Cap Channel Design - Lateral Torsional Buckling

[rharting]

I'm currently designing the runway beams for a 26 Ton crane with columns at 20'. I'm having significant difficulty trying to determine the best way to design for lateral torsional buckling. For the purposes of this discussion, I will be looking at a W30x116 with a C15x33.9 Cap Channel with using all Gr 50 steel.

According to the Design Guide 7 (1993 Edition) Appendix A Table 2 - The "maximum span for Fb=0.6 Fy" is 20.69'. After digging into it, this reference uses the green book and uses the equation Lb=20,000/(d/Af*Fy) but does not include the equation 76bf/sqrt(Fy) - (I'm not sure why). While this equation appears simple, I find it hard to believe that the lateral torsional buckling criteria is based only on the depth to area of steel ratio.

According to a paper in the engineering journal in 1996 by Jeffrey Laman, Lp is defined as 300Ry/Sqrt(Fy)which can be found in the blue book (although its LRFD Lp is not impacted by load factors) and would reduce that Lb to 16.2' (A 22% reduction). Jeffrey gives his equations that he uses in a fortran program (the Ry he uses is slightly different than the Ry in the combination sections in the green book).

If I were to use the black book (the code I most often use), the governing section would be section F4 (singly symmetric I-shaped members... bent about their major axis). This defines Lb=1.1*rT*sqrt(E/Fy). The rT found in the combination sections in the green book for this section is listed as 4.34". This would give an Lb=1.1*4.34*sqrt(29000/50)= 9.58' (less than half of the design guide and a 40% reduction from the blue book). The user note on page 16.1-52 approximates rt as "radius of gyration of the compression flange plus one-third of the compression portion of the web, in other words = Bfc/(sqrt(12*(1+aw/6)". I feel this book gives poor definitions, but the best I can tell (using the channel depth as Bfc and aw as 2*hc*tw/(Atotal/2-hc*tw)) I get rT=4.08" (slightly less than the 4.34 in the green book).

Given the importance and weight of the crane, I don't want to be unconservative however I want to be economical. Given the drastic difference in Lb, how would you guys proceed?

Lb=20.69' (Design Guide 7)
LB=16.2' (paper in engineering journal and on AISC website)
Lb=9.58' (appears applicable to the black book)

Sorry it's so long. I can insert some calcs if that would help.

 

[JAE]

Using the 360-05 AISC specifications (which I think is the black book) I get Lp = 9.8 ft and Lr = 37.3 ft.





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[rharting]

That's about what I'm getting JAE. Thanks for the reply.

It just seems odd that AISC published a design guide in 2004 with Lp over 20', but then literally the next year published new codes that cut it in half. I still see a lot of people referring to the design guide 7 for crane girder design which is somewhat scary.

 

[SlideRuleEra]

I'm currently designing the runway beams...I will be looking at a W30x116 with a C15x33.9 Cap Channel ...

That combination of W30 and C15 is a common choice for the bridge beam, but why are you considering it for the runway beams? Usually, the runway beams are heavy W sections, without a cap.

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[rharting]

First, this design is for a replacement of an existing section for a runway beam which is starting to fail (the original is concrete encased and the concrete is showing preliminary signs of failure). The original design was modified some years ago to include a cap channel for lateral stability and to increase the capacity of the crane. I am planning on matching the as designed condition.

Also, I'm not sure I agree with your assessment that the W30 w/ C15 isn't a common runway beam design. If you look at the newer design guides and papers on runway beams they include a cap channel.

 

[jec67]

I believe Lr should be used (black book) to compare with the value in the green book. Lp is for the maximum unbraced length for full plastic. This is similar to Lr in the green book.

Sorry for the brief response. I will elaborate/clarify later.

 

[rharting]

I believe the value of Lp as defined in section F4-7 of the black book should be comparable to Lb as defined in F1-2 in the green book. Both of them essentially maximize the allowable moment capacity and removed the lateral torsional requirement.

 

[Hokie93]

Jeffrey Laman and Patrick Johnson authored a fourth quarter 2010 Engineering Journal paper ("Singly Symmetric Combination Section Crane Girder Design Aids") that includes capacity tables per the 2005 AISC Specification. From Table 3 of that paper, L_p = 9.61 feet and L_r = 36.5 feet for a W30x116 + C15x33.9 section (F_y = 50 ksi).

L_c from the 1989 AISC Specification (green AISC Manual) should be approximately equal to L_p from the 2005 AISC Specification. I would expect the maximum span for F_b = 0.60Fy to be greater than L_c since L_c is based on being able to achieve 0.66Fy bending stress. I would not have expected the difference to be a factor of two or more, however.

I believe Laman (in his 1996 paper) ignored the 76b_f/sqrt(F_y) because it will not govern when you have a large (very wide) compression flange.

Since your unbraced length will exceed L_p, don't forget that you may be able to use C_b > 1 for some added economy.

 

[rharting]

Hokie,

thanks for that reference. That is just what I was looking for. tough to swallow... but just what I was looking for.

Just wanted to mention that in Laman's paper I'm pretty sure he used the Third edition (dark blue lrfd book). He included his fortran which has LP=300*Ry/SQRT(fy) which equates to 1.76ry*sqrt(E/FY).

I will probably have fatigue considerations (it is for a crane that operates 24/7 and is the lifeblood of the plant. If that crane goes down, they stop production. would you still include Cb in your calculations? I may be very conservative, but I typically try to stay away from Cb unless I'm in an existing conditions situation.

 

[Hokie93]

I would most likely not use C_b > 1 for a runway beam that supports a "lifeblood" crane. It probably makes little, if any, difference but the 1996 Laman paper was written around the 1993 AISC Specification, which was included in the silver AISC Manual. The dark blue manual included the 1999 AISC Specification.