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Stresses in Thin-walled Pressure Vessels (I)

Stresses in Thin-walled Pressure Vessels (I). (Hoop Stress). (Longitudinal Stress). Stresses in Thin-walled Pressure Vessels (II). Stress State under General Combined Loading. Plane Stress Transformation. Mohr’s Circle for Plane Stress. Principal Stresses. Maximum Shear Stress.

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Stresses in Thin-walled Pressure Vessels (I)

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  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/4 + γxy/4 εmin gmax εc = εx/4 + 3εy/4 - 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) σ1 σ1 |σ1| = σY σ2 |σ2| = σY σ2

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

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