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

 

[gwynn]

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.

I am unsure about what you mean in the first sentence. Are you setting a second W section on its side, atop and parallel to the main section?

If so:
Using the simplified method you are suggesting, I would size this for 2% of the compressive force in the compression flange, not 2% of half the beam reaction. With the second section spanning the entire length of the main section, this will result in a varying force with the same shape as the main beam's moment diagram.

However, an analysis of the actual moment resistance of the new section may result in a smaller section being required, as the combined section will have greater lateral and vertical stiffness than the two added together. I would go this route, as you will need to design the connection between the two members for shear flow anyway (even if you aren't counting on it, it is there and not designing fot it could fail the connection).

And it should be 2% of the total worst case loads.

 

[hokie66]

I think gwynn has answered your question correctly. The capping beam only has to take 2%, or whatever percent is applicable, of the compression flange force. As the capping beam will in itself be most of the compressive flange, I would first do the permutations necessary to select the sections to resist the vertical load, then check horizontally.

 

[Grizzman]

I think you'd be better off in your circumstance to use torsional bracing to laterally stabilize the beam.
It will make your profile smaller as the strut beams will frame into the side of the girder (versus sitting on top)
This allows for a cleaner moment connection to the girder too. Also, you can design the other end as a pin connection and don't have to worry so much about adding any additional loads into the original building components(aside from the vertical reaction)
Appendix 6.3 of AISC 13 does a fine job of walking you through the process.

 

[JAE]

I wouldn't use the 2% rule of thumb in this case.

What you are doing is creating a new section comprised of the two wide flanges. Simple calculate new section properties and design the beam accordingly as a unit.

With LRFD, you'd use appendix F, calculating all the required [λ] factors and using the beams new cross sectional properties (you will still have a singularly symmetric shape).

With ASD, you now have a different r[sub]T[/sub] factor (a very large compression flange) and design according to the beam formulae given.

 

[faromic]

By compression flange force do you mean decoupling the moment and just taking that load. When I want to calculate the horizontal shear at the edge, it's 0 obviously because it's at the end of the member. Additionally, the decoupled moment is 28.8 kips. 2% of this is .576 kips. I'll apply this load per linear foot and design for it. The combined section analysis is not my call. I'm designing each seperately, altough very conservative.

 

[JAE]

Actually, the horizontal shear is maximum at the ends.

Pretending that the new capping beam is somehow an independent thing that laterally braces another beam is pie-in-the-sky simplification.

The two will work together as a single flexural element in reality.

By adding the WF on top, you are greatly altering the cross sectional properties, and the neutral axis location.

Design it as a combined section. Calculate the horizontal shear using q = VQ/I and design the longitudinal connecting welds accordingly and in accordance with Chapter B in the AISC Spec.

 

[faromic]

correction the decoupled moment is 345 k 2% of this 6.9 kips. Even if I do design as a combined section, how do I know determine what the lateral force to resist is? That's what I'm struggling with. As of right now I'm using 2% of the beam reaction. which is .02*44.925 = .8985 k applied per linear foot. I'll look into the combined section. Am I supposed to take 2% of the horiz shear?

 

[faromic]

I was reading in section 2.3 of blodgett that the horizontal shear is 0 at the ends, and it sounded suspicious to me.

 

[apsix]

It should be designed as a combined section with no lateral restraint (assuming that there are no transverse members along the beam length).

The problem with using a horizontal beam to resist the lateral restraint force is its lack of stiffness. It may have the strength to resist the 2% of flange force but, unless proven otherwise, I would assume that it doesn't have sufficient stiffness.

 

[faromic]

Thanks you guys have been a great help. I sized the beam for L/360 deflection not based on strength. This is 75'*12/360=2.5". I calculated the Ix based on this deflection (which governed and easily satisfies strength requirements) and sized it for this.

 

[miecz]

With all due respect, for an unsupported length of 75 ft, I don't think deflection governs the design of a rolled section.

 

[ctcray]

Yikes. I have to concur with miecz. I think with 2.5" of (lateral) deflection of the top flange, your saying that it would be acceptable for the beam to essentially twist 2.5" out of plumb?

Incidentally, you might want to review how shear flow is calculated....the shear is definitely not zero at the interface between the 2 sections.

 

[miecz]

ctcray

I'm understanding this differently than you are. If I understand faromic, he has abandoned the idea of providing lateral support to a 75 foot beam with a horizontal beam attached to the top flange, and wants to use a hot rolled shape with no lateral support, and design it for deflection of L/360. He said that deflection will govern over strength, and I disagreed with that.

 

[faromic]

No, no, no. That's crazy. Of course I have not abandoned the the idea of using a horizontal beam for lateral support. What I'm saying is that deflection governs the vertical beam based on a fully braced analysis (.6*fy allowable compressive flange stress). Based on this, I want to design a horizontal beam (attached to the top of the vertical beam) to resist the lateral buckling force of the top flange of the vertical beam. My first question in the thread was what lateral force to design to top flange for? I was designing it for 2% of the beam reaction (per linear foot). At first I was going to design it for 2% of the compression force in the top flange but the moment was 1031 k*ft. d=36.9 for W36x262. This gives a top flange compressive force of 336 kips*.02=6.7 k*ft!!! THis is huge applied per linear foot and didn't seem reasonable. I am basically ignored the advantages of the combined section and designing each seperately as described above. What I'm saying about deflection is that I'm designing both beams for a deflection of L/360.

 

[JAE]

I am basically ignored the advantages of the combined section and designing each seperately as described above.

faromic - I think that is just plain wrong. There is no prescribed design method in any specification (AISC or otherwise) that suggests you design a compound beam by first designing the "vertical" beam as fully braced and then providing a "horizontal" beam to brace it using some rule of thumb 2% rule.

I honestly, and humbly, suggest you design it as a compound beam using the AISC prescribed methods for single symmetric shapes.

Just my opinion. But do show me where AISC suggests you can do it your way...I'm all ears.

 

[faromic]

I understand, and I'm going to do a calculation analyzing it this way. I'm not that familiar with this type of lateral bracing, but I was told to do the calc like this at work and am unsure of the result I got for the horizontal beam. I know I shouldn't just listen to what someone tells me and have my own thoughts. I'm going to start the calc now and see what I come up with.

I'll keep you posted. Thanks a lot.

 

[Grizzman]

you need to refer to appendix 6 of AISC 13th. It plainly explains how to calculate your load and also the required stiffness to the bracing member. In you case this would be the top members bending stiffness.
If you're not going to design the member as composite, you must design the connection between them to not carry any shear. do not weld them together. you'll require some kind of angle configuration butted against the top flange of the lower beam and welded to the (I assume)web of the top beam rotated horizontally.
It can be done but is probably not as efficient as using a combined section. the top member will have to be designed as fully unbraced along the 75 foot span as well and you need to limits its deflection to prevent twist in the lower beam from horizontal deflection as ctcray suggested.
your best bet would be to find a way to laterally brace the lower beam with perpendicular members bearing somewhere along a column line or building perimeter. torsional restraint pinned at the far end will put the least additional load on the existing building.

 

[miecz]

ctcray-

Guess you had it right. I must be going crazy.

faromic-

Sorry, misunderstood you. Research has shown that lateral bracing needs a certain stiffness as well as strength. The 2% rule is not always adequate. It may provide the required strength, but not the required stiffness, for the type of bracing you are proposing. As others have said, you need to refer to Appendix 6 for the stiffness (and strength) requirements. I expect you'll find that you cannot meet the stiffness requirements, and need to design as a combined section, as JAE has suggested.

 

[faromic]

OK, I'll work on that and keep you posted.