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Location of Principal Planes Formula

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The Theta is the angle subtended by a plane of a body when stress is applied. Check FAQs

θ = (((\frac{1}{2}) \cdot a \tan (\frac{2 \cdot τ xy}{σ y - σ x})))

θ - Theta?τ_xy - Shear Stress xy?σ_y - Stress along y Direction?σ_x - Stress along x Direction?

Location of Principal Planes Example

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Here is how the Location of Principal Planes equation looks like with Values.

Here is how the Location of Principal Planes equation looks like with Units.

Here is how the Location of Principal Planes equation looks like.

6.2457 = (((\frac{1}{2}) \cdot a \tan (\frac{2 \cdot 7.2}{110 - 45})))

6.2457° = (((\frac{1}{2}) \cdot a \tan (\frac{2 \cdot 7.2MPa}{110MPa - 45MPa})))

6.2457 = (((\frac{1}{2}) \cdot a \tan (\frac{2 \cdot 7.2}{110 - 45})))

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Location of Principal Planes Solution

Follow our step by step solution on how to calculate Location of Principal Planes?

FIRST Step Consider the formula

θ = (((\frac{1}{2}) \cdot a \tan (\frac{2 \cdot τ xy}{σ y - σ x})))

Next Step Substitute values of Variables

∴

θ = (((\frac{1}{2}) \cdot a \tan (\frac{2 \cdot 7.2MPa}{110MPa - 45MPa})))

Next Step Convert Units

∴

θ = (((\frac{1}{2}) \cdot a \tan (\frac{2 \cdot 7.2E+6Pa}{1.1E+8Pa - 4.5E+7Pa})))

Next Step Prepare to Evaluate

∴

θ = (((\frac{1}{2}) \cdot a \tan (\frac{2 \cdot 7.2E+6}{1.1E+8 - 4.5E+7})))

Next Step Evaluate

∴

θ = 0.109008633947581rad

Next Step Convert to Output's Unit

∴

θ = 6.24573465568406°

LAST Step Rounding Answer

∴

θ = 6.2457°

Location of Principal Planes Formula Elements

Variables

Functions

Theta

The Theta is the angle subtended by a plane of a body when stress is applied.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Theta

Shear Stress xy

Shear Stress xy is the Stress acting along xy plane.

Symbol: τ_xy

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Shear Stress xy

Stress along y Direction

The Stress along y Direction can be described as axial stress along the given direction.

Symbol: σ_y

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress along y Direction

Stress along x Direction

The Stress along x Direction can be described as axial stress along the given direction.

Symbol: σ_x

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Stress along x 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 in Equivalent Bending Moment and Torque category

Go Maximum Shear Stress due to Equivalent Torque

τ max = \frac{16 \cdot T e}{π \cdot (Φ^{3})}

Go Bending Stress of Circular Shaft given Equivalent Bending Moment

σ b = \frac{32 \cdot M e}{π \cdot (Φ^{3})}

Go Diameter of Circular Shaft given Equivalent Bending Stress

Φ = {(\frac{32 \cdot M e}{π \cdot (σ b)})}^{\frac{1}{3}}

Go Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress

Φ = {(\frac{16 \cdot T e}{π \cdot (τ max)})}^{\frac{1}{3}}

How to Evaluate Location of Principal Planes?

Location of Principal Planes evaluator uses Theta = (((1/2)*atan((2*Shear Stress xy)/(Stress along y Direction-Stress along x Direction)))) to evaluate the Theta, The Location of Principal Planes formula is defined as the angle made with the principal planes along which the shear stress is zero. Theta is denoted by θ symbol.

How to evaluate Location of Principal Planes using this online evaluator? To use this online evaluator for Location of Principal Planes, enter Shear Stress xy (τ_xy), Stress along y Direction (σ_y) & Stress along x Direction (σ_x) and hit the calculate button.

FAQs on Location of Principal Planes

What is the formula to find Location of Principal Planes?

The formula of Location of Principal Planes is expressed as Theta = (((1/2)*atan((2*Shear Stress xy)/(Stress along y Direction-Stress along x Direction)))). Here is an example- 357.8542 = (((1/2)*atan((2*7200000)/(110000000-45000000)))).

How to calculate Location of Principal Planes?

With Shear Stress xy (τ_xy), Stress along y Direction (σ_y) & Stress along x Direction (σ_x) we can find Location of Principal Planes using the formula - Theta = (((1/2)*atan((2*Shear Stress xy)/(Stress along y Direction-Stress along x Direction)))). This formula also uses Tangent (tan), Inverse Tan (atan) function(s).

Can the Location of Principal Planes be negative?

No, the Location of Principal Planes, measured in Angle cannot be negative.

Which unit is used to measure Location of Principal Planes?

Location of Principal Planes is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Location of Principal Planes can be measured.

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Location of Principal Planes Formula

Location of Principal Planes Example

Location of Principal Planes Solution

Location of Principal Planes Formula Elements

Other formulas in Equivalent Bending Moment and Torque category

How to Evaluate Location of Principal Planes?

FAQs on Location of Principal Planes

Variable Name