Hoop stress in thin cylinder Calculator

✖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.ⓘ Density Of Disc [ρ]			+10% -10%
✖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.ⓘ Angular Velocity [ω]			+10% -10%
✖Disc Radius is a radial line from the focus to any point of a curve.ⓘ Disc Radius [r_disc]			+10% -10%

✖Hoop Stress in Disc is the circumferential stress in a cylinder.ⓘ Hoop stress in thin cylinder [σ_θ]

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Formula

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Hoop stress in thin cylinder

Formula

σ θ = ρ \cdot ω \cdot r disc

Example

22.4 N/m² = 2 kg/m³ \cdot 11.2 rad/s \cdot 1000 mm

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Hoop stress in thin cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hoop Stress in Disc = Density Of Disc*Angular Velocity*Disc Radius
σ_θ = ρ*ω*r_disc
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

σ_θ = ρ*ω*r_disc --> 2*11.2*1

Evaluating ... ...

σ_θ = 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 00.004 seconds)

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Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Mechanical » Expression for Stresses in Rotating Thin Disc » Hoop stress in thin cylinder

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

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< Expression for Stresses in Rotating Thin Disc Calculators

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

Hoop stress in thin cylinder Formula

Hoop Stress in Disc = Density Of Disc*Angular Velocity*Disc Radius
σ_θ = ρ*ω*r_disc

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 σ_θ 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 (r_disc) 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 σ_θ = ρ*ω*r_disc 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 (r_disc). 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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