Stress field in cylindrical coordinates

In summary, the stress fields in cylindrical coordinates involve radial and azimuthal directions, with the latter being normal to the former. The difference between σ_{rz} and σ_{\theta z} is that the former refers to shear stress while the latter refers to normal force. In terms of stress in the r and θ axes, one deals with tensile or compressive forces rather than shear forces.
  • #1
leumas614
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Can anyone please explain the stress fields in cylindrical coordinates? What is the difference between [tex]\sigma_{rz}[/tex] and [tex]\sigma_{\theta z}[/tex]? What is the difference between stress in the [tex]r[/tex] axis and stress in the [tex]\theta[/tex] axis? Thanks
 
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  • #2
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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What is a stress field in cylindrical coordinates?

A stress field in cylindrical coordinates is a mathematical description of the distribution of stress (force per unit area) within a cylindrical object. It takes into account both the magnitude and direction of the stress at each point in the object.

What are the advantages of using cylindrical coordinates to describe a stress field?

Using cylindrical coordinates allows for a more simplified and efficient mathematical representation of stress fields in cylindrical objects. It also takes into account the symmetry of the object, making it easier to analyze and solve for stress distributions.

How is a stress field in cylindrical coordinates calculated?

A stress field in cylindrical coordinates is calculated using the equations of equilibrium, which take into account the forces and moments acting on the object, as well as the geometry and material properties of the object.

What are some real-world applications of understanding stress fields in cylindrical coordinates?

Understanding stress fields in cylindrical coordinates is important in engineering and design, as it allows for the prediction and prevention of potential failures in cylindrical structures such as pipes, tanks, and pressure vessels. It also plays a role in material selection and optimizing the design of these structures.

Can a stress field in cylindrical coordinates change over time?

Yes, a stress field in cylindrical coordinates can change over time due to external forces, changes in temperature, and other factors. This is why it is important to continuously monitor and analyze stress fields in real-world applications to ensure the safety and integrity of cylindrical structures.

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