Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses Calculator

✖Major Principal Stress is the maximum normal stress acting on the principal plane.ⓘ Major Principal Stress [σ_major]			+10% -10%
✖Minor Principal Stress is the minimum normal stress acting on the principal plane.ⓘ Minor Principal Stress [σ_minor]			+10% -10%
✖Plane Angle is the measure of the inclination between two intersecting lines in a flat surface, usually expressed in degrees.ⓘ Plane Angle [θ_plane]			+10% -10%

✖Normal Stress on Oblique Plane is the stress acting normally to its oblique plane.ⓘ Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses [σ_θ]

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Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses

Formula

`"σ"_{"θ"} = ("σ"_{"major"}+"σ"_{"minor"})/2+("σ"_{"major"}-"σ"_{"minor"})/2*cos(2*"θ"_{"plane"})`

Example

`"62.25MPa"=("75MPa"+"24MPa")/2+("75MPa"-"24MPa")/2*cos(2*"30°")`

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Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses Solution

STEP 0: Pre-Calculation Summary

Formula Used

Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle)
σ_θ = (σ_major+σ_minor)/2+(σ_major-σ_minor)/2*cos(2*θ_plane)
This formula uses 1 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Normal Stress on Oblique Plane - (Measured in Pascal) - Normal Stress on Oblique Plane is the stress acting normally to its oblique plane.
Major Principal Stress - (Measured in Pascal) - Major Principal Stress is the maximum normal stress acting on the principal plane.
Minor Principal Stress - (Measured in Pascal) - Minor Principal Stress is the minimum normal stress acting on the principal plane.
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.

STEP 1: Convert Input(s) to Base Unit

Major Principal Stress: 75 Megapascal --> 75000000 Pascal (Check conversion here)
Minor Principal Stress: 24 Megapascal --> 24000000 Pascal (Check conversion here)
Plane Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_θ = (σ_major+σ_minor)/2+(σ_major-σ_minor)/2*cos(2*θ_plane) --> (75000000+24000000)/2+(75000000-24000000)/2*cos(2*0.5235987755982)

Evaluating ... ...

σ_θ = 62250000.0000044

STEP 3: Convert Result to Output's Unit

62250000.0000044 Pascal -->62.2500000000044 Megapascal (Check conversion here)

FINAL ANSWER

62.2500000000044 ≈ 62.25 Megapascal <-- Normal Stress on Oblique Plane

(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 » Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses

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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

Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses Formula

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 Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses?

Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses calculator uses Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle) to calculate the Normal Stress on Oblique Plane, The Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses formula is defined as the ratio of total normal stress acting on the plane to the cross-sectional area. Normal Stress on Oblique Plane is denoted by σ_θ symbol.

How to calculate Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses using this online calculator? To use this online calculator for Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses, enter Major Principal Stress (σ_major), Minor Principal Stress (σ_minor) & Plane Angle (θ_plane) and hit the calculate button. Here is how the Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses calculation can be explained with given input values -> 6.2E-5 = (75000000+24000000)/2+(75000000-24000000)/2*cos(2*0.5235987755982).

FAQ

What is Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses?

The Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses formula is defined as the ratio of total normal stress acting on the plane to the cross-sectional area and is represented as σ_θ = (σ_major+σ_minor)/2+(σ_major-σ_minor)/2*cos(2*θ_plane) or Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle). Major Principal Stress is the maximum normal stress acting on the principal plane, Minor Principal Stress is the minimum normal stress acting on the principal plane & Plane Angle is the measure of the inclination between two intersecting lines in a flat surface, usually expressed in degrees.

How to calculate Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses?

The Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses formula is defined as the ratio of total normal stress acting on the plane to the cross-sectional area is calculated using Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle). To calculate Normal Stress on Oblique Plane with Two Mutually Perpendicular Unequal Stresses, you need Major Principal Stress (σ_major), Minor Principal Stress (σ_minor) & Plane Angle (θ_plane). With our tool, you need to enter the respective value for Major Principal Stress, Minor Principal Stress & Plane Angle 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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