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Ian B
10-12-2005, 05:10 AM
Anyone know how to calculate the axial compressive strength of a piece of pipe, say, 2" diameter and 3/16" wall thickness, 3 feet long, low carbon steel?

At what point (length to diameter ratio) does buckling become the method of failure rather than plain compressive failure? Larger diameters would probably be less likely to buckle, but how to calculate it?

Thanks,

Ian

phil burman
10-12-2005, 10:02 AM
Try this link to an Excel spread sheet. It looks like it might be of use. If not google for the keywords.

http://www.eaa.org/benefits/sportaviation/0305_stucture_wksht_v5.xls

Regards
Phil Burman

SGW
10-12-2005, 01:55 PM
Dunno the exact answer, except that it's "a lot." One time in college a friend and I tested the compressive strength of an ordinary soup can, with the ends cut out, and it supported over a thousand pounds before it began to buckle.

That was slow, uniform loading though.

Ian B
10-12-2005, 02:07 PM
Thanks Phil,

Exactly what I was looking for!

Ian

JDF
10-12-2005, 02:27 PM
The basic equation for column buckling is:

Pcr=(pi)^2*E*I/(Le^2)

where:
Pcr = critical load where buckling occurs
E = Young's modulus, 30x10^6psi for most steels
I = moment of inertia. For a round hollow section: I=pi*(OD^4-ID^4)/64

Le = equivalent column length based on end conditions. Can range from .65L for two fixed ends to 2.1L for one fixed end and one free end.

So for your example
I=pi(2^4-(2-2*.1875)^4)/64=0.4431

for Le=.65L (least conservative)
Pcr=(pi)^2*30x10^6*.4431/(.65*3)^2=3.45x10^7

for Le=2.1L (most conservative)
Pcr=(pi)^2*30x10^6*.4431/(2.1*3)^2=3.31x10^6

[edit: forgot to square the bottom term in these two equations. Dropped Scr below by quite a bit.]

And now if you find critical compressive stress due to these loads:

Scr=P/A
A=pi(OD^2-ID^2)/4=1.0676
Scr=3.31^6/1.0676

Scr=3,080,000---this is WAY over the ultimate stress for any low carbon steel, so compressive failure would occur long before buckling becomes an issue. "a lot" as SGW said.

This is a very basic equation for idealized conditions that will give you an idea of how buckling and compressive failures relate, but keep in mind that actual failures will occur below the load and stress levels given by the Pcr and Scr equations. There are more detailed methods used for more realistic situations.

[This message has been edited by JDF (edited 10-12-2005).]

CCWKen
10-12-2005, 02:52 PM
My brain is about to explode! http://bbs.homeshopmachinist.net//eek.gif http://bbs.homeshopmachinist.net//biggrin.gif

Thanks for the detailed explanation JDF. (And the headache) http://bbs.homeshopmachinist.net//biggrin.gif

JDF
10-12-2005, 03:58 PM
Yeah, I confused myself too--had a couple of errors which are now fixed.

I think all these equations are in the strength of materials section of Machinery's Handbook, but don't have in front of me now to check.

Flatline's Up!
10-12-2005, 04:03 PM
I just alwasy smack it a hard one and if it dents, get the next bigger pipe/tube... http://bbs.homeshopmachinist.net//wink.gif

webowser
10-12-2005, 07:07 PM
The AISC (Amer. Inst. of Steel Const.) manual has formulas for calculating the allowable stress for members subjected to compression loads (columns). The allowable stress varies inversely with the unsupported length and directly with the radius of gyration.

E-mail me if you want me to get out my AISC manual and look up the formulas.

Bill