Condition for Minimum Normal Stress Calculator

✖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%
✖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%

✖Plane Angle is the measure of the inclination between two intersecting lines in a flat surface, usually expressed in degrees.ⓘ Condition for Minimum Normal Stress [θ_plane]

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Condition for Minimum Normal Stress

Formula

`"θ"_{"plane"} = (atan((2*"τ")/("σ"_{"x"}-"σ"_{"y"})))/2`

Example

`"24.33389°"=(atan((2*"41.5MPa")/("95MPa"-"22MPa")))/2`

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Condition for Minimum Normal Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2
θ_plane = (atan((2*τ)/(σ_x-σ_y)))/2
This formula uses 2 Functions, 4 Variables

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Plane Angle - (Measured in Radian) - Plane Angle is the measure of the inclination between two intersecting lines in a flat surface, usually expressed in degrees.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Shear Stress in Mpa: 41.5 Megapascal --> 41500000 Pascal (Check conversion here)
Stress Along x Direction: 95 Megapascal --> 95000000 Pascal (Check conversion here)
Stress Along y Direction: 22 Megapascal --> 22000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_plane = (atan((2*τ)/(σ_x-σ_y)))/2 --> (atan((2*41500000)/(95000000-22000000)))/2

Evaluating ... ...

θ_plane = 0.424706570615896

STEP 3: Convert Result to Output's Unit

0.424706570615896 Radian -->24.3338940277703 Degree (Check conversion here)

FINAL ANSWER

24.3338940277703 ≈ 24.33389 Degree <-- Plane Angle

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Stress and Strain » Mohr's Circle » Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular and a Simple Shear Stress » Condition for Minimum Normal Stress

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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

Condition for Minimum Normal Stress Formula

Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2
θ_plane = (atan((2*τ)/(σ_x-σ_y)))/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 Condition for Minimum Normal Stress?

Condition for Minimum Normal Stress calculator uses Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2 to calculate the Plane Angle, The Condition for Minimum Normal Stress formula is defined as when twice the angle of the plane is equal to the inverse tangent of the ratio of twice the value of shear stress to the difference of stress along x and y-direction. Plane Angle is denoted by θ_plane symbol.

How to calculate Condition for Minimum Normal Stress using this online calculator? To use this online calculator for Condition for Minimum Normal Stress, enter Shear Stress in Mpa (τ), Stress Along x Direction (σ_x) & Stress Along y Direction (σ_y) and hit the calculate button. Here is how the Condition for Minimum Normal Stress calculation can be explained with given input values -> 1394.229 = (atan((2*41500000)/(95000000-22000000)))/2.

FAQ

What is Condition for Minimum Normal Stress?

The Condition for Minimum Normal Stress formula is defined as when twice the angle of the plane is equal to the inverse tangent of the ratio of twice the value of shear stress to the difference of stress along x and y-direction and is represented as θ_plane = (atan((2*τ)/(σ_x-σ_y)))/2 or Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2. Shear Stress in Mpa, force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress, 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.

How to calculate Condition for Minimum Normal Stress?

The Condition for Minimum Normal Stress formula is defined as when twice the angle of the plane is equal to the inverse tangent of the ratio of twice the value of shear stress to the difference of stress along x and y-direction is calculated using Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2. To calculate Condition for Minimum Normal Stress, you need Shear Stress in Mpa (τ), Stress Along x Direction (σ_x) & Stress Along y Direction (σ_y). With our tool, you need to enter the respective value for Shear Stress in Mpa, Stress Along x Direction & Stress Along y Direction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Plane Angle?

In this formula, Plane Angle uses Shear Stress in Mpa, Stress Along x Direction & Stress Along y Direction. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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