Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced Calculator

✖Normal Stress on Oblique Plane is the stress acting normally to its oblique plane.ⓘ Normal Stress on Oblique Plane [σ_θ]			+10% -10%
✖Shear Stress, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress [τ]			+10% -10%

✖The Theta is the angle subtended by a plane of a body when stress is applied.ⓘ Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced [θ]

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Formula

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Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced

Formula

`"θ" = (asin("σ"_{"θ"}/"τ"))/2`

Example

`"44.4537°"=(asin("54.99MPa"/"55MPa"))/2`

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Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theta = (asin(Normal Stress on Oblique Plane/Shear Stress))/2
θ = (asin(σ_θ/τ))/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)
asin - The inverse sine 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., asin(Number)

Variables Used

Theta - (Measured in Radian) - The Theta is the angle subtended by a plane of a body when stress is applied.
Normal Stress on Oblique Plane - (Measured in Pascal) - Normal Stress on Oblique Plane is the stress acting normally to its oblique plane.
Shear Stress - (Measured in Pascal) - Shear Stress, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

STEP 1: Convert Input(s) to Base Unit

Normal Stress on Oblique Plane: 54.99 Megapascal --> 54990000 Pascal (Check conversion here)
Shear Stress: 55 Megapascal --> 55000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = (asin(σ_θ/τ))/2 --> (asin(54990000/55000000))/2

Evaluating ... ...

θ = 0.775863393035054

STEP 3: Convert Result to Output's Unit

0.775863393035054 Radian -->44.4536978996167 Degree (Check conversion here)

FINAL ANSWER

44.4536978996167 ≈ 44.4537 Degree <-- Theta

(Calculation completed in 00.004 seconds)

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< 6 Complementary Induced Stress Calculators

Angle of Oblique Plane using Shear Stress when Complementary Shear Stresses Induced

Go Theta = 0.5*arccos(Shear Stress on Oblique Plane/Shear Stress)

Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced

Go Theta = (asin(Normal Stress on Oblique Plane/Shear Stress))/2

Shear Stress due to Induced Complementary Shear Stresses and Normal Stress on Oblique Plane

Go Shear Stress = Normal Stress on Oblique Plane/sin(2*Theta)

Normal Stress when Complementary Shear Stresses Induced

Go Normal Stress on Oblique Plane = Shear Stress*sin(2*Theta)

Shear Stress due to Effect of Complementary Shear Stresses and Shear Stress in Oblique Plane

Go Shear Stress = Shear Stress on Oblique Plane/cos(2*Theta)

Shear Stress along Oblique Plane when Complementary Shear Stresses Induced

Go Shear Stress on Oblique Plane = Shear Stress*cos(2*Theta)

Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced Formula

Theta = (asin(Normal Stress on Oblique Plane/Shear Stress))/2
θ = (asin(σ_θ/τ))/2

What are Complentary Shear Stresses?

A set of shear stresses acting across a plane will always be accompanied by a set of balancing shear stresses of similar intensity across the plane and acting normal to it.

What is Induced Stress ?

The force of resistance per unit area, offered by a body against deformation is known as stress. The external force acting on the body is called the load or force. The load is applied on the body while the stress is induced in the material of the body.

How to Calculate Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced?

Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced calculator uses Theta = (asin(Normal Stress on Oblique Plane/Shear Stress))/2 to calculate the Theta, The Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced formula is defined as the angle between the vertical and inclination of the plane to the vertical. Theta is denoted by θ symbol.

How to calculate Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced using this online calculator? To use this online calculator for Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced, enter Normal Stress on Oblique Plane (σ_θ) & Shear Stress (τ) and hit the calculate button. Here is how the Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced calculation can be explained with given input values -> 2578.31 = (asin(54990000/55000000))/2.

FAQ

What is Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced?

The Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced formula is defined as the angle between the vertical and inclination of the plane to the vertical and is represented as θ = (asin(σ_θ/τ))/2 or Theta = (asin(Normal Stress on Oblique Plane/Shear Stress))/2. Normal Stress on Oblique Plane is the stress acting normally to its oblique plane & Shear Stress, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

How to calculate Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced?

The Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced formula is defined as the angle between the vertical and inclination of the plane to the vertical is calculated using Theta = (asin(Normal Stress on Oblique Plane/Shear Stress))/2. To calculate Angle of Oblique Plane using Normal Stress when Complementary Shear Stresses Induced, you need Normal Stress on Oblique Plane (σ_θ) & Shear Stress (τ). With our tool, you need to enter the respective value for Normal Stress on Oblique Plane & Shear Stress 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 Normal Stress on Oblique Plane & Shear Stress. We can use 1 other way(s) to calculate the same, which is/are as follows -

Theta = 0.5*arccos(Shear Stress on Oblique Plane/Shear Stress)

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