Elasticity lecture 5
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This document discusses different types of stresses and how to represent stress tensors in 2D and 3D. It introduces normal stresses that act perpendicular to a plane, and shear stresses that act parallel to a surface. It then describes using a stress vector and unit vector n to represent the stress tensor in 3D as an ellipsoid equation. For 2D representation, it recommends using a Mohr circle diagram to show the range of stresses in any direction in a hatched region.
Elasticity lecture 5
- 1. Elasticity-Lecture 5 More About Stress
- 2. Normal stresses acts normal to the plane, whereas Shear stresses acts parallel to the surface
- 3. The unit vector n is defined usually normal to the plane with components : n1 , n2, n3 The stress vector is thus:
- 4. Since n is a unit vector Because: Equation of ellipsoid The ellipsoid equation is a good choice to represent the stress tensor in 3-D But what about 2-D representation?
- 5. A good choice is the Mohr circle The stress in any direction will lie in the hatched region of the diagram How?
- 7. Since n1 2 >= 0 and since
- 9. Vectors can be defined as The vector ca also be written as
- 10. The rules are: