Elasticity lecture 5
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Elasticity-Lecture 5 More About Stress
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Undergraduate elasticity lecture
Transcript of Elasticity lecture 5
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: