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Condition for Minimum Normal Stress Formula

GoCondition for Maximum Value of Normal Stress Formula

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Plane Angle is the measure of the inclination between two intersecting lines in a flat surface, usually expressed in degrees. Check FAQs

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

θ_plane - Plane Angle?τ - Shear Stress in Mpa?σ_x - Stress Along x Direction?σ_y - Stress Along y Direction?

Condition for Minimum Normal Stress Example

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Here is how the Condition for Minimum Normal Stress equation looks like with Values.

Here is how the Condition for Minimum Normal Stress equation looks like with Units.

Here is how the Condition for Minimum Normal Stress equation looks like.

24.3339 = \frac{a \tan (\frac{2 \cdot 41.5}{95 - 22})}{2}

24.3339° = \frac{a \tan (\frac{2 \cdot 41.5MPa}{95MPa - 22MPa})}{2}

24.3339 = \frac{a \tan (\frac{2 \cdot 41.5}{95 - 22})}{2}

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Condition for Minimum Normal Stress Solution

Follow our step by step solution on how to calculate Condition for Minimum Normal Stress?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ plane = \frac{a \tan (\frac{2 \cdot 41.5MPa}{95MPa - 22MPa})}{2}

Next Step Convert Units

∴

θ plane = \frac{a \tan (\frac{2 \cdot 4.2E+7Pa}{9.5E+7Pa - 2.2E+7Pa})}{2}

Next Step Prepare to Evaluate

∴

θ plane = \frac{a \tan (\frac{2 \cdot 4.2E+7}{9.5E+7 - 2.2E+7})}{2}

Next Step Evaluate

∴

θ plane = 0.424706570615896rad

Next Step Convert to Output's Unit

∴

θ plane = 24.3338940277703°

LAST Step Rounding Answer

∴

θ plane = 24.3339°

Condition for Minimum Normal Stress Formula Elements

Variables

Functions

Plane Angle

Plane Angle is the measure of the inclination between two intersecting lines in a flat surface, usually expressed in degrees.

Symbol: θ_plane

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Plane Angle

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

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

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

Other Formulas to find Plane Angle

Go Condition for Maximum Value of Normal Stress

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

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

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}}

Go Minimum Value of Normal Stress

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

Go Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses

σ θ = \frac{σ major + σ minor}{2} + \frac{σ major - σ minor}{2} \cdot \cos (2 \cdot θ plane)

How to Evaluate Condition for Minimum Normal Stress?

Condition for Minimum Normal Stress evaluator uses Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2 to evaluate the Plane Angle, The Condition for Minimum Normal Stress formula is defined as when twice the angle of the plane is equal to the inverse tangent of the ratio of twice the value of shear stress to the difference of stress along x and y-direction. Plane Angle is denoted by θ_plane symbol.

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

FAQs on Condition for Minimum Normal Stress

What is the formula to find Condition for Minimum Normal Stress?

The formula of Condition for Minimum Normal Stress is expressed as Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2. Here is an example- 1394.229 = (atan((2*41500000)/(95000000-22000000)))/2.

How to calculate Condition for Minimum Normal Stress?

With Shear Stress in Mpa (τ), Stress Along x Direction (σ_x) & Stress Along y Direction (σ_y) we can find Condition for Minimum Normal Stress using the formula - Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2. This formula also uses Tangent (tan), Inverse Tan (atan) function(s).

What are the other ways to Calculate Plane Angle?

Here are the different ways to Calculate Plane Angle-

Plane Angle=(atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2

Can the Condition for Minimum Normal Stress be negative?

No, the Condition for Minimum Normal Stress, measured in Angle cannot be negative.

Which unit is used to measure Condition for Minimum Normal Stress?

Condition for Minimum Normal Stress is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Condition for Minimum Normal Stress can be measured.

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Condition for Minimum Normal Stress Formula

​GoCondition for Maximum Value of Normal Stress Formula

Condition for Minimum Normal Stress Example

Condition for Minimum Normal Stress Solution

Condition for Minimum Normal Stress Formula Elements

Other Formulas to find Plane Angle

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

How to Evaluate Condition for Minimum Normal Stress?

FAQs on Condition for Minimum Normal Stress

Variable Name

GoCondition for Maximum Value of Normal Stress Formula