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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 refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis. 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 refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis.

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 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 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