Stress along Y-direction given Shear Stress in Member subjected to 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 Theta is the angle subtended by a plane of a body when stress is applied.ⓘ Theta [θ]			+10% -10%

✖The Stress along y Direction can be described as axial stress along the given direction.ⓘ Stress along Y-direction given Shear Stress in Member subjected to Axial Load [σ_y]

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Formula

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

Formula

`"σ"_{"y"} = "τ"_{"θ"}/(0.5*sin(2*"θ"))`

Example

`"64.99809MPa"="28.145MPa"/(0.5*sin(2*"30°"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Stress along y Direction = Shear Stress on Oblique Plane/(0.5*sin(2*Theta))
σ_y = τ_θ/(0.5*sin(2*θ))
This formula uses 1 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)

Variables Used

Stress along y Direction - (Measured in Pascal) - The Stress along y Direction can be described as axial stress along the given direction.
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.
Theta - (Measured in Radian) - The Theta is the angle subtended by a plane of a body when stress is applied.

STEP 1: Convert Input(s) to Base Unit

Shear Stress on Oblique Plane: 28.145 Megapascal --> 28145000 Pascal (Check conversion here)
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_y = τ_θ/(0.5*sin(2*θ)) --> 28145000/(0.5*sin(2*0.5235987755982))

Evaluating ... ...

σ_y = 64998093.3053755

STEP 3: Convert Result to Output's Unit

64998093.3053755 Pascal -->64.9980933053755 Megapascal (Check conversion here)

FINAL ANSWER

64.9980933053755 ≈ 64.99809 Megapascal <-- Stress along y Direction

(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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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)

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

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

What is Principal Stress?

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

Stress along Y-direction given Shear Stress in Member subjected to Axial Load calculator uses Stress along y Direction = Shear Stress on Oblique Plane/(0.5*sin(2*Theta)) to calculate the Stress along y Direction, The Stress along Y-direction given Shear Stress in Member subjected to Axial Load formula is defined as calculating principal stress in the Y direction when a member is acted upon by axial load only and shear stress acting on it is already given. Stress along y Direction is denoted by σ_y symbol.

How to calculate Stress along Y-direction given Shear Stress in Member subjected to Axial Load using this online calculator? To use this online calculator for Stress along Y-direction given Shear Stress in Member subjected to Axial Load, enter Shear Stress on Oblique Plane (τ_θ) & Theta (θ) and hit the calculate button. Here is how the Stress along Y-direction given Shear Stress in Member subjected to Axial Load calculation can be explained with given input values -> 6.5E-5 = 28145000/(0.5*sin(2*0.5235987755982)).

FAQ

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

The Stress along Y-direction given Shear Stress in Member subjected to Axial Load formula is defined as calculating principal stress in the Y direction when a member is acted upon by axial load only and shear stress acting on it is already given and is represented as σ_y = τ_θ/(0.5*sin(2*θ)) or Stress along y Direction = Shear Stress on Oblique Plane/(0.5*sin(2*Theta)). The Shear Stress on Oblique Plane is the shear stress experienced by a body at any θ angle & The Theta is the angle subtended by a plane of a body when stress is applied.

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

The Stress along Y-direction given Shear Stress in Member subjected to Axial Load formula is defined as calculating principal stress in the Y direction when a member is acted upon by axial load only and shear stress acting on it is already given is calculated using Stress along y Direction = Shear Stress on Oblique Plane/(0.5*sin(2*Theta)). To calculate Stress along Y-direction given Shear Stress in Member subjected to Axial Load, you need Shear Stress on Oblique Plane (τ_θ) & Theta (θ). With our tool, you need to enter the respective value for Shear Stress on Oblique Plane & Theta 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 Stress along y Direction?

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

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

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