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# Stresses in Thin-walled Pressure Vessels (I) PowerPoint PPT Presentation

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.

Stresses in Thin-walled Pressure Vessels (I)

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### Stresses in Thin-walled Pressure Vessels (I)

(Hoop Stress)

(Longitudinal Stress)

### 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

### Stress Field in Beams

Stress trajectories indicating the direction of principal stress of the same magnitude.

### Dilatation and Bulk Modulus

σx = σy = σz = –p

where DV/V is called Dilatation or Volumetric Strain.

Define Bulk Modulus K as

σ1

σ1

|σ1| = σY

σ2

|σ2| = σY

σ2

### Comparison of Yielding Criteria

Tresca Criterion

(Max. Shear Stress)

|σ1| = σY

|σ2| = σY

|σ1 – σ2| = σY

Von Mises Criterion

(Max. Distortion Energy)