Trial Percentage of Composite Action (AISC Examples) 1

[CrabbyT]

I'm trying to figure out the composite strength of an existing W24x55 using the AISC 14th SCM.

I started by working my way through the AISC example problems I.1 and I.2 for the 14th edition manual. They calculate the limit states of concrete crushing and tensile yielding of the steel section, and they take the minimum of those 2 things. Then, seemingly randomly, they make this statement: "Fifty percent is used as a trial percentage of composite action as follows" and they multiply the minimum limit state by 50%.

I don't see any mention of this in the code, and I don't get why they're doing this. It seems like voodoo to me, it's like... "Here! Just pick some number between 0 and 1 and that's how composite this system is! Use 0.5, that means it's 50% composite!"

What does it mean if something is 50% composite? I don't know if it even matters for what I'm doing, the W24x55 only has 10 studs between the max moment and the end of the beam, so the max compressive force is something like 10*17.1 = 171 kips, which is well below the limits of concrete crushing and steel yielding in my case.

The commentary in the steel book goes on to state "a fully composite beam corresponds to the case of C governed by the yield strength of the steel beam or the compressive strength of the concrete slab, as in Equation C-I3-6 or C-I3-7. The number and strength of steel headed stud anchors govern C for a partially composite beam as in Equation C-I3-8" (16.1-358).

Based on the design example, they seem to imply that something can be fully composite, but also 50% composite. It sounds like a George Carlin joke.

Can please someone help me make sense of this? Did I miss the trial percentage thing in the code?? Should I throw the trial percentage out the window in my calcs???

 

[KootK]

1) Often, providing full composite capacity is not the most efficient way to provide the required composite capacity. So, in new construction, it's common to provide less than 100% for efficiency. Fewer studs.

2) Being 50% composite means that you've got the horizontal shear capacity in the studs to a achieve a shear resistance that is 50% of that which would be required for 100% composite behavior.

3) As you've rightly surmised, %composite should not affect your evaluation other than for you to acknowledge that you can, in fact, have some composite capacity without having enough studs to provide full composite capacity. It's not an all or nothing situation.

 

[CrabbyT]

Thanks for the reply KootK - that's more or less how I was interpreting it. You only need as much strength as what's required - more studs might mean more strength, but if the strength is unnecessary then so are the extra studs.

What bugs me is that if I change the trial percentage, it changes the location of the PNA, or at least that's what the example implies. It seems like the PNA is a function of the actual geometry and material properties, and that maybe it would be better to calculate the location of the PNA after the quantity of studs has been determined. Then again, maybe it doesn't really matter and it's accounted for with the φ_b = 0.9 safety factor.

 

[271828]

It was just picked to have a starting point. 40-50% is about where many composite beams end up.

In the following Steel Interchange, there's a Q&A on this subject. I would start being concerned with stud ductility below about 40%.

https://www.aisc.org/globalassets/modern-steel/archives/2016/03/si.pdf

 

[Agent666]

The reason the PNA moves is, that you're altering the total stud force which is also the maximum force transferred to the concrete. So in effect you're altering the compression block depth, so the PNA depth naturally changes.

I'd suggest working out some scenarios by hand to get a good feel for what's going on.

https://engineervsheep.com

 

[CrabbyT]

In the following Steel Interchange, there's a Q&A on this subject.

Thank you for sharing this, that's insightful.

So in effect you're altering the compression block depth, so the PNA depth naturally changes.

After thinking about this for a while now, my understanding is that there's implicit upper and lower limits on where we define the PNA, and those limits are based on how many studs exist. For instance, based on the calcs, let's say you mess with the percentage and notice that from between 50% and 60% it would require 12 studs. Then, at 60.1%, the calcs might say you need 13 studs. This is hypothetical of course, but that's how it works out.

What bugs me about this is that the true location of the PNA is based on the geometry and the material properties. Personally, I think that using a trial percentage should only be used to determine the number of studs required to make the system work. After the number of studs is determined, it seems like we should iterate the process and re-calculate the location of the PNA based on the shear strength of the studs (or concrete crushing, or steel yielding - whichever controls). Maybe it's not so important, maybe the 0.9 LRFD factor accounts for the uncertainty in the moment arm lengths.

* * *

I found a very helpful article for anyone who is interested. It's free if you're an AISC member. It provides some very straight forward equations for determining the moment capacity of a composite slab based on the 3 possible scenarios where the PNA might exist (the slab, the beam flange, or the beam web). I was able to obtain the exact same results using these equations as what are obtained in the AISC 14th Edtiion Design Examples.

Design of Partially or Fully Composite Beams with Ribbed Metal Deck Using LRFD Specifications

 

[KootK]

Sweet. Foley and Vinnakota were actually my graduate school professors at Marquette.

 

[Agent666]

What bugs me about this is that the true location of the PNA is based on the geometry and the material properties. Personally, I think that using a trial percentage should only be used to determine the number of studs required to make the system work. After the number of studs is determined, it seems like we should iterate the process and re-calculate the location of the PNA based on the shear strength of the studs (or concrete crushing, or steel yielding - whichever controls). Maybe it's not so important, maybe the 0.9 LRFD factor accounts for the uncertainty in the moment arm lengths.

Yeah you've got it, Trial percentage is just a preliminary design approach to ballpark the number of studs you'll need. At some point you'll be replacing with an actual stud capacity and working out the percentage from that and ensuring the percentage composite action is higher than any minimums outlined in your code.

https://engineervsheep.com