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)
σr = (C1/2)-((ρ*(ω^2)*(rdisc^2)*(3+𝛎))/8)
This formula uses 6 Variables
Variables Used
Radial Stress - (Measured in Pascal) - Radial Stress induced by a bending moment in a member of constant cross section.
Constant at boundary condition - Constant at boundary condition is value obtained for stress in solid disc.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - 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.
Angular Velocity - (Measured in Radian per Second) - 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.
Disc Radius - (Measured in Meter) - Disc Radius is a radial line from the focus to any point of a curve.
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.
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
σr = (C1/2)-((ρ*(ω^2)*(rdisc^2)*(3+𝛎))/8) --> (300/2)-((2*(11.2^2)*(1^2)*(3+0.3))/8)
Evaluating ... ...
σr = 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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19 Expression for Stresses in Solid Disc Calculators

Circumferential stress in solid disc given Outer radius
Go Circumferential Stress = ((Density Of Disc*(Angular Velocity^2))*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2)))/8
Poisson's ratio given Circumferential stress in solid disc
Go Poisson's Ratio = (((((Constant at boundary condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)))-1)/3
Constant at boundary condition given Circumferential stress in solid disc
Go Constant at boundary condition = 2*(Circumferential Stress+((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8))
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 and outer radius
Go Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*((Outer Radius Disc^2)-(Radius of Element^2))))-3
Radial stress in solid disc given Outer radius
Go Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2)))/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
Poisson's ratio given constant at boundary condition for circular disc
Go Poisson's Ratio = ((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Constant at boundary condition for circular disc
Go Constant at boundary condition = (Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))/8
Poisson's ratio given Circumferential stress at center of solid disc
Go Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Poisson's Ratio given max circumferential stress in solid disc
Go Poisson's Ratio = ((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Circumferential stress at center of solid disc
Go Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8
Maximum circumferential stress in solid disc
Go Circumferential Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8
Poisson's ratio given Radial stress at center of solid disc
Go Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Poisson's ratio given maximum radial stress in solid disc
Go Poisson's Ratio = ((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)))-3
Maximum Radial Stress in solid disc
Go Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc ^2))/8
Radial stress at center of solid disc
Go Radial Stress = (Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2))/8

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)
σr = (C1/2)-((ρ*(ω^2)*(rdisc^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 σr 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 (rdisc) & 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 σr = (C1/2)-((ρ*(ω^2)*(rdisc^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 value obtained for stress in solid 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, 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, Disc Radius is a radial line from the focus to any point of a curve & 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.
How to calculate 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 is calculated using Radial Stress = (Constant at boundary condition/2)-((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8). To calculate Radial stress in solid disc, you need Constant at boundary condition (C1), Density Of Disc (ρ), Angular Velocity (ω), Disc Radius (rdisc) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Constant at boundary condition, Density Of Disc, Angular Velocity, Disc Radius & Poisson's Ratio and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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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