8}

Next Step Evaluate

∴

σ c = 52.4645744Pa

Next Step Convert to Output's Unit

∴

σ c = 52.4645744N/m²

LAST Step Rounding Answer

∴

σ c = 52.4646N/m²

Circumferential stress in solid disc given Outer radius Formula Elements

Variables

Circumferential Stress

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.

Symbol: σ_c

Measurement: StressUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Circumferential Stress

Density Of Disc

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.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density Of Disc

Angular Velocity

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.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity

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.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value should be between -1 to 10.

Formulas to find Poisson's Ratio

Outer Radius Disc

Outer radius disc is the distance from the center of the disc to its outer edge or boundary.

Symbol: r_outer

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Radius Disc

Radius of Element

Radius of element often referred to as the atomic radius, is a measure of the size of an atom, typically defined as the distance from the center of the nucleus to the outermost shell of electrons.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Element

Other Formulas to find Circumferential Stress

Go Circumferential stress in solid disc

σ c = (\frac{C 1}{2}) - (\frac{ρ \cdot (ω^{2}) \cdot ({r disc}^{2}) \cdot ((3 \cdot 𝛎) + 1)}{8})

Go Circumferential stress at center of solid disc

σ c = \frac{ρ \cdot (ω^{2}) \cdot (3 + 𝛎) \cdot ({r outer}^{2})}{8}

Go Maximum circumferential stress in solid disc

σ c = \frac{ρ \cdot (ω^{2}) \cdot (3 + 𝛎) \cdot ({r outer}^{2})}{8}

Other formulas in Stresses in Disc category

Go Radial stress in solid disc

σ r = (\frac{C 1}{2}) - (\frac{ρ \cdot (ω^{2}) \cdot ({r disc}^{2}) \cdot (3 + 𝛎)}{8})

Go Constant at boundary condition given Radial stress in solid disc

C 1 = 2 \cdot (σ r + (\frac{ρ \cdot (ω^{2}) \cdot ({r disc}^{2}) \cdot (3 + 𝛎)}{8}))

Go Poisson's ratio given Radial stress in solid disc

𝛎 = (\frac{((\frac{C}{2}) - σ r) \cdot 8}{ρ \cdot (ω^{2}) \cdot ({r disc}^{2})}) - 3

Go Constant at boundary condition given Circumferential stress in solid disc

C 1 = 2 \cdot (σ c + (\frac{ρ \cdot (ω^{2}) \cdot ({r disc}^{2}) \cdot ((3 \cdot 𝛎) + 1)}{8}))

How to Evaluate Circumferential stress in solid disc given Outer radius?

Circumferential stress in solid disc given Outer radius evaluator uses 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 to evaluate the Circumferential Stress, The Circumferential stress in solid disc given Outer radius formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction. Circumferential Stress is denoted by σ_c symbol.

How to evaluate Circumferential stress in solid disc given Outer radius using this online evaluator? To use this online evaluator for Circumferential stress in solid disc given Outer radius, enter Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (R) and hit the calculate button.

FAQs on Circumferential stress in solid disc given Outer radius

What is the formula to find Circumferential stress in solid disc given Outer radius?

The formula of Circumferential stress in solid disc given Outer radius is expressed as 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. Here is an example- 52.46457 = ((2*(11.2^2))*(((3+0.3)*0.9^2)-(1+(3*0.3)*0.005^2)))/8.

How to calculate Circumferential stress in solid disc given Outer radius?

With Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (R) we can find Circumferential stress in solid disc given Outer radius using the formula - 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.

What are the other ways to Calculate Circumferential Stress?

Here are the different ways to Calculate Circumferential Stress-

Circumferential Stress=(Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/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

Can the Circumferential stress in solid disc given Outer radius be negative?

No, the Circumferential stress in solid disc given Outer radius, measured in Stress cannot be negative.

Which unit is used to measure Circumferential stress in solid disc given Outer radius?

Circumferential stress in solid disc given Outer radius is usually measured using the Newton per Square Meter[N/m²] for Stress. Pascal[N/m²], Newton per Square Millimeter[N/m²], Kilonewton per Square Meter[N/m²] are the few other units in which Circumferential stress in solid disc given Outer radius can be measured.

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Circumferential stress in solid disc given Outer radius Formula

​GoCircumferential stress in solid disc Formula

​GoCircumferential stress at center of solid disc Formula

Circumferential stress in solid disc given Outer radius Example

Circumferential stress in solid disc given Outer radius Solution

Circumferential stress in solid disc given Outer radius Formula Elements

Other Formulas to find Circumferential Stress

Other formulas in Stresses in Disc category

How to Evaluate Circumferential stress in solid disc given Outer radius?

FAQs on Circumferential stress in solid disc given Outer radius

Variable Name

GoCircumferential stress in solid disc Formula

GoCircumferential stress at center of solid disc Formula