Hoop Stress

[MatrixEnvironmental]

Using Lame' Equation for Hoop stress the equation states

Hoop Stress=(a^2pi-b^2po) - (pi-po)a^2b^2
b^2-a^2 (a^2-b^2)r^2

pi=interior pressure
po=exterior pressure
a=interior radius
b=exterior radius

What does the r stand for? is it the total radius or is it the thickness of the cylinder?

 

[EMTEC]

The r in Lame' equations is a radius with a value between a and b used to compute the stress at that particular radius. Compute the equation with a series of increasing r values ranging from a to b to get values for a plot of the stress across the wall. The denominator in the second half of the equation should be (b^2-a^2)r^2. Because of the negative sign in the middle, I believe the equation you presented is for radial stress NOT "hoop" or tangential stress. This equation is for thick walled cylinders, only. See this site for a simpler equation when Po=0, equation development, and definitions. Example calculations can be found on related pages at this site:

http://www.utm.edu/departments/engin/lemaster/Machine Design/Notes 13.pdf

 

[MatrixEnvironmental]

Thanks for the advice EMTEC. The equation typed in was an error on my part, but thanks for telling me what the r value stood for. I appreciate it.

Matrixenvironmental