Thick walled cylinder: find required thickness

[mylovelyamber]

1. given that the yield stress σy of the material is 475 Mpa, internal radius ri is 24.47mm, internal pressure pi is 6.07 Mpa, external pressure po is atmospheric, find the thickness required of the cylinder such that it does not undergo failure. (ro≥ r ≥ri)2. σr = [(pi ri^2 - po ro^2) / (ro^2 - ri^2)] + [ri^2 ro^2 (po - pi) / r^2 (ro^2 - ri^2)]
3. I set σr=σy/1.5 and Po as 101.325 kPa
i also set r=ro
i sub the values into the calculation but the value of ro that i get is the same as ri, which is not possible.

can someone please enlighten me what i should set as r?

 

[edgepflow]

These Lame's formulas are a function of r. Since you are given ri, assume a wall thickness t. Then ro = ri + t. And then check the stress at ri, ro, and a few points in between.

You will have to iterate to find the thickness so your stress is within limits.

 

[mylovelyamber]

hi,

thank you for the reply, but i still can't get rid of the r term...
if i let ro=ri+t,
there is still that r term that i can't get rid of...
σr = [(pi ri^2 - po ro^2) / (ro^2 - ri^2)] + [ri^2 ro^2 (po - pi) / r^2 (ro^2 - ri^2)]

 

[edgepflow]

hi,

thank you for the reply, but i still can't get rid of the r term...
if i let ro=ri+t,
there is still that r term that i can't get rid of...
σr = [(pi ri^2 - po ro^2) / (ro^2 - ri^2)] + [ri^2 ro^2 (po - pi) / r^2 (ro^2 - ri^2)]

Let me try to clarify.

You are given ri = 24.47 mm. So suppose the wall thickness is t = 3 mm. So, ro = ri + t = 24.47 mm + 3 mm = 27.47 mm.

Now for the r in the formula, plug in these values one at a time and write down the stress for each one:

(1) r = ri
(2) r = ri + 0.2 t
(3) r = ri + 0.4 t
(4) r = ri + 0.6 t
(5) r = ri + 0.8 t
(6) r = ro

Then see which stress is the largest and if it is under your allowable stress limit.