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)
σθ = (σmajor+σminor)/2+(σmajor-σminor)/2*cos(2*θplane)
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
σθ = (σmajorminor)/2+(σmajorminor)/2*cos(2*θplane) --> (75000000+24000000)/2+(75000000-24000000)/2*cos(2*0.5235987755982)
Evaluating ... ...
σθ = 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)

Credits

Creator Image
Created by Vaibhav Malani
National Institute of Technology (NIT), Tiruchirapalli
Vaibhav Malani has created this Calculator and 600+ more calculators!
Verifier Image
Verified by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
Anshika Arya has verified this Calculator and 2500+ more calculators!

Mohr's Circle when a Body is Subjected to Two Mutual Perpendicular and a Simple Shear Stress Calculators

Maximum Value of Normal Stress
​ LaTeX ​ 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
​ LaTeX ​ 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
​ LaTeX ​ 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 given Two Mutually Perpendicular and Unequal Stress
​ LaTeX ​ Go Tangential Stress on Oblique Plane = (Major Principal Stress-Minor Principal Stress)/2*sin(2*Plane Angle)

When a Body is subjected to two Mutual Perpendicular Principal Tensile stresses along with Simple Shear Stress Calculators

Maximum Value of Normal Stress
​ LaTeX ​ 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)
Maximum Value of Shear Stress
​ LaTeX ​ Go Maximum Shear Stress = sqrt(((Stress Along x Direction-Stress Along y Direction)/2)^2+Shear Stress in Mpa^2)
Condition for Maximum Value of Normal Stress
​ LaTeX ​ Go Plane Angle = (atan((2*Shear Stress in Mpa)/(Stress Along x Direction-Stress Along y Direction)))/2
Condition for Minimum Normal Stress
​ LaTeX ​ 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

​LaTeX ​Go
Normal Stress on Oblique Plane = (Major Principal Stress+Minor Principal Stress)/2+(Major Principal Stress-Minor Principal Stress)/2*cos(2*Plane Angle)
σθ = (σmajor+σminor)/2+(σmajor-σminor)/2*cos(2*θplane)

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 σθ 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 major), Minor Principal Stress minor) & Plane Angle 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 σθ = (σmajorminor)/2+(σmajorminor)/2*cos(2*θplane) 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 major), Minor Principal Stress minor) & Plane Angle 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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!