Principal Plane & Principal Stress (Stress and Strain Part-4)

Before proceeding to two dimensional stress system. Let’s us understand few technical terms which are generally asked during interview questions.

Principal Plane: A plane at which shear stress is Zero, is known as principal plane.

Principal Stress: When on principal plane normal stress is acting ,then it is known as principal stress.

There are two types of principal stresses as follows:

  1. Major Principal Stress: Maximum normal stress at principal plane is called major principal stress and the plane at which it is acting is called major principal plane.
  2. Minor Principal stress: Minimum normal stress at principal plane is called minor principal stress and the plane at which it is acting is called minor principal plane.
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Two-Dimensional Stress System

If normal stress and shear stress both acting on a body then principal stress is determined by:

At this point sometimes we get confused that at principal plane shear stress is zero, so how can there be normal stress, shear stress, and principal plane. But the thing is Principal plane will be some plane at an angle on a body where those above-defined conditions will meet.

Let’s consider a triangular block having unit depth.

Resolving components we get following equations:

As we have already discussed at any angle θ, there will be a plane where shear stress will be zero, that plane will be principal plane.

So to find that angle we put eq. (2) = 0 and we get the value of angle θ.

As it can be seen in eq. (4) there are two signs, that means two values of Principal stress.

If we take positive sign then we get major principal stress.

If we take negative sign then we get minor principal stress.

We also know that there will be a plane where shear stress will be maximum, let’s find out what is the value of maximum shear stress and how it is related with principal plane.

Putting this value in eq. (3) , we get 

So, we have seen in eq (4) there were two values of principal stress we can say that these principal stress major and minor are perpendicular to each other i.e. at 90º to each other .
Similarly one more point that can be concluded is maximum shear stress plane and principal plane are at 45º to each other .
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