Minimum Value of Normal Stress Solution

STEP 0: Pre-Calculation Summary
Formula Used
Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
σn,min = (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
Minimum Normal Stress - (Measured in Pascal) - Minimum Normal Stress is equal to the minor principal stress value or minimum principal stress value.
Stress Along x Direction - (Measured in Pascal) - Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation.
Stress Along y Direction - (Measured in Pascal) - Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure.
Shear Stress in Mpa - (Measured in Pascal) - Shear Stress in Mpa, 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 Along x Direction: 95 Megapascal --> 95000000 Pascal (Check conversion here)
Stress Along y Direction: 22 Megapascal --> 22000000 Pascal (Check conversion here)
Shear Stress in Mpa: 41.5 Megapascal --> 41500000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σn,min = (σxy)/2-sqrt(((σxy)/2)^2+τ^2) --> (95000000+22000000)/2-sqrt(((95000000-22000000)/2)^2+41500000^2)
Evaluating ... ...
σn,min = 3232468.84471861
STEP 3: Convert Result to Output's Unit
3232468.84471861 Pascal -->3.23246884471861 Megapascal (Check conversion here)
FINAL ANSWER
3.23246884471861 3.232469 Megapascal <-- Minimum Normal Stress
(Calculation completed in 00.020 seconds)

Credits

Created by Vaibhav Malani
National Institute of Technology (NIT), Tiruchirapalli
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7 Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular and a Simple Shear Stress Calculators

Maximum Value of Normal Stress
Go Maximum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2+sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Minimum Value of Normal Stress
Go Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses
Go Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle)
Maximum Value of Shear Stress
Go Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress
Go Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle)
Condition for Maximum Value of Normal Stress
Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2
Condition for Minimum Normal Stress
Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2

7 When a Body is subjected to two Mutual Perpendicular Principal Tensile stresses along with Simple Shear Stress Calculators

Maximum Value of Normal Stress
Go Maximum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2+sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Minimum Value of Normal Stress
Go Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses
Go Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle)
Maximum Value of Shear Stress
Go Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress
Go Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle)
Condition for Maximum Value of Normal Stress
Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2
Condition for Minimum Normal Stress
Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2

Minimum Value of Normal Stress Formula

Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
σn,min = (σx+σy)/2-sqrt(((σx-σy)/2)^2+τ^2)

What is Normal Stress?

The intensity of net force acting per unit area normal to the cross-section under consideration is called normal stress.

What is Shear Stress?

When an external force acts on an object, It undergoes deformation. If the direction of the force is parallel to the plane of the object. The deformation will be along that plane. The stress experienced by the object here is shear stress or tangential stress.

It arises when the force vector components are parallel to the cross-sectional area of the material. In the case of normal/longitudinal stress, the force vectors will be perpendicular to the cross-sectional area on which it acts.

How to Calculate Minimum Value of Normal Stress?

Minimum Value of Normal Stress calculator uses Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2) to calculate the Minimum Normal Stress, The Minimum Value of Normal Stress formula is defined as equal to the minor principal stress value or minimum principal stress value. Minimum Normal Stress is denoted by σn,min symbol.

How to calculate Minimum Value of Normal Stress using this online calculator? To use this online calculator for Minimum Value of Normal Stress, enter Stress Along x Direction x), Stress Along y Direction y) & Shear Stress in Mpa (τ) and hit the calculate button. Here is how the Minimum Value of Normal Stress calculation can be explained with given input values -> 3.2E-6 = (95000000+22000000)/2-sqrt(((95000000-22000000)/2)^2+41500000^2).

FAQ

What is Minimum Value of Normal Stress?
The Minimum Value of Normal Stress formula is defined as equal to the minor principal stress value or minimum principal stress value and is represented as σn,min = (σxy)/2-sqrt(((σxy)/2)^2+τ^2) or Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2). Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation, Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure & Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.
How to calculate Minimum Value of Normal Stress?
The Minimum Value of Normal Stress formula is defined as equal to the minor principal stress value or minimum principal stress value is calculated using Minimum Normal Stress = (Stress Along x Direction+Stress Along y Direction)/2-sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2). To calculate Minimum Value of Normal Stress, you need Stress Along x Direction x), Stress Along y Direction y) & Shear Stress in Mpa (τ). With our tool, you need to enter the respective value for Stress Along x Direction, Stress Along y Direction & Shear Stress in Mpa 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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