Length of the column where buckling is likely to occur

1. mattyh3

25
1. The problem statement, all variables and given/known data
i am struggling with a question i have.. i cant find the right equation to use to find what the minimum length of the column at which buckling is likely to occur??
can anyone offer any help with this as my lesson books show me nothing on how you find length?
i have D=80mm d=60mm
youngs modulus 200GNm-2
yield stress 140MNm-2

2. Relevant equations

3. The attempt at a solution

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2. PhanthomJay

6,149
The minimum length at which the column will buckle depends on the applied axial compressive load which is not given...

3. pongo38

707
The question seems to be a tube. IN that case there are at least two modes of buckling. First, there is the overall buckling of the member as if it were a long thin rod and Euler's formula might be said to apply. But this could be preceded by a local buckling of the tube, especially if it is thin in relation to the diameter. I think you are probably looking to apply the Euler equation of buckling, in which you will be interested in the EFFECTIVE length.

4. mattyh3

25
well at present i am trying to find the length so been looking at using these...

to find I... I = (D^4-d^4)*pi / 64
and for area,,,, A = (D^2-d^2)*pi / 4

E.S.R = (sq) (pi^2*E)/oc(critical stress)
and then
L = E.S.R * (sq) I/A

am i going down the right route with these as someone has told me the answer for length 5.94 but i need to find it my self as i cant just put that lol

5. PhanthomJay

6,149
Since P_cr = pi^2(EI)/(kL)^2, you cannot solve for the effective length unless you know the value of the compressive load. Are you sure you have stated the problem correctly as worded?

Edit: Maybe the problem is looking for the max length before buckling occurs prior to the material reaching its yield stress?? If so, P_cr = (yield stress)*A, then solve for L using the buckling formula for a fixed-fixed column. I can't do the math...too many zeros.

Last edited: Jul 14, 2012
6. mattyh3

25
my question i have says... what is the minimum length of the column at which buckling is likely to occur ... and the values i have put down are all i have on the sheet..
then i have what will mode of failure be and at what load..

i have included an image of my workings out so far for length,, which i have seen on the internet that 5.94 is the length just needed to find it myself... could anyone confirm this???

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Last edited: Jul 15, 2012
7. PhanthomJay

6,149
I painstakingly did the math and i get about 6 meters length when the column buckles at yield stress $\sigma_{cr} = \sigma_y$ , hope the math is Ok but in any event the problem statement is poorly worded.

8. forexpipz

7
That all pans out. I get the same.

9. andytb1232000

3
Isn't the diagram in post 1 a annulus? which would mean that second moment of area formula is pi (R^4 - r^4) / 4?

10. PhanthomJay

6,149
Hi there newbie, at this time we wish to welcome you to these Forums!

Yes, sir, pi (R^4 - r^4) / 4 is the same as pi(D^4-d^4)/ 64