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

✖The stress acting along x-direction.ⓘ Stress acting along x-direction [σ_x]			+10% -10%
✖The Stress acting along y-direction is denoted by the symbol σ_y.ⓘ 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%

✖Minor Principal Stress is the minimum normal stress acting on the Principal plane.ⓘ Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress [σ_minor]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
σ_minor = (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

Minor Principal Stress - (Measured in Pascal) - Minor Principal Stress is the minimum 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 σ_y.
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_minor = (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_minor = -1754682.93128221

STEP 3: Convert Result to Output's Unit

-1754682.93128221 Pascal -->-1.75468293128221 Megapascal (Check conversion here)

FINAL ANSWER

-1.75468293128221 ≈ -1.754683 Megapascal <-- Minor 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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National Institute Of Technology (NIT), Hamirpur

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< Stress Relations Calculators

Resultant Stress on Oblique Section given Stress in Perpendicular Directions

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

Angle of Obliquity

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

Stress along Maximum Axial Force

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

Maximum Axial Force

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

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

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

Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress calculator uses 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) to calculate the Minor Principal Stress, The Minor principal stress if Member is subjected to two perpendicular direct stress and shear stress is the minimum value of principal stress. Minor Principal Stress is denoted by σ_minor symbol.

How to calculate Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress using this online calculator? To use this online calculator for Minor 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 Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress calculation can be explained with given input values -> -1.8E-6 = (500000+800000)/2-sqrt(((500000-800000)/2)^2+2400000^2).

FAQ

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

The Minor principal stress if Member is subjected to two perpendicular direct stress and shear stress is the minimum value of principal stress and is represented as σ_minor = (σ_x+σ_y)/2-sqrt(((σ_x-σ_y)/2)^2+𝜏^2) or 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). The stress acting along x-direction, The Stress acting along y-direction is denoted by the symbol σ_y & 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 Minor Principal Stress if Member is Subjected to Two Perpendicular Direct Stress and Shear Stress?

The Minor principal stress if Member is subjected to two perpendicular direct stress and shear stress is the minimum value of principal stress is calculated using 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). To calculate Minor 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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