LTB Calculation of Stacked Beams

[TEDstruc]

My situation is an S6x12.5 monorail that spans too far without some sort of reinforcing (24'-5") simple span without any lateral bracing between supports. My supervisor (not a licensed engineer) wants me to weld a W8x18 or similar larger beam to the top of the S6x12.5.

My question is how should I calculate the LTB capacity of the combined section? If I used the old ASD method of Fb = 12000 * Cb / Lb * (d/Af), it seems like I am limiting myself due to the increased depth of the section without accounting for any resistance to rotation from the top flange of the S6 and bottom Flange of the W8 (located near the neutral axis of the combined section). It's seams like the newer method in 13th or 14th edition may take into account weak axis stiffness and torsional/rotational stiffness and may yield a higher capacity.

A W14x22 (Sx = 29, Ix=199) by itself just barely works for this loading, and my combined section has just slightly lower section properties (Sx = 26.8, Ix = 192). But my gut feeling is that the combined section would be able to resist more torsional rotation than a W14x22 and if so, you could increase Lp and therefore increase LTB capacity.

Side notes - I may lobby to use a WT in lieu of a W-Shape to reinforce the monorail (thoughts)? A larger S-Shape for the monorail is not an option.

Any advice would be appreciated.

Thanks,

-T

 

[RPMG]

A WT with a wide flange (large bf) is the best option because the top welds are easier for the welder. I would suggest a channel (minor axis), but the S6 is too shallow for 25' span.

However, you should use an HSS to eliminate LTB as a failure mode. That's the only way you can be certain that you've done it correctly, without understanding what you're doing.

 

[JAE]

I think you make LTB worse by stacking beams. Not sure but it seems that there would be even more instability with it. I'd have to run through some sample sections to see.

Usually a flat channel cap can be used on top. This significantly increases the shape's lateral stiffness (Iy goes up for LRFD) and increases the old ASD rT of the shape and helps LTB considerably.



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[Lomarandil]

Yes, adding a channel cap (or some other section) will increase the lateral stiffness as JAE mentioned. I haven't used the old ASD method you mention, but it certainly does not seem to capture the intricacy of this situation. I'd recommend using bending analysis from a more recent edition (the spec is free from AISC).

Typically, the choice of retrofit section is dictated by fabrication and serviceability concerns. I've personally seen the channel cap used or HSS sections on each top flange tip. I've heard of adding a WT or another beam entirely (as JAE mentions, this can be a mixed bag depending on the section).



----
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[SAIL3]

I would just check the W6 for the loads and LTB and assume the S6 goes along for the ride....

 

[TEDstruc]

Thanks for all of the replies. My specific question is how to calculate the capacity of the combined section. Let's say I welded a WT on top, which section becomes applicable in the 13th edition? Would it be F4, "Other I-Shaped Members....about Major Axis"?

Also, to clarify, this is not a retrofit and the monorail will be hung from the top WT or W-shape Stiffener.

 

[jayrod12]

If this isn't a retrofit, why go to all this effort when you could just up the size of the original section as required.

 

[canwesteng]

There is no rational method to account for the additional warping resistance of a "middle flange", and you take a hit for non symmetric I sections as well. I question how much a monorail beam really wants to buckle in an LT mode, as the load seems like it should be restorative (create a couteracting torsional moment during LTB), but no idea how you take account of this. A WT allows an overhand weld, but might have issues if the monorail is against the ceiling, a channel cap is an overhead weld but is easier to access. Pick your poison.

 

[WARose]

My approach for built-up shapes (unless it conforms to a shape that is specifically covered by code) has always been to figure the limit states of the individual components (i.e. local buckling, LTB, etc).....and then figure stresses based on the entire [combined] section and compare.

I've seen LTB values figured for built-up shapes before (as a single piece) and it's not that much extra capacity most of the time. (At least enough that justifies a lot of time & expense to pour into it.)

 

[TEDstruc]

Thanks WARose. I'll proceed in that direction.

jayrod12 - I have to use an S6x12.5 per the client specifications for compatibility with their existing trolleys. They have service rails all over this plant and all are S6x12.5.

 

[RPMG]

Yes, you can use section F4 if you want to include the composite strength, but you can also just pick a beam from the tables and ignore the S6. The S6 will not create instability or reduce the strength of the section. Even if there was a perfect math proof showing the design equations predict a lower moment capacity, we can use the larger moment capacity. That's per the Lower Bound Theorem.

Loading the bottom flange does not create a restorative moment because the top flange can displace laterally and twist torsionally. Lateral-torsional buckling is not a flexural tension failure.

 

[canwesteng]

Bottom flange loading does provide a stabilizing effect against LTB - during twist the load becomes eccentric to the centre and creates a restorative moment. There was a recent discussion here

http://www.eng-tips.com/viewthread.cfm?qid=429665

relevant to the topic at hand.

The only caution with adding a W14 to the S6 is that lateral loading from the monorail creates additional torsion on the W14 as the lever arm is bigger. Rationalize it as the torsion is resisted by the S6, or check the W14 for the load... any way statics is satisfied and you have capacity in the system.

 

[RPMG]

That topic is about unbraced lengths with intermediate hangers and reverse curvature in the monorail. They're discussing bottom flange buckling at the hanger. In that case, the bottom flange kicks out, but is being pulled down by gravity. P-delta creates a stabilizing force.

There is no stabilizing P-delta in simply supported monorails. The tension flange doesn't buckle laterally or torsionally. The compression element of a W14 will not buckle because you added an S6 below it. This isn't torsion. It's buckling resisted by lateral-torsional strength of the compression element.