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Radial stress in solid disc given Outer radius Formula

GoRadial stress in solid disc Formula

GoRadial stress at center of solid disc Formula

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Radial Stress induced by a bending moment in a member of constant cross section. Check FAQs

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

σ_r - Radial Stress?ρ - Density Of Disc?ω - Angular Velocity?𝛎 - Poisson's Ratio?r_outer - Outer Radius Disc?r - Radius of Element?

Radial stress in solid disc given Outer radius Example

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

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

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

83.8227 = \frac{2 \cdot ({11.2}^{2}) \cdot (3 + 0.3) \cdot ((900^{2}) - (5^{2}))}{8}

83.8227N/m² = \frac{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot (3 + 0.3) \cdot (({900mm}^{2}) - ({5mm}^{2}))}{8}

83.8227 = \frac{2 \cdot ({11.2}^{2}) \cdot (3 + 0.3) \cdot ((900^{2}) - (5^{2}))}{8}

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Radial stress in solid disc given Outer radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

σ r = 83.8226928Pa

Next Step Convert to Output's Unit

∴

σ r = 83.8226928N/m²

LAST Step Rounding Answer

∴

σ r = 83.8227N/m²

Radial stress in solid disc given Outer radius Formula Elements

Variables

Radial Stress

Radial Stress induced by a bending moment in a member of constant cross section.

Symbol: σ_r

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Radial 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 Radial Stress

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 Radial stress at center of solid disc

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

Go Maximum Radial Stress in solid disc

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

Other formulas in Stresses in Disc category

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 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 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 Radial stress in solid disc given Outer radius?

Radial stress in solid disc given Outer radius evaluator uses Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))/8 to evaluate the Radial Stress, The Radial stress in solid disc given Outer radius formula is defined as stress towards or away from the central axis of a component. Radial Stress is denoted by σ_r symbol.

How to evaluate Radial stress in solid disc given Outer radius using this online evaluator? To use this online evaluator for Radial 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 Radial stress in solid disc given Outer radius

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

The formula of Radial stress in solid disc given Outer radius is expressed as Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))/8. Here is an example- 83.82269 = (2*(11.2^2)*(3+0.3)*((0.9^2)-(0.005^2)))/8.

How to calculate Radial 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 Radial stress in solid disc given Outer radius using the formula - Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))/8.

What are the other ways to Calculate Radial Stress?

Here are the different ways to Calculate Radial Stress-

Radial Stress=(Constant at boundary condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8)
Radial Stress=(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8
Radial Stress=(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8

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

No, the Radial stress in solid disc given Outer radius, measured in Pressure cannot be negative.

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

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

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Radial stress in solid disc given Outer radius Formula

​GoRadial stress in solid disc Formula

​GoRadial stress at center of solid disc Formula

Radial stress in solid disc given Outer radius Example

Radial stress in solid disc given Outer radius Solution

Radial stress in solid disc given Outer radius Formula Elements

Other Formulas to find Radial Stress

Other formulas in Stresses in Disc category

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

FAQs on Radial stress in solid disc given Outer radius

Variable Name

GoRadial stress in solid disc Formula

GoRadial stress at center of solid disc Formula