1. Stresses in Thin-walled Pressure Vessels (I)
(Hoop Stress)
(Longitudinal Stress)

2. Stresses in Thin-walled Pressure Vessels (II)

3. Stress State under General Combined Loading

4. Plane Stress Transformation

5. Mohr’s Circle for Plane Stress

6. Principal Stresses

7. Maximum Shear Stress

8. Mohr’s Circle for 3-D Stress Analysis

9. Mohr’s Circle for Plane Strain

10. Strain Analysis with Rosette

11. Typical Rosette Analysis
εmax
εa = εx
εb = εx/2 + εy/2 + γxy/2
εmin
εc = εy
gmax
εa = εx
εmax
εb = εx/4 + 3εy/ γxy/4
εmin
gmax
εc = εx/4 + 3εy/ γxy/4

12. Stress Analysis on a Cross-section of Beams

13. Stress Field in Beams
Stress trajectories indicating the direction of principal stress of the same magnitude.

14. Re-visit of Pressure Vessel Stress Analysis

15. Relations among Elastic Constants

16. Constitutive Relations under Tri-axial Loading

17. Dilatation and Bulk Modulus
For the special case of “hydrostatic” loading -----
σx = σy = σz = –p
where DV/V is called Dilatation or Volumetric Strain.
Define Bulk Modulus K as

18. Failure Criterion for Ductile Materials (Yielding Criterion)σ2
|σ2| = σY
|σ1| = σY σ1

19. Comparison of Yielding Criteria
Tresca Criterion
(Max. Shear Stress)
|σ1| = σY
|σ2| = σY
|σ1 – σ2| = σY
Von Mises Criterion
(Max. Distortion Energy)