Buckling of a thin-walled cylinder
Buckling of a thin-walled cylinder
(OP)
I am trying to determine at what point a long thin-walled cylinder will buckle under external pressure. I'm sure there is most likely a simple equation I could use, but I haven't been able to find one. Any suggestions?





RE: Buckling of a thin-walled cylinder
http://naca.larc.nasa.gov/reports/1951/naca-report-1027/
RE: Buckling of a thin-walled cylinder
p' = 3EI/(r^3)
where p' is the buckling load per unit length of cricumference. In his Edition 5, it is Table 34, Case 8.
This is readily extendable to your case of a LONG thin-walled cylinder. Don't forget the (1-n^2) correction, where n is Poisson's ratio.
NOTE however that most texts warn that formulae such as this one are critically (no pun intended) dependent upon the shape having perfect geometry. Slight imperfections lead to large reduction in load-carrying capacity.
HTH.
RE: Buckling of a thin-walled cylinder
table 35 case 19 is probably the one you need.
Cheers
Greg Locock
RE: Buckling of a thin-walled cylinder
Are you sure Table 34 / Case 8 of Edition 5, "Uniform circular ring under uniform radial pressure", is for out-of-plane buckling of the ring? I have always taken it as applying to in-plane buckling.
And now that you draw my attention to Case 19 of Table 35, "Thin tube under uniform lateral external pressure", for which my thanks, I believe that the two formulae are the same (mutatis mutandis).
As an aside to a fellow user of Table 34, there is an error in Case 4, "Uniform straight bar under end load P ... elastically supported by lateral pressure p proportional to deflection". The pi^2 in the denominator of the formula for P' should actually be pi^4. I passed this error on to the Australian office of the publisher (McGraw-Hill) in 1993, but am not sure whether the error has been corrected in any subsequent edition. Does anyone out there know?
RE: Buckling of a thin-walled cylinder
34/8 is pcrit=3*E*I/r^3/b, ie 1/4*E*t^3/r^3
35/9 is pcrit=E*t^3/(4*(1-nu^2)*r^3)
That's about a 10% difference.
However, since they are so similar I think you are right, the 34/8 is for an in-plane buckle.
Cheers
Greg Locock
RE: Buckling of a thin-walled cylinder
2Et 1 t2 2n2-1-ν
pcr= ----{--------------------- + ---------- [n2-1 + -----------]}
Do (n2-1)[1+(2nL/πDo)2]2 3(1-ν2)Do2 (2nL/πDo)2-1
prex
http://www.xcalcs.com
Online tools for structural design
RE: Buckling of a thin-walled cylinder
The tube is constrained against deforming in this manner, by virtue of its large axial length. It is therefore stiffer in response to any such bending. This additional effective stiffness leads to the slightly larger resistance to buckling.
I alluded to this effect in both my above posts, perhaps too cryptically.
RE: Buckling of a thin-walled cylinder
Or am I concentrating too much on the idea of pushing my thumb into the side of Pepsi (tm) can?
Cheers
Greg Locock
RE: Buckling of a thin-walled cylinder
Pushing your thumb into the side of a can is not "uniform radial pressure" - it is closer to a point load.
Regards,
Cory
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.
RE: Buckling of a thin-walled cylinder
Also, there's an old ASME paper, #48-A-123 "Allowable Working Pressure for long tubes subject to External Pressure" by M.B. Higgins.
RE: Buckling of a thin-walled cylinder
Burst: Pb = (7/8)(2 Yp [t/D])
Yield Strength Collapse: Pyc = 2Yp([(D/t) - 1]/(D/t)^2)
Elastic Collapse: Pe = [2E/(1-v^2)](1/[(D/t)(D/t - 1)^2]
for Yp=yield strength (2% offset), D=Outside Diameter, t=wall thickness, E=Young's Modulus, v=Poisson Ratio.
I prefer a wrap fist around a Budweiser can as an analogy myself, I've never personally taken the Pepsi Challenge.
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada
RE: Buckling of a thin-walled cylinder
http://naca.larc.nasa.gov/reports/1952/naca-tn-2612/naca-tn-2612.pdf
Admittedly, it's for internal pressure, but it's a starting point.
Steven Fahey, CET
"Simplicate, and add more lightness" - Bill Stout