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Minimum Principal Stress Formula

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Minimum principal stress can be defined as the plane carrying minimum normal stress is known as minor. principal plane and the stress acting on it is called as minor principal stress. Check FAQs

σ min = \frac{σ x + σ y}{2} - \sqrt{{(\frac{σ x - σ y}{2})}^{2} + {ζ xy}^{2}}

σ_min - Minimum principal stress?σ_x - Normal stress along x direction?σ_y - Normal stress along y direction?ζ_xy - Shear stress acting in xy plane?

Minimum Principal Stress Example

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Here is how the Minimum Principal Stress equation looks like with Values.

Here is how the Minimum Principal Stress equation looks like with Units.

Here is how the Minimum Principal Stress equation looks like.

23.9445 = \frac{80 + 40}{2} - \sqrt{{(\frac{80 - 40}{2})}^{2} + 30^{2}}

23.9445MPa = \frac{80MPa + 40MPa}{2} - \sqrt{{(\frac{80MPa - 40MPa}{2})}^{2} + {30MPa}^{2}}

23.9445 = \frac{80 + 40}{2} - \sqrt{{(\frac{80 - 40}{2})}^{2} + 30^{2}}

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Minimum Principal Stress Solution

Follow our step by step solution on how to calculate Minimum Principal Stress?

FIRST Step Consider the formula

σ min = \frac{σ x + σ y}{2} - \sqrt{{(\frac{σ x - σ y}{2})}^{2} + {ζ xy}^{2}}

Next Step Substitute values of Variables

∴

σ min = \frac{80MPa + 40MPa}{2} - \sqrt{{(\frac{80MPa - 40MPa}{2})}^{2} + {30MPa}^{2}}

Next Step Convert Units

∴

σ min = \frac{8E+7Pa + 4E+7Pa}{2} - \sqrt{{(\frac{8E+7Pa - 4E+7Pa}{2})}^{2} + {3E+7Pa}^{2}}

Next Step Prepare to Evaluate

∴

σ min = \frac{8E+7 + 4E+7}{2} - \sqrt{{(\frac{8E+7 - 4E+7}{2})}^{2} + {3E+7}^{2}}

Next Step Evaluate

∴

σ min = 23944487.2453601Pa

Next Step Convert to Output's Unit

∴

σ min = 23.9444872453601MPa

LAST Step Rounding Answer

∴

σ min = 23.9445MPa

Minimum Principal Stress Formula Elements

Variables

Functions

Minimum principal stress

Minimum principal stress can be defined as the plane carrying minimum normal stress is known as minor. principal plane and the stress acting on it is called as minor principal stress.

Symbol: σ_min

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Minimum principal stress

Normal stress along x direction

Normal stress along x direction is the internal resistive force acting longitudinally.

Symbol: σ_x

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Normal stress along x direction

Normal stress along y direction

Normal stress along y direction is the internal resistive force per unit area acting along y direction.

Symbol: σ_y

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Normal stress along y direction

Shear stress acting in xy plane

Shear stress acting in xy plane is the shear stress on xy plane.

Symbol: ζ_xy

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Shear stress acting in xy plane

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 in Analysis of Stresses category

Go Stress on Inclined Plane

σ i = \frac{P t \cdot {(\cos (θ))}^{2}}{A i}

Go Shear Stress on Inclined Plane

ζ i = - P t \cdot \sin (θ) \cdot \frac{\cos (θ)}{A i}

Go Maximum Principal Stress

σ max = \frac{σ x + σ y}{2} + \sqrt{{(\frac{σ x - σ y}{2})}^{2} + {ζ xy}^{2}}

Go Area of Inclined Plane given Stress

A i = \frac{P t \cdot {(\cos (θ))}^{2}}{σ i}

How to Evaluate Minimum Principal Stress?

Minimum Principal Stress evaluator uses Minimum principal stress = (Normal stress along x direction+Normal stress along y direction)/2-sqrt(((Normal stress along x direction-Normal stress along y direction)/2)^2+Shear stress acting in xy plane^2) to evaluate the Minimum principal stress, The Minimum principal stress formula is defined as the plane carrying minimum normal stress is known as minor. principal plane and the stress acting on it is called as minor principal stress. Minimum principal stress is denoted by σ_min symbol.

How to evaluate Minimum Principal Stress using this online evaluator? To use this online evaluator for Minimum Principal Stress, enter Normal stress along x direction (σ_x), Normal stress along y direction (σ_y) & Shear stress acting in xy plane (ζ_xy) and hit the calculate button.

FAQs on Minimum Principal Stress

What is the formula to find Minimum Principal Stress?

The formula of Minimum Principal Stress is expressed as Minimum principal stress = (Normal stress along x direction+Normal stress along y direction)/2-sqrt(((Normal stress along x direction-Normal stress along y direction)/2)^2+Shear stress acting in xy plane^2). Here is an example- 2.4E-5 = (80000000+40000000)/2-sqrt(((80000000-40000000)/2)^2+30000000^2).

How to calculate Minimum Principal Stress?

With Normal stress along x direction (σ_x), Normal stress along y direction (σ_y) & Shear stress acting in xy plane (ζ_xy) we can find Minimum Principal Stress using the formula - Minimum principal stress = (Normal stress along x direction+Normal stress along y direction)/2-sqrt(((Normal stress along x direction-Normal stress along y direction)/2)^2+Shear stress acting in xy plane^2). This formula also uses Square Root Function function(s).

Can the Minimum Principal Stress be negative?

Yes, the Minimum Principal Stress, measured in Pressure can be negative.

Which unit is used to measure Minimum Principal Stress?

Minimum Principal Stress is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Minimum Principal Stress can be measured.

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Minimum Principal Stress Formula

Minimum Principal Stress Example

Minimum Principal Stress Solution

Minimum Principal Stress Formula Elements

Other formulas in Analysis of Stresses category

How to Evaluate Minimum Principal Stress?

FAQs on Minimum Principal Stress

Variable Name