Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress Calculator

✖Stress Acting Along X Direction is the stress acting along x-direction.ⓘ Stress Acting Along X Direction [σ_x]			+10% -10%
✖Stress Acting Along Y Direction is stress acting along y direction is denoted by σy.ⓘ Stress Acting Along Y Direction [σ_y]			+10% -10%
✖Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress [𝜏]			+10% -10%

✖Major Principal Stress can be defined as the maximum normal stress acting on the principal plane.ⓘ Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress [σ_m]

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Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Major Principal Stress = (Stress Acting Along X Direction+Stress Acting Along Y Direction)/2+sqrt(((Stress Acting Along X Direction-Stress Acting Along Y Direction)/2)^2+Shear Stress^2)
σ_m = (σ_x+σ_y)/2+sqrt(((σ_x-σ_y)/2)^2+𝜏^2)
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Major Principal Stress - (Measured in Pascal) - Major Principal Stress can be defined as the maximum normal stress acting on the principal plane.
Stress Acting Along X Direction - (Measured in Pascal) - Stress Acting Along X Direction is the stress acting along x-direction.
Stress Acting Along Y Direction - (Measured in Pascal) - Stress Acting Along Y Direction is stress acting along y direction is denoted by σy.
Shear Stress - (Measured in Pascal) - Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

STEP 1: Convert Input(s) to Base Unit

Stress Acting Along X Direction: 0.5 Megapascal --> 500000 Pascal (Check conversion here)
Stress Acting Along Y Direction: 0.8 Megapascal --> 800000 Pascal (Check conversion here)
Shear Stress: 2.4 Megapascal --> 2400000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_m = (σ_x+σ_y)/2+sqrt(((σ_x-σ_y)/2)^2+𝜏^2) --> (500000+800000)/2+sqrt(((500000-800000)/2)^2+2400000^2)

Evaluating ... ...

σ_m = 3054682.93128221

STEP 3: Convert Result to Output's Unit

3054682.93128221 Pascal -->3.05468293128221 Megapascal (Check conversion here)

FINAL ANSWER

3.05468293128221 ≈ 3.054683 Megapascal <-- Major Principal Stress

(Calculation completed in 00.004 seconds)

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

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< Stress Relations Calculators

Resultant Stress on Oblique Section given Stress in Perpendicular Directions

Go Resultant Stress = sqrt(Normal Stress^2+Shear Stress^2)

Angle of Obliquity

Go Angle of Obliquity = atan(Shear Stress/Normal Stress)

Stress along Maximum Axial Force

Go Stress in Bar = Maximum Axial Force/Area of Cross Section

Maximum Axial Force

Go Maximum Axial Force = Stress in Bar*Area of Cross Section

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress Formula

What is principal stress?

When a stress tensor acts on a body, the plane along which the shear stress terms vanish is called the principal plane, and the stress on such planes is called principal stress.

How to Calculate Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress calculator uses Major Principal Stress = (Stress Acting Along X Direction+Stress Acting Along Y Direction)/2+sqrt(((Stress Acting Along X Direction-Stress Acting Along Y Direction)/2)^2+Shear Stress^2) to calculate the Major Principal Stress, Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress formula is defined as the maximum normal stress that occurs in a member when it is subjected to two perpendicular direct stresses and a shear stress, resulting in a complex state of stress. Major Principal Stress is denoted by σ_m symbol.

How to calculate Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress using this online calculator? To use this online calculator for Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress, enter Stress Acting Along X Direction (σ_x), Stress Acting Along Y Direction (σ_y) & Shear Stress (𝜏) and hit the calculate button. Here is how the Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress calculation can be explained with given input values -> 3.1E-6 = (500000+800000)/2+sqrt(((500000-800000)/2)^2+2400000^2).

FAQ

What is Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress formula is defined as the maximum normal stress that occurs in a member when it is subjected to two perpendicular direct stresses and a shear stress, resulting in a complex state of stress and is represented as σ_m = (σ_x+σ_y)/2+sqrt(((σ_x-σ_y)/2)^2+𝜏^2) or Major Principal Stress = (Stress Acting Along X Direction+Stress Acting Along Y Direction)/2+sqrt(((Stress Acting Along X Direction-Stress Acting Along Y Direction)/2)^2+Shear Stress^2). Stress Acting Along X Direction is the stress acting along x-direction, Stress Acting Along Y Direction is stress acting along y direction is denoted by σy & Shear Stress is force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.

How to calculate Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress formula is defined as the maximum normal stress that occurs in a member when it is subjected to two perpendicular direct stresses and a shear stress, resulting in a complex state of stress is calculated using Major Principal Stress = (Stress Acting Along X Direction+Stress Acting Along Y Direction)/2+sqrt(((Stress Acting Along X Direction-Stress Acting Along Y Direction)/2)^2+Shear Stress^2). To calculate Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress, you need Stress Acting Along X Direction (σ_x), Stress Acting Along Y Direction (σ_y) & Shear Stress (𝜏). With our tool, you need to enter the respective value for Stress Acting Along X Direction, Stress Acting Along Y Direction & Shear Stress 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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