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Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces Calculator

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Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular Tensile Stress of Unequal Intensity 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

✖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.ⓘ Plane Angle [θ_plane]			+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%

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

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Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces Solution

STEP 0: Pre-Calculation Summary

Formula Used

Normal Stress on Oblique Plane = (Stress Along x Direction+Stress Along y Direction)/2+(Stress Along x Direction-Stress Along y Direction)/2*cos(2*Plane Angle)+Shear Stress in Mpa*sin(2*Plane Angle)
σ_θ = (σ_x+σ_y)/2+(σ_x-σ_y)/2*cos(2*θ_plane)+τ*sin(2*θ_plane)
This formula uses 2 Functions, 5 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)
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 Megapascal) - Normal Stress on Oblique Plane is the stress acting normally to its oblique plane.
Stress Along x Direction - (Measured in Megapascal) - 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 Megapascal) - Stress Along y Direction is the force per unit area acting perpendicular to the y-axis in a material or structure.
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 Megapascal) - 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 --> 95 Megapascal No Conversion Required
Stress Along y Direction: 22 Megapascal --> 22 Megapascal No Conversion Required
Plane Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Shear Stress in Mpa: 41.5 Megapascal --> 41.5 Megapascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_θ = (σ_x+σ_y)/2+(σ_x-σ_y)/2*cos(2*θ_plane)+τ*sin(2*θ_plane) --> (95+22)/2+(95-22)/2*cos(2*0.5235987755982)+41.5*sin(2*0.5235987755982)

Evaluating ... ...

σ_θ = 112.690054257056

STEP 3: Convert Result to Output's Unit

112690054.257056 Pascal -->112.690054257056 Megapascal (Check conversion here)

FINAL ANSWER

112.690054257056 ≈ 112.6901 Megapascal <-- Normal Stress on Oblique Plane

(Calculation completed in 00.020 seconds)

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Created by Vaibhav Malani

National Institute of Technology (NIT), Tiruchirapalli

Vaibhav Malani has created this Calculator and 600+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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< Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular Tensile Stress of Unequal Intensity Calculators

Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces

LaTeX Go Normal Stress on Oblique Plane = (Stress Along x Direction+Stress Along y Direction)/2+(Stress Along x Direction-Stress Along y Direction)/2*cos(2*Plane Angle)+Shear Stress in Mpa*sin(2*Plane Angle)

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces

LaTeX Go Tangential Stress on Oblique Plane = (Stress Along x Direction-Stress Along y Direction)/2*sin(2*Plane Angle)-Shear Stress in Mpa*cos(2*Plane Angle)

Maximum Shear Stress

LaTeX Go Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2

Radius of Mohr's Circle for Two Mutually Perpendicular Stresses of Unequal Intensities

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

< When a Body is subjected to two Mutual Perpendicular Principal Tensile stresses of Unequal Intensity Calculators

Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces

LaTeX Go Tangential Stress on Oblique Plane = (Stress Along x Direction-Stress Along y Direction)/2*sin(2*Plane Angle)-Shear Stress in Mpa*cos(2*Plane Angle)

Maximum Shear Stress

LaTeX Go Maximum Shear Stress = sqrt((Stress Along x Direction-Stress Along y Direction)^2+4*Shear Stress in Mpa^2)/2

Radius of Mohr's Circle for Two Mutually Perpendicular Stresses of Unequal Intensities

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

Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces Formula

LaTeX Go

What is Normal Stress & Principal Stress?

The intensity of net force acting per unit area normal to the cross-section under consideration is called normal stress.
When a stress tensor acts on a body, the plane along which the shear stress terms vanish is called the principal plane, and the stress on such planes is called principal stress.

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.

How to Calculate Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces?

Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces calculator uses Normal Stress on Oblique Plane = (Stress Along x Direction+Stress Along y Direction)/2+(Stress Along x Direction-Stress Along y Direction)/2*cos(2*Plane Angle)+Shear Stress in Mpa*sin(2*Plane Angle) to calculate the Normal Stress on Oblique Plane, The Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces formula is defined as the total normal force ratio to the cross-section area. Normal Stress on Oblique Plane is denoted by σ_θ symbol.

How to calculate Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces using this online calculator? To use this online calculator for Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces, enter Stress Along x Direction (σ_x), Stress Along y Direction (σ_y), Plane Angle (θ_plane) & Shear Stress in Mpa (τ) and hit the calculate button. Here is how the Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces calculation can be explained with given input values -> 0.000113 = (95000000+22000000)/2+(95000000-22000000)/2*cos(2*0.5235987755982)+41500000*sin(2*0.5235987755982).

FAQ

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

The Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces formula is defined as the total normal force ratio to the cross-section area and is represented as σ_θ = (σ_x+σ_y)/2+(σ_x-σ_y)/2*cos(2*θ_plane)+τ*sin(2*θ_plane) or Normal Stress on Oblique Plane = (Stress Along x Direction+Stress Along y Direction)/2+(Stress Along x Direction-Stress Along y Direction)/2*cos(2*Plane Angle)+Shear Stress in Mpa*sin(2*Plane Angle). 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, Plane Angle is the measure of the inclination between two intersecting lines in a flat surface, usually expressed in degrees & 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 Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces?

The Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces formula is defined as the total normal force ratio to the cross-section area is calculated using Normal Stress on Oblique Plane = (Stress Along x Direction+Stress Along y Direction)/2+(Stress Along x Direction-Stress Along y Direction)/2*cos(2*Plane Angle)+Shear Stress in Mpa*sin(2*Plane Angle). To calculate Normal Stress on Oblique Plane with Two Mutually Perpendicular Forces, you need Stress Along x Direction (σ_x), Stress Along y Direction (σ_y), Plane Angle (θ_plane) & Shear Stress in Mpa (τ). With our tool, you need to enter the respective value for Stress Along x Direction, Stress Along y Direction, Plane Angle & 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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