LTB of built of members / Radius of gyration

[ColinPearson]

Hi all:
I am analyzing an existing beam built up of a W12x26 with a W6x25 bolted along it's top flange to see if it is suitable to support a valve. I'd like to include in this analysis a certain amount of lateral loading to allow for actual field conditions when removing the valve.

My question revolves around determining the rT to then use with Eqs F1-6 & F1-7 from the AISC green book (9th edition)to arrive at the allowable bending stress.

I have not found anything for a section close to this; the closet I found was a suggestion from a member regarding a C-cap on top of an S where he used the entire C plus the compression flange of the S, together with 1/3 of the S web. This differs significantly in my mind due to the geometry of the two W combination.

Any thoughts on this folks? Thanks in advance.

 

[hokie66]

Using the combined section would depend on the capacity of the bolts in shear to make the two sections work together. Without an assessment of the shear flow, I would assume the two members work together rather than compositely. The deflection of the two beams will be the same, so allow for stiffness compatibility.

 

[ColinPearson]

Yes, agreed about the shear flow. I feel like the beam is fine, but as I'm sure you well know, I've got to hash out the details on paper before I tell someone else it's okay. I will check the bolts in shear, but there's quite a few and the valve is not that heavy. I am more concerned about the (ridiculous) unbraced length affecting the allowable bending stress at this point. Thanks hokie66 for the quick reply.

 

[JAE]

You can do either of these two methods:

Option 1
Assume the two beams act compositely.
Do a gravity (vertical) analysis and compute the relevent V, Q, and I values of the combined shape.
Design the bolts to take the horizontal shear.
Check the composite shape calculating rT based upon the horizontal W6, the top flange of the W12, and the 1/3 compression web of the W12.
Use the unbraced length as the span of the beam.
Apply the horizontal load only to the W6 and to the top flange of the W12 (assuming the loading comes in at the W6) -conservative.
Check the stresses using the fc/Fc + fb/Fb combined formula.

Option 2
Assume that the two beams do not act compositely.
Do a gravity (vertical) analysis and distribute the forces to the two beams in proportion to their stiffnesses (per hokie66 above).
Use the unbraced length as the span of the W12 beam.
Use an unbraced length of 0 (or 1 ft) for the W6 assuming the W12 braces it laterally.
Apply the horizontal load only to the W6 and to the top flange of the W12 (assuming the loading comes in at the W6) -conservative.
Check the stresses for each beam individually using the fc/Fc + fb/Fb combined formula.

I think the above is correct but would also encourage suggestions.

 

[hokie66]

One thing which requires clarification...the orientation of the W6. I assumed it was web vertical, while JAE is thinking web horizontal.

 

[JAE]

Yes, you are correct hokie - I was thinking the W6 was laid flat - sort of like the cap channel on a crane runway beam.

 

[ToadJones]

I run into this a lot with built up columns and sections.
I have always developed rT they way the green book describes.
It is always a gray area. I tend to be conservative when determining allowable stresses in situations like this.

If your beams are stacked with webs vertical on both, I'd really tend to be conservative with a long Lb.

 

[ColinPearson]

Sorry for the missing info folks, both beams are web vertical.

Thanks to all for the help.