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Radial stress at center of solid disc Formula

GoRadial stress in solid disc Formula

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

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

Radial stress at center of solid disc Example

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Here is how the Radial stress at center of solid disc equation looks like with Values.

Here is how the Radial stress at center of solid disc equation looks like with Units.

Here is how the Radial stress at center of 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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Radial stress at center of solid disc Solution

Follow our step by step solution on how to calculate Radial stress at center of solid disc?

FIRST Step Consider the formula

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

σ r = 83.82528Pa

Next Step Convert to Output's Unit

∴

σ r = 83.82528N/m²

LAST Step Rounding Answer

∴

σ r = 83.8253N/m²

Radial stress at center of 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

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

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 in solid disc given Outer radius

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

Radial stress at center of solid disc evaluator uses Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8 to evaluate the Radial Stress, The Radial stress at center of solid disc 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 at center of solid disc using this online evaluator? To use this online evaluator for Radial stress at center of 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 Radial stress at center of solid disc

What is the formula to find Radial stress at center of solid disc?

The formula of Radial stress at center of solid disc is expressed as Radial 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 Radial stress at center of solid disc?

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

Can the Radial stress at center of solid disc be negative?

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

Which unit is used to measure Radial stress at center of solid disc?

Radial stress at center of 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 at center of solid disc can be measured.

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Radial stress at center of solid disc Formula

​GoRadial stress in solid disc Formula

​GoRadial stress in solid disc given Outer radius Formula

Radial stress at center of solid disc Example

Radial stress at center of solid disc Solution

Radial stress at center of solid disc Formula Elements

Other Formulas to find Radial Stress

Other formulas in Stresses in Disc category

How to Evaluate Radial stress at center of solid disc?

FAQs on Radial stress at center of solid disc

Variable Name

GoRadial stress in solid disc Formula

GoRadial stress in solid disc given Outer radius Formula