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

✖Tangential Stress on Oblique Plane is the total force acting in the tangential direction divided by the area of the surface.ⓘ Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress [σ_t]

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Formula

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

Formula

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

Example

`"22.08365MPa"=("75MPa"-"24MPa")/2*sin(2*"30°")`

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

STEP 0: Pre-Calculation Summary

Formula Used

Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle)
σ_t = (σ_major-σ_minor)/2*sin(2*θ_plane)
This formula uses 1 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Tangential Stress on Oblique Plane - (Measured in Pascal) - Tangential Stress on Oblique Plane is the total force acting in the tangential direction divided by the area of the surface.
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_t = (σ_major-σ_minor)/2*sin(2*θ_plane) --> (75000000-24000000)/2*sin(2*0.5235987755982)

Evaluating ... ...

σ_t = 22083647.7965007

STEP 3: Convert Result to Output's Unit

22083647.7965007 Pascal -->22.0836477965007 Megapascal (Check conversion here)

FINAL ANSWER

22.0836477965007 ≈ 22.08365 Megapascal <-- Tangential Stress on Oblique Plane

(Calculation completed in 00.004 seconds)

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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

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

Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle)
σ_t = (σ_major-σ_minor)/2*sin(2*θ_plane)

What is Tangential Force?

The tangential force, also known as the 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.

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

Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress calculator uses Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle) to calculate the Tangential Stress on Oblique Plane, The Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress formula is defined as the total force acting in the tangential direction divided by the area of the surface. Tangential Stress on Oblique Plane is denoted by σ_t symbol.

How to calculate Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress using this online calculator? To use this online calculator for Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal 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 Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress calculation can be explained with given input values -> 2.2E-5 = (75000000-24000000)/2*sin(2*0.5235987755982).

FAQ

What is Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress?

The Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress formula is defined as the total force acting in the tangential direction divided by the area of the surface and is represented as σ_t = (σ_major-σ_minor)/2*sin(2*θ_plane) or Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(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 Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress?

The Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal Stress formula is defined as the total force acting in the tangential direction divided by the area of the surface is calculated using Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle). To calculate Shear Stress on Oblique Plane given Two Mutually Perpendicular and Unequal 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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