Angle of Oblique Plane using Shear Stress and Axial Load Calculator

✖The Shear Stress on Oblique Plane is the shear stress experienced by a body at any θ angle.ⓘ Shear Stress on Oblique Plane [τ_θ]			+10% -10%
✖The Stress along y Direction can be described as axial stress along the given direction.ⓘ Stress along y Direction [σ_y]			+10% -10%

✖The Theta is the angle subtended by a plane of a body when stress is applied.ⓘ Angle of Oblique Plane using Shear Stress and Axial Load [θ]

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Formula

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Angle of Oblique Plane using Shear Stress and Axial Load

Formula

`"θ" = (arsin(((2*"τ"_{"θ"})/"σ"_{"y"})))/2`

Example

`"15.38948°"=(arsin(((2*"28.145MPa")/"110MPa")))/2`

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Angle of Oblique Plane using Shear Stress and Axial Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theta = (arsin(((2*Shear Stress on Oblique Plane)/Stress along y Direction)))/2
θ = (arsin(((2*τ_θ)/σ_y)))/2
This formula uses 2 Functions, 3 Variables

Functions Used

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., sin(Angle)
arsin - Arcsine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., arsin(Number)

Variables Used

Theta - (Measured in Radian) - The Theta is the angle subtended by a plane of a body when stress is applied.
Shear Stress on Oblique Plane - (Measured in Pascal) - The Shear Stress on Oblique Plane is the shear stress experienced by a body at any θ angle.
Stress along y Direction - (Measured in Pascal) - The Stress along y Direction can be described as axial stress along the given direction.

STEP 1: Convert Input(s) to Base Unit

Shear Stress on Oblique Plane: 28.145 Megapascal --> 28145000 Pascal (Check conversion here)
Stress along y Direction: 110 Megapascal --> 110000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = (arsin(((2*τ_θ)/σ_y)))/2 --> (arsin(((2*28145000)/110000000)))/2

Evaluating ... ...

θ = 0.268597018934037

STEP 3: Convert Result to Output's Unit

0.268597018934037 Radian -->15.3894755747187 Degree (Check conversion here)

FINAL ANSWER

15.3894755747187 ≈ 15.38948 Degree <-- Theta

(Calculation completed in 00.004 seconds)

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< 6 Stresses of Members Subjected to Axial Loading Calculators

Angle of Oblique Plane using Shear Stress and Axial Load

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

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

Go Stress along y Direction = Shear Stress on Oblique Plane/(0.5*sin(2*Theta))

Angle of Oblique plane when Member Subjected to Axial Loading

Go Theta = (acos(Normal Stress on Oblique Plane/Stress along y Direction))/2

Shear Stress when Member Subjected to Axial Load

Go Shear Stress on Oblique Plane = 0.5*Stress along y Direction*sin(2*Theta)

Stress along Y-direction when Member Subjected to Axial Load

Go Stress along y Direction = Normal Stress on Oblique Plane/(cos(2*Theta))

Normal Stress when Member Subjected to Axial Load

Go Normal Stress on Oblique Plane = Stress along y Direction*cos(2*Theta)

Angle of Oblique Plane using Shear Stress and Axial Load Formula

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

What is Principal Stress?

The Principal Stress is the maximum normal stress a body can have at its some point. It represents purely normal stress. If at some point principal stress is said to have acted it does not have any shear stress component.

How to Calculate Angle of Oblique Plane using Shear Stress and Axial Load?

Angle of Oblique Plane using Shear Stress and Axial Load calculator uses Theta = (arsin(((2*Shear Stress on Oblique Plane)/Stress along y Direction)))/2 to calculate the Theta, The Angle of Oblique Plane using Shear Stress and Axial Load formula is defined as the angle between the plane and the vertical line. Theta is denoted by θ symbol.

How to calculate Angle of Oblique Plane using Shear Stress and Axial Load using this online calculator? To use this online calculator for Angle of Oblique Plane using Shear Stress and Axial Load, enter Shear Stress on Oblique Plane (τ_θ) & Stress along y Direction (σ_y) and hit the calculate button. Here is how the Angle of Oblique Plane using Shear Stress and Axial Load calculation can be explained with given input values -> 881.752 = (arsin(((2*28145000)/110000000)))/2.

FAQ

What is Angle of Oblique Plane using Shear Stress and Axial Load?

The Angle of Oblique Plane using Shear Stress and Axial Load formula is defined as the angle between the plane and the vertical line and is represented as θ = (arsin(((2*τ_θ)/σ_y)))/2 or Theta = (arsin(((2*Shear Stress on Oblique Plane)/Stress along y Direction)))/2. The Shear Stress on Oblique Plane is the shear stress experienced by a body at any θ angle & The Stress along y Direction can be described as axial stress along the given direction.

How to calculate Angle of Oblique Plane using Shear Stress and Axial Load?

The Angle of Oblique Plane using Shear Stress and Axial Load formula is defined as the angle between the plane and the vertical line is calculated using Theta = (arsin(((2*Shear Stress on Oblique Plane)/Stress along y Direction)))/2. To calculate Angle of Oblique Plane using Shear Stress and Axial Load, you need Shear Stress on Oblique Plane (τ_θ) & Stress along y Direction (σ_y). With our tool, you need to enter the respective value for Shear Stress on Oblique Plane & Stress along y Direction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Theta?

In this formula, Theta uses Shear Stress on Oblique Plane & Stress along y Direction. We can use 1 other way(s) to calculate the same, which is/are as follows -

Theta = (acos(Normal Stress on Oblique Plane/Stress along y Direction))/2

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