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)
σmajor = (σx+σy)/2+sqrt(((σx-σy)/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) - The stress acting along x-direction.
Stress acting along y-direction - (Measured in Pascal) - The Stress acting along y-direction is denoted by the symbol 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
σmajor = (σxy)/2+sqrt(((σxy)/2)^2+𝜏^2) --> (500000+800000)/2+sqrt(((500000-800000)/2)^2+2400000^2)
Evaluating ... ...
σmajor = 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)

Credits

Created by Vaibhav Malani
National Institute of Technology (NIT), Tiruchirapalli
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National Institute Of Technology (NIT), Hamirpur
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8 Principal Stresses Calculators

Major Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress
Go 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)
Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress
Go Minor 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)
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)
Safe Stress given Safe Value of Axial Pull
Go Stress in Bar = Safe Value of Axial Pull/Area of Cross-Section
Safe Value of Axial Pull
Go Safe Value of Axial Pull = Safe Stress*Area of Cross-Section
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

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)
σmajor = (σx+σy)/2+sqrt(((σx-σy)/2)^2+𝜏^2)

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, The Major principal stress if Member is subjected to two perpendicular direct stress and shear stress is the maximum value of principal stress. Major Principal Stress is denoted by σmajor 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 x), Stress acting along y-direction 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?
The Major principal stress if Member is subjected to two perpendicular direct stress and shear stress is the maximum value of principal stress and is represented as σmajor = (σxy)/2+sqrt(((σxy)/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). The stress acting along x-direction, The Stress acting along y-direction is denoted by the symbol 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?
The Major principal stress if Member is subjected to two perpendicular direct stress and shear stress is the maximum value of principal 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 x), Stress acting along y-direction 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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