Torsion properties of Built-up W-sections

[EPSTR]

A current project in our office has required us to size a very large W-section. A height restriction of 24" has been set by the architect to make the beam more "interesting" for us. The beam spans 45' and with its cont. and point. loads must resist a 154K-ft moment. We have just recently chosen to design a built-up beam that will consist of (2) W21x147 beams w/ a cont. 1/2" plate above and below. One of the point loads is 77k and must be set into the webs of one of the beams, thus generating a torsional moment on the beam. We have treated the built-up beam as an open and closed section while generating its properties. We have been looking for additional information on such built-up/composite sections as we have not been able to calculate what we feel is an acceptable F.O.S.
Does anyone have any experience with any beams of similar construction? Does anyone have additional concerns for the performance of the beam (welds, web stiffeners etc.)?
Thank you

 

[burtonli]

If you calculated the section character, you would find that open section can hardly bear torsion load.

 

[ishvaaag]

Once you prove the space (and shape) allowances for structures are not enough to meet the requirements, there's no other thing to do that to introduce proper changes. Logically, and in the intent of affect little what proposed, you first try a box beam, but if this is neither able to cope with the problem within the terms of reasonable and even a bit over reasonable fabrication, you will need further change, typically size, or maybe buttressing one beam against the other etc... anything that the building design can (and must) stand ... because it needs.

 

[JedClampett]

Maybe I'm missing something, but if you have two W21's running side by side with top and bottom plates, you do have a closed section. The closed section has dimensions of 12.5 inches by 22 inches. I'm guessing that this section can take a pretty big torsion (2 x A x t x allowable torsion, where A is the enclosed area). Ignore the projecting flanges for the torsional analysis.
Once you make sure that your connections can take the torsion out to the supporting structure, you're in business.

 

[JAE]

JedClampett is right... I agree with his points. Also, you do have another consideration in that if your point load is applied to only one of the W21's, then not only is torsion developed, but there could be a tendancy for the top and bottom plates to bend... allowing one W21 to deflect downward relative to the other, creating a kind of parallelogram (sorry on the spelling). This can be accommodated by adding interior stiffener plates to support and transfer the isolated concentrated load to the total cross section and avoid local bending problems.

 

[ishvaaag]

"... as we have not been able to calculate what we feel is an acceptable F.O.S."

Calculate the J for the closed section JAE and JedClampett refer to, in absence of more exact way, assume a box.

The welds from the closing plates need pass the shear flow in code terms.

Then you will get your (approximate yet reasonably acceptable) safety factor.

Most likely your check is one with moment, anc eccentric shear, hence torsion. If you don't remember how to exactly proceed one of us might give further advice.

 

[EPSTR]

thank you everyone for the help. your feedback has been great and it provides us with some answers on our assumptions and solution process.
I had placed a more detailed explanation of the situation on the following thread in the general structural area:
thread507-69213 some of you may have a stand on using the total section (inluding the flanges) for the combined stress situation from bending and torsion. The welds and the webs are the critical sections as the shear flow carries through the weld and the webs are critical with the warping shear generated from the eccentric loads.

JAE-
great point with regard to the additional stresses in the plates. We currently have some web stiffeners detailed at the locations where a beam hangs into the box girder.
ALthough not a "HEAVY SECTION", do you guys have any welding concerns with the material at these locations for a W21 x147 ?

thanks again

ecastle

 

[JAE]

When you say "welding concerns" - not sure what you mean exactly. Assuming you do not have a fatigue situation, there should not be any significant issues with stiffeners as they do not have to be extremely thick to get the job done - thus the welds of stiffeners to beam tend to be based on minimum sizes (per AISC per plate thickness).

 

[fkd]

Quoting myself as posted on the other thread,

Please correct me if I'm wrong, cause I'm facin an analoge situation here.

" For the torsion strenght I would take in account only the section properties of an equivalent RHS formed by the two W's inner half flanges and their respective webs.. but this aproach depends on the welding arrangement utilized to join the W's and the cover plates. When dealing with open
shapes, the torion can be "broken down" into St. Venant torsion (pure shear stresses) and Warping torsion (both shear stresses and axial/bending stresses as result you avoid to get in a very complex issue."

You should check AISC's Design Guide 9 and also Salmon & Johnson here you can find a very good theory discussion on
torsional stresses.

See also SCI's advisory 249 Design of Members Subjected to Torsion