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

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Normal Stress on Oblique Plane is the stress acting normally to its oblique plane. Check FAQs

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

σ_θ - Normal Stress on Oblique Plane?σ_major - Major Principal Stress?σ_minor - Minor Principal Stress?θ_plane - Plane Angle?

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

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Here is how the Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses equation looks like with Values.

Here is how the Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses equation looks like with Units.

Here is how the Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses equation looks like.

62.25 = \frac{75 + 24}{2} + \frac{75 - 24}{2} \cdot \cos (2 \cdot 30)

62.25MPa = \frac{75MPa + 24MPa}{2} + \frac{75MPa - 24MPa}{2} \cdot \cos (2 \cdot 30°)

62.25 = \frac{75 + 24}{2} + \frac{75 - 24}{2} \cdot \cos (2 \cdot 30)

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

Follow our step by step solution on how to calculate Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

σ θ = \frac{75MPa + 24MPa}{2} + \frac{75MPa - 24MPa}{2} \cdot \cos (2 \cdot 30°)

Next Step Convert Units

∴

σ θ = \frac{7.5E+7Pa + 2.4E+7Pa}{2} + \frac{7.5E+7Pa - 2.4E+7Pa}{2} \cdot \cos (2 \cdot 0.5236rad)

Next Step Prepare to Evaluate

∴

σ θ = \frac{7.5E+7 + 2.4E+7}{2} + \frac{7.5E+7 - 2.4E+7}{2} \cdot \cos (2 \cdot 0.5236)

Next Step Evaluate

∴

σ θ = 62250000.0000044Pa

Next Step Convert to Output's Unit

∴

σ θ = 62.2500000000044MPa

LAST Step Rounding Answer

∴

σ θ = 62.25MPa

Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses Formula Elements

Variables

Functions

Normal Stress on Oblique Plane

Normal Stress on Oblique Plane is the stress acting normally to its oblique plane.

Symbol: σ_θ

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Normal Stress on Oblique Plane

Major Principal Stress

Major Principal Stress is the maximum normal stress acting on the principal plane.

Symbol: σ_major

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Major Principal Stress

Minor Principal Stress

Minor Principal Stress is the minimum normal stress acting on the principal plane.

Symbol: σ_minor

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Minor Principal Stress

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

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

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

Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses evaluator uses Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle) to evaluate the Normal Stress on Oblique Plane, The Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses formula is defined as the ratio of total normal stress acting on the plane to the cross-sectional area. Normal Stress on Oblique Plane is denoted by σ_θ symbol.

How to evaluate Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses using this online evaluator? To use this online evaluator for Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses, enter Major Principal Stress (σ_major), Minor Principal Stress (σ_minor) & Plane Angle (θ_plane) and hit the calculate button.

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

What is the formula to find Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses?

The formula of Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses is expressed as Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle). Here is an example- 6.2E-5 = (75000000+24000000)/2+(75000000-24000000)/2*cos(2*0.5235987755982).

How to calculate Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses?

With Major Principal Stress (σ_major), Minor Principal Stress (σ_minor) & Plane Angle (θ_plane) we can find Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses using the formula - Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle). This formula also uses Cosine function(s).

Can the Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses be negative?

No, the Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses, measured in Stress cannot be negative.

Which unit is used to measure Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses?

Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses 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 Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses can be measured.

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

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

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

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

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

Variable Name