Module 14
Complex stress and strain
Stress on any plane through a point, principal stresses, Mohr's circle, strain gauges and when materials yield.
What this module covers
- Describe the state of stress at a point using components on two perpendicular planes
- Derive the transformation equations from equilibrium of a wedge
- Find principal stresses, their directions and the maximum shear stress
- Use Mohr's circle and connect every construction to a physical plane
- Convert strain-gauge rosette readings into stresses
- Apply the Tresca and von Mises yield criteria
Lessons
Why the answer depends on the plane, and deriving the transformation equations.
Start lesson →The planes with no shear, the largest shear, and the picture that ties it all together.
Start lesson →Measuring strain on a real structure, and deciding whether the material will yield.
Start lesson →Following the principal stresses through a beam, and why cracks go where they go.
Start lesson →The same circle again, with one factor of two that catches everybody.
Start lesson →
Module checkpoint
Check what you have taken in
3 questions
Question 1
At a point σx = 100 N/mm², σy = 40 N/mm² and τxy = 40 N/mm². What is the major principal stress?
Question 2
For that same state, what is the maximum in-plane shear stress?
Question 3
Rotating a physical plane by 20° moves you how far around Mohr's circle?