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


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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)

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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


Mohr’s Circle for 3-D Stress Analysis


Mohr’s Circle for Plane Strain


Strain Analysis with Rosette


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 Analysis on a Cross-section of Beams


Stress Field in Beams

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


Re-visit of Pressure Vessel Stress Analysis


Relations among Elastic Constants


Constitutive Relations under Tri-axial Loading


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)

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)


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