Stress field in cylindrical coordinates

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SUMMARY

The discussion focuses on understanding stress fields in cylindrical coordinates, specifically the differences between the stress components \(\sigma_{rz}\) and \(\sigma_{\theta z}\). The radial direction (r) and the azimuthal direction (θ) are crucial for analyzing stresses and strains in cylindrical systems. It is established that when subscripts differ, they indicate shear stress, while identical subscripts denote normal stress, which can be either tensile or compressive.

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  • Understanding of cylindrical coordinate systems
  • Familiarity with stress and strain concepts in solid mechanics
  • Knowledge of normal and shear stress definitions
  • Basic grasp of tensor notation in mechanics
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leumas614
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Can anyone please explain the stress fields in cylindrical coordinates? What is the difference between \sigma_{rz} and \sigma_{\theta z}? What is the difference between stress in the r axis and stress in the \theta axis? Thanks
 
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In the polar directions, one deals with radial, r, and azimuthal (hoop), θ, directions/stresses/strains. The hoop direction is normal or perpendicular to the radial direction.

σxy, x refers to direction of surface normal on which force acts, and y refers to direction of force component, i.e. σxy = stress on x plane acting in y direction.

cf - http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/stress.cfm

When the two subscripts are different, they refer to a shear stress. When the same, they refer to a normal force, which is purely tensile or compressive, but not shear.
 
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