AISC Chapter I - Composite Section: Stress and Strain Distribution in Composite Section 2

[CivilSigma]

I'm studying the design of composite members (concrete deck over wide flange steel beam).

Per AISC we typically we design the PNA to be in the steel section (either flange or web) by choosing a stud connection capacity less than 100% of either the AsFy or 0.85fcb.
Lets say we chose studs to provide 50% composite action of AsFy, then the PNA will be somewhere in the steel section. By design, anything above the PNA will be in compression.

Here's the contradiction that is confusing me:

So if you have a 7" slab on top of a steel beam, my understanding is that the entire 7" concrete slab would be in compression since the PNA is in the steel beam ?
But, that is not true and the depth of compression block is: a = Q / (0.85fc*b), where Q is cumulative the stud shear capacity.
How does this work? Does the strain reverse at the shear studs such that the concrete slab is not entierly in compression?

Can someone draw the strain diagram? In my head its linear through the PNA, but from the above I don't think that may be true becuase otherwise the entire concrete slab would be in compression.

Thank you

 

[JoshPlumSE]

CivilSigma -

First let's talk about a regular concrete beam. When you draw the strain diagram for a reinforced concrete beam you start to have compression in the concrete at the neutral axis, right? But, your assumed compression block at failure is based on 0.85 f'c * a where "a" is something like 85% of the total compression area. Right? Why is this? It's because we're trying to find the capacity of the beam when the beam reaches it's compressive failure. Right? And, that assumed stress block matches up nicely with test data (or so we're told).

Well, I look at composite beams basically the same way. We ignore a portion of the concrete slab that is in compression because we're more concerned about the concrete block at the ultimate failure. Also remember that we're not generally looking for a 100% accurate model to compute our capacity. We generally prefer to use a model that is reasonably simple and conservative.

I agree that it is a little weird though. I don't think the concrete block is really the failure location for these partial composite beams. Right? It's limited by the shear studs and their ability to transmit this force. My guess is that they researchers started with this concrete block assumption because it would be easy and consistent with what we do for reinforced concrete beams. When this seemed to match reasonably well to the test data, they were satisfied and we got our procedure..... This is just conjecture, of course.

I'm also guessing that there are PhD candidates trying to come up with insanely complicated methods to better approximate the test data. Whether they get funding or come up with a procedure that any of us would like to adopt is a different story.

 

[CivilSigma]

So this is a miracle in AISC ? Fine I won't question it

 

[JoshPlumSE]

Well, it's not explained very well in the commentary. Or, I don't see papers that are directly referenced. I've been pulling various references (and older version of the code) off my shelf the last day or two because it bugs me too. I did find one example "strain diagram" for partial slip for "incomplete interaction" that you see below.

 

[CivilSigma]

Thank you for this ! What book is the diagram from ?

 

[Eng16080]

I did a little research on this awhile ago. I forget some of the details now, but my understanding was that the analysis procedure for composite sections in AISC didn’t exactly match the method found in ACI 318. I think there may have been some simplifying assumptions which were found to be more or less in agreement with test data.

 

[icebloom]

Oehlers and Bradford have written two books on composite design which go in depth into all aspects (Composite Steel and concrete structures: fundamental behaviour, and Composite steel and concrete structures, elementary behaviour). There are also design guides and books by RP Johnston with focus on eurocodes but which also cover fundamental behaviour. A more easily accessible resource free on the internet is SCI P359 (google it, should pop up as top result), which is design guide for composite beams written by Steel Construction Institute in the UK. SCI has a few guides on composite design all freely accessible on their website.

 

[JoshPlumSE]

That diagram was from a book published by ASCE / McGraw Hill called "Composite Construction: Design for Buildings". Viest, Colaco, Furlong, Griffis, Leio, Wyllie.

I've probably had that book for more than 20 years. I bought it when the company I worked for (RISA) was developing the first version of RISAFloor and I wanted to learn more about the miscellaneous details of composite design..... I've barely used it during that time. Not that it's a terrible book. But, it isn't exactly a definitive reference on the subject like I was hoping for.

 

[Celt83]

That diagram was from a book published by ASCE / McGraw Hill called "Composite Construction: Design for Buildings". Viest, Colaco, Furlong, Griffis, Leio, Wyllie.

I've probably had that book for more than 20 years. I bought it when the company I worked for (RISA) was developing the first version of RISAFloor and I wanted to learn more about the miscellaneous details of composite design..... I've barely used it during that time. Not that it's a terrible book. But, it isn't exactly a definitive reference on the subject like I was hoping for.

Have the book as well and agree it has a lot of good info but not necessarily the best if you were looking to get in the weeds on calculations.

@JoshPlumSE is there a more in depth text you would recommend on the topic?

 

[JoshPlumSE]

Celt83: @JoshPlumSE is there a more in depth text you would recommend on the topic?

Not that I've found. When getting into the weeds of the calculations, I often like the AISC examples.

However, there are just a lot of considerations for composite beams that you won't find much code guidance on.
a) How to establish effective width for floor systems that aren't all parallel.
b) What to do with openings or such.
c) Do you ignore some behavior (i.e. opening or such) close to the ends of a beam.
d) What loads (or percentage of load) do you use to determine camber.
e) What loads do you use for certain deflection checks. Do you reduce live loads for deflection? Do you subtract out camber for deflection checks?
f) What happens if you have a small amount of negative bending (like a short cantilever at one or both ends)?

Most of the software companies that have done this come up with answers to all of these questions. Regardless, all of them are based on some engineering judgment and some people will do it differently. Which is why so many of these programs allow the user to over ride the default assumptions to get the behavior they want.