Normal Stress Induced in Oblique Plane due to Biaxial Loading Calculator

✖The Stress along x Direction can be described as axial stress along the given direction.ⓘ Stress along x Direction [σ_x]			+10% -10%
✖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%
✖Shear Stress xy is the Stress acting along xy plane.ⓘ Shear Stress xy [τ_xy]			+10% -10%

✖Normal Stress on Oblique Plane is the stress acting normally to its oblique plane.ⓘ Normal Stress Induced in Oblique Plane due to Biaxial Loading [σ_θ]

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Formula

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Normal Stress Induced in Oblique Plane due to Biaxial Loading

Formula

`"σ"_{"θ"} = (1/2*("σ"_{"x"}+"σ"_{"y"}))+(1/2*("σ"_{"x"}-"σ"_{"y"})*(cos(2*"θ")))+("τ"_{"xy"}*sin(2*"θ"))`

Example

`"67.48538MPa"=(1/2*("45MPa"+"110MPa"))+(1/2*("45MPa"-"110MPa")*(cos(2*"30°")))+("7.2MPa"*sin(2*"30°"))`

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Normal Stress Induced in Oblique Plane due to Biaxial Loading Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
σ_θ = (1/2*(σ_x+σ_y))+(1/2*(σ_x-σ_y)*(cos(2*θ)))+(τ_xy*sin(2*θ))
This formula uses 2 Functions, 5 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)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Normal Stress on Oblique Plane - (Measured in Pascal) - Normal Stress on Oblique Plane is the stress acting normally to its oblique plane.
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.
Theta - (Measured in Radian) - The Theta is the angle subtended by a plane of a body when stress is applied.
Shear Stress xy - (Measured in Pascal) - Shear Stress xy is the Stress acting along xy plane.

STEP 1: Convert Input(s) to Base Unit

Stress along x Direction: 45 Megapascal --> 45000000 Pascal (Check conversion here)
Stress along y Direction: 110 Megapascal --> 110000000 Pascal (Check conversion here)
Theta: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Shear Stress xy: 7.2 Megapascal --> 7200000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_θ = (1/2*(σ_x+σ_y))+(1/2*(σ_x-σ_y)*(cos(2*θ)))+(τ_xy*sin(2*θ)) --> (1/2*(45000000+110000000))+(1/2*(45000000-110000000)*(cos(2*0.5235987755982)))+(7200000*sin(2*0.5235987755982))

Evaluating ... ...

σ_θ = 67485382.9072417

STEP 3: Convert Result to Output's Unit

67485382.9072417 Pascal -->67.4853829072417 Megapascal (Check conversion here)

FINAL ANSWER

67.4853829072417 ≈ 67.48538 Megapascal <-- Normal Stress on Oblique Plane

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Strength of Materials » Principal Stress » Stresses in Bi-Axial Loading » Normal Stress Induced in Oblique Plane due to Biaxial Loading

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< 4 Stresses in Bi-Axial Loading Calculators

Normal Stress Induced in Oblique Plane due to Biaxial Loading

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

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

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

Go Stress along y Direction = Stress along x Direction+((Shear Stress on Oblique Plane*2)/sin(2*Theta))

Normal Stress Induced in Oblique Plane due to Biaxial Loading Formula

What is Normal Stress?

The Normal stress is a stress that occurs when a member is loaded by an axial force. Normal stresses are assumed positive if tensile and negative if compressive.

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 Normal Stress Induced in Oblique Plane due to Biaxial Loading?

Normal Stress Induced in Oblique Plane due to Biaxial Loading calculator uses 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)) to calculate the Normal Stress on Oblique Plane, The Normal Stress Induced in Oblique Plane due to Biaxial Loading formula is defined as calculating stress subjected to a combination of direct stresses (σx) and (σy) in two mutually perpendicular planes, accompanied by simple shear stress (τxy). Normal Stress on Oblique Plane is denoted by σ_θ symbol.

How to calculate Normal Stress Induced in Oblique Plane due to Biaxial Loading using this online calculator? To use this online calculator for Normal Stress Induced in Oblique Plane due to Biaxial Loading, enter Stress along x Direction (σ_x), Stress along y Direction (σ_y), Theta (θ) & Shear Stress xy (τ_xy) and hit the calculate button. Here is how the Normal Stress Induced in Oblique Plane due to Biaxial Loading calculation can be explained with given input values -> 6.7E-5 = (1/2*(45000000+110000000))+(1/2*(45000000-110000000)*(cos(2*0.5235987755982)))+(7200000*sin(2*0.5235987755982)).

FAQ

What is Normal Stress Induced in Oblique Plane due to Biaxial Loading?

The Normal Stress Induced in Oblique Plane due to Biaxial Loading formula is defined as calculating stress subjected to a combination of direct stresses (σx) and (σy) in two mutually perpendicular planes, accompanied by simple shear stress (τxy) and is represented as σ_θ = (1/2*(σ_x+σ_y))+(1/2*(σ_x-σ_y)*(cos(2*θ)))+(τ_xy*sin(2*θ)) or 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)). The Stress along x Direction can be described as axial stress along the given direction, 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 & Shear Stress xy is the Stress acting along xy plane.

How to calculate Normal Stress Induced in Oblique Plane due to Biaxial Loading?

The Normal Stress Induced in Oblique Plane due to Biaxial Loading formula is defined as calculating stress subjected to a combination of direct stresses (σx) and (σy) in two mutually perpendicular planes, accompanied by simple shear stress (τxy) is calculated using 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)). To calculate Normal Stress Induced in Oblique Plane due to Biaxial Loading, you need Stress along x Direction (σ_x), Stress along y Direction (σ_y), Theta (θ) & Shear Stress xy (τ_xy). With our tool, you need to enter the respective value for Stress along x Direction, Stress along y Direction, Theta & Shear Stress xy 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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