# On the physical meaning of principal stress

Hi everyone, I was looking up Mohr's circle on planar stress and stress/strain relation and all that

and I read a context on principal stress. It said that if there is both normal (tensile) stress and shear stress in a given area, then the principal stress at that location is greater than the normal stress.

Well, I was just wondering what really is the importance of principal stress in real world applications...

does principal stress mean the MAXIMUM stress an object can be under in a given area dA???
And when there is a principal stress then there is no shear stress, but I didn't get that either because how could there be no shear stress?

SteamKing
Staff Emeritus
Homework Helper
It depends on the plane within the object for which the stress is calculated. Normal (as in perpendicular) stresses and shear stresses act differently on a given plane. In a sense, the principal stress acts to combine normal stresses and shear stresses to produce a maximum (or a minimum) stress.

A meatier article on stress is here: http://en.wikipedia.org/wiki/Stress_(mechanics)

SteamKing's right on about principal stress. As you look at a material under stress, the stresses are different when you look at it in different directions (the T = n * σ part of Cauchy's stress tensor). The idea is to find an orientation for a differential volume such that the shear stress is zero for that element. That means all the stresses are normal stresses, and these stresses are called principal stresses. Mohr's circle tells you the orientation that satisfies that condition.

You use it all the time in the real world. Usually you're given material allowables in design, but they don't specify at some normal stress what the max shear stresses need to be. You usually get a tension (and maybe a compression) allowable, so using Mohr's circle, you can get principal stresses and check those against your allowables.