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

### 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:

#### 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 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

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