Hoop stress in thin cylinder Solution

STEP 0: Pre-Calculation Summary
Formula Used
Hoop Stress in Disc = Density Of Disc*Angular Velocity*Disc Radius
σθ = ρ*ω*rdisc
This formula uses 4 Variables
Variables Used
Hoop Stress in Disc - (Measured in Pascal) - Hoop Stress in Disc is the circumferential stress in a cylinder.
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.
STEP 1: Convert Input(s) to Base Unit
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)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σθ = ρ*ω*rdisc --> 2*11.2*1
Evaluating ... ...
σθ = 22.4
STEP 3: Convert Result to Output's Unit
22.4 Pascal -->22.4 Newton per Square Meter (Check conversion here)
FINAL ANSWER
22.4 Newton per Square Meter <-- Hoop Stress in Disc
(Calculation completed in 00.020 seconds)

Credits

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National Institute Of Technology (NIT), Hamirpur
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21 Expression for Stresses in Rotating Thin Disc Calculators

Poisson's ratio given initial radial width of disc
Go Poisson's Ratio = (Radial Stress-((Increase in Radial Width/Initial Radial Width)*Modulus Of Elasticity Of Disc))/(Circumferential Stress)
Modulus of elasticity given initial radial width of disc
Go Modulus Of Elasticity Of Disc = (Radial Stress-(Poisson's Ratio*Circumferential Stress))/(Increase in Radial Width/Initial Radial Width)
Modulus of elasticity given radius of disc
Go Modulus Of Elasticity Of Disc = ((Circumferential Stress-(Poisson's Ratio*Radial Stress))/(Increase in radius/Disc Radius))
Increase in radius of disc given stresses
Go Increase in radius = ((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc)*Disc Radius
Radius of disc given stresses on disc
Go Disc Radius = Increase in radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc)
Poisson's ratio given radius of disc
Go Poisson's Ratio = (Circumferential Stress-((Increase in radius/Disc Radius)*Modulus Of Elasticity Of Disc))/Radial Stress
Poisson's ratio given circumferential strain on disc
Go Poisson's Ratio = (Circumferential Stress-(Circumferential strain*Modulus Of Elasticity Of Disc))/(Radial Stress)
Modulus of elasticity given circumferential strain on disc
Go Modulus Of Elasticity Of Disc = (Circumferential Stress-(Poisson's Ratio*Radial Stress))/Circumferential strain
Poisson's ratio given radial strain on disc
Go Poisson's Ratio = (Radial Stress-(Radial strain*Modulus Of Elasticity Of Disc))/(Circumferential Stress)
Modulus of elasticity given radial strain on disc
Go Modulus Of Elasticity Of Disc = (Radial Stress-(Poisson's Ratio*Circumferential Stress))/Radial strain
Angular speed of rotation for thin cylinder given hoop stress in thin cylinder
Go Angular Velocity = Hoop Stress in Disc/(Density Of Disc*Disc Radius)
Density of cylinder material given hoop stress (for thin cylinder)
Go Density Of Disc = Hoop Stress in Disc/(Angular Velocity*Disc Radius)
Mean radius of cylinder given hoop stress in thin cylinder
Go Disc Radius = Hoop Stress in Disc/(Density Of Disc*Angular Velocity)
Hoop stress in thin cylinder
Go Hoop Stress in Disc = Density Of Disc*Angular Velocity*Disc Radius
Initial circumference given circumferential strain for rotating thin disc
Go Initial circumference = Final Circumference/(Circumferential strain+1)
Final circumference given circumferential strain for rotating thin disc
Go Final Circumference = (Circumferential strain+1)*Initial circumference
Tangential velocity of cylinder given hoop stress in thin cylinder
Go Tangential Velocity = Hoop Stress in Disc/(Density Of Disc)
Density of material of cylinder given hoop stress and tangential velocity
Go Density Of Disc = Hoop Stress in Disc/Tangential Velocity
Hoop stress in thin cylinder given tangential velocity of cylinder
Go Hoop Stress in Disc = Tangential Velocity*Density Of Disc
Increase in radius given circumferential strain for rotating thin disc
Go Increase in radius = Circumferential strain*Disc Radius
Radius of disc given circumferential strain for rotating thin disc
Go Disc Radius = Increase in radius/Circumferential strain

Hoop stress in thin cylinder Formula

Hoop Stress in Disc = Density Of Disc*Angular Velocity*Disc Radius
σθ = ρ*ω*rdisc

What is the allowable stress?

Allowable stress, or allowable strength, is the maximum stress that can be safely applied to a structure. Allowable stress is the stress at which a member is not expected to fail under the given loading conditions.

How to Calculate Hoop stress in thin cylinder?

Hoop stress in thin cylinder calculator uses Hoop Stress in Disc = Density Of Disc*Angular Velocity*Disc Radius to calculate the Hoop Stress in Disc, The Hoop stress in thin cylinder formula is defined as force over area exerted circumferentially perpendicular to axis and radius. Hoop Stress in Disc is denoted by σθ symbol.

How to calculate Hoop stress in thin cylinder using this online calculator? To use this online calculator for Hoop stress in thin cylinder, enter Density Of Disc (ρ), Angular Velocity (ω) & Disc Radius (rdisc) and hit the calculate button. Here is how the Hoop stress in thin cylinder calculation can be explained with given input values -> 28.4 = 2*11.2*1.

FAQ

What is Hoop stress in thin cylinder?
The Hoop stress in thin cylinder formula is defined as force over area exerted circumferentially perpendicular to axis and radius and is represented as σθ = ρ*ω*rdisc or Hoop Stress in Disc = Density Of Disc*Angular Velocity*Disc Radius. 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.
How to calculate Hoop stress in thin cylinder?
The Hoop stress in thin cylinder formula is defined as force over area exerted circumferentially perpendicular to axis and radius is calculated using Hoop Stress in Disc = Density Of Disc*Angular Velocity*Disc Radius. To calculate Hoop stress in thin cylinder, you need Density Of Disc (ρ), Angular Velocity (ω) & Disc Radius (rdisc). With our tool, you need to enter the respective value for Density Of Disc, Angular Velocity & Disc Radius 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 Hoop Stress in Disc?
In this formula, Hoop Stress in Disc uses Density Of Disc, Angular Velocity & Disc Radius. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Hoop Stress in Disc = Tangential Velocity*Density Of Disc
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