Combined Compression/Bending in a Column

[Binary]

I'm looking at analysis performed by an engineer no longer with the company and I'm concerned that it's incorrect but I'm not confident enough to push the issue. I'd appreciate any input.

Structure consists of two 20-ft sections of 8-in pipe bolted together through 1-in flanges. Top section is sch 40, bottom is sch 80.

Loading is from an FM antenna array and windloads (approx 2 kip compression/30 ft-kip moment at base).

He disregarded compression and treated the whole thing as a simple Mc/I bending problem saying that it's OK because ó < Sy.

However, when I follow AISC Manual of Steel Construction approach for combined column loading, looking just at the lower sch 80 section, I find the eqns in sec'n H are > 1 which says the design is insufficient.

The reason for my lack of confidence is that the axial stress is only about 0.2 ksi which seems to say this thing is basically a vertical cantilever beam in bending so Mc/I approach is right.

I'm losing sleep over this and any help would be greatly appreciated.

Thanks!

 

[steve1]

You should be able to take advantage of the 1/3 increase in allowable stress when under wind loading. I interprete this 1/3 increase to mean that your interaction equation need only be less than 1.33.

By the way, what value did you use for your effective length factor (K)? If it's a straight cantilever K should be 2.1 per Table C-C2.1 in the Commentary.

 

[scofie]

How is it that 200 psi of compression stress causes the pole to fail the unity equation while ignoring 200 psi of compression does not? There is something wrong here. I get that the buckling stress is 9.35 ksi, so allowable axial compression stress is 4.88 ksi, so applied over allowable ratio for compression is just 0.04?

 

[Binary]

Here's the summary of my analysis:

Top 20-ft section:
L = 240 inches
W(incl pole) = 930 lb, F_lateral = 840 lb at middle of pole.

Bottom 20-ft section:
L = 240 in A=12.75 in², I=105.7 in⁴ r=sqrt(I/A)=2.88 in

W (incl pole) = 1060 lb, F_lat = 730 lb at 180 inches from base of pole.


Therefore, looking at bottom pole:

F_axial = W_top + W_bottom - W_{bottom pole} = 930+1060-870 = 1,120 lb

and f_a = F/A = 1.1 kip/12.75 in² = 86 psi

M = F_{lat top} * (.5L_top+L_bottom) + F_{lat bottom} * 180
= 840 lb * (.5*240 in +240 in) + (730 lb * 180 in) = 434 in-kip

and f_b = Mc/I = (434 in-kip)(8.63/2 in)/(105.7 in⁴) = 17.7 ksi

Obviously very little compressive stress, mostly bending stress.
K=2.1 so KL/r = 175; C_c = sqrt(2*pi²*E/F_y =

sqrt(2*3.14²*29000/36) = 126

Since KL/r > C_c, F_a = 4.88 ksi
F_b = .66F_y = 23.7 ksi

Plugging these numbers into eqns H1-1 and H1-2 gives 1.57 and 1.52 respectively.
Even setting f_a = 0 only lowers them to 1.49 which still indicates failure.

I guess my concern is this:

[ul][li]The compressive stress is way below the allowable so it's A-OK as a column[/li] [li]Bending stress is well below allowable so it's A-OK as a cantilever[li]So, why does the combined approach predict failure even with compressive stress set to zero[/li][/ul]

Like I said, the guy who did the original analysis just treated it from an Mc/I < S_y perspective - no consideration of &quot;pushing a rope&quot; - and that's not OK. But, before I make an issue out of it I'd like to make sure my analysis is right.

Thanks for any and all comments.

 

[steve1]

If fa/Fa is less than .15 (your case) then Equation H1-3 governs.

 

[Binary]

Thanks Steve.

In this case, H1-3 doesn't show an appreciable difference.

I think I found a flaw in my analysis, though. For the bending stresses, the equations have both an x and a y component. Because I have a uniform cross-section, F_bx = F_by. I erroneously also set f_bx = f_by. As it turns out, they are definitely not equal. I haven't run the analysis yet but I'm guessing that I'll be much more comfortable with the result at that point.

scofie - Thanks for the There's something wrong here comment. That helped me persist in looking for the problem.

 

[ick2]

may i ask why a mechanical engineer is designing a column??

 

[Binary]

Sure, you can ask.

The straight answer is because the person who provides the money that keeps my family able to buy food, see a doctor, and from losing our home asked me to.