What is the increase in outer radius of the annulus?

Question

http://i33.tinypic.com/25p45u1.jpg

An annular region (inner radius R/2 and outer radius R) is subject to a uniform stress σ on its outer edges. Find an expression for the increase in the outer radius of the annulus.

Young’s modulus = E

Poisson’s ration = ν

Follow up to: http://answers.yahoo.com/question/index;_ylt=AndcsczxygXfTKxdhN0ZK1rsy6IX;_ylv=3?qid=20080728070747AA68TGA

I hope I don't get a violation for say annulus.

Answer 1

Calculate hoop stress and then it's just the elongation of the section.

Answer 2

ΔR = (1 - 4/3*Poisson's ratio)/(Young's modulus) σR

Just a guess based on the decrease in area of the disk.

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Re: Hint.  lol.  Already thought of that.  It is no different then a pressure vessel.  

But I could not find an equation for a thick wall pressure vessel.  And I abhor the thought of trying to integrate anything.

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Ahh, re-googled.  Add the word "formula" to "thick walled pressure vessel" (which I previously googled) and I got: http://courses.washington.edu/me354a/cha...

The only difference, is axial stress.  There is no axial stress.

Radial stress = Ri^2 p/(Ro^2 - Ri^2) (1- Ro^2/r^2)

Ri= 1/2 Ro

Ro = R

ergo

Rad Stress = p1/4R^2/(R^2 - 1/4R^2) (1-R^2/r^2)

= -p/3(1- (R/r)^2)

Let x = r/R

rad stress = -p/3(1-1/x^2)

Integrate 1/2 to 1

=-p/3 (x + 1/x)

=-p/3 [2- 2.5]

= p/6

*To be continued ....... maybe

**I will continue -- probably tonight.  It has been a long time, and I no longer have reference books but I recalled how to finish it off.  And yes, I caught that typo too in 12.5 of the reference.