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Minimum Principal Stress Calculator

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Stress Strain Stress and Strain

✖Normal stress along x direction is the internal resistive force acting longitudinally.ⓘ Normal Stress along x Direction [σ_x]			+10% -10%
✖Normal stress along y direction is the internal resistive force per unit area acting along y direction.ⓘ Normal Stress along y Direction [σ_y]			+10% -10%
✖Shear stress acting in xy plane is the shear stress on xy plane.ⓘ Shear Stress acting in xy Plane [ζ_xy]			+10% -10%

✖Minimum principal stress can be defined as the plane carrying minimum normal stress is known as minor. principal plane and the stress acting on it is called as minor principal stress.ⓘ Minimum Principal Stress [σ_min]

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Minimum Principal Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Minimum Principal Stress = (Normal Stress along x Direction+Normal Stress along y Direction)/2-sqrt(((Normal Stress along x Direction-Normal Stress along y Direction)/2)^2+Shear Stress acting in xy Plane^2)
σ_min = (σ_x+σ_y)/2-sqrt(((σ_x-σ_y)/2)^2+ζ_xy^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

Minimum Principal Stress - (Measured in Pascal) - Minimum principal stress can be defined as the plane carrying minimum normal stress is known as minor. principal plane and the stress acting on it is called as minor principal stress.
Normal Stress along x Direction - (Measured in Pascal) - Normal stress along x direction is the internal resistive force acting longitudinally.
Normal Stress along y Direction - (Measured in Pascal) - Normal stress along y direction is the internal resistive force per unit area acting along y direction.
Shear Stress acting in xy Plane - (Measured in Pascal) - Shear stress acting in xy plane is the shear stress on xy plane.

STEP 1: Convert Input(s) to Base Unit

Normal Stress along x Direction: 80 Megapascal --> 80000000 Pascal (Check conversion here)
Normal Stress along y Direction: 40 Megapascal --> 40000000 Pascal (Check conversion here)
Shear Stress acting in xy Plane: 30 Megapascal --> 30000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_min = (σ_x+σ_y)/2-sqrt(((σ_x-σ_y)/2)^2+ζ_xy^2) --> (80000000+40000000)/2-sqrt(((80000000-40000000)/2)^2+30000000^2)

Evaluating ... ...

σ_min = 23944487.2453601

STEP 3: Convert Result to Output's Unit

23944487.2453601 Pascal -->23.9444872453601 Megapascal (Check conversion here)

FINAL ANSWER

23.9444872453601 ≈ 23.94449 Megapascal <-- Minimum Principal Stress

(Calculation completed in 00.004 seconds)

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< Stress Calculators

Beam Shear Stress

Go Beam Shear Stress = (Total Shear Force*First Moment of Area)/(Moment of Inertia*Thickness of Material)

Bending Stress

Go Bending Stress = Bending Moment*Distance from Neutral Axis/Moment of Inertia

Bulk Stress

Go Bulk Stress = Normal Inward Force/Cross Sectional Area

Direct Stress

Go Direct Stress = Axial Thrust/Cross Sectional Area

Minimum Principal Stress Formula

What is Principal Stress and it's Types?

Principal stress is the maximum or minimum normal stress which may be developed on a loaded body. It is classified as major principal stress and minor principal stress. On the plane of principal stress shear stress value is termed as zero.

How to Calculate Minimum Principal Stress?

Minimum Principal Stress calculator uses Minimum Principal Stress = (Normal Stress along x Direction+Normal Stress along y Direction)/2-sqrt(((Normal Stress along x Direction-Normal Stress along y Direction)/2)^2+Shear Stress acting in xy Plane^2) to calculate the Minimum Principal Stress, The Minimum principal stress formula is defined as the plane carrying minimum normal stress is known as minor. principal plane and the stress acting on it is called as minor principal stress. Minimum Principal Stress is denoted by σ_min symbol.

How to calculate Minimum Principal Stress using this online calculator? To use this online calculator for Minimum Principal Stress, enter Normal Stress along x Direction (σ_x), Normal Stress along y Direction (σ_y) & Shear Stress acting in xy Plane (ζ_xy) and hit the calculate button. Here is how the Minimum Principal Stress calculation can be explained with given input values -> 2.4E-5 = (80000000+40000000)/2-sqrt(((80000000-40000000)/2)^2+30000000^2).

FAQ

What is Minimum Principal Stress?

The Minimum principal stress formula is defined as the plane carrying minimum normal stress is known as minor. principal plane and the stress acting on it is called as minor principal stress and is represented as σ_min = (σ_x+σ_y)/2-sqrt(((σ_x-σ_y)/2)^2+ζ_xy^2) or Minimum Principal Stress = (Normal Stress along x Direction+Normal Stress along y Direction)/2-sqrt(((Normal Stress along x Direction-Normal Stress along y Direction)/2)^2+Shear Stress acting in xy Plane^2). Normal stress along x direction is the internal resistive force acting longitudinally, Normal stress along y direction is the internal resistive force per unit area acting along y direction & Shear stress acting in xy plane is the shear stress on xy plane.

How to calculate Minimum Principal Stress?

The Minimum principal stress formula is defined as the plane carrying minimum normal stress is known as minor. principal plane and the stress acting on it is called as minor principal stress is calculated using Minimum Principal Stress = (Normal Stress along x Direction+Normal Stress along y Direction)/2-sqrt(((Normal Stress along x Direction-Normal Stress along y Direction)/2)^2+Shear Stress acting in xy Plane^2). To calculate Minimum Principal Stress, you need Normal Stress along x Direction (σ_x), Normal Stress along y Direction (σ_y) & Shear Stress acting in xy Plane (ζ_xy). With our tool, you need to enter the respective value for Normal Stress along x Direction, Normal Stress along y Direction & Shear Stress acting in xy Plane 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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