Hoop stress given decrease in outer radius of inner cylinder Calculator

✖Decrease in radius is the decrease in outer radius of inner cylinder of compound cylinder.ⓘ Decrease in radius [R_d]			+10% -10%
✖The Radius at Junction is the radius value at the junction of compound cylinders.ⓘ Radius at Junction [r_*]			+10% -10%
✖Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.ⓘ Modulus of Elasticity Of Thick Shell [E]			+10% -10%
✖Radial Pressure is pressure towards or away from the central axis of a component.ⓘ Radial Pressure [P_v]			+10% -10%
✖Mass Of Shell is the quantity of matter in a body regardless of its volume or of any forces acting on it.ⓘ Mass Of Shell [M]			+10% -10%

✖Hoop Stress on thick shell is the circumferential stress in a cylinder.ⓘ Hoop stress given decrease in outer radius of inner cylinder [σ_θ]

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Formula

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Hoop stress given decrease in outer radius of inner cylinder

Formula

`"σ"_{"θ"} = ("R"_{"d"}/("r"_{"*"}/"E"))-("P"_{"v"}/"M")`

Example

`"0.004805MPa"=("8mm"/("4000mm"/"2.6MPa"))-("0.014MPa/m²"/"35.45kg")`

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Hoop stress given decrease in outer radius of inner cylinder Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hoop Stress on thick shell = (Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell)
σ_θ = (R_d/(r_*/E))-(P_v/M)
This formula uses 6 Variables

Variables Used

Hoop Stress on thick shell - (Measured in Pascal) - Hoop Stress on thick shell is the circumferential stress in a cylinder.
Decrease in radius - (Measured in Meter) - Decrease in radius is the decrease in outer radius of inner cylinder of compound cylinder.
Radius at Junction - (Measured in Meter) - The Radius at Junction is the radius value at the junction of compound cylinders.
Modulus of Elasticity Of Thick Shell - (Measured in Pascal) - Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.
Radial Pressure - (Measured in Pascal per Square Meter) - Radial Pressure is pressure towards or away from the central axis of a component.
Mass Of Shell - (Measured in Kilogram) - Mass Of Shell is the quantity of matter in a body regardless of its volume or of any forces acting on it.

STEP 1: Convert Input(s) to Base Unit

Decrease in radius: 8 Millimeter --> 0.008 Meter (Check conversion here)
Radius at Junction: 4000 Millimeter --> 4 Meter (Check conversion here)
Modulus of Elasticity Of Thick Shell: 2.6 Megapascal --> 2600000 Pascal (Check conversion here)
Radial Pressure: 0.014 Megapascal per Square Meter --> 14000 Pascal per Square Meter (Check conversion here)
Mass Of Shell: 35.45 Kilogram --> 35.45 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_θ = (R_d/(r_*/E))-(P_v/M) --> (0.008/(4/2600000))-(14000/35.45)

Evaluating ... ...

σ_θ = 4805.07757404795

STEP 3: Convert Result to Output's Unit

4805.07757404795 Pascal -->0.00480507757404795 Megapascal (Check conversion here)

FINAL ANSWER

0.00480507757404795 ≈ 0.004805 Megapascal <-- Hoop Stress on thick shell

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Thick Cylinders And Spheres » Compound Cylinder Shrinkage Radii Change » Hoop stress given decrease in outer radius of inner cylinder

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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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< 21 Compound Cylinder Shrinkage Radii Change Calculators

Decrease in outer radius of inner cylinder at junction given constants of lame equation

Go Decrease in radius = -Radius at Junction*(((1/Modulus of Elasticity Of Thick Shell)*((Constant 'b' for inner cylinder/Radius at Junction)+Constant 'a' for inner cylinder))+((1/Modulus of Elasticity Of Thick Shell*Mass Of Shell)*((Constant 'b' for inner cylinder/Radius at Junction)-Constant 'a' for inner cylinder)))

Increase in inner radius of outer cylinder at junction given constants of lame equation

Go Increase in radius = Radius at Junction*(((1/Modulus of Elasticity Of Thick Shell)*((Constant 'b' for outer cylinder/Radius at Junction)+Constant 'a' for outer cylinder))+((1/Modulus of Elasticity Of Thick Shell*Mass Of Shell)*((Constant 'b' for outer cylinder/Radius at Junction)-Constant 'a' for outer cylinder)))

Modulus of elasticity given decrease in outer radius of inner cylinder and constants

Go Modulus of Elasticity Of Thick Shell = -Radius at Junction*(((1/Decrease in radius)*((Constant 'b' for inner cylinder/Radius at Junction)+Constant 'a' for inner cylinder))+((1/Decrease in radius*Mass Of Shell)*((Constant 'b' for inner cylinder/Radius at Junction)-Constant 'a' for inner cylinder)))

Modulus of elasticity given increase in inner radius of outer cylinder and constants

Go Modulus of Elasticity Of Thick Shell = Radius at Junction*(((1/Increase in radius)*((Constant 'b' for outer cylinder/Radius at Junction)+Constant 'a' for outer cylinder))+((1/Increase in radius*Mass Of Shell)*((Constant 'b' for outer cylinder/Radius at Junction)-Constant 'a' for outer cylinder)))

Radius at junction of compound cylinder given increase in inner radius of outer cylinder

Go Radius at Junction = (Increase in radius*Modulus of Elasticity Of Thick Shell)/(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Radius at junction of compound cylinder given decrease in outer radius of inner cylinder

Go Radius at Junction = (Decrease in radius*Modulus of Elasticity Of Thick Shell)/(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Increase in inner radius of outer cylinder at junction of compound cylinder

Go Increase in radius = (Radius at Junction/Modulus of Elasticity Of Thick Shell)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Decrease in outer radius of inner cylinder at junction of compound cylinder

Go Decrease in radius = (Radius at Junction/Modulus of Elasticity Of Thick Shell)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Mass of compound cylinder given increase in inner radius of outer cylinder

Go Mass Of Shell = Radial Pressure/((Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)

Mass of compound cylinder given decrease in outer radius of inner cylinder

Go Mass Of Shell = Radial Pressure/((Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)

Modulus of elasticity given increase in inner radius of outer cylinder

Go Modulus of Elasticity Of Thick Shell = (Radius at Junction/Increase in radius)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Radial pressure given increase in inner radius of outer cylinder

Go Radial Pressure = ((Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)*Mass Of Shell

Radial pressure given decrease in outer radius of inner cylinder

Go Radial Pressure = ((Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)*Mass Of Shell

Modulus of elasticity decrease in outer radius of inner cylinder

Go Modulus of Elasticity Of Thick Shell = (Radius at Junction/Decrease in radius)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Hoop stress given increase in inner radius of outer cylinder

Go Hoop Stress on thick shell = (Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell)

Hoop stress given decrease in outer radius of inner cylinder

Go Hoop Stress on thick shell = (Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell)

Radius at junction of compound cylinder given original difference of radii at junction

Go Radius at Junction = Original difference of radii/(2*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Modulus of Elasticity Of Thick Shell)

Constant 'a' for inner cylinder given original difference of radii at junction

Go Constant 'a' for inner cylinder = Constant 'a' for outer cylinder-(Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))

Constant for outer cylinder given original difference of radii at junction

Go Constant 'a' for outer cylinder = (Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))+Constant 'a' for inner cylinder

Modulus of elasticity given original difference of radii at junction

Go Modulus of Elasticity Of Thick Shell = 2*Radius at Junction*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Original difference of radii

Original difference of radii at junction

Go Original difference of radii = 2*Radius at Junction*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Modulus of Elasticity Of Thick Shell

Hoop stress given decrease in outer radius of inner cylinder Formula

Hoop Stress on thick shell = (Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell)
σ_θ = (R_d/(r_*/E))-(P_v/M)

What is meant by hoop stress?

The hoop stress is the force over the area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall.

How to Calculate Hoop stress given decrease in outer radius of inner cylinder?

Hoop stress given decrease in outer radius of inner cylinder calculator uses Hoop Stress on thick shell = (Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell) to calculate the Hoop Stress on thick shell, The Hoop stress given decrease in outer radius of inner cylinder formula is defined as the force over area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall. Hoop Stress on thick shell is denoted by σ_θ symbol.

How to calculate Hoop stress given decrease in outer radius of inner cylinder using this online calculator? To use this online calculator for Hoop stress given decrease in outer radius of inner cylinder, enter Decrease in radius (R_d), Radius at Junction (r_*), Modulus of Elasticity Of Thick Shell (E), Radial Pressure (P_v) & Mass Of Shell (M) and hit the calculate button. Here is how the Hoop stress given decrease in outer radius of inner cylinder calculation can be explained with given input values -> 4.8E-9 = (0.008/(4/2600000))-(14000/35.45).

FAQ

What is Hoop stress given decrease in outer radius of inner cylinder?

The Hoop stress given decrease in outer radius of inner cylinder formula is defined as the force over area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall and is represented as σ_θ = (R_d/(r_*/E))-(P_v/M) or Hoop Stress on thick shell = (Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell). Decrease in radius is the decrease in outer radius of inner cylinder of compound cylinder, The Radius at Junction is the radius value at the junction of compound cylinders, Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it, Radial Pressure is pressure towards or away from the central axis of a component & Mass Of Shell is the quantity of matter in a body regardless of its volume or of any forces acting on it.

How to calculate Hoop stress given decrease in outer radius of inner cylinder?

The Hoop stress given decrease in outer radius of inner cylinder formula is defined as the force over area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall is calculated using Hoop Stress on thick shell = (Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell). To calculate Hoop stress given decrease in outer radius of inner cylinder, you need Decrease in radius (R_d), Radius at Junction (r_*), Modulus of Elasticity Of Thick Shell (E), Radial Pressure (P_v) & Mass Of Shell (M). With our tool, you need to enter the respective value for Decrease in radius, Radius at Junction, Modulus of Elasticity Of Thick Shell, Radial Pressure & Mass Of Shell 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 on thick shell?

In this formula, Hoop Stress on thick shell uses Decrease in radius, Radius at Junction, Modulus of Elasticity Of Thick Shell, Radial Pressure & Mass Of Shell. We can use 1 other way(s) to calculate the same, which is/are as follows -

Hoop Stress on thick shell = (Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell)

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