Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress 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 for Two Perpendicular Unequal and Unlike Stress [σ_θ]

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Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress

Formula

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

Example

`"50.25MPa"=("75MPa"-"24MPa")/2+("75MPa"+"24MPa")/2*cos(2*"30°")`

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Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress 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 = 50250000.0000085

STEP 3: Convert Result to Output's Unit

50250000.0000085 Pascal -->50.2500000000085 Megapascal (Check conversion here)

FINAL ANSWER

50.2500000000085 ≈ 50.25 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 Stress which are Unequal and Unlike » Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress

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< 3 Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular Stress which are Unequal and Unlike Calculators

Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress

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 for Two Perpendicular Unequal and Unlike Stress

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

Radius of Mohr's Circle for Unequal and Unlike Mutually Perpendicular Stresses

Go Radius of Mohr's circle = (Major Principal Stress+Minor Principal Stress)/2

< 3 When a Body is subjected to two Mutual Perpendicular Principal Tensile stresses which are Unequal and Unlike Calculators

Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress

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 for Two Perpendicular Unequal and Unlike Stress

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

Radius of Mohr's Circle for Unequal and Unlike Mutually Perpendicular Stresses

Go Radius of Mohr's circle = (Major Principal Stress+Minor Principal Stress)/2

Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress 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 Tangential Force?

The tangential force, also known as shear force, is the force acting parallel to the surface. When the direction of the deforming force or external force is parallel to the cross-sectional area, the stress experienced by the object is called shearing stress or tangential stress.

How to Calculate Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress?

Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress 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 for Two Perpendicular Unequal and Unlike Stress formula is defined as the ratio of the total normal force to cross-sectional area. Normal Stress on Oblique Plane is denoted by σ_θ symbol.

How to calculate Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress using this online calculator? To use this online calculator for Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress, 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 for Two Perpendicular Unequal and Unlike Stress calculation can be explained with given input values -> 5E-5 = (75000000-24000000)/2+(75000000+24000000)/2*cos(2*0.5235987755982).

FAQ

What is Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress?

The Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress formula is defined as the ratio of the total normal force to 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 for Two Perpendicular Unequal and Unlike Stress?

The Normal Stress on Oblique Plane for Two Perpendicular Unequal and Unlike Stress formula is defined as the ratio of the total normal force to 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 for Two Perpendicular Unequal and Unlike Stress, 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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