Elasticity-Lecture 5

More About Stress

Normal Stress

Shea

ring s

tress

Normal stresses acts normal to the plane, whereasShear stresses acts parallel to the surface

The unit vector n is defined usually normal to the plane with components :n1 , n2, n3

The stress vector is thus:

Since n is a unit vector

Because:

Equation of ellipsoid

The ellipsoid equation is a good choice to represent the stress tensor in 3-DBut what about 2-D representation?

A good choice is theMohr circle

The stress in any direction will lie in the hatched region of the diagram How?

Since n12 >= 0 and since

Then

Vectors can be defined as

The vector ca also be written as

The rules are: