Continuous Beam Questions

[Steel5]

What’s the most appropriate way to analyze a continuous steel wide flange beam over steel columns for flexure?

Consider a simple example:
-100 ft. long continuous steel wide flange beam (if there are any splices in the beam consider them CJP, effectively making it continuous. This may be unreasonable in practical applications, but it’s a needed simplification for me to ask my questions below)
-Beam supported on steel columns at 20 ft. O.C.
-Beam’s top flange braced by purlins every 5 ft.
-Beam’s bottom flange not braced by purlins
-Supports uniform gravity loads only

I’ve seen a lot of discussions on inflection points used at brace points in the past, but that AISC doesn’t allow that any more. What is the appropriate way to analyze the strength of this beam? To clarify, I’m not looking for advice on how to provide bracing to the bottom flange, I’m wondering what the proper way is to determine the strength of the beam as is.

Specifically, I have 2 questions:
1. What Cb value should be used? Do I use AISC 360-10 Equation F1-1, or some other equation? If I use F1-1, Do I use quarter points between the columns (as in, MA, MB, and MC would be 5ft. away from eachother), or something else?
2. What Lb value should be used? This seems to get overlooked in many of the discussions I’ve found on this subject. Taking Lb = 100 ft. seems way too unreasonable, the bending strength becomes so small that even a large Cb can’t make up for it. Taking Lb = 20 ft. for the column spacing might be reasonable, but I can’t find anything in the code that suggests you can do this. If you were to use the distance between inflection points for the negative moment you might get an Lb = 10ft.+/-, but this isn’t allowed by code.

To explain why Lb = 100 ft. for the full beam length is unreasonable, another way of looking at it is that if the beam were 200 ft. long (and Lb = 200 ft.) the bending strength would be even further reduced, but common sense tells us that a continuous 100 ft. beam over columns at 20 ft. O.C. should perform similarly to a 200 ft. continuous beam over columns at 20 ft. O.C.

Hopefully you understand where my confusion is coming from. Thanks for any help.

 

[mtu1972]

dik -
I see your point for this 5-span situation. You'd have 3 pieces, 2 connections, and 3 crane positions. I'd have 5 pieces, 4 connections, and 3 crane positions. My connections would be shear only web plate connections and I would probably use slotted holes to accommodate any construction tolerances.

Cantilever pieces would be close to your sizes and hung pieces maybe could be slightly smaller. Probably not much overall cost differences.


gjc

 

[Celt83]

I was thinking of the Gerber beams.

Dik:
Is the plastic design covered in most steel texts or do you have a preferred reference for it? I have a very very vague memory of looking at this in college but really have not done much steel design in my career so far so very rusty.

 

[Steel5]

Regarding stiffener plates on the beams over columns, what do you think about partial height stiffeners? Such as stiffeners that are roughly 3/4 the height of the beam, welded to the bottom flange and web. I imagine there’d be some fabrication cost savings in using partial height vs. full height.

Maybe partial height stiffeners would be appropriate in a situation where the purlins frame into the side of the beam; but for the hypothetical where purlins run over the top of the beam you would still want full height stiffeners. What do you think?

Edit: To clarify, I mean wide flange purlins with shear tab or double clip angle connections to the side of the beam. If it were OWSJ's I imagine it'd be similar to wide flange beams running over the top situation in which case you'd maybe want full height stiffeners (or some other way of bracing the bottom flange).

 

[JAE]

For me - full height stiffeners.
I just don't like bending webs from lateral forces.

Check out Eng-Tips Forum's Policies here:
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[dik]

Celt83:

All my references had whiskers... they were that old. I had a couple of texts by Maissonette(sp?) and Save and also "The Steel Skeleton" by Baker and a couple of others... The first two volumes by M&S are extremely good... I don't know if you can still find them. I loaned the M&S to an engineer... that took off with them, never to be seen again, and, I gave the Baker book to a Mexican engineer about 40 years ago... There are likely good books on plastic design and most steel codes accommodate it and some concrete codes, often by allowing a moment redistribution. FYI, lower strength concrete behaves more plastically. About 45 years ago, I did a large warehouse for an engineer that had lost his license and used the Gerber system (only time I used it) and the engineer asked why I didn't use plastic design... read up on it over the weekend and have used it since... over the years have had numerous engineers comment that plastic design was 15% more expensive... but, any projects that I've had costed were 5% to 10% less expensive... I almost 'go out of my way' to use it.

 

[dik]

Steel5:

I'm with JAE... even if not needed, if I have a beam going over a column, I use full height stiffeners. Personal quirk...

Dik

 

[Ingenuity]

Regarding stiffener plates on the beams over columns, what do you think about partial height stiffeners? Such as stiffeners that are roughly 3/4 the height of the beam, welded to the bottom flange and web. I imagine there’d be some fabrication cost savings in using partial height vs. full height.

Prof Joe Yura did some research work on the subject of torsional brace stiffness requirements considering no, partial and full depth stiffeners.

Simply supported beam W12x14 wide flange, 24 foot span, midspan vertically-applied top flange loading, resulting in top flange in compression (bottom flange in tension) and he considered the following cases:

CASE A: TORSIONAL BRACE TO COMPRESSION FLANGE WITH NO STIFFENER.

CASE B: TORSIONAL BRACE TO COMPRESSION FLANGE WITH ¾ DEPTH STIFFENER FROM TENSION FLANGE.

CASE C: TORSIONAL BRACE TO TENSION FLANGE WITH ½ DEPTH STIFFENER FROM TENSION FLANGE.

CASE D: TORSIONAL BRACE TO COMPRESSION FLANGE WITH ½ DEPTH STIFFENER FROM COMPRESSION FLANGE.

CASE E: TORSIONAL BRACE TO COMPRESSION FLANGE WITH ½ DEPTH STIFFENER AT CENTROID.

CASE F: TORSIONAL BRACE TO COMPRESSION FLANGE WITH ¾ DEPTH STIFFENER FROM COMPRESSION FLANGE.

CASE G: TORSIONAL BRACE TO COMPRESSION FLANGE WITH FULL DEPTH STIFFENER.​

 

[dik]

Ingenuity:

Where was the torsional brace applied? At the supports or at the point of load application.

Did he have a curve for the condition where the entire flange was laterally braced or a curve showing the full elastic moment capacity?

Dik

 

[Ingenuity]

dik:

End supports are laterally and torsionally fully restrained, and variable torsional brace stiffness was at MIDSPAN.

'Ideal' brace stiffness was determined based upon achieving the critical load (approx 6.5 kips = the plateau on the graph) that represents a load level where the L_b = 12'.

 

[dik]

Thanks...

 

[Steel5]

Good news everyone, I had posed my original question to AISC at the same time I posted here and they finally responded back. The information they sent was really helpful and hopefully it’s helpful to you as well.

The first thing they pointed me to was pg. 2-19 of the AISC Steel Construction Manual 14th Edition, there’s a section titled “Beams and Girders Framing Continuously over Columns”. It’s a very short section with lots of good figures, highly recommend giving it a read. Mostly in line with the information you’ve already provided.

Another thing they pointed me to was equation C-F1-5 in the commentary for calculating the Cb value for gravity loaded beams with the top flange laterally restrained. Until now I only knew of equation F1-1 for calculating Cb, I didn’t realize there were more equations for Cb in the commentary.

Some of you probably already knew all of this, but sharing just in case.