Lateral Bracing for Long Span Beam

[faromic]

Hi,
I have a question about lateral bracing for a beam I'm designing. It's an existing 2 story structure, built 2 years ago. The setup is repetitive. Anyway, they want to remove the 2nd story mezzanine and and 2 interior columns from the interior of the building and hang the roof from a new beam stubbed up from the roof. The span is 75', with 2 point loads (interior columns)acting symmetrically. I sized it as continuously braced, but have questions about the lateral bracing. I am going to attach another W section horizontally to the top flange of the beam. This horizontal section will resist the lateral forces due to Lateral torsional buckling. I'm sizing it for lateral load of 2% * half the reaction of the beam.
The point loads are equal to 35 kips. The reaction of the beam is 35k + .262k*75'/2 = 44.9k. 2% of this is .8985 kips. This is applied per foot so the moment is .8985*75^2/8 = 632 k*ft. I also designed it for L/360 -> Ix required =8823 in^4. I get a W24x250. Does this sound reasonable for this kind of span? Or is it 2% of the reaction from self-weight only? I don't think that's the case, buy it yields a much smaller section, W21x93. I know it's a 75' span so the lateral loads are large but I just want to justify my calc.

Thanks

 

[faromic]

Ok, so what I did was design the the vertical beam as fully braced. I sized it based on an allowable deflection L/360=2.5". The strength did not govern the design. I designed the bottom (tension) flange for the load on it by decoupling the moment. I get a tension of 366 kips. Then I designed the top flange for the compressive load of 366 kips with the horizontal beam on top. The compression flange consisted of the horizontal W21x93 and 1/3 of the web in compression. I calculated the r of this section and designed the top flange as a column to resist the compressive force in the top flange. I also accounted for the P delta effect from the 2.5" allowable deflection. So it behaved as a beam column. I checked that it wouldn't buckle about the horizontal (weak) axis. The interaction ratio was exactly 1, so it is ok. There are no horizontal reactions (due to lateral) that I need to account for at the beam ends, is there?

 

[miecz]

OK, so ignoring the conventional way of designing a steel beam for the moment, you have a 75 foot long column with 366 kips on it. You are not welding the two shapes into a combined section. Your r[sub]y[/sub] for a W21x93 plus your flange is on the order of 6 or 7 inches. Assuming K=1, you have KL/r of 150 or so. Allowable axial stress is around 7 ksi. So you need a flange with 366/7=52 square inches. What is the size of your vertical beam?

 

[faromic]

w21x93

 

[miecz]

I must be missing something. As I understand it, you have two W21x93 sections, one with the web vertical and one with the web horizontal. The beam is 75 feet long and has two 35 kip loads, located at the third points. For that configuration, I get deflections between 9 and 18 inches, depending on whether or not the section is composite, which isn't yet clear to me.

 

[faromic]

the vertical section is a W36x262, horiz is w21x93

 

[JAE]

I get the following:

Combined section properties:
W36x260 and W21x93(laid flat on top flange of W36)

St = 1362 in3
Sb = 1054 in3
I[sub]T[/sub] = 2614
A[sub]T[/sub] = 51.1
Sx(top) = 1361.9 in3
Sx(bott) = 1054 in3

r[sub]T[/sub] = 7.15"
l = 900"
l/r[sub]T[/sub] = 98.4
Cb = 1.0
Fy = 50 ksi

Fb(comp) = 17.51 ksi per AISC Eq F1-7
Fb(tens) = 30 ksi per AISC Eq F1-5

M = 1123 ft-kips (2 - 35k loads plus 355 plf self weight on 75 ft span)

fb(tension in bottom) = 12.8 ksi OK - less than 17.51 ksi
fb (comp in top) = 9.89 ksi OK - less than 17.51 ksi

Forget the 2% stuff.

 

[csd72]

Agree with JAE.

Use v = VQ/It to check the welds between the sections under longitudinal shear. Usually a staggered half on half off will do the job.

 

[faromic]

that's much easier than the new AISC code, which I was trying to use and it confused the hell out of me.

 

[miecz]

You may want to use a deeper cap beam or a main beam with a narrower flange. It could be tough to get a decent weld with a 16.6" flange between the flanges of a W21.

 

[csd72]

Whats sitting on top? - have you considered using a channel so something can more easily sit on top?

 

[faromic]

I did, but didn't think it would work. with such a long span