Verifying Stress Components in a Circular Cylinder

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SUMMARY

The discussion focuses on verifying the stress components in a circular cylinder, specifically the equilibrium equations and the behavior of the stress vector on the cylinder's surface. The stress components are defined as sigmaij=[Ay+Bz, Cz, -Cy; Cz, 0, 0; -Cy, 0, 0]. It is established that in the absence of body forces, the equilibrium equations are satisfied. Additionally, it is confirmed that the stress vector, defined as t_i=n_j * sigma_ij, vanishes at all points on the curved surface of the cylinder.

PREREQUISITES
  • Understanding of stress tensors in continuum mechanics
  • Familiarity with equilibrium equations in solid mechanics
  • Knowledge of stress vectors and their definitions
  • Basic concepts of cylindrical coordinates in mechanics
NEXT STEPS
  • Study the derivation of equilibrium equations in solid mechanics
  • Learn about stress vector calculations in different geometries
  • Explore the application of cylindrical coordinates in stress analysis
  • Investigate the implications of body forces on stress components
USEFUL FOR

This discussion is beneficial for mechanical engineers, structural analysts, and students studying solid mechanics, particularly those focusing on stress analysis in cylindrical structures.

maros522
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The stress components in a circular cylinder of length L and radius r
are given by

sigmaij=[Ay+Bz, Cz, -Cy; Cz, 0, 0; -Cy, 0, 0]

(a) Verify that in the absence of body forces the equilibrium equations
are satisfied.
(b) Show that the stress vector vanishes at all points on the curved
surface of the cylinder.

I have problem with this example, especialy with point b. Do You have some idea?
 
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I've never heard of a "stress vector"; stress is a tensor. Perhaps this is referring to a resolved external force at the surface?
 
In this example the stress vector is defined as t_i=n_j * sigma_ij
 

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