Cb for Jib Crane Boom 1

[RWW0002]

I am verifying the capacity of a jib crane boom arm (see attached sketch). The crane arm is free to swing 180° about the column, and the hoist load acts at the bottom flange of the boom arm. The design is fairly straightforward with some conservative assumptions concerning unbraced length and Cb (beam stability factor).

However, for the attached jib boom, I am wanting to take advantage of Cb>1.0 for the section of the boom between the support rod and the column (node A to node B in the sketch). From the AISC spec and commentary, it is implied that the Cb equations and published values are only valid for sections of members "between brace points." There is definitely not much in terms of lateral or torsional bracing for a jib crane. I know that Cb should be 1.0 (or possibly <1.0) for the unbraced cantilever portion of the arm (between B and C), but is Cb=1.67 (Calculated from AISC Eq F1-1) justifiable for the portion of beam between nodes A and B?

Thanks in advance for your thoughts.

 

[SteelPE]

The definition of "Cb = lateral torsional buckling modification factor for the nonuniform moment diagrams when both ends of the unsupported segment are braced".

In this particular instance you are only really braced against torsion (in my opinion) at the beam-column interface therefore you are not allowed to use a Cb modification and Cb = 1.0. Also, it says the Cb is permitted to be conservatively taken as 1.0 for all cases therefore, you will never have a case where Cb < 1.0.

 

[BAretired]

I would say that the effective buckling length of the beam is A-C or 24' but the moment diagram varies from 0 at A and C to a maximum at point B so the variation in moment must be considered. It is no different than a 24' long beam hinged at A and roller at C with a concentrated load acting at point B in the direction of the rod.

The fact that the connection at point B is above the neutral axis and the reaction at point C is below the neutral axis increases the buckling load of the beam (see Timoshenko & Gere, "Theory of Elastic Stability").

BA

 

[RWW0002]

Thanks for your replies.

@ Steel PE, I agree that the AISC formulation of Cb is intended for beams laterally braced at the ends. I had not seen the definition the you pointed to, but that seems to confirm my suspicion. However, I am wondering of there is any research out there that would still take into account the variation of moment along the beam length and its effect on LTB for a case similar to the one presented. Also, in regards to Cb conservatively being taken as 1.0, the commentary for chapter F states that unbraced cantilevers have a Cb<1.0 as well as "members with no bracing within the span with significant loading to the top flange"

@ BA, By " buckling length " are you referring to Lateral Torsional Buckling or Compression Buckling? I am assuming unbraced compression flange length (Lb) for LTB would be 24', but an effective length (KL) for compression buckling of 16'.

I like your upside-down beam analogy. Do you think it still applies since there is no lateral support provided at point B (as there would be with the pin-roller condition you present)?

As far as the load location, when the load is applied to the flange nearest to the direction of loading, I think there would be a stabilizing effect as opposed to a tipping effect on the beam. Is that what you are getting at then you say that the loading would "increases the buckling load of the beam"?

Thanks again for your time and comments.

 

[SteelPE]

My definition of Cb came from AISC 360-05 section F1.... and at the end of this section they say "For cantilevers or overhangs where the free end is unbraced Cb = 1.0". So it's interesting that they say otherwise in the commentary.

 

[BAretired]

@ BA, By " buckling length " are you referring to Lateral Torsional Buckling or Compression Buckling? I am assuming unbraced compression flange length (Lb) for LTB would be 24', but an effective length (KL) for compression buckling of 16'.

I like your upside-down beam analogy. Do you think it still applies since there is no lateral support provided at point B (as there would be with the pin-roller condition you present)?

As far as the load location, when the load is applied to the flange nearest to the direction of loading, I think there would be a stabilizing effect as opposed to a tipping effect on the beam. Is that what you are getting at then you say that the loading would "increases the buckling load of the beam"?

In the Canadian code, CSA S16-01, the term used in the Beam Selection Table is "unbraced length". I used the term "buckling length" which I intended to be equivalent. If the beam buckles in lateral torsional buckling, it buckles over a 24' length, not 16'. Thus, I would take the effective length as 24'.

The upside-down beam analogy is justified by the fact that the joint at A is free to rotate about a vertical axis, so a downward load at C must always be precisely aligned with the neutral axis of the jib beam. That provides an equivalent result to a roller support at C. Point B is not braced laterally for either the jib beam or the equivalent upside-down beam.

Yes, the position of the load above or below the neutral axis of the beam has a stabilizing or a tipping effect on the beam. In your case, it is stabilizing.

BA

 

[RWW0002]

Thanks for the explanation BA. So I take it you feel like a Cb of 1.67 is justifiable for the A-B segment (with a 24' unbraced length).

This makes sense, since I saw this jib crane in action and I am pretty sure it was lifting more than the calculated load for Cb=1.0 with no apparent problems.

Thanks for the help.

 

[BAretired]

Sorry RWW, I am not familiar with the AISC code, so I am not clear on the meaning of Cb or how it is applied to the problem. I tend to think of segment A-C with variable moment, not segment A-B in isolation.


BA

 

[RFreund]

Here is some further info on effective length:

http://www.eng-tips.com/viewthread.cfm?qid=235560

http://files.engineering.com/getfil..._Interchange_»_Design_of_Cantilever_Beams.pdf

http://files.engineering.com/getfil...levers_Nethercot_Effective_Length_Factors.pdf

EIT

http://www.HowToEngineer.com

 

[RWW0002]

Thanks for all of the information.
RFreund - I was not able to download the second attached file (from the AISC steel interchange) for some reason.

@BA - I assume that you would design based on an approach similar to the one presented in the information RFreund posted. Therefore, if I am interpreting this correctly, you would use a K of 3.o for segment A-C?


For anyone that is familiar with the ASIC 360-05 approach, any opinions on the use of a Cb of 1.41 per Eq. F1-1 for the beam segment A-C based on the "upside-down" beam approach that BA suggests above?