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Minimum Value of Normal Stress Calculator

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Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular and a Simple Shear Stress Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular Stress which are Unequal and Unlike Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular Tensile Stress of Unequal Intensity

✖Stress Along x Direction is the force per unit area acting on a material in the positive x-axis orientation.ⓘ Stress Along x Direction [σ_x]			+10% -10%
✖Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure.ⓘ Stress Along y Direction [σ_y]			+10% -10%
✖Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress.ⓘ Shear Stress in Mpa [τ]			+10% -10%

✖Minimum Normal Stress is equal to the minor principal stress value or minimum principal stress value.ⓘ Minimum Value of Normal Stress [σ_n,min]

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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)
σ_n,min = (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

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

σ_n,min = (σ_x+σ_y)/2-sqrt(((σ_x-σ_y)/2)^2+τ^2) --> (95000000+22000000)/2-sqrt(((95000000-22000000)/2)^2+41500000^2)

Evaluating ... ...

σ_n,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 00.007 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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< Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular and a Simple Shear Stress Calculators

Maximum Value of Normal Stress

LaTeX 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

LaTeX 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

LaTeX Go Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle)

Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress

LaTeX Go Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle)

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

Maximum Value of Normal Stress

LaTeX 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)

Maximum Value of Shear Stress

LaTeX Go Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)

Condition for Maximum Value of Normal Stress

LaTeX Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2

Condition for Minimum Normal Stress

LaTeX Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2

Minimum Value of Normal Stress Formula

LaTeX Go

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 σ_n,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 (σ_x), Stress Along y Direction (σ_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 σ_n,min = (σ_x+σ_y)/2-sqrt(((σ_x-σ_y)/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 (σ_x), Stress Along y Direction (σ_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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