Double Web Plate Girder Bending Capacity 2

[andriver]

Ladies and gents,

I am in the process of designing a double web plate girder, the girder tapers towards the ends. At the center of my plate girder, where the flanges are the widest is where my questions applies.

I have been treating my double web plate girder as a box girder, using section F7 in AISC. At the center though, where my flange is the widest, the flange sticking outside of my "box" girder are non-compact. I had originally used equation F7-2 for Flange Local Buckling, using the entire section/plastic modulus of the shape. When my calculations were first checked, a more senior engineer said I should be using section F3, where I used EQ F3-1. This lowered my capacity significantly.

I checked my results with a Bentley structural analysis software, that has a double web plate girder section. When I run through it's printout, it uses Section F7 EQ F7-2 for the bending capacity. This jives with my original approach, however I noticed the capacity was significantly higher in the model output. Digging through the numbers, it is because on EQ F7-2, it uses my entire girder flange width as b in the b/tf term. I however had only used the flange width between my box girder as my b in the b/tf term.

My questions are, how would you approach solving this problem. If you agree with treating it as a box girder (even though the flanges outside the box are non-compact), which value would you use for b?

Thanks for any help. Attachment hopefully helps clear up any confusion.

 

[TehMightyEngineer]

I'd be inclined to agree with your senior engineer, the flange buckling will be similar to a non-compact I-section flange. From my understanding, the non-compact flange section wont care much if you have two webs or one. I imagine there's some middle ground where you would really need a hybrid between the equations of F7-2 and F3-1 but I don't know of anything off the top of my head that demonstrates this and using F3-1 would be conservative and probably fairly accurate.

I would not think taking the entire flange width as b is appropriate.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries

http://www.americanconcrete.com

 

[andriver]

Thanks for the input, the software results is what has us debating the issue. I also have RISA 3D and wanted to check the capacity there, but never saw an option for a double web plate girder option.

The difference is significant enough that it is worth the investigation. Especially because I only fail at this section, every other section along the girder works with a maximum UC of 0.6. Just when it gets to the point that the flanges become non-compact do things blow up.

 

[Shu Jiang PEng SE]

Treating the member as box girder per AISC F7. Check the slenderness of flange outside of the webs per AISC Table B4.1 case 11 for W member; check the slenderness of the flange between the webs per case 17. Convert the width of the flange outside of the webs to effective width per the compact criteria if the flange is not compact.

 

[andriver]

Convert the width of the flange outside of the webs to effective width per the compact criteria if the flange is not compact.

Can you expand on this?

 

[Shu Jiang PEng SE]

AISC Table B4.1 Case 11 specifies the compact flange b/t should be less than 10.79 (assuming fy=36ksi), calculate the member section properties as a box per the effective width of the flange outside the web of 10.79t. you do not need to consider the flange local buckle failure mode.

 

[andriver]

Thanks Jiang, that approach yields about a 9% reduction when compared to treating it as a box girder using Flange Local Buckling. Unfortunately it leaves me a little bit short. When compared to using section F3 I get about a 15% increase in capacity. So, by using section F3, my increase in section yields a lower capacity due to crossing into non-compact land. Is this evidence I should be using F7 over F3?

To make up the difference, couldn't I design stiffeners below the compression flange to prevent the flange local buckling?

 

[Shu Jiang PEng SE]

Suggest to weld two steel strips to the bottom surfaces of the top flange outside the webs. The steel strip needs to extend beyond the section not needing strengthening some distance to transfer the force in the strips.

 

[dhengr]

Andriver:
Why does the width of the flanges vary/taper over the length of the girder? That is kinda strange and difficult to deal with, unless there is really a good reason for it. Ripping a long plate to provide that flg. taper wastes a lot of material and requires considerable labor and flg. edge clean-up, and potential for distortion. Why not make the middle third (in length) of the flgs. from a thicker plate or a plate of higher strength? We can’t see it from here, and your kiddy CAD sketch doesn’t help much. As is so often the case these days on E-Tips, there is so little meaningful engineering info. provided on your problem that it is tough to know how to comment. How about providing some real engineering details, loads and load conditions, span length, material dimensions and strengths ( along with the ASTM Mat’l. specs.), what is the girder going to be used for, etc. etc., you might generate some serious discussion with some detailed info. I don’t have the last few eds. of the AISC Manual, so I can’t comment on specific formulas unless you show them and the surrounding commentary.

 

[Lomarandil]

dhengr, the AISC manual is of course protected by copyright, but the AISC specification (equations and commentary) can always be found here:

http://www.aisc.org/2010spec

 

[KootK]

I also agree with your reviewer. You want the procedure where the allowable flange stress is reduced to a value that won't initiate buckling. Stiffeners would work but the spacing would need to be fairly tight for them to be effective.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[andriver]

I appreciate (most) comments.

dhengr, my question (and kiddy) sketch was very precise. I asked for help in a very specific situation, that is, how would you analyze a double web girder with non compact flanges in bending?

I did not ask you to design a girder for me, if I had, I would have provided lengths, loads, purpose, etc. Take my word for it, that there has been a great deal of thought that has gone into this design, and there is a purpose for my tapered flange, and overall geometry. If you don't understand the question, refrain from commenting. Too often on eng-tips, there are comments that provide no value, you can add yours to the pot.

If I give out the exact specifics, no doubt a client engineer could stumble upon this which would open up a can I am trying to avoid. My senior engineer and I were just debating internally whether F3 or F7 apply, and you provided no opinion on the matter. Thanks anyway.

As for everyone else's comments, I will roll with F3 because that is the most conservative value, although I was just trying to understand the code better. I did not want to leave any strength on the table.

 

[Lomarandil]

Although I'm having trouble remembering a reference for it, I've also used Jiang's method in the past -- neglecting the "slender bit" of steel at the flange tips

 

[andriver]

After applying jiang's method, my results have either confused me more or confirmed a suspicion.

I have analyzed this three ways.

1) Treated it as a box girder with non compact flanges using the whole area, using F7-2​

2) Treated it as a built up shape with non compact flanges using the whole area, using F3-1​

3) Used Jiangs method, that is a box girder using only the compact portion of the flanges using F7​

The capacities are as such: 2 < 3 < 1

The fact that just using the compact portion of the flanges yields a higher capacity than using the whole shape and treating it as a built up I shape is what concerns me. This is either confirmation to me, that method one is the correct procedure because intuitively, a wider flange should add some capacity to the box portion not weaken the whole section. Or, it's a confirmation to me, that I should not be treating it as a box girder because my outer flanges are likely to buckle which will cause the compact section to knuckle too. I can intuitively argue it both ways.

 

[Shu Jiang PEng SE]

The member will not experience lateral torsion failure, web local buckling and flange local buckling if the section properties are calculated per the reduced flange width. The governing failure mode is yielding, therefore the moment resistance M=smaller (1.6SFy, ZFy) and it does not matter the section is box or W

 

[andriver]

Thanks Jiang,

I have computed the critical buckling stress using Roarks and Blodgett as references (almost identical) and confirmed the critical buckling stress is greater than my yield stress confirming your approach in my eyes.

 

[KootK]

I don't support treating the flange as a reduced width element satisfying b/t. Flange local buckling is a buckling mode that involves the entire flange width with the flange transverse flexural stiffness adjacent to the web being the most critical aspect. It's not as though the flange will buckle in a J-shape with the b/t bit remaining straight. I've no doubt that some portion of outstanding flange remains effective, just as with cold formed steel. I don think that it's correct to assume that b/t properly represents the width of that portion however.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[jayrod12]

KootK,

I believe the cisc and I assume the aisc propose doing exactly as jiang has prescribed?

Perhaps you don't agree with it, but it is a directly codified method of shape analysis.

 

[KootK]

If I'm wrong I'm wrong. It wouldn't be the first time. I'll track it down when I get back to Canada

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[FLCraneBuilder]

As I read the inquiry, I was envisioning the shape of the girder to be a plate box girder similar to what we use in the bridge crane world for long span cranes

then looked at the sketch and wondered why the flanges are "hanging out there" at all

for crane girders we only leave about 1-1/2" protruding beyond the web

Note Also, CMAA has guidelines for proportions that may give you some clues
and... there is a good bit of info on the calculation approaches -
para 3.5