Stresses in Thin-walled Pressure Vessels (I) (Hoop Stress

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Stresses in Thin-walled Pressure Vessels (I)
(Hoop Stress)
(Longitudinal Stress)
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Stresses in Thin-walled Pressure Vessels (II)
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Stress State under General Combined Loading
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Plane Stress Transformation
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Mohrs Circle for Plane Stress
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Principal Stresses
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Maximum Shear Stress
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Mohrs Circle for 3-D Stress Analysis
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Mohrs Circle for Plane Strain
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Strain Analysis with Rosette
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Typical Rosette Analysis
emax
ea ex
eb ex/2 ey/2 ?xy/2
emin
ec ey
gmax
ea ex
emax
eb ex/4 3ey/4 ?xy/4
emin
gmax
ec ex/4 3ey/4 - ?xy/4
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Stress Analysis on a Cross-section of Beams
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Stress Field in Beams
Stress trajectories indicating the direction of
principal stress of the same magnitude.
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Re-visit of Pressure Vessel Stress Analysis
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Relations among Elastic Constants
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Constitutive Relations under Tri-axial Loading
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Dilatation and Bulk Modulus
For the special case of hydrostatic loading
-----
sx sy sz p
where DV/V is called Dilatation or Volumetric
Strain.
Define Bulk Modulus K as
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Failure Criterion for Ductile Materials(Yielding
Criterion)
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Comparison of Yielding Criteria
Tresca Criterion (Max. Shear Stress)
s1 sY
s2 sY
s1 s2 sY
Von Mises Criterion (Max. Distortion Energy)