Shear Stress when Member Subjected to Axial Load Calculator

✖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.ⓘ Theta [θ]			+10% -10%

✖The Shear Stress on Oblique Plane is the shear stress experienced by a body at any θ angle.ⓘ Shear Stress when Member Subjected to Axial Load [τ_θ]

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Formula

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Shear Stress when Member Subjected to Axial Load

Formula

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

Example

`"47.6314MPa"=0.5*"110MPa"*sin(2*"30°")`

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Shear Stress when Member Subjected to Axial Load Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

Stress along y Direction: 110 Megapascal --> 110000000 Pascal (Check conversion here)
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ_θ = 0.5*σ_y*sin(2*θ) --> 0.5*110000000*sin(2*0.5235987755982)

Evaluating ... ...

τ_θ = 47631397.2081387

STEP 3: Convert Result to Output's Unit

47631397.2081387 Pascal -->47.6313972081387 Megapascal (Check conversion here)

FINAL ANSWER

47.6313972081387 ≈ 47.6314 Megapascal <-- Shear Stress on Oblique Plane

(Calculation completed in 00.004 seconds)

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Created by Rithik Agrawal

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)

Shear Stress when Member Subjected to Axial Load Formula

Shear Stress on Oblique Plane = 0.5*Stress along y Direction*sin(2*Theta)
τ_θ = 0.5*σ_y*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 Shear Stress when Member Subjected to Axial Load?

Shear Stress when Member Subjected to Axial Load calculator uses Shear Stress on Oblique Plane = 0.5*Stress along y Direction*sin(2*Theta) to calculate the Shear Stress on Oblique Plane, The Shear Stress when Member Subjected to Axial Load formula is defined as stress at which plane gets distorted along the action of force. Shear Stress on Oblique Plane is denoted by τ_θ symbol.

How to calculate Shear Stress when Member Subjected to Axial Load using this online calculator? To use this online calculator for Shear Stress when Member Subjected to Axial Load, enter Stress along y Direction (σ_y) & Theta (θ) and hit the calculate button. Here is how the Shear Stress when Member Subjected to Axial Load calculation can be explained with given input values -> 9.5E-6 = 0.5*110000000*sin(2*0.5235987755982).

FAQ

What is Shear Stress when Member Subjected to Axial Load?

The Shear Stress when Member Subjected to Axial Load formula is defined as stress at which plane gets distorted along the action of force and is represented as τ_θ = 0.5*σ_y*sin(2*θ) or Shear Stress on Oblique Plane = 0.5*Stress along y Direction*sin(2*Theta). The Stress along y Direction can be described as axial stress along the given direction & The Theta is the angle subtended by a plane of a body when stress is applied.

How to calculate Shear Stress when Member Subjected to Axial Load?

The Shear Stress when Member Subjected to Axial Load formula is defined as stress at which plane gets distorted along the action of force is calculated using Shear Stress on Oblique Plane = 0.5*Stress along y Direction*sin(2*Theta). To calculate Shear Stress when Member Subjected to Axial Load, you need Stress along y Direction (σ_y) & Theta (θ). With our tool, you need to enter the respective value for Stress along y Direction & Theta and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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