Stress along X- Direction with known Shear Stress in Bi-Axial Loading 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 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 x Direction can be described as axial stress along the given direction.ⓘ Stress along X- Direction with known Shear Stress in Bi-Axial Loading [σ_x]

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Stress along X- Direction with known Shear Stress in Bi-Axial Loading Solution

STEP 0: Pre-Calculation Summary

Formula Used

Stress along x Direction = Stress along y Direction-((Shear Stress on Oblique Plane*2)/sin(2*Theta))
σ_x = σ_y-((τ_θ*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 x Direction - (Measured in Pascal) - The Stress along x Direction can be described as axial stress along the given direction.
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

Stress along y Direction: 110 Megapascal --> 110000000 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

σ_x = σ_y-((τ_θ*2)/sin(2*θ)) --> 110000000-((28145000*2)/sin(2*0.5235987755982))

Evaluating ... ...

σ_x = 45001906.6946245

STEP 3: Convert Result to Output's Unit

45001906.6946245 Pascal -->45.0019066946245 Megapascal (Check conversion here)

FINAL ANSWER

45.0019066946245 ≈ 45.00191 Megapascal <-- Stress along x Direction

(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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< 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 X- Direction with known Shear Stress in Bi-Axial Loading Formula

LaTeX Go

Stress along x Direction = Stress along y Direction-((Shear Stress on Oblique Plane*2)/sin(2*Theta))
σ_x = σ_y-((τ_θ*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 X- Direction with known Shear Stress in Bi-Axial Loading?

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

How to calculate Stress along X- Direction with known Shear Stress in Bi-Axial Loading using this online calculator? To use this online calculator for Stress along X- Direction with known Shear Stress in Bi-Axial Loading, enter Stress along y Direction (σ_y), Shear Stress on Oblique Plane (τ_θ) & Theta (θ) and hit the calculate button. Here is how the Stress along X- Direction with known Shear Stress in Bi-Axial Loading calculation can be explained with given input values -> -4.3E-5 = 110000000-((28145000*2)/sin(2*0.5235987755982)).

FAQ

What is Stress along X- Direction with known Shear Stress in Bi-Axial Loading?

The Stress along X- Direction with known Shear Stress in Bi-Axial Loading formula is defined as stress along a particular direction and is represented as σ_x = σ_y-((τ_θ*2)/sin(2*θ)) or Stress along x Direction = Stress along y Direction-((Shear Stress on Oblique Plane*2)/sin(2*Theta)). The Stress along y 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 X- Direction with known Shear Stress in Bi-Axial Loading?

The Stress along X- Direction with known Shear Stress in Bi-Axial Loading formula is defined as stress along a particular direction is calculated using Stress along x Direction = Stress along y Direction-((Shear Stress on Oblique Plane*2)/sin(2*Theta)). To calculate Stress along X- Direction with known Shear Stress in Bi-Axial Loading, you need Stress along y Direction (σ_y), Shear Stress on Oblique Plane (τ_θ) & Theta (θ). With our tool, you need to enter the respective value for Stress along y 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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