Verifying Stress Components in a Circular Cylinder

AI Thread Summary
The discussion focuses on verifying stress components in a circular cylinder, specifically addressing equilibrium equations and the stress vector on the cylinder's surface. The stress components are defined in a tensor format, and the participants clarify that the stress vector is derived from the stress tensor using the normal vector at the surface. Concerns are raised about understanding the concept of a stress vector, with suggestions that it relates to external forces acting on the surface. The discussion emphasizes the need to confirm that the stress vector equals zero at the curved surface of the cylinder. Overall, the thread seeks clarity on the mathematical verification of these stress components and their implications.
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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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