Cap Channel Design - Lateral Torsional Buckling
Cap Channel Design - Lateral Torsional Buckling
(OP)
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.
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.






RE: Cap Channel Design - Lateral Torsional Buckling
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RE: Cap Channel Design - Lateral Torsional Buckling
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.
RE: Cap Channel Design - Lateral Torsional Buckling
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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RE: Cap Channel Design - Lateral Torsional Buckling
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.
RE: Cap Channel Design - Lateral Torsional Buckling
Sorry for the brief response. I will elaborate/clarify later.
RE: Cap Channel Design - Lateral Torsional Buckling
RE: Cap Channel Design - Lateral Torsional Buckling
Lc from the 1989 AISC Specification (green AISC Manual) should be approximately equal to Lp from the 2005 AISC Specification. I would expect the maximum span for Fb = 0.60Fy to be greater than Lc since Lc 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 76bf/sqrt(Fy) because it will not govern when you have a large (very wide) compression flange.
Since your unbraced length will exceed Lp, don't forget that you may be able to use Cb > 1 for some added economy.
RE: Cap Channel Design - Lateral Torsional Buckling
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.
RE: Cap Channel Design - Lateral Torsional Buckling