AISC Torsional Bracing of Beams (Appendix 6)

[Hokie93]

Has anyone noticed that Equation (A-6-9) in AISC 360-05 Appendix 6 gives a significantly greater required bracing moment (M_br) than the equation from which it is derived? Equation (A-6-9) is based on Equation (15) from "Fundamentals of Beam Bracing" by Joseph Yura, 2001, first quarter, AISC Engineering Journal. The equations are provided below. These equations pertain to nodal torsional bracing for a wide-flange beam or girder. The Appendix 6 Commentary derives Equation (A-6-9) but it isn't clear to me why it would return a required bracing moment that is 3-5 times (in my case) that required by the equation from which it is derived. My guess is the simplification incorprated into the derivation essentially makes Equation (A-6-9) an upper bound for the required moment.

AISC Equation (A-6-9): M_br = 0.024(M_r)L/[n(C_b)L_b]
Yura Equation (15): M_br = 0.005LL_bM_r²/[nhEI_yC²_bb]

For what it is worth, the Guide to Stability Design Criteria for Metal Structures (6th edition) shows the same equation as Yura.

The required bracing moments are not large in either event (for my case) and I am going to follow the code requirement, of course (the AISC equation).

 

[JoshPlumSE]

Yes, equation A-6-9 is a conservative simplification of the Yura equation (C-A-6-8). I don't get as involved in Appendix 6 as I get in the other analysis / stability provisions. So, I'm not expert. However, I do know that the AISC task committee responsible for this appendix has been exploring the possibility of two things for the next code cycle:

1) Swapping the two equations for the next code cycle. Meaning the more exact Yura equation would be in the appendix and the approximation would be in the commentary.

2) Leaving it as it currently exists but adding additional commentary about the extra conservatism inherent in the simplified equation.

Based on a draft version of the next spec given out at the last committee meeting, it appears that they are going with option #2.

If I had to guess, I'd say that the extra conservativeness stems from the fact that Mr/ho is assumed to equal the flange force Pf... which is assumed to be at its buckling load.... rather than the maximum flange force seen by the member.

 

[Hokie93]

Thank you for the insight and I agree with your assumption regarding the conservativeness of the 'simplified' equation. Incorporating Option #1 into the next Specification makes more sense to me but adding clarifying language in the Commentary certainly will help. Thanks again.