# Principal Stress & Strain Study Notes for Mechanical Engineering

By Akhil Gupta|Updated : December 22nd, 2021

Principal Stress & Strain is a very important topic in Mechanical Engineering, especially if you are preparing for the GATE 2022 exam. We have listed below the complete study notes on Principal Stress & Strain for your GATE ME exam preparation.

Principal Stress & Strain is a very important topic in Mechanical Engineering, especially if you are preparing for the GATE 2022 exam. We have listed below the complete study notes on Principal Stress & Strain for your GATE ME exam preparation.

These topic-wise study notes are helpful for the preparation of various upcoming exams like GATE MEIESBARCISROSSC-JE/ State Engineering Services examinations and other important forthcoming competitive exams.

The article contains fundamental study notes on the "Principal Stress & Strain" topic of the "Strength of Materials" subject.

Stress on Inclined Section PQ due to Uniaxial Stress

Consider a rectangular beam and we have to calculate the stress on an inclined section as shown in the figure.

Induced stress is divided into two components which are given as-
Normal stress
Normal Stress on an inclined section.

Tangential stress
Shear Stress on an inclined section.

Stress on Inclined Section PQ due to Shear Stress

Induced stress is divided into two components which are given as -
Normal stress
Normal Stress on an inclined section.

Tangential Stress
Shear Stress on an inclined section.

Stress on Inclined Section PQ due to the combination of Axial Stress and Shear Stress
Induced stress is divided into two components which are given as -
Normal stress
Normal Stress on an inclined section.

Tangential stress
Shear Stress on an inclined section.

Principal Stresses and Principal Planes
The plane carrying the maximum normal stress is called the major principal plane and normal stress is called major principal stress.
The plane carrying the minimum normal stress is known as minor principal plane and normal stress is called minor principal stress.
Major principal stress
Minor principal stress
Major & Minor principal plane angle
Note: Across maximum normal stresses acting in plane shear stresses are zero.

Computation of Principal Stress from Principal Strain
The three stresses normal to shear principal planes are called principal stress, while a plane at which shear strain is zero is called principal strain.
For two-dimensional stress system, σ3 = 0
Maximum Shear Stress
The maximum shear stress is equal of one half the difference between the largest and smallest principal stresses and acts on the plane that bisects the angle between the directions of the largest and smallest principal stress, i.e. the plane of the maximum shear stress is oriented 45° from the principal stress planes.

Principal Strain
For two-dimensional strain system,
Where, εx = Strain in x-direction
εy = Strain in y-direction
γxy = Shearing strain

Maximum Shear Strain
The maximum shear strain also contains normal strain which is given as

Strain Measuring Method - 45° Strain Rosette or Rectangular Strain Rosette
Rectangular strains Rosette is inclined 45° to each other
Principal strains can be calculated from the above equations.

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write a comment

8498943063Jul 18, 2018

Tq sir
Thankyou

Siva RockzzJul 25, 2018

Thank u sir for sharing  ur beautiful  knowlege  with  us
Can u explain briefly how stress where derived

Ajay MoreFeb 11, 2019

I don't get the stress induced by state simple shear and axial and normal stress
Can u explain both terms with example

Chirag ShahAug 15, 2019

This comment is hidden because it was marked spam.

Can you explain clearly difference between ductile and brittle

Vijay ChollangiAug 5, 2020

Thank you  sir🧑

Amar BareAug 14, 2020

Mistake in Principle stress formulae (bracket inside square root)

SrinivasOct 5, 2020

thank you sir
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