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Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces 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 x - σ y}{2} \cdot \sin (2 \cdot θ plane) - τ \cdot \cos (2 \cdot θ plane)

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

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces Example

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Here is how the Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces equation looks like with Values.

Here is how the Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces equation looks like with Units.

Here is how the Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces equation looks like.

10.8599 = \frac{95 - 22}{2} \cdot \sin (2 \cdot 30) - 41.5 \cdot \cos (2 \cdot 30)

10.8599MPa = \frac{95MPa - 22MPa}{2} \cdot \sin (2 \cdot 30°) - 41.5MPa \cdot \cos (2 \cdot 30°)

10.8599 = \frac{95 - 22}{2} \cdot \sin (2 \cdot 30) - 41.5 \cdot \cos (2 \cdot 30)

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Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces Solution

Follow our step by step solution on how to calculate Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces?

FIRST Step Consider the formula

σ t = \frac{σ x - σ y}{2} \cdot \sin (2 \cdot θ plane) - τ \cdot \cos (2 \cdot θ plane)

Next Step Substitute values of Variables

∴

σ t = \frac{95MPa - 22MPa}{2} \cdot \sin (2 \cdot 30°) - 41.5MPa \cdot \cos (2 \cdot 30°)

Next Step Convert Units

∴

σ t = \frac{95MPa - 22MPa}{2} \cdot \sin (2 \cdot 0.5236rad) - 41.5MPa \cdot \cos (2 \cdot 0.5236rad)

Next Step Prepare to Evaluate

∴

σ t = \frac{95 - 22}{2} \cdot \sin (2 \cdot 0.5236) - 41.5 \cdot \cos (2 \cdot 0.5236)

Next Step Evaluate

∴

σ t = 10859927.2381213Pa

Next Step Convert to Output's Unit

∴

σ t = 10.8599272381213MPa

LAST Step Rounding Answer

∴

σ t = 10.8599MPa

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces 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

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

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

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)

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 Tensile Stress of Unequal Intensity category

Go Maximum Shear Stress

τ max = \frac{\sqrt{{(σ x - σ y)}^{2} + 4 \cdot τ^{2}}}{2}

Go Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces

σ θ = \frac{σ x + σ y}{2} + \frac{σ x - σ y}{2} \cdot \cos (2 \cdot θ plane) + τ \cdot \sin (2 \cdot θ plane)

Go Radius of Mohr's Circle for Two Mutually Perpendicular Stresses of Unequal Intensities

R = \frac{σ major - σ minor}{2}

How to Evaluate Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces?

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces evaluator uses Tangential Stress on Oblique Plane = (Stress Along x Direction-Stress Along y Direction)/2*sin(2*Plane Angle)-Shear Stress in Mpa*cos(2*Plane Angle) to evaluate the Tangential Stress on Oblique Plane, The Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces 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 Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces using this online evaluator? To use this online evaluator for Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces, enter Stress Along x Direction (σ_x), Stress Along y Direction (σ_y), Plane Angle (θ_plane) & Shear Stress in Mpa (τ) and hit the calculate button.

FAQs on Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces

What is the formula to find Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces?

The formula of Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces is expressed as Tangential Stress on Oblique Plane = (Stress Along x Direction-Stress Along y Direction)/2*sin(2*Plane Angle)-Shear Stress in Mpa*cos(2*Plane Angle). Here is an example- 1.1E-5 = (95000000-22000000)/2*sin(2*0.5235987755982)-41500000*cos(2*0.5235987755982).

How to calculate Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces?

With Stress Along x Direction (σ_x), Stress Along y Direction (σ_y), Plane Angle (θ_plane) & Shear Stress in Mpa (τ) we can find Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces using the formula - Tangential Stress on Oblique Plane = (Stress Along x Direction-Stress Along y Direction)/2*sin(2*Plane Angle)-Shear Stress in Mpa*cos(2*Plane Angle). This formula also uses Sine (sin), Cosine (cos) function(s).

Can the Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces be negative?

No, the Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces, measured in Stress cannot be negative.

Which unit is used to measure Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces?

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces 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 Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces can be measured.

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Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces Formula

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces Example

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces Solution

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces Formula Elements

Other formulas in Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular Tensile Stress of Unequal Intensity category

How to Evaluate Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces?

FAQs on Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces

Variable Name