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Minimum Value of Normal Stress Formula

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Minimum Normal Stress is equal to the minor principal stress value or minimum principal stress value. Check FAQs

σ n,min = \frac{σ x + σ y}{2} - \sqrt{{(\frac{σ x - σ y}{2})}^{2} + τ^{2}}

σ_n,min - Minimum Normal Stress?σ_x - Stress Along x Direction?σ_y - Stress Along y Direction?τ - Shear Stress in Mpa?

Minimum Value of Normal Stress Example

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Here is how the Minimum Value of Normal Stress equation looks like with Values.

Here is how the Minimum Value of Normal Stress equation looks like with Units.

Here is how the Minimum Value of Normal Stress equation looks like.

3.2325 = \frac{95 + 22}{2} - \sqrt{{(\frac{95 - 22}{2})}^{2} + {41.5}^{2}}

3.2325MPa = \frac{95MPa + 22MPa}{2} - \sqrt{{(\frac{95MPa - 22MPa}{2})}^{2} + {41.5MPa}^{2}}

3.2325 = \frac{95 + 22}{2} - \sqrt{{(\frac{95 - 22}{2})}^{2} + {41.5}^{2}}

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Minimum Value of Normal Stress Solution

Follow our step by step solution on how to calculate Minimum Value of Normal Stress?

FIRST Step Consider the formula

σ n,min = \frac{σ x + σ y}{2} - \sqrt{{(\frac{σ x - σ y}{2})}^{2} + τ^{2}}

Next Step Substitute values of Variables

∴

σ n,min = \frac{95MPa + 22MPa}{2} - \sqrt{{(\frac{95MPa - 22MPa}{2})}^{2} + {41.5MPa}^{2}}

Next Step Convert Units

∴

σ n,min = \frac{9.5E+7Pa + 2.2E+7Pa}{2} - \sqrt{{(\frac{9.5E+7Pa - 2.2E+7Pa}{2})}^{2} + {4.2E+7Pa}^{2}}

Next Step Prepare to Evaluate

∴

σ n,min = \frac{9.5E+7 + 2.2E+7}{2} - \sqrt{{(\frac{9.5E+7 - 2.2E+7}{2})}^{2} + {4.2E+7}^{2}}

Next Step Evaluate

∴

σ n,min = 3232468.84471861Pa

Next Step Convert to Output's Unit

∴

σ n,min = 3.23246884471861MPa

LAST Step Rounding Answer

∴

σ n,min = 3.2325MPa

Minimum Value of Normal Stress Formula Elements

Variables

Functions

Minimum Normal Stress

Minimum Normal Stress is equal to the minor principal stress value or minimum principal stress value.

Symbol: σ_n,min

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Minimum Normal Stress

Stress Along x Direction

Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation.

Symbol: σ_x

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress Along x Direction

Stress Along y Direction

Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure.

Symbol: σ_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress Along y Direction

Shear Stress in Mpa

Shear Stress in Mpa, 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 Mpa

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 Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular and a Simple Shear Stress category

Go Condition for Maximum Value of Normal Stress

θ plane = \frac{a \tan (\frac{2 \cdot τ}{σ x - σ y})}{2}

Go Condition for Minimum Normal Stress

θ plane = \frac{a \tan (\frac{2 \cdot τ}{σ x - σ y})}{2}

Go Maximum Value of Normal Stress

σ n,max = \frac{σ x + σ y}{2} + \sqrt{{(\frac{σ x - σ y}{2})}^{2} + τ^{2}}

Go Maximum Value of Shear Stress

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

How to Evaluate Minimum Value of Normal Stress?

Minimum Value of Normal Stress evaluator uses Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2) to evaluate the Minimum Normal Stress, The Minimum Value of Normal Stress formula is defined as equal to the minor principal stress value or minimum principal stress value. Minimum Normal Stress is denoted by σ_n,min symbol.

How to evaluate Minimum Value of Normal Stress using this online evaluator? To use this online evaluator for Minimum Value of Normal Stress, enter Stress Along x Direction (σ_x), Stress Along y Direction (σ_y) & Shear Stress in Mpa (τ) and hit the calculate button.

FAQs on Minimum Value of Normal Stress

What is the formula to find Minimum Value of Normal Stress?

The formula of Minimum Value of Normal Stress is expressed as Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2). Here is an example- 3.2E-6 = (95000000+22000000)/2-sqrt(((95000000-22000000)/2)^2+41500000^2).

How to calculate Minimum Value of Normal Stress?

With Stress Along x Direction (σ_x), Stress Along y Direction (σ_y) & Shear Stress in Mpa (τ) we can find Minimum Value of Normal Stress using the formula - Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2). This formula also uses Square Root (sqrt) function(s).

Can the Minimum Value of Normal Stress be negative?

No, the Minimum Value of Normal Stress, measured in Stress cannot be negative.

Which unit is used to measure Minimum Value of Normal Stress?

Minimum Value of Normal 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 Minimum Value of Normal Stress can be measured.

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Minimum Value of Normal Stress Formula

Minimum Value of Normal Stress Example

Minimum Value of Normal Stress Solution

Minimum Value of Normal Stress Formula Elements

Other formulas in Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular and a Simple Shear Stress category

How to Evaluate Minimum Value of Normal Stress?

FAQs on Minimum Value of Normal Stress

Variable Name