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Major principal stress in thin cylindrical stress Formula

GoMajor principal stress in thin cylindrical stress given maximum shear stress Formula

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The Major Principal Stress Value. Check FAQs

σ max = (\frac{σ θ + σ l}{2}) + (\sqrt{({(\frac{σ θ + σ l}{2})}^{2}) + (𝜏^{2})})

σ_max - Major Principal Stress?σ_θ - Hoop Stress in Thin shell?σ_l - Longitudinal Stress?𝜏 - Shear Stress in Cylindrical Shell?

Major principal stress in thin cylindrical stress Example

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Here is how the Major principal stress in thin cylindrical stress equation looks like with Values.

Here is how the Major principal stress in thin cylindrical stress equation looks like with Units.

Here is how the Major principal stress in thin cylindrical stress equation looks like.

25.1299 = (\frac{25.03 + 0.09}{2}) + (\sqrt{({(\frac{25.03 + 0.09}{2})}^{2}) + ({0.5}^{2})})

25.1299MPa = (\frac{25.03MPa + 0.09MPa}{2}) + (\sqrt{({(\frac{25.03MPa + 0.09MPa}{2})}^{2}) + ({0.5MPa}^{2})})

25.1299 = (\frac{25.03 + 0.09}{2}) + (\sqrt{({(\frac{25.03 + 0.09}{2})}^{2}) + ({0.5}^{2})})

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Major principal stress in thin cylindrical stress Solution

Follow our step by step solution on how to calculate Major principal stress in thin cylindrical stress?

FIRST Step Consider the formula

σ max = (\frac{σ θ + σ l}{2}) + (\sqrt{({(\frac{σ θ + σ l}{2})}^{2}) + (𝜏^{2})})

Next Step Substitute values of Variables

∴

σ max = (\frac{25.03MPa + 0.09MPa}{2}) + (\sqrt{({(\frac{25.03MPa + 0.09MPa}{2})}^{2}) + ({0.5MPa}^{2})})

Next Step Convert Units

∴

σ max = (\frac{2.5E+7Pa + 90000Pa}{2}) + (\sqrt{({(\frac{2.5E+7Pa + 90000Pa}{2})}^{2}) + ({500000Pa}^{2})})

Next Step Prepare to Evaluate

∴

σ max = (\frac{2.5E+7 + 90000}{2}) + (\sqrt{({(\frac{2.5E+7 + 90000}{2})}^{2}) + (500000^{2})})

Next Step Evaluate

∴

σ max = 25129948.289472Pa

Next Step Convert to Output's Unit

∴

σ max = 25.129948289472MPa

LAST Step Rounding Answer

∴

σ max = 25.1299MPa

Major principal stress in thin cylindrical stress Formula Elements

Variables

Functions

Major Principal Stress

The Major Principal Stress Value.

Symbol: σ_max

Measurement: StressUnit: MPa

Note: Value can be positive or negative.

Formulas to find Major Principal Stress

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

Longitudinal Stress

Longitudinal Stress is defined as the stress produced when a pipe is subjected to internal pressure.

Symbol: σ_l

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Longitudinal Stress

Shear Stress in Cylindrical Shell

Shear Stress in Cylindrical Shell is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

Symbol: 𝜏

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress in Cylindrical Shell

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Major Principal Stress

Go Major principal stress in thin cylindrical stress given maximum shear stress

σ max = (2 \cdot 𝜏 max) + σ min

Other formulas in Thin Cylindrical Vessel Subjected to Internal Fluid Pressure and Torque category

Go Minor principal stress in thin cylindrical stress

σ min = (\frac{σ θ + σ l}{2}) - (\sqrt{({(\frac{σ θ + σ l}{2})}^{2}) + (𝜏^{2})})

Go Maximum shear stress in thin cylindrical stress

𝜏 max = (\frac{1}{2}) \cdot (σ max - σ min)

Go Minor principal stress in thin cylindrical stress given maximum shear stress

σ min = σ max - (2 \cdot 𝜏 max)

How to Evaluate Major principal stress in thin cylindrical stress?

Major principal stress in thin cylindrical stress evaluator uses Major Principal Stress = ((Hoop Stress in Thin shell+Longitudinal Stress)/2)+(sqrt((((Hoop Stress in Thin shell+Longitudinal Stress)/2)^2)+(Shear Stress in Cylindrical Shell^2))) to evaluate the Major Principal Stress, Major principal stress in thin cylindrical stress is the major normal stress acting on the principle plane. Major Principal Stress is denoted by σ_max symbol.

How to evaluate Major principal stress in thin cylindrical stress using this online evaluator? To use this online evaluator for Major principal stress in thin cylindrical stress, enter Hoop Stress in Thin shell (σ_θ), Longitudinal Stress (σ_l) & Shear Stress in Cylindrical Shell (𝜏) and hit the calculate button.

FAQs on Major principal stress in thin cylindrical stress

What is the formula to find Major principal stress in thin cylindrical stress?

The formula of Major principal stress in thin cylindrical stress is expressed as Major Principal Stress = ((Hoop Stress in Thin shell+Longitudinal Stress)/2)+(sqrt((((Hoop Stress in Thin shell+Longitudinal Stress)/2)^2)+(Shear Stress in Cylindrical Shell^2))). Here is an example- 2.9E-5 = ((25030000+90000)/2)+(sqrt((((25030000+90000)/2)^2)+(500000^2))).

How to calculate Major principal stress in thin cylindrical stress?

With Hoop Stress in Thin shell (σ_θ), Longitudinal Stress (σ_l) & Shear Stress in Cylindrical Shell (𝜏) we can find Major principal stress in thin cylindrical stress using the formula - Major Principal Stress = ((Hoop Stress in Thin shell+Longitudinal Stress)/2)+(sqrt((((Hoop Stress in Thin shell+Longitudinal Stress)/2)^2)+(Shear Stress in Cylindrical Shell^2))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Major Principal Stress?

Here are the different ways to Calculate Major Principal Stress-

Major Principal Stress=(2*Maximum shear stress)+Minor Principal Stress

Can the Major principal stress in thin cylindrical stress be negative?

Yes, the Major principal stress in thin cylindrical stress, measured in Stress can be negative.

Which unit is used to measure Major principal stress in thin cylindrical stress?

Major principal stress in thin cylindrical stress 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 Major principal stress in thin cylindrical stress can be measured.

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Major principal stress in thin cylindrical stress Formula

​GoMajor principal stress in thin cylindrical stress given maximum shear stress Formula

Major principal stress in thin cylindrical stress Example

Major principal stress in thin cylindrical stress Solution

Major principal stress in thin cylindrical stress Formula Elements

Other Formulas to find Major Principal Stress

Other formulas in Thin Cylindrical Vessel Subjected to Internal Fluid Pressure and Torque category

How to Evaluate Major principal stress in thin cylindrical stress?

FAQs on Major principal stress in thin cylindrical stress

Variable Name

GoMajor principal stress in thin cylindrical stress given maximum shear stress Formula