On Sun, 09 Apr 2017 15:51:39 -0500, dpb wrote:
On 04/09/2017 3:16 PM, James Waldby wrote:
... I calculated via the formula shown at
https://en.wikipedia.org/wiki/Euler%27s_critical_load with K=1
for the case "rotation free and translation fixed" at both ends
of the column. I think that's correct for the bottom ends of
your columns, but wasn't sure that the top is translation fixed.
Here is the Python code for several cases:

from math import pi, sqrt
od=1.9; id=1.77; r1=id/2; r2=od/2; I=(r2**4 - r1**4)*pi/2; K=1; L=96; ...

Here are the results:
Pcr=9808.7 at od=1.900, id=1.770, I=0.31583
...

I just typed in command window w/ Matlab...

OD=1.9;ID=1.77;
E=29E6;
L=8*12;
I=pi*(ID^4-OD^4)/64;
Pcr=pi^2*E*I/L^2;
num2str(Pcr,'%.0f')
ans = 4904

Your I is off by a factor of
Ipy=((OD/2)^4 - (ID/2)^4)*pi/2
Ipy = 0.3158
I/Ipy
ans = 0.5000

which accounts for the difference. When you used radii instead of
diameters missed one factor of 2 in denominator it seems.

Instead of the problem being due to radii vs. diameters, it was
due to using wrong-axis I. As shown in following link, I_z
(which I used by mistake) is twice as big as either of I_x or I_y.
https://en.wikipedia.org/wiki/List_of_second_moments_of_area#Second_moments_of_a rea

With that fixed we get the same results. Thanks for the help!

--
jiw