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)
σmin = (σx+σy)/2-sqrt( ((σx-σy)/2)^2+ζxy^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
σmin = (σxy)/2-sqrt( ((σxy)/2)^2+ζxy^2) --> (80000000+40000000)/2-sqrt( ((80000000-40000000)/2)^2+30000000^2)
Evaluating ... ...
σmin = 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)

Credits

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BMS COLLEGE OF ENGINEERING (BMSCE), BANGALORE
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6 Analysis of Stresses Calculators

Maximum Principal Stress
Go Maximum 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)
Minimum Principal Stress
Go 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)
Shear Stress on Inclined Plane
Go Shear stress on inclined plane = -Tensile load*sin(Theta)*cos(Theta)/Area of inclined plane
Area of Inclined Plane given Stress
Go Area of inclined plane = (Tensile load*(cos(Theta))^2)/Stress on inclined plane
Load of Inclined Plane given Stress
Go Tensile load = (Stress on inclined plane*Area of inclined plane)/(cos(Theta))^2
Stress on Inclined Plane
Go Stress on inclined plane = (Tensile load*(cos(Theta))^2)/Area of inclined plane

Minimum Principal Stress Formula

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)
σmin = (σx+σy)/2-sqrt( ((σx-σy)/2)^2+ζxy^2)

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 σmin 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 x), Normal stress along y direction y) & Shear stress acting in xy plane 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 σmin = (σxy)/2-sqrt( ((σxy)/2)^2+ζxy^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 x), Normal stress along y direction y) & Shear stress acting in xy plane 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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