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Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress Formula

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Tangential Stress on Oblique Plane is the total force acting in the tangential direction divided by the area of the surface. Check FAQs

σ t = \frac{σ major - σ minor}{2} \cdot \sin (2 \cdot θ plane)

σ_t - Tangential Stress on Oblique Plane?σ_major - Major Principal Stress?σ_minor - Minor Principal Stress?θ_plane - Plane Angle?

Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress Example

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Here is how the Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress equation looks like with Values.

Here is how the Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress equation looks like with Units.

Here is how the Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress equation looks like.

22.0836 = \frac{75 - 24}{2} \cdot \sin (2 \cdot 30)

22.0836MPa = \frac{75MPa - 24MPa}{2} \cdot \sin (2 \cdot 30°)

22.0836 = \frac{75 - 24}{2} \cdot \sin (2 \cdot 30)

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Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress Solution

Follow our step by step solution on how to calculate Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress?

FIRST Step Consider the formula

σ t = \frac{σ major - σ minor}{2} \cdot \sin (2 \cdot θ plane)

Next Step Substitute values of Variables

∴

σ t = \frac{75MPa - 24MPa}{2} \cdot \sin (2 \cdot 30°)

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

σ t = 22083647.7965007Pa

Next Step Convert to Output's Unit

∴

σ t = 22.0836477965007MPa

LAST Step Rounding Answer

∴

σ t = 22.0836MPa

Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress Formula Elements

Variables

Functions

Tangential Stress on Oblique Plane

Tangential Stress on Oblique Plane is the total force acting in the tangential direction divided by the area of the surface.

Symbol: σ_t

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Tangential 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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(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 Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress?

Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress evaluator uses Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle) to evaluate the Tangential Stress on Oblique Plane, The Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress formula is defined as the total force acting in the tangential direction divided by the area of the surface. Tangential Stress on Oblique Plane is denoted by σ_t symbol.

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

FAQs on Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress

What is the formula to find Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress?

The formula of Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress is expressed as Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle). Here is an example- 2.2E-5 = (75000000-24000000)/2*sin(2*0.5235987755982).

How to calculate Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress?

With Major Principal Stress (σ_major), Minor Principal Stress (σ_minor) & Plane Angle (θ_plane) we can find Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress using the formula - Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle). This formula also uses Sine function(s).

Can the Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress be negative?

No, the Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress, measured in Stress cannot be negative.

Which unit is used to measure Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress?

Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal 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 Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress can be measured.

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Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress Formula

Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress Example

Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress Solution

Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal 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 Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress?

FAQs on Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress

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