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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 is the force over area exerted circumferentially perpendicular to the axis and the radius. 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 is the force over area exerted circumferentially perpendicular to the axis and the radius.

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 shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density Of Disc

Angular Velocity

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.

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 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.

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 radius of the larger of the two concentric circles that form its boundary.

Symbol: r_outer

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Radius Disc

Radius of Element

The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

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