Flexible Diaphragm Design - Shear Strength and Rollover Capacity 1

[VT17]

Hello all,

I've been searching on this forum and online as to how to design flexible roof diaphragms in a steel building but there are some things I'm still not clear about which I would really appreciate your input on.

Please see the attached document that has a roof plan and which I'm using as a reference for my below questions. For simplification purposes, let's assume all factors (LRFD or ASD) are 1.0 when selecting an appropriate diaphragm and each question is unrelated to the next unless stated otherwise.

1) When analyzing at the interior frame (BF2) to size the diaphragm for w1, does the shear strength of the diaphragm have to be greater than 50k/150ft or 100k/150ft? If you say it's 50k/150ft would the attachment pattern along this beam line only have to be double (i.e. if a 36/7 pattern works, would the pattern along this beam line have to be 36/14)?

2) How do you actually determine the shear demand on the diaphragm? For instance, when sizing the diaphragm for w2, would you consider the shear demand to be 100k/200ft and then also design the 3 other beams (in red at the bottom) as collector elements? Or could you say its 100k/100ft and only design one beam as a chord element (like shown in red at the top)

3) Assume that when designing for w1 (ignore the loads provided in that direction) you choose a diaphragm that has the capacity of 2klf. When checking if it works for the w2 load stated, it's obvious the deck can transfer all 100kips to BF4 (or BF5) across the length of the brace frame only. In that case, (ignoring the potential rollover capacity of the joists), is there a need to design any of the adjacent beams as collector elements?

4) Related to question 3. Even if there's no need to design the other beams as collector elements, wouldn't the lateral load on the joist seats at BF4 then be 100k/10 = 10k which would far exceed its rollover capacity? If you were adamant about your connection detail in this direction to not include an hss (or similar) member between each joist to prevent rollover of the joist seats, wouldn't you then have to design all 3 of the beams along that line as collector elements so that the lateral load per joist seat would then be 100k/40 = 2.5k which is around the rollover capacity?

My apologies if this is a lot. I think I've honestly put good effort into trying to figure this out but I either can't find a source that explains the above or when I think I have made sense out of it, I double guess myself and as a recent grad, I do not want to improperly design this aspect of a building. Thank you everyone in advance!

 

[P205]

1) The shear strength has to be 100k/150ft. I think of this as this line is the reaction (if you consider the beam analogy). I believe you are thinking of the shear on either side of the reaction as being half the reaction load, like the shear either side of a beam with a UDL.

2) You design the whole line as collectors. On the BF5 line, the first beam "collects" from 0 to 25k, the second beam collects from 25 to 50k. Now, things change from here on depending if you have an "X" brace or "/\" brace, and if the "X" is tension only. Assuming it's an "X" with tension only, then the 3rd beam collects from 50 to 75k. These are all compression collector forces. The 4th beam, on the other side of the brace "collects" tension loads from 0 to 25k. Giving you a total of 75k compression, and 25k of tension on the right-hand side of BF5, for a total of 100k. (75k pushing and 25k pulling at that joint. Then, the brace takes those through the diagonal brace down to the foundation).

3) I don't quite understand this question.

4) Yes, but if the diaphragm is connected, the beams before and after the brace will collect load. Yes you would have to design all three of the beams along that line as collectors.

SIDE NOTE: You can state (or should state rather) on your drawings the rollover force that you want the joist supplier to design the joist shoes for.

 

[Hokie93]

Responses to your questions follow. As a general comment, diaphragm analysis and design are generally complicated and often not given good coverage in academic courses or structural textbooks. Two of the best documents I have found for diaphragm analysis and design are NEHRP Seismic Design Technical Brief No. 3 (Seismic Design of Cast-In-Place Concrete Diaphragms, Chords, and Collectors) and NEHRP Seismic Design Technical Brief No. 5 (Seismic Design of Composite Steel Deck and Concrete-filled Diaphragms). Despite the title of Technical Brief No. 5, it gives some coverage to bare steel deck diaphragms. Both Technical Briefs are available free of charge from the NEHRP website (

http://www.nehrp.gov/library/techbriefs.htm).

1.) In the north-south direction (up and down the page), the flexible diaphragm spans between BF-1 and BF-2 and between BF-2 and BF-3 as simply-supported beams. The diaphragm reactions are as you have indicated (50k, 100k, and 50k). The maximum shear in the diaphragm at BF-2 is 50 kips, which occurs on each side of BF-2. With all three beams at BF-2 designed as collectors, the design diaphragm shear is 50k/150 ft, or 333 lb/ft. The connection between the diaphragm and the collector beams at the column line on BF-2 would need to be designed for the diaphragm reaction (100 kips, or twice the diaphragm shear).

2.) I recommend designing all four beams at BF-4 and BF-5 as collector elements and, thus, the diaphragm shear when subject to load w2 is 100k/200 ft, or 500 lb/ft.

3.) I would argue the answer is "yes", that it is preferable to distribute the diaphragm reaction over a greater length (depth) rather than concentrate it over a very short length (depth). Having said that, it is certainly permissible to have a partial-depth collector and local chords. In any event, the analysis, design, and detailing must be consistent. As an aside, I don't believe you will find a bare steel deck with an allowable diaphragm shear capacity equal to 2000 lb/ft. Perhaps that is just a value you made up for this example but, in case not, it is something to keep in mind.

4.) Yes, to both questions. You could also check with a joist manufacturer regarding the maximum feasible joist seat rollover capacity. Based a Vulcraft publication, the service-level rollover capacity of a K-series joist is approximately 2 kips. This value corresponds to 1/4" deflection at the top of the joist seat. Providing an HSS member to transfer the shear directly from the steel deck diaphragm to the collector is preferable in my opinion. Such a connection is far stiffer (and stronger) than that provided by the rollover resistance of a joist seat.

 

[Once20036]

1) When analyzing at the interior frame (BF2)... does the shear strength of the diaphragm have to be greater than 50k/150ft or 100k/150ft?

...the design diaphragm shear is 50k/150 ft, or 333 lb/ft. The connection between the diaphragm and the collector beams at the column line on BF-2 would need to be designed for the diaphragm reaction (100 kips, or twice the diaphragm shear).

Agreed with Hokie. There are 4 variables to be checked for the diaphragm capacity, per SDI. I believe that you need to compare PhiSne to the 100k/ft to make sure that the connection to the collectors are adequate. The other 3 variables are compared to the 50k/ft force in the diaphragm on either side of the collector. My understanding is based primarily on a couple long conversations with Vulcraft's deck guys.

2)...then also design the 3 other beams (in red at the bottom) as collector elements?
3)...the deck can transfer all 100kips to BF4 (or BF5) across the length of the brace frame only.

I think that these two questions are really two options to the same question. I believe that if the deck is strong enough to get the force out of the diaphragms and into the collectors, than no collectors are needed. This assumes that you have a complete load path (joist seat rollover, in this case), proper chord elements, and proper connections. You could design for 100k over 50 ft (2klf) or 100k over 200' (0.5 klf).

4)...which would far exceed its rollover capacity? If you were adamant about your connection detail in this direction to not include an hss (or similar) member between each joist to prevent rollover of the joist seats, wouldn't you then have to design all 3 of the beams along that line as collector elements so that the lateral load per joist seat would then be 100k/40 = 2.5k which is around the rollover capacity?

You need a complete load path. While a stock K seat may be good for 2k rollover, you can certainly provide higher values in your bid documents and have those additional forces accounted for in the joist design. I've gone up to 3.5k +/-. Last time I compared the economics, the premium for reinforced seats was ~25% of the price to add HSSs between joist seats. I`m not sure what the max force would be on a reinforced seat.

The above questions all focus on collectors and getting the forces into the braced frames. Please don't forget about your chords.
There have been two interesting threads recently on chord forces, if you scroll through the threads a week or so...

 

[VT17]

P205, Hokie93, and Once20036:

Thank you for taking the time to respond. Your answers have been helpful. I think I'm clear pertaining to questions 2-4.

However, if I understood correctly, it seems P205's opinion regarding question 1 is to design the diaphragm for a shear strength of 667plf. On the other hand, Hokie93 and Once20036 think that the diaphragm should only be designed for 333plf but that the connection of the diaphragm to the collectors should be designed for 667plf. Is this a fair summary? Would P205 care to elaborate as to why you think differently?

I believe that you need to compare PhiSne to the 100k/ft to make sure that the connection to the collectors are adequate

Lastly, Once20036, per your above statement, are you suggesting that to check the appropriate connection capacity to the collectors, I should check the edge fastener limitations (Sne)? I was looking through the Diaphragm Design Manual 3rd Edition and Section 2.2 addresses Sne. Would I have to go through this check [ Sne = (2*alpha1 + np*alpha2 + ne)*Qf/l ] to figure this out? But then, aren't the values in the tables provided Sn which is the min of Sne, Sni, and Snc and wouldn't I effectively at that point be sizing a diaphragm for 667plf which is what P205 mentioned?

Thank you Hokie93 for those references. I appreciate it.

 

[P205]

@VT17 I agree with Hokie93 and Once20036, their answers are more thorough and point out that there is more than just one thing to check. I only touched on the deck-to-collector.

Edit: spelling

 

[Once20036]

Lastly, Once20036, per your above statement, are you suggesting that to check the appropriate connection capacity to the collectors, I should check the edge fastener limitations (Sne)? I was looking through the Diaphragm Design Manual 3rd Edition and Section 2.2 addresses Sne. Would I have to go through this check [ Sne = (2*alpha1 + np*alpha2 + ne)*Qf/l ] to figure this out? But then, aren't the values in the tables provided Sn which is the min of Sne, Sni, and Snc and wouldn't I effectively at that point be sizing a diaphragm for 667plf which is what P205 mentioned?
Thank you Hokie93 for those references. I appreciate it.

This gets into your design procedure. A year or two ago, I went through a diaphragm design using SDI, using the Hilti Manual, and using the Hilti Software. The answers from the three methods were vastly different.

I called Hilti's engineers to understand the differences. They said that SDI was based on equations, and therefore different than the testing they performed on their products. I think that they said the difference between the manual and the program had to do with how current the information was, but I don`t really remember this second part.
Comparing these results, the hilti software provided the most conservative answers, and that's what I've used ever since.
I input the 333 plf, check the fasteners, then go into the results and check Sne. Typically the result has been fine with no modifications necessary.

If you're using SDI, it wouldn't be practical to separate out the different values, and I`d just use 667plf as the design value. This guarantees that Sne is good enough, and your capacity of the deck adjacent to the collectors has a little extra strength.

Likewise - thanks for those references Hokie. I haven't found much formal information on diaphragm design and I`m looking forward to reading those. There's also guide #13 which deals with diaphragms in precast buildings. It may be similar to guide 3 for CIP concrete, but might have some additional wisdom hidden in there.

 

[VT17]

Thanks for the additional clarification P205 and Once20036! I do wish this topic was covered in more depth in school. Looking back we barely touch upon it compared to other topics and I didn't realize at the time how critical it is to the load path.

 

[KootK]

I didn't realize at the time how critical it is to the load path.

I would argue that it's not that critical really. A lot of buildings have done just fine for a very long time without any explicit attention to diaphragm strength. While I certainly wouldn't advocate ignoring diaphragm design, I can see how it might not make it onto the short list of things that university courses are able to cover. Diaphragms certainly aren't as important as, say, columns/ .

The only thing that I'll add wrt to technical matters is that I usually prefer to design diaphragms for wind as though they are never any deeper than they are wide. At some point, I think that one needs a reality check on how far away an applied diaphragm load is going to be "felt". To each his own in the absence of a published recommendation of course.

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.