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Radial stress in solid disc Formula

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

σ_r - Radial Stress?C₁ - Constant at boundary condition?ρ - Density Of Disc?ω - Angular Velocity?r_disc - Disc Radius?𝛎 - Poisson's Ratio?

Radial stress in solid disc Example

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

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

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

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

46.512N/m² = (\frac{300}{2}) - (\frac{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({1000mm}^{2}) \cdot (3 + 0.3)}{8})

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

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Radial stress in solid disc Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

σ r = 46.512Pa

LAST Step Convert to Output's Unit

∴

σ r = 46.512N/m²

Radial stress in solid disc 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

Constant at boundary condition

Constant at boundary condition is value obtained for stress in solid disc.

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 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

Disc Radius

Disc Radius is a radial line from the focus to any point of a curve.

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 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

Other Formulas to find Radial Stress

Go Radial stress in solid disc given Outer radius

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

Radial stress in solid disc evaluator uses Radial Stress = (Constant at boundary condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8) to evaluate the Radial Stress, The Radial stress in solid disc formula is defined as stress towards or away from the central axis of a component. The “radial stress” this stress attempts to separate the pipe or disc wall in the circumferential direction. This stress is caused by internal pressure. Radial Stress is denoted by σ_r symbol.

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

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

The formula of Radial stress in solid disc is expressed as Radial Stress = (Constant at boundary condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8). Here is an example- 46.512 = (300/2)-((2*(11.2^2)*(1^2)*(3+0.3))/8).

How to calculate Radial 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 Radial stress in solid disc using the formula - Radial Stress = (Constant at boundary condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8).

What are the other ways to Calculate Radial Stress?

Here are the different ways to Calculate Radial Stress-

Radial Stress=(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))/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 be negative?

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

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

Radial stress in solid disc 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 can be measured.

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Radial stress in solid disc Formula

​GoRadial stress in solid disc given Outer radius Formula

​GoRadial stress at center of solid disc Formula

Radial stress in solid disc Example

Radial stress in solid disc Solution

Radial stress in solid disc Formula Elements

Other Formulas to find Radial Stress

Other formulas in Stresses in Disc category

How to Evaluate Radial stress in solid disc?

FAQs on Radial stress in solid disc

Variable Name

GoRadial stress in solid disc given Outer radius Formula

GoRadial stress at center of solid disc Formula