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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
Stresses in Thin-walled Pressure Vessels (I)

(Hoop Stress)

(Longitudinal Stress)

typical rosette analysis
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 Field in Beams

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

dilatation and bulk modulus
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

comparison of yielding criteria
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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