Global Lateral Torsional Buckling of Twin Tapered 3-Plate Girders

[azogr]

I have two simply supported twin girders that are 24" apart. They span 50' and have a start depth of 18", taper to 42" at the midspan, and then back to 18" at the opposite support. They are each carrying a point load at midspan loaded through the centroid of the beam. I am planning to lace the top flanges together with angles to reduce the unbraced length of the compression flange. I am also planning to build cross frames at about 12'-6" on center to brace the bottom flange since the point load can become uplift under wind loading conditions.

Given the depth of the member at midspan, and the fact that the girders are only 2' apart, I am concerned about global lateral buckling of the system. I have read through "Global Lateral Buckling of I-Shaped Girder Systems" by Yura, Helwig, Herman, and Zhou. They have formulas for a doubly symmetric members of uniform depth but nothing about tapered members. Any suggestions on how to approach calculating the Ieff for a tapered section in this situation? Do I even need to worry about it if I am lacing the top flange all the way to the supports? If so, do I need to design for a cumulative bracing effect at each panel point or at least at each cross frame? This could add up to a significant lateral force at my supports.

 

[WARose]

See this thread for info on designing with tapered girders:

http://www.eng-tips.com/viewthread.cfm?qid=302826

DG 25 seems to be the weapon of choice but I've heard some complaints about it elsewhere as well.

I am planning to lace the top flanges together with angles to reduce the unbraced length of the compression flange. I am also planning to build cross frames at about 12'-6" on center to brace the bottom flange since the point load can become uplift under wind loading conditions.

The thing to remember when (laterally) bracing any beam is the fact it has to have both strength and stiffness. As far as the latter goes, you have to tie most lateral bracing (for LTB) into the Lateral Force Resisting System. Otherwise you will not have the necessary out of plane stiffness required. (See Appendix 6 of AISC 13th edition.) Hopefully you are running your bracing back to the support. (To form what looks like (in plan view) a horizontal truss.)

 

[JoshPlumSE]

DG-25 is probably the place to start. My belief is that the design guide doesn't address multi-tapered members. So, if the span is not braced in some way at the mid point, then the provisions would not quite work. But, it is still probably the best place to start.

 

[Ingenuity]

This paper considers instability/flexural-torsional buckling with width tapers, depth tapers and thickness tapers (with reference to British and Australian standards) using elastic critical load analysis: "Stability of Tapered I-Beams" by Mark Bradford: Link

 

[azogr]

Thank you for the comments. Josh you are correct, I don't see where the Design Guide 25 addresses this twin beam global buckling situation. I calculated the global buckling capacity of the system per the Yura document assuming average section properties and it checks out. I am not sure if this is a valid approach. The laced top flanges should increase the safety factor on this was well.

 

[WillisV]

Does Iy (minor) for the combined twin section exceed the combined Ix for each of the girders at all locations along the length of the section? If so - no instability.

 

[azogr]

At the 18" depth it does at the 42" depth it does not.

 

[WillisV]

Then there is a potential concern that I would check with FE models of a swept system (similar to what Helwig used to develop the paper)

 

[Lomarandil]

Just to be clear, a linear taper from 18" to 42" and back?

LTB behavior is driven by the properties of the beam in the middle ~60% of the unbraced length. So much so, that for beams with cover plates, AASHTO allows the end regions to be ignored in certain circumstances (see C6.10.8.2). Even if you can't entirely ignore it, you can usually compensate for it using an analogy to a stepped column. I don't think an FE model is required (yet).

I wouldn't necessarily consider a calculation with average section properties to cover things, but does it work with both the 18" and 42" sections?



----
The name is a long story -- just call me Lo.

 

[structSU10]

I would probably plot out the capacity for varying depths from 18" to 42" and study that trend. Your actual condition should fall between the two extremes, and how the function changes between the two may help in understanding the critical aspects of the twin beam system.

 

[azogr]

Lomarandi, yes this is a linear taper from 18" to 42" and back to 18". StructSU10, per your suggestion I put a quick spreadsheet together (see attached) based on the equations in this document:

https://ascelibrary.org/doi/10.1061/(ASCE)0733-9445(2008)134:9(1487)

The blue line is Equation 9 with a normal condition and the orange line is equation 9 with an end-restrained condition. The red line is my required moment at that beam depth with the dashed line representing the maximum required moment. It looks like even with the cross frames I am going to require top flange diagonal bracing on at least part of the span. Due to the unknowns I am leaning towards just doing the entire span.

 

[Lomarandil]

Yes, I'd be surprised if you meet an "end restained" condition. So I'd use top flange bracing.

I'd probably take it all the way back -- you might be able to save one or two bays at the ends (resolving the brace forces into axial and weak axis) but for the size of bracing you're talking about, you'll generate more headache and contractor anguish checking that than the extra steel will cost.

(To be honest, we probably already analyzed past the point of ideal economics... but it is just too darn fun!)

----
The name is a long story -- just call me Lo.