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Circumferential stress in solid disc Formula

GoCircumferential stress in solid disc given Outer radius 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{C 1}{2}) - (\frac{ρ \cdot (ω^{2}) \cdot ({r disc}^{2}) \cdot ((3 \cdot 𝛎) + 1)}{8})

σ_c - Circumferential Stress?C₁ - Constant at Boundary Condition?ρ - Density Of Disc?ω - Angular Velocity?r_disc - Disc Radius?𝛎 - Poisson's Ratio?

Circumferential stress in solid disc Example

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

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

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

90.416 = (\frac{300}{2}) - (\frac{2 \cdot ({11.2}^{2}) \cdot (1000^{2}) \cdot ((3 \cdot 0.3) + 1)}{8})

90.416N/m² = (\frac{300}{2}) - (\frac{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({1000mm}^{2}) \cdot ((3 \cdot 0.3) + 1)}{8})

90.416 = (\frac{300}{2}) - (\frac{2 \cdot ({11.2}^{2}) \cdot (1000^{2}) \cdot ((3 \cdot 0.3) + 1)}{8})

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Circumferential stress in solid disc Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ c = (\frac{300}{2}) - (\frac{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({1000mm}^{2}) \cdot ((3 \cdot 0.3) + 1)}{8})

Next Step Convert Units

∴

σ c = (\frac{300}{2}) - (\frac{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({1m}^{2}) \cdot ((3 \cdot 0.3) + 1)}{8})

Next Step Prepare to Evaluate

∴

σ c = (\frac{300}{2}) - (\frac{2 \cdot ({11.2}^{2}) \cdot (1^{2}) \cdot ((3 \cdot 0.3) + 1)}{8})

Next Step Evaluate

∴

σ c = 90.416Pa

LAST Step Convert to Output's Unit

∴

σ c = 90.416N/m²

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

Constant at Boundary Condition

Constant at boundary condition is a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain.

Symbol: C₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant at Boundary Condition

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

Disc Radius

Disc radius is the distance from the center of the disc to any point on its circumference.

Symbol: r_disc

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Disc Radius

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

Other Formulas to find Circumferential Stress

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}

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?

Circumferential stress in solid disc evaluator uses Circumferential Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8) to evaluate the Circumferential Stress, The 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 Circumferential stress in solid disc using this online evaluator? To use this online evaluator for Circumferential stress in solid disc, enter Constant at Boundary Condition (C₁), Density Of Disc (ρ), Angular Velocity (ω), Disc Radius (r_disc) & Poisson's Ratio (𝛎) and hit the calculate button.

FAQs on Circumferential stress in solid disc

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

The formula of Circumferential stress in solid disc is expressed as Circumferential Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8). Here is an example- 90.416 = (300/2)-((2*(11.2^2)*(1^2)*((3*0.3)+1))/8).

How to calculate Circumferential stress in solid disc?

With Constant at Boundary Condition (C₁), Density Of Disc (ρ), Angular Velocity (ω), Disc Radius (r_disc) & Poisson's Ratio (𝛎) we can find Circumferential stress in solid disc using the formula - Circumferential Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8).

What are the other ways to Calculate Circumferential Stress?

Here are the different ways to Calculate Circumferential Stress-

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
Circumferential Stress=(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8

Can the Circumferential stress in solid disc be negative?

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

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

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 Circumferential stress in solid disc can be measured.

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Circumferential stress in solid disc Formula

​GoCircumferential stress in solid disc given Outer radius Formula

​GoCircumferential stress at center of solid disc Formula

Circumferential stress in solid disc Example

Circumferential stress in solid disc Solution

Circumferential stress in solid disc Formula Elements

Other Formulas to find Circumferential Stress

Other formulas in Stresses in Disc category

How to Evaluate Circumferential stress in solid disc?

FAQs on Circumferential stress in solid disc

Variable Name

GoCircumferential stress in solid disc given Outer radius Formula

GoCircumferential stress at center of solid disc Formula