Radial stress in solid disc Calculator

✖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.ⓘ Constant at Boundary Condition [C₁]			+10% -10%
✖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.ⓘ Density Of Disc [ρ]			+10% -10%
✖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.ⓘ Angular Velocity [ω]			+10% -10%
✖Disc radius is the distance from the center of the disc to any point on its circumference.ⓘ Disc Radius [r_disc]			+10% -10%
✖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.ⓘ Poisson's Ratio [𝛎]			+10% -10%

✖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.ⓘ Radial stress in solid disc [σ_r]

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Radial stress in solid disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radial Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8)
σ_r = (C₁/2)-((ρ*(ω^2)*(r_disc^2)*(3+𝛎))/8)
This formula uses 6 Variables

Variables Used

Radial Stress - (Measured in Pascal) - 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.
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.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - 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.
Angular Velocity - (Measured in Radian per Second) - 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.
Disc Radius - (Measured in Meter) - Disc radius is the distance from the center of the disc to any point on its circumference.
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.

STEP 1: Convert Input(s) to Base Unit

Constant at Boundary Condition: 300 --> No Conversion Required
Density Of Disc: 2 Kilogram per Cubic Meter --> 2 Kilogram per Cubic Meter No Conversion Required
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required
Disc Radius: 1000 Millimeter --> 1 Meter (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_r = (C₁/2)-((ρ*(ω^2)*(r_disc^2)*(3+𝛎))/8) --> (300/2)-((2*(11.2^2)*(1^2)*(3+0.3))/8)

Evaluating ... ...

σ_r = 46.512

STEP 3: Convert Result to Output's Unit

46.512 Pascal -->46.512 Newton per Square Meter (Check conversion here)

FINAL ANSWER

46.512 Newton per Square Meter <-- Radial Stress

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Solid Disc » Mechanical » Stresses in Disc » Radial stress in solid disc

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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< Stresses in Disc Calculators

Circumferential stress in solid disc

Go Circumferential Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8)

Constant at boundary condition given Radial stress in solid disc

Go Constant at Boundary Condition = 2*(Radial Stress+((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8))

Radial stress in solid disc

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

Poisson's ratio given Radial stress in solid disc

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

Radial stress in solid disc Formula

Radial Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8)
σ_r = (C₁/2)-((ρ*(ω^2)*(r_disc^2)*(3+𝛎))/8)

What is radial and tangential stress?

The “Hoop Stress” or “Tangential Stress” acts on a line perpendicular to the “longitudinal “and the “radial stress” this stress attempts to separate the pipe wall in the circumferential direction. This stress is caused by internal pressure.

How to Calculate Radial stress in solid disc?

Radial stress in solid disc calculator uses Radial Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8) to calculate 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 calculate Radial stress in solid disc using this online calculator? To use this online calculator 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. Here is how the Radial stress in solid disc calculation can be explained with given input values -> 46.512 = (300/2)-((2*(11.2^2)*(1^2)*(3+0.3))/8).

FAQ

What is Radial stress in solid disc?

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 and is represented as σ_r = (C₁/2)-((ρ*(ω^2)*(r_disc^2)*(3+𝛎))/8) or Radial Stress = (Constant at Boundary Condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8). 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, 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, 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, Disc radius is the distance from the center of the disc to any point on its circumference & 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.

How to calculate Radial stress in solid disc?

How many ways are there to calculate Radial Stress?

In this formula, Radial Stress uses Constant at Boundary Condition, Density Of Disc, Angular Velocity, Disc Radius & Poisson's Ratio. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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