OK.
Been working on some other things..........
Anyways,
I understand what you're saying about using the whole length. I also looked at a picture yesterday in Crawl Magazine of a Jeep standing up trying to climb a ledge. You can see the drivers side rear lower link. It's straight up and down like a column falling more in to a buckling issue at that point.
Let's say my Ranger weighs 5,000lbs and is mostly horizontal. The left rear lower link is resting centered on a rock with the wheel off the ground. To keep things simple we'll say the weight is evenly distributed so that link has 1,250lbs (5,000lbs / 4) on it.
Using the same formula above I would get this:
1.5X.125 (1.5 OD - .125 wall - 1.25 ID)
I = .1284
Z = .1712
1250x48 / 4x.1712
= 60,000 / .6848 =
87,616 PSI
1.75X.250 (1.75 OD - .250 wall - 1.25 ID)
I = .3400
Z = .3885
1250x48 / 4x.3885
= 60,000 / 1.554 =
38,610 PSI
Looking at it that way, The 1.5" tubing would fail because of the 70,000 yield strength and the examples 87,616 PSI calculation but the 1.75" would be fine.
Does it look like I'm calculating that correctly now?
I wonder how you would take the torque applied to the links under accelleration in to consideration?
As far as your equation for buckling:
Fcr = (pi^2*E*A)/(l/k)^2
Fcr = minimum critical load
pi = 3.14159....
E = modulus of elasticity (stiffness)
A = area of cross-section
l = length of beam
k = radius of gyration
k = sqrt(I/A)
I = second moment of area (for a tube I = (pi/64)*(Do^4-Di^4))
Where Do and Di are the outside and inside diameters.
You give the formula for k as k = sqrt(I/A). I've also seen Radius of Gyration for the tubing listed as k = sqrt(D^2 + d^2)/4. When I do both I get different results, so which formula is correct for the tubing. Also, you didn't mention the formula for A (Area of Section). For tubing I have A = pi(D^2 - d^2)/4 or A = 0.7854(D^2 - d^2). Is that correct?
You're going to need to know how much force is going to be applied to your links and then find a tube that has a higher minimum critical bucking load, or you could resolve the equation for the outside and inside diameters if you know the force that will be applied. (To do that, you would need a second equation relating the inside and outside diameters, i.e. if you know the wall thickness you want to use).
What formula are you referring too?
I haven't worked the buckling formula yet.
I find all the math fascinating. I'm dorky like that. I'm surprised some of the other people lurking with engineering knowledge aren't speaking up.
There's not a lot on the net on this, and one chart I looked at didn't look right. I'd rather know how to get the information than rely on what I see on the net.