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Maximum circumferential stress in solid disc Formula

GoCircumferential stress in solid disc Formula

GoCircumferential stress in solid disc given Outer radius 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})}{8}

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

Maximum circumferential stress in solid disc Example

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Here is how the Maximum circumferential stress in solid disc equation looks like with Values.

Here is how the Maximum circumferential stress in solid disc equation looks like with Units.

Here is how the Maximum circumferential stress in solid disc equation looks like.

83.8253 = \frac{2 \cdot ({11.2}^{2}) \cdot (3 + 0.3) \cdot (900^{2})}{8}

83.8253N/m² = \frac{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot (3 + 0.3) \cdot ({900mm}^{2})}{8}

83.8253 = \frac{2 \cdot ({11.2}^{2}) \cdot (3 + 0.3) \cdot (900^{2})}{8}

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Maximum circumferential stress in solid disc Solution

Follow our step by step solution on how to calculate Maximum circumferential stress in solid disc?

FIRST Step Consider the formula

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

σ c = 83.82528Pa

Next Step Convert to Output's Unit

∴

σ c = 83.82528N/m²

LAST Step Rounding Answer

∴

σ c = 83.8253N/m²

Maximum circumferential stress in solid disc 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

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 in solid disc given Outer radius

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

Go Circumferential stress at center of 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 Maximum circumferential stress in solid disc?

Maximum circumferential stress in solid disc evaluator uses Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8 to evaluate the Circumferential Stress, The Maximum circumferential stress in solid disc 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 Maximum circumferential stress in solid disc using this online evaluator? To use this online evaluator for Maximum circumferential stress in solid disc, enter Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Outer Radius Disc (r_outer) and hit the calculate button.

FAQs on Maximum circumferential stress in solid disc

What is the formula to find Maximum circumferential stress in solid disc?

The formula of Maximum circumferential stress in solid disc is expressed as Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8. Here is an example- 83.82528 = (2*(11.2^2)*(3+0.3)*(0.9^2))/8.

How to calculate Maximum circumferential stress in solid disc?

With Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Outer Radius Disc (r_outer) we can find Maximum circumferential stress in solid disc using the formula - Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^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)-(1+(3*Poisson's Ratio)*Radius of Element^2)))/8
Circumferential Stress=(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8

Can the Maximum circumferential stress in solid disc be negative?

No, the Maximum circumferential stress in solid disc, measured in Stress cannot be negative.

Which unit is used to measure Maximum circumferential stress in solid disc?

Maximum circumferential stress in solid disc 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 Maximum circumferential stress in solid disc can be measured.

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Maximum circumferential stress in solid disc Formula

​GoCircumferential stress in solid disc Formula

​GoCircumferential stress in solid disc given Outer radius Formula

Maximum circumferential stress in solid disc Example

Maximum circumferential stress in solid disc Solution

Maximum circumferential stress in solid disc Formula Elements

Other Formulas to find Circumferential Stress

Other formulas in Stresses in Disc category

How to Evaluate Maximum circumferential stress in solid disc?

FAQs on Maximum circumferential stress in solid disc

Variable Name

GoCircumferential stress in solid disc Formula

GoCircumferential stress in solid disc given Outer radius Formula