Hoop stress given tensile circumferential strain for thick spherical shell Calculator

✖Circumferential strain represents the change in length.ⓘ Circumferential strain [e₁]			+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 tensile circumferential strain for thick spherical shell [σ_θ]

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Formula

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Hoop stress given tensile circumferential strain for thick spherical shell

Formula

`"σ"_{"θ"} = (("e"_{"1"}*"E")-("P"_{"v"}/"M"))/(("M"-1)/"M")`

Example

`"6.688273MPa"=(("2.5"*"2.6MPa")-("0.014MPa/m²"/"35.45kg"))/(("35.45kg"-1)/"35.45kg")`

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Hoop stress given tensile circumferential strain for thick spherical shell Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hoop Stress on thick shell = ((Circumferential strain*Modulus of Elasticity Of Thick Shell)-(Radial Pressure/Mass Of Shell))/((Mass Of Shell-1)/Mass Of Shell)
σ_θ = ((e₁*E)-(P_v/M))/((M-1)/M)
This formula uses 5 Variables

Variables Used

Hoop Stress on thick shell - (Measured in Pascal) - Hoop Stress on thick shell is the circumferential stress in a cylinder.
Circumferential strain - Circumferential strain represents the change in length.
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

Circumferential strain: 2.5 --> No Conversion Required
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 = ((e₁*E)-(P_v/M))/((M-1)/M) --> ((2.5*2600000)-(14000/35.45))/((35.45-1)/35.45)

Evaluating ... ...

σ_θ = 6688272.85921626

STEP 3: Convert Result to Output's Unit

6688272.85921626 Pascal -->6.68827285921626 Megapascal (Check conversion here)

FINAL ANSWER

6.68827285921626 ≈ 6.688273 Megapascal <-- Hoop Stress on thick shell

(Calculation completed in 00.004 seconds)

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< 24 Thick Spherical Shells Calculators

Hoop stress given tensile circumferential strain for thick spherical shell

Go Hoop Stress on thick shell = ((Circumferential strain*Modulus of Elasticity Of Thick Shell)-(Radial Pressure/Mass Of Shell))/((Mass Of Shell-1)/Mass Of Shell)

Radial pressure given tensile circumferential strain for thick spherical shell

Go Radial Pressure = ((Circumferential strain*Modulus of Elasticity Of Thick Shell)-Hoop Stress on thick shell*((Mass Of Shell-1)/Mass Of Shell))*Mass Of Shell

Modulus of elasticity given tensile circumferential strain for thick spherical shell

Go Adjusted design value = (Hoop Stress on thick shell*((Mass Of Shell-1)/Mass Of Shell)+(Radial Pressure/Mass Of Shell))/Circumferential strain

Tensile circumferential strain for thick spherical shell

Go Circumferential strain = (Hoop Stress on thick shell*((Mass Of Shell-1)/Mass Of Shell)+(Radial Pressure/Mass Of Shell))/Adjusted design value

Poisson's ratio for thick spherical shell given compressive radial strain

Go Poisson's Ratio = 1/((2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure))

Poisson's Ratio for Thick Spherical Shell given Tensile Radial Strain

Go Poisson's Ratio = (1/(2*Hoop Stress on thick shell))*((-Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)

Hoop stress on thick spherical shell given compressive radial strain and Poisson's ratio

Go Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)/(2*Poisson's Ratio)

Mass of thick spherical shell given compressive radial strain

Go Mass Of Shell = (2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)

Hoop stress on thick spherical shell given tensile radial strain and Poisson's ratio

Go Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)/(2*Poisson's Ratio)

Hoop stress on thick spherical shell given compressive radial strain

Go Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)*Mass Of Shell/2

Mass of thick spherical shell given tensile radial strain

Go Mass Of Shell = (2*Hoop Stress on thick shell)/((Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)

Hoop stress on thick spherical shell given tensile radial strain

Go Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)*Mass Of Shell/2

Radial pressure on thick spherical shell given compressive radial strain and Poisson's ratio

Go Radial Pressure = (Adjusted design value*Compressive Strain)-(2*Hoop Stress on thick shell*Poisson's Ratio)

Compressive radial strain given Poisson's ratio for thick spherical shell

Go Compressive Strain = (Radial Pressure+(2*Hoop Stress on thick shell*Poisson's Ratio))/Adjusted design value

Modulus of elasticity given compressive radial strain and Poisson's ratio

Go Adjusted design value = (Radial Pressure+(2*Hoop Stress on thick shell*Poisson's Ratio))/Compressive Strain

Modulus of elasticity for thick spherical shell given compressive radial strain

Go Adjusted design value = (Radial Pressure+(2*Hoop Stress on thick shell/Mass Of Shell))/Compressive Strain

Radial pressure on thick spherical shell given compressive radial strain

Go Radial Pressure = (Adjusted design value*Compressive Strain)-(2*Hoop Stress on thick shell/Mass Of Shell)

Tensile radial strain given Poisson's ratio for thick spherical shell

Go Tensile Strain = ((Radial Pressure+(2*Hoop Stress on thick shell*Poisson's Ratio))/Adjusted design value)

Modulus of elasticity given tensile radial strain and Poisson's ratio

Go Adjusted design value = ((Radial Pressure+(2*Hoop Stress on thick shell*Poisson's Ratio))/Tensile Strain)

Compressive radial strain for thick spherical shells

Go Compressive Strain = (Radial Pressure+(2*Hoop Stress on thick shell/Mass Of Shell))/Adjusted design value

Radial pressure on thick spherical shell given tensile radial strain and Poisson's ratio

Go Radial Pressure = (Adjusted design value*Tensile Strain)-(2*Hoop Stress on thick shell*Poisson's Ratio)

Modulus of elasticity thick spherical shell given tensile radial strain

Go Adjusted design value = ((Radial Pressure+(2*Hoop Stress on thick shell/Mass Of Shell))/Tensile Strain)

Radial pressure on thick spherical shell given tensile radial strain

Go Radial Pressure = ((Adjusted design value*Tensile Strain)-(2*Hoop Stress on thick shell/Mass Of Shell))

Tensile radial strain for thick spherical shell

Go Tensile Strain = ((Radial Pressure+(2*Hoop Stress on thick shell/Mass Of Shell))/Adjusted design value)

Hoop stress given tensile circumferential strain for thick spherical shell Formula

Hoop Stress on thick shell = ((Circumferential strain*Modulus of Elasticity Of Thick Shell)-(Radial Pressure/Mass Of Shell))/((Mass Of Shell-1)/Mass Of Shell)
σ_θ = ((e₁*E)-(P_v/M))/((M-1)/M)

Where is bending stress maximum?

The bottom die has a large deflection due to the bending force. The maximum bending stress occurs at the top surface of the die, and its location is corresponding to the inner bumps of the bottom die. The deflection of the beam is proportional to the bending moment, which is also proportional to the bending force.

How to Calculate Hoop stress given tensile circumferential strain for thick spherical shell?

Hoop stress given tensile circumferential strain for thick spherical shell calculator uses Hoop Stress on thick shell = ((Circumferential strain*Modulus of Elasticity Of Thick Shell)-(Radial Pressure/Mass Of Shell))/((Mass Of Shell-1)/Mass Of Shell) to calculate the Hoop Stress on thick shell, Hoop stress given tensile circumferential strain for thick spherical shell 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 tensile circumferential strain for thick spherical shell using this online calculator? To use this online calculator for Hoop stress given tensile circumferential strain for thick spherical shell, enter Circumferential strain (e₁), 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 tensile circumferential strain for thick spherical shell calculation can be explained with given input values -> 6.7E-6 = ((2.5*2600000)-(14000/35.45))/((35.45-1)/35.45).

FAQ

What is Hoop stress given tensile circumferential strain for thick spherical shell?

Hoop stress given tensile circumferential strain for thick spherical shell 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 = ((e₁*E)-(P_v/M))/((M-1)/M) or Hoop Stress on thick shell = ((Circumferential strain*Modulus of Elasticity Of Thick Shell)-(Radial Pressure/Mass Of Shell))/((Mass Of Shell-1)/Mass Of Shell). Circumferential strain represents the change in length, 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 tensile circumferential strain for thick spherical shell?

Hoop stress given tensile circumferential strain for thick spherical shell 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 = ((Circumferential strain*Modulus of Elasticity Of Thick Shell)-(Radial Pressure/Mass Of Shell))/((Mass Of Shell-1)/Mass Of Shell). To calculate Hoop stress given tensile circumferential strain for thick spherical shell, you need Circumferential strain (e₁), 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 Circumferential strain, 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 Circumferential strain, Modulus of Elasticity Of Thick Shell, Radial Pressure & Mass Of Shell. We can use 4 other way(s) to calculate the same, which is/are as follows -

Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)*Mass Of Shell/2
Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Compressive Strain)-Radial Pressure)/(2*Poisson's Ratio)
Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)*Mass Of Shell/2
Hoop Stress on thick shell = ((Modulus of Elasticity Of Thick Shell*Tensile Strain)-Radial Pressure)/(2*Poisson's Ratio)

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