When you design any structural component, You need to know the critical values of stress, So that, you can design for the greater capacities.
So there are only 2 major types of stresses
A material can fail due to shear even though a tensile load(Normal load) is applied. So the point is you cannot design for normal stress nor shear stress as they can act together to cause failure.
In simple terms principal stresses gives us the critical values of stress due to shear,normal,combination of both.
Therefore, it is necessary to compute principal stresses.
I hope the solution is clear.
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