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Angle of Oblique plane when Member Subjected to Axial Loading Formula

GoAngle of Oblique Plane using Shear Stress and Axial Load 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{a \cos (\frac{σ θ}{σ y})}{2}

θ - Theta?σ_θ - Normal Stress on Oblique Plane?σ_y - Stress along y Direction?

Angle of Oblique plane when Member Subjected to Axial Loading Example

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Here is how the Angle of Oblique plane when Member Subjected to Axial Loading equation looks like with Values.

Here is how the Angle of Oblique plane when Member Subjected to Axial Loading equation looks like with Units.

Here is how the Angle of Oblique plane when Member Subjected to Axial Loading equation looks like.

30.003 = \frac{a \cos (\frac{54.99}{110})}{2}

30.003° = \frac{a \cos (\frac{54.99MPa}{110MPa})}{2}

30.003 = \frac{a \cos (\frac{54.99}{110})}{2}

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Angle of Oblique plane when Member Subjected to Axial Loading Solution

Follow our step by step solution on how to calculate Angle of Oblique plane when Member Subjected to Axial Loading?

FIRST Step Consider the formula

θ = \frac{a \cos (\frac{σ θ}{σ y})}{2}

Next Step Substitute values of Variables

∴

θ = \frac{a \cos (\frac{54.99MPa}{110MPa})}{2}

Next Step Convert Units

∴

θ = \frac{a \cos (\frac{5.5E+7Pa}{1.1E+8Pa})}{2}

Next Step Prepare to Evaluate

∴

θ = \frac{a \cos (\frac{5.5E+7}{1.1E+8})}{2}

Next Step Evaluate

∴

θ = 0.523651260396103rad

Next Step Convert to Output's Unit

∴

θ = 30.0030071574084°

LAST Step Rounding Answer

∴

θ = 30.003°

Angle of Oblique plane when Member Subjected to Axial Loading 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

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 can be positive or negative.

Formulas to find Normal Stress on Oblique Plane

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

cos

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

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

Other Formulas to find Theta

Go Angle of Oblique Plane using Shear Stress and Axial Load

θ = \frac{a r \sin ((\frac{2 \cdot τ θ}{σ y}))}{2}

Other formulas in Stresses of Members Subjected to Axial Loading category

Go Normal Stress when Member Subjected to Axial Load

σ θ = σ y \cdot \cos (2 \cdot θ)

Go Stress along Y-direction when Member Subjected to Axial Load

σ y = \frac{σ θ}{\cos (2 \cdot θ)}

Go Shear Stress when Member Subjected to Axial Load

τ θ = 0.5 \cdot σ y \cdot \sin (2 \cdot θ)

Go Stress along Y-direction given Shear Stress in Member subjected to Axial Load

σ y = \frac{τ θ}{0.5 \cdot \sin (2 \cdot θ)}

How to Evaluate Angle of Oblique plane when Member Subjected to Axial Loading?

Angle of Oblique plane when Member Subjected to Axial Loading evaluator uses Theta = (acos(Normal Stress on Oblique Plane/Stress along y Direction))/2 to evaluate the Theta, The Angle of Oblique plane when Member Subjected to Axial Loading formula is defined as calculating the angle of an oblique plane which is being acted upon by normal stress and stress in the x-direction. Theta is denoted by θ symbol.

How to evaluate Angle of Oblique plane when Member Subjected to Axial Loading using this online evaluator? To use this online evaluator for Angle of Oblique plane when Member Subjected to Axial Loading, enter Normal Stress on Oblique Plane (σ_θ) & Stress along y Direction (σ_y) and hit the calculate button.

FAQs on Angle of Oblique plane when Member Subjected to Axial Loading

What is the formula to find Angle of Oblique plane when Member Subjected to Axial Loading?

The formula of Angle of Oblique plane when Member Subjected to Axial Loading is expressed as Theta = (acos(Normal Stress on Oblique Plane/Stress along y Direction))/2. Here is an example- 1718.873 = (acos(54990000/110000000))/2.

How to calculate Angle of Oblique plane when Member Subjected to Axial Loading?

With Normal Stress on Oblique Plane (σ_θ) & Stress along y Direction (σ_y) we can find Angle of Oblique plane when Member Subjected to Axial Loading using the formula - Theta = (acos(Normal Stress on Oblique Plane/Stress along y Direction))/2. This formula also uses Cosine (cos), Inverse Cosine (acos) function(s).

What are the other ways to Calculate Theta?

Here are the different ways to Calculate Theta-

Theta=(arsin(((2*Shear Stress on Oblique Plane)/Stress along y Direction)))/2

Can the Angle of Oblique plane when Member Subjected to Axial Loading be negative?

No, the Angle of Oblique plane when Member Subjected to Axial Loading, measured in Angle cannot be negative.

Which unit is used to measure Angle of Oblique plane when Member Subjected to Axial Loading?

Angle of Oblique plane when Member Subjected to Axial Loading is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Angle of Oblique plane when Member Subjected to Axial Loading can be measured.

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