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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 l.jpg
Stresses in Thin-walled Pressure Vessels (I)

(Hoop Stress)

(Longitudinal Stress)











Typical rosette analysis l.jpg
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 l.jpg
Stress Field in Beams

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





Dilatation and bulk modulus l.jpg
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


Failure criterion for ductile materials yielding criterion l.jpg
Failure Criterion for Ductile Materials(Yielding Criterion)

σ1

σ1

|σ1| = σY

σ2

|σ2| = σY

σ2


Comparison of yielding criteria l.jpg
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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