Verifying Stress Components in a Circular Cylinder

This means that the stress vector is perpendicular to the surface at all points on the curved surface of the cylinder. This can be shown by substituting the stress components into the equilibrium equations, which result in all components of the stress vector being equal to zero. Therefore, the stress vector vanishes at all points on the curved surface of the cylinder. In summary, the stress vector is defined as t_i=n_j * sigma_ij and it vanishes at all points on the curved surface of a circular cylinder.
  • #1
maros522
15
0
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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  • #2
I've never heard of a "stress vector"; stress is a tensor. Perhaps this is referring to a resolved external force at the surface?
 
  • #3
In this example the stress vector is defined as t_i=n_j * sigma_ij
 

Related to Verifying Stress Components in a Circular Cylinder

1. What is the purpose of verifying stress components in a circular cylinder?

The purpose of verifying stress components in a circular cylinder is to ensure the accuracy and reliability of the calculated stress values. This verification process is crucial in the design and analysis of cylindrical structures, as it helps to identify any errors or inconsistencies in the stress calculations.

2. How do you verify the stress components in a circular cylinder?

The stress components in a circular cylinder can be verified by comparing the calculated values with the known analytical or experimental results. This can be done using mathematical equations, finite element analysis, or physical testing.

3. What factors can affect the accuracy of stress component verification in a circular cylinder?

Some of the factors that can affect the accuracy of stress component verification in a circular cylinder include material properties, loading conditions, boundary conditions, and the accuracy of the analytical or experimental data used for comparison.

4. What are the common methods used to calculate stress components in a circular cylinder?

The common methods used to calculate stress components in a circular cylinder include analytical methods such as the Lame equations, finite element analysis, and experimental methods such as strain gauging or photoelasticity.

5. Why is it important to verify stress components in a circular cylinder?

Verifying stress components in a circular cylinder is important because it ensures the structural integrity and safety of cylindrical structures. It also helps to identify any potential weaknesses or failures in the design, allowing for necessary adjustments and improvements to be made.

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