Reinforcing existing steel column

[GalileoG]

I have an existing steel column with 8ft deep trusses that frame into it on each of its 4 sides. These trusses will transfer new load to the column and so the column will need to be reinforced. I am looking at welding plates to the column to form a boxed section. The reinforcing plates will extend to just 4in below the truss bottom chord.

How would I go about analyzing the capacity of this new reinforced column? As the reinforcing does not extend the full height of the column (to the truss top chord where the load is imparted) is the reinforcing even effective given that there is a weak link, the top 8ft?

So if the reinforced column is 30ft tall and the unreinforced section is 8ft tall above it, should each segment be designed for the full unbraced length of 38ft or their respective lengths only (30ft and 8ft)?

My understanding is that it is the former, and so the column reinforcing as suggested is not effective at all. Intuitively, I feel that is not the case, but I can not rationalize it.

Any suggestions?

 

[JedClampett]

A couple of things:
Can you temporarily support the trusses and reinforce to the top? This will remove the "locked in" stresses and make the reinforcing more effective. Plus now you've reinforced the whole column.
If you can only reinforce part of the column and it increases your "r", there's a way to combine the "r"s over the whole length. This should increase the capacity of the column, maybe enough to just use the smaller section above the reinforcing.

 

[KootK]

As I understand your situation, namely that the column is braced by the truss bottom chords in both directions, I sgree with your intuition and your suggestion that the upper and lower column segments can be designed as two seperate columns. I suppose that your column effective length might still be the full height for the purely torsional buckling mode. That mode almost never governs conventional column sections however. Just oddball shapes like cruciform that lack torsional stiffness.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[KootK]

8' is a whole lot of truss. Sounds like a pretty cool project.

If your column is not braced by the truss bottom chords, you'll probably want to treat it as a stepped column for buckling. Let us know if that's the case and we'll help you prosecute that.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Teguci]

Full axial load (new + old) on original column for the first 8 ft from the top. Verify that the top and bottom chords of the trusses adequately brace the column in both directions (ie - they are connected/no sliding or slots).

For the new section, use the composite shape and analyze over the full height for buckling. You could do a two step stress analysis but I think the residual stress on the original column will not harm the performance of the boxed out section (probably the opposite).

If the trusses do not laterally brace the column at the bottom chord due to sliding or slots, then you should analyze the column as unbraced for the full 38 ft. I would recommend not changing the sliding condition.
For this case, you could model the lateral buckling deflection based on the column with 2 different curvatures corresponding to the two different column stiffnesses.

 

[KootK]

Also, regardless of the effective length that you go with, reinforcing 70% of the column ought to substantially improve your buckling strength. Interestingly, if you reinforce below the bottom chords and above the bottom chords but left a gap at the bottom chords, that would probably be as good as complete reinforcement from a buckling perspective. We'll cross that bridge if we come to it.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JoshPlumSE]

There is an analysis procedure described in appendix C of the AISC design guide on tapered members (DG-25?). It's called the Method of Successive Approximations. It does a really good job of predicting the elastic buckling capacity of members whose properties change along the height of the member. My belief it that it could be used to give a better prediction of elastic buckling strength of your column.

 

[Lomarandil]

This is absolutely a stepped column problem -- that term should lead you to some papers by Dalal and Kitipornchai (or older steel analysis texts) that can give you a published basis for the advice you're getting here.

Reinforcing the bottom 30' of a 38' column will do a lot for the capacity of a buckling-driven column. I know I was surprised the first time I tried to make it work.

Most practical approaches develop a modified effective length factor based on the ratio of lengths and Is of your two cross sections. If the column passes a buckling check with the modified K and total length, the unreinforced sections only need to be adequate for yield (or local buckling issues, I suppose).

Typically, if the radius of gyration of the reinforced section is at least 85% of the radius of the original section, the reinforcement can be considered "stabilizing" and the pre-load can be neglected. If not, you'll need to consider additive pre- and post-reinforcement stresses on your original cross section.

(all of this assumes that the column is in fact not braced by the truss bottom flange)

 

[hokie66]

If the trusses frame into the column on all four sides, you may want to rethink the philosophy of the bottom chord connections. These are typically allowed to slide to avoid bending the column, but in this case, that may not be important. If you lock up the bottom chords, the length of the column would be reduced, with one end having a degree of fixity. The way the trusses sees the forces would change, but that may be of little consequence.