Stress along Y- Direction using Shear Stress in Bi-Axial Loading Solution

STEP 0: Pre-Calculation Summary
Formula Used
Stress along y Direction = Stress along x Direction+((Shear Stress on Oblique Plane*2)/sin(2*Theta))
σy = σx+((τθ*2)/sin(2*θ))
This formula uses 1 Functions, 4 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.
Stress along x Direction - (Measured in Pascal) - The Stress along x 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
Stress along x Direction: 45 Megapascal --> 45000000 Pascal (Check conversion ​here)
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
σy = σx+((τθ*2)/sin(2*θ)) --> 45000000+((28145000*2)/sin(2*0.5235987755982))
Evaluating ... ...
σy = 109998093.305375
STEP 3: Convert Result to Output's Unit
109998093.305375 Pascal -->109.998093305375 Megapascal (Check conversion ​here)
FINAL ANSWER
109.998093305375 109.9981 Megapascal <-- Stress along y Direction
(Calculation completed in 00.020 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal
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National Institute of Technology (NIT), Warangal
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Stresses in Bi Axial Loading Calculators

Normal Stress Induced in Oblique Plane due to Biaxial Loading
​ LaTeX ​ Go Normal Stress on Oblique Plane = (1/2*(Stress along x Direction+Stress along y Direction))+(1/2*(Stress along x Direction-Stress along y Direction)*(cos(2*Theta)))+(Shear Stress xy*sin(2*Theta))
Shear Stress Induced in Oblique Plane due to Biaxial Loading
​ LaTeX ​ Go Shear Stress on Oblique Plane = -(1/2*(Stress along x Direction-Stress along y Direction)*sin(2*Theta))+(Shear Stress xy*cos(2*Theta))
Stress along X- Direction with known Shear Stress in Bi-Axial Loading
​ LaTeX ​ Go Stress along x Direction = Stress along y Direction-((Shear Stress on Oblique Plane*2)/sin(2*Theta))
Stress along Y- Direction using Shear Stress in Bi-Axial Loading
​ LaTeX ​ Go Stress along y Direction = Stress along x Direction+((Shear Stress on Oblique Plane*2)/sin(2*Theta))

Stress along Y- Direction using Shear Stress in Bi-Axial Loading Formula

​LaTeX ​Go
Stress along y Direction = Stress along x Direction+((Shear Stress on Oblique Plane*2)/sin(2*Theta))
σy = σx+((τθ*2)/sin(2*θ))

What is Principal Stress?

The Principal stresses are the maximum and minimum (extremum) extensional (normal) stresses in a stress state at a point. The principal directions are the corresponding directions. The principal directions have no shear stresses associated with them.

What is a Biaxial State of Stress?

A two-dimensional state of stress in which only two normal stresses are present is called biaxial stress. When a body is subjected to biaxial stress, it is acted upon by direct stresses (σx) and (σy) in two mutually perpendicular planes accompanied by a simple shear stress (τxy).

How to Calculate Stress along Y- Direction using Shear Stress in Bi-Axial Loading?

Stress along Y- Direction using Shear Stress in Bi-Axial Loading calculator uses Stress along y Direction = Stress along x Direction+((Shear Stress on Oblique Plane*2)/sin(2*Theta)) to calculate the Stress along y Direction, The Stress along Y- Direction using Shear Stress in Bi-Axial Loading formula is defined as stress along a particular direction. Stress along y Direction is denoted by σy symbol.

How to calculate Stress along Y- Direction using Shear Stress in Bi-Axial Loading using this online calculator? To use this online calculator for Stress along Y- Direction using Shear Stress in Bi-Axial Loading, enter Stress along x Direction x), Shear Stress on Oblique Plane θ) & Theta (θ) and hit the calculate button. Here is how the Stress along Y- Direction using Shear Stress in Bi-Axial Loading calculation can be explained with given input values -> 0.00011 = 45000000+((28145000*2)/sin(2*0.5235987755982)).

FAQ

What is Stress along Y- Direction using Shear Stress in Bi-Axial Loading?
The Stress along Y- Direction using Shear Stress in Bi-Axial Loading formula is defined as stress along a particular direction and is represented as σy = σx+((τθ*2)/sin(2*θ)) or Stress along y Direction = Stress along x Direction+((Shear Stress on Oblique Plane*2)/sin(2*Theta)). The Stress along x Direction can be described as axial stress along the given direction, 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 using Shear Stress in Bi-Axial Loading?
The Stress along Y- Direction using Shear Stress in Bi-Axial Loading formula is defined as stress along a particular direction is calculated using Stress along y Direction = Stress along x Direction+((Shear Stress on Oblique Plane*2)/sin(2*Theta)). To calculate Stress along Y- Direction using Shear Stress in Bi-Axial Loading, you need Stress along x Direction x), Shear Stress on Oblique Plane θ) & Theta (θ). With our tool, you need to enter the respective value for Stress along x Direction, 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.
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