Bracing of 2-Beam System 1

[darogers]

I did not have much steel design in school and have never gotten too in depth in the theory behind lateral bracing. My experience with bracing requirements for steel beams involves specifying standard details provided by the state DOT.

I have a temporary 2-beam steel system that is only supporting a small utility line during construction (wt. of utility is negligible). It will be spanning 2 120' spans; both beams are identical and spaced ~ 4' apart. The contractor wants to bolt 4x4 angles perpendicular between the beams every 15' to both the top and bottom flanges. The utility line will sit on the angle that is bolted to the bottom of the bottom flange.

I have read through "Fundamentals of Beam Bracing" by Yura and I have read Chapter C and Appendix 6, but I'm still having trouble knowing how to determine if the bracing noted above is sufficient and how to prove it. Can anyone provide some further insight on how to interpret these guidelines for my situation?

Thanks in advance,

Dan

 

[WillisV]

You need to address both local and global buckling of the twin girder system.

Note that the information in Appendix C does not adequately cover a two-beam "global" buckling mode. A closed form solution is provided by Yura and Helwig in this paper which I highly recommend reading for this type of system:

Global Lateral Buckling of I-Shaped Girder Systems
J. Struct. Engrg. Volume 134, Issue 9, pp. 1487-1494 (September 2008)

Obtainable here:

http://scitation.aip.org/getabs/ser...00134000009001487000001&idtype=cvips&gifs=yes

As a quick and dirty guesstimate - if the moment of inertia of the twin girder system about the system's y-axis (using the parallel axis theorem - i.e. sum of Ad^2 about the centerline between the two beams) exceeds the sum of the moments of inertia of each individual beam about their strong axis, then you will not have a global buckling problem. This is not always the case though as indicated in the above referenced paper.

Assuming that the global buckling mode is satisfied, this then leaves the design of the individual cross-frames to serve as brace points to reduce the unbraced length for the buckling of the individual beams between each frame. The angle between the top (compression) flange will be serving as a nodal brace (Appendix 6.3.1b) and will need to supply the required brace strength from eqn. A-6-7 and required stiffness from eqn A-6-8. The supplied stiffness will be equal to 6EI/L of the brace member assuming it is bent in double curvature between the two beams. The other possibility since you have top and bottom bracing is to treat them together as a torsional nodal brace per A6.3.2a and break the required moment down into a axial couple for each member as well as satisfy the stiffness requirements.

 

[darogers]

WillisV -

Thanks for the great response - this is exactly what I was looking for. I'll look into what you have said.

One question about the design of the individual cross frames. You mention that that top flange brace will be serving as a nodal brace. I was under the impression that a nodal brace must be tied to a rigid support. That was part of my confusion - if it isn't a nodal brace and it isn't a relative brace since they aren't diagonal, what type of bracing is it?

Thanks

 

[WillisV]

darogers - you are correct re: standard nodal lateral bracing needing an external lateral restraint point - your situation should really be treated as a torsional (nodal) brace. I would probably look into using k or cross-brasing in lieu of just top and bottom angles. See the following for a discussion on how to design such a system to meet the torsional brace requirements:

http://www.aisc.org/WorkArea/showcontent.aspx?id=20484

 

[ishvaaag]

In any case this is not a problem that falls out of the scope of general stability, and hence, creating a 3D model with proper representation of the joint connections and explicit initial tolerances on out of straightness, and letting the wind and seismic forces go to increment such initial deformation, if you find a design that meets the limit strength and deflections (so P-Delta converging to solution) for your set of hypotheses, you will have a satisfactory design as long you have reduced if required the stiffness of the beam on account of inelasticity if the standing stresses so demand.

At 120´, the temporary situation is not outrightly discardable on stability concerns, and you need to ensure stability at the then permitted safey factors for the then standing set of loads and structural systems. Some of the remarkable failures of long beams have been on just improper consideration of constructibility.