Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
σt = (σx-σy)/2*sin(2*θplane)-τ*cos(2*θplane)
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
Tangential Stress on Oblique Plane - (Measured in Megapascal) - Tangential Stress on Oblique Plane is the total force acting in the tangential direction divided by the area of the surface.
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
σt = (σxy)/2*sin(2*θplane)-τ*cos(2*θplane) --> (95-22)/2*sin(2*0.5235987755982)-41.5*cos(2*0.5235987755982)
Evaluating ... ...
σt = 10.8599272381213
STEP 3: Convert Result to Output's Unit
10859927.2381213 Pascal -->10.8599272381213 Megapascal (Check conversion here)
FINAL ANSWER
10.8599272381213 10.85993 Megapascal <-- Tangential Stress on Oblique Plane
(Calculation completed in 00.004 seconds)

Credits

Created by Vaibhav Malani
National Institute of Technology (NIT), Tiruchirapalli
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National Institute Of Technology (NIT), Hamirpur
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4 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
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
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
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
Go Radius of Mohr's circle = (Major Principal Stress-Minor Principal Stress)/2

4 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
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
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
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
Go Radius of Mohr's circle = (Major Principal Stress-Minor Principal Stress)/2

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces Formula

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)
σt = (σx-σy)/2*sin(2*θplane)-τ*cos(2*θplane)

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 Principal Stress & 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.
The intensity of net force acting per unit area normal to the cross-section under consideration is called normal stress.

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

Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces calculator uses 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) to calculate the Tangential Stress on Oblique Plane, The Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces 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 σt symbol.

How to calculate Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces using this online calculator? To use this online calculator for Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces, enter Stress Along x Direction x), Stress Along y Direction y), Plane Angle plane) & Shear Stress in Mpa (τ) and hit the calculate button. Here is how the Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces calculation can be explained with given input values -> 1.1E-5 = (95000000-22000000)/2*sin(2*0.5235987755982)-41500000*cos(2*0.5235987755982).

FAQ

What is Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces?
The Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces formula is defined as the total force acting in the tangential direction divided by the area of the surface and is represented as σt = (σxy)/2*sin(2*θplane)-τ*cos(2*θplane) or 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). 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 Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces?
The Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces 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 = (Stress Along x Direction-Stress Along y Direction)/2*sin(2*Plane Angle)-Shear Stress in Mpa*cos(2*Plane Angle). To calculate Tangential Stress on Oblique Plane with Two Mutually Perpendicular Forces, you need Stress Along x Direction x), Stress Along y Direction y), Plane Angle 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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