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

σ_θ - Normal 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?

Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces Example

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

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

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

112.6901 = \frac{95 + 22}{2} + \frac{95 - 22}{2} \cdot \cos (2 \cdot 30) + 41.5 \cdot \sin (2 \cdot 30)

112.6901MPa = \frac{95MPa + 22MPa}{2} + \frac{95MPa - 22MPa}{2} \cdot \cos (2 \cdot 30°) + 41.5MPa \cdot \sin (2 \cdot 30°)

112.6901 = \frac{95 + 22}{2} + \frac{95 - 22}{2} \cdot \cos (2 \cdot 30) + 41.5 \cdot \sin (2 \cdot 30)

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Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces Solution

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

FIRST Step Consider the formula

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)

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

σ θ = 112690054.257056Pa

Next Step Convert to Output's Unit

∴

σ θ = 112.690054257056MPa

LAST Step Rounding Answer

∴

σ θ = 112.6901MPa

Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces 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

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

R = \frac{σ major - σ minor}{2}

Go Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces

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

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

Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces evaluator uses Normal Stress on Oblique Plane = (Stress Along x Direction+Stress Along y Direction)/2+(Stress Along x Direction-Stress Along y Direction)/2*cos(2*Plane Angle)+Shear Stress in Mpa*sin(2*Plane Angle) to evaluate the Normal Stress on Oblique Plane, The Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces formula is defined as the total normal force ratio to the cross-section area. Normal Stress on Oblique Plane is denoted by σ_θ symbol.

How to evaluate Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces using this online evaluator? To use this online evaluator for Normal 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 Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces

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

The formula of Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces is expressed as Normal Stress on Oblique Plane = (Stress Along x Direction+Stress Along y Direction)/2+(Stress Along x Direction-Stress Along y Direction)/2*cos(2*Plane Angle)+Shear Stress in Mpa*sin(2*Plane Angle). Here is an example- 0.000113 = (95000000+22000000)/2+(95000000-22000000)/2*cos(2*0.5235987755982)+41500000*sin(2*0.5235987755982).

How to calculate Normal 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 Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces using the formula - Normal Stress on Oblique Plane = (Stress Along x Direction+Stress Along y Direction)/2+(Stress Along x Direction-Stress Along y Direction)/2*cos(2*Plane Angle)+Shear Stress in Mpa*sin(2*Plane Angle). This formula also uses Sine (sin), Cosine (cos) function(s).

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

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

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

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

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Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces Formula

Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces Example

Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces Solution

Normal 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 Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces?

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

Variable Name