Determining the State of Stress for a combination of loads and moments, and maybe internal pressure

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Determining the State of Stress for a combination
of loads and moments, and maybe internal pressure

• P, Vy, Vz, T, My, Mz, p

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Statics Make cut through point where stress is
to be determined, here A, B, C, or D might be
the point.
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Cylinder with diameter 100mm
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For example, if VVy and x is perpendicular to
this surface ?xy
V and ?

?xz (-) ?xy()
?xy(-) ?xz ()
If MxT then depending on where the stress is to
be determined the subscripts change
Y Z
T and ?
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See the following slides for details about points
B, C, and D
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Principal stresses and Maximum shear stress (MPa)
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Procedure

• Identify point (eg, pt A) where stress state is
  to be determined
• Create a FBD by cutting through the object at
  point A and define x,y,z axes (here assume x
  perpendicular to the surface)
• Do statics using centroid of surface created to
  determine P, Vy, Vz, MxT, My, Mz (Note may be
  necessary to determine location of centroid)
• Establish orientation of stress cube for keeping
  track of various stress components
• Determine magnitude and orientation of individual
  stress components properly place on stress cube
• Add/subtract components to determine the state of
  stress
• Where necessary determine principal stresses and
  maximum shear stress

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8.32
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8.34
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8.41
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8.39
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8.44
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8.45
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8.49
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8.69
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8.70