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Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio Formula

GoHoop stress induced in thin spherical shell given strain in any one direction Formula

GoHoop stress given efficiency of longitudinal joint Formula

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Hoop Stress in Thin shell is the circumferential stress in a cylinder. Check FAQs

σ θ = (\frac{ε}{1 - 𝛎}) \cdot E

σ_θ - Hoop Stress in Thin shell?ε - Strain in thin shell?𝛎 - Poisson's Ratio?E - Modulus of Elasticity Of Thin Shell?

Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio Example

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Here is how the Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio equation looks like with Values.

Here is how the Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio equation looks like with Units.

Here is how the Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio equation looks like.

42.8571 = (\frac{3}{1 - 0.3}) \cdot 10

42.8571MPa = (\frac{3}{1 - 0.3}) \cdot 10MPa

42.8571 = (\frac{3}{1 - 0.3}) \cdot 10

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Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio Solution

Follow our step by step solution on how to calculate Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio?

FIRST Step Consider the formula

σ θ = (\frac{ε}{1 - 𝛎}) \cdot E

Next Step Substitute values of Variables

∴

σ θ = (\frac{3}{1 - 0.3}) \cdot 10MPa

Next Step Convert Units

∴

σ θ = (\frac{3}{1 - 0.3}) \cdot 1E+7Pa

Next Step Prepare to Evaluate

∴

σ θ = (\frac{3}{1 - 0.3}) \cdot 1E+7

Next Step Evaluate

∴

σ θ = 42857142.8571429Pa

Next Step Convert to Output's Unit

∴

σ θ = 42.8571428571429MPa

LAST Step Rounding Answer

∴

σ θ = 42.8571MPa

Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio Formula Elements

Variables

Hoop Stress in Thin shell

Hoop Stress in Thin shell is the circumferential stress in a cylinder.

Symbol: σ_θ

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Hoop Stress in Thin shell

Strain in thin shell

Strain in thin shell is simply the measure of how much an object is stretched or deformed.

Symbol: ε

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Strain in thin shell

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.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Poisson's Ratio

Modulus of Elasticity Of Thin Shell

Modulus of Elasticity Of Thin Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.

Symbol: E

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity Of Thin Shell

Other Formulas to find Hoop Stress in Thin shell

Go Hoop stress induced in thin spherical shell given strain in any one direction

σ θ = (\frac{ε}{1 - 𝛎}) \cdot E

Go Hoop stress given efficiency of longitudinal joint

σ θ = \frac{P i \cdot D i}{2 \cdot t \cdot η l}

Other formulas in Change in Dimension of Thin Spherical Shell due to Internal Pressure category

Go Hoop stress given circumferential strain

σ θ = (e 1 \cdot E) + (𝛎 \cdot σ l)

Go Hoop stress in thin cylindrical vessel given Longitudinal strain

σ θ = \frac{- (ε longitudinal \cdot E) + σ l}{𝛎}

Go Hoop stress

σ θ = \frac{P i \cdot D i}{2 \cdot t}

Go Hoop stress given force due to circumferential stress in thin cylindrical vessel

σ θ = \frac{F}{2 \cdot L cylinder \cdot t}

How to Evaluate Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio?

Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio evaluator uses Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell to evaluate the Hoop Stress in Thin shell, Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio 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 in Thin shell is denoted by σ_θ symbol.

How to evaluate Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio using this online evaluator? To use this online evaluator for Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio, enter Strain in thin shell (ε), Poisson's Ratio (𝛎) & Modulus of Elasticity Of Thin Shell (E) and hit the calculate button.

FAQs on Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio

What is the formula to find Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio?

The formula of Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio is expressed as Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell. Here is an example- 4.3E-5 = (3/(1-0.3))*10000000.

How to calculate Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio?

With Strain in thin shell (ε), Poisson's Ratio (𝛎) & Modulus of Elasticity Of Thin Shell (E) we can find Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio using the formula - Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell.

What are the other ways to Calculate Hoop Stress in Thin shell?

Here are the different ways to Calculate Hoop Stress in Thin shell-

Hoop Stress in Thin shell=(Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell
Hoop Stress in Thin shell=(Internal Pressure in thin shell*Inner Diameter of Cylinderical Vessel)/(2*Thickness Of Thin Shell*Efficiency of Longitudinal Joint)

Can the Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio be negative?

Yes, the Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio, measured in Stress can be negative.

Which unit is used to measure Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio?

Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio is usually measured using the Megapascal[MPa] for Stress. Pascal[MPa], Newton per Square Meter[MPa], Newton per Square Millimeter[MPa] are the few other units in which Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio can be measured.

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