Lateral brace near middle of section will help in resisting Lateral Torsional Buckling?

[patelam]

I have a W12 beam split into two spans of 20ft each with column support between two spans. The outer ends of both spans are simple supported. I am removing a column support, which results the beam into one span of 40ft long. I am adding WT above top flange of W12 beam. The W12 beam is braced for lateral movements near the top (compression) flange at every 4ft spacings. My questions are:-

1. Can the current lateral brace at W12 beam be used as a brace to resist Lateral torsional buckling of the new cross-section after adding WT? In other words, if I want to calculate moment resistance of beam reinforced with WT, can I account for existing lateral brace in calculating effective braced length of beam?

2. The stem and flange of WT section are stiff enough not to locally buckle. In other words, it meets width/thickness limitation criteria of standard that ensures that the components of section won't buckle individually. Do you see any other type of failure as a major concern, other than lateral torsional buckling?

 

[Baffled Engineer]

For your first question:

I would say no. If you are checking the capacity of the built-up section as a whole, the lateral brace near the middle of the built-up section is not going to provide sufficient restraint on the compression flange of the built-up section (i.e. the flange of the WT), but if you can weld stiffeners beside the WT-section and connect it to the lateral brace near the middle, then you can maybe consider it as LTB restraint for the built-up section depending on how much torsional restraint you have on the top flange of the W12 beam. You may also be able to take advantage of where the load is relative to the shear centre of the built-up section in determining the effective unbraced length of the built-up section.

For your second question:

I think for your case, it depends on the residual stresses on the W12 beam. If you are not shoring and relieving existing stresses in the W12 beam, then the W12 beam can fail first prior to the LTB or yield capacity of the built-up section as a whole.
You may need stiffeners near the ends of the WT section to transfer vertical shear forces.
I usually go with welded W-sections instead of welded WT in reinforcing beams if possible because the stem of the WT can warp while welding which makes the WT crooked. Speaking of welding, the weld direction & method matters as well to minimize warping of the WT stem.

AISC has a webinar that discusses welding WT sections to reinforce beams. I think you should look that up since it's a great resource. I just can't remember what it's called...

I hope that helps. I'm interested to know what others think as well since I do encounter this problem often but for my case the WT is usually below the beam not on top like yours.

 

[KootK]

The mid-height lateral bracing will prevent the "lateral" in lateral torsional buckling. So, then, you'll be left with purely torsional buckling as your governing failure mode. This will usually have a much higher capacity than does traditional lateral torsional buckling. Do some searching for the term "constrained axis lateral torsional buckling" and you'll likely discover the applicable design methods. There's an example in AISC's seismic design manual. The math is pretty messy.