Rigid Diaphragm with Chevron Bracing – Collectors & ASCE 7 Section Overstrength Requirements

[Futzin]

Consider if you will the 6-bay frame arrangement (attached) utilizing chevron bracing as the LFRS elements along with the following parameters/assumptions:

1) The structure is SDC C.
2) R = 3 for structures not specifically detailed for seismic resistance (i.e., AISC 341 requirements are not invoked)
3) There are no structural irregularities as defined by ASCE 7.
4) The frame supports a reinforced concrete slab-on-metal-deck which acts as the roof diaphragm. Contribution of the decking to the diaphragm strength/stiffness is neglected.
5) The diaphragm can be idealized as rigid per Section 12.3.1.2 of ASC 7-16 and a 3D structural analysis utilizing semi-rigid plate elements suggests the behavior of the diaphragm is practically rigid.
6) The slab has sufficient strength and rigidity and is provided with sufficient reinforcement such that diaphragm shears can be transmitted over the length of the chevron beams only as opposed to treating the non-chevron beams as collectors for transmission of diaphragm shears to the braced frames.
7) The headed studs are sufficient to transmit the diaphragm shears over the length of the chevron beams only.

Some background. I had modeled the structure utilizing plate elements to represent the diaphragm. I acknowledge that I could have modeled the diaphragm utilizing rigid nodal restraints and gotten approximately the same force distribution to the braced frames, but the use of plates was advantageous for my load application methodology.

I had initially/incorrectly assumed that axial diaphragm forces would manifest in the beams adjacent to/in between the braced bays (i.e. these beams would act as collectors) from the analysis. After reviewing the results, I realized this wasn’t the case. A majority of the force was concentrating and being transmitted directly to the node at the intersection point of the braces and plate elements. Upon reflection, I realized this made sense due to the stiffness of the plate elements and that if I were to instead represent the diaphragm utilizing a rigid nodal restraint that I should expect zero axial force to manifest in these beams (no stress/no strain, etc.). Clearly, however, the diaphragm shears cannot all be transferred through an infinitesimally discreet point. So I decided to take the force delivered to the braced frames and consider them evenly distributed along the entire column line for the purposes of collector connection design (therefore all beams along the line would be provided with shear studs for force transfer) like I had initially the model would act. Sure, I was applying the traditional flexible diaphragm force distribution method to a rigid diaphragm, but no harm/no foul right?

Enter ASCE 7-16 Section 12.10.2.1 which requires collectors and their connections be designed for loads considering seismic overstrength (omega factor). I was getting fairly massive connections and beginning to wonder if these “collectors” were actually necessary. If the diaphragm had the strength to transfer the loads over a shorter distance (say, the length of the chevron beams themselves), then why not neglect putting studs on the beams in-between and adjacent to the frames and not have collectors at all? The following paper seemed support my conclusion:

https://datacenterhub.org/resources/12268/download/10NCEE-000933.pdf

Up to this point, I feel comfortable with the direction I’m going in. I welcome any disagreements or comment on/with my thought process above. I had a few lingering questions though:
- As far as ASCE 7 is concerned, where does a collector end and the SFRS begin?
- Is the chevron beam itself a “collector”?
- If so, does the gusset plate to beam weld need to consider overstrength forces? Does the bolted connection between the gusset plate and a brace need to consider overstrength forces?
- If that’s the case, then why aren’t the column base brace connections required to be designed for overstrength forces? (It’s acknowledged that ACI 318 anchorage ductility requirements require consideration of overstrength in certain situations.) It doesn’t seem to make much sense for one end connection of a brace to have 3x the capacity of the other end.

TIA for your input and thanks to all the regular contributors through the years who have provided such valuable insights.

 

[driftLimiter]

I'm not following the reasoning behind ommiting steel collectors and shear studs along the line of the frame. Did you make this choice simply because of the results of the analysis model? Really not thrilled about a diaphragm that intentionally isn't connected on most of it's perimeter.

It is well established practice to utilize full length collectors in this arrangement. And to me the argument that the model says something different isn't enough to radically change my approach. The assumption that all of the shear is taken out of 1 single point is an error of analysis in my mind. Are you sure you have meshed the perimeter of the slab so that it is compatible with collectors? Seems like maybe the diaphragm is only being compatibly meshed at that single point.

Besides one could still make the argument that the beams inline with the chevron are collectors because they have to collect their own seismic forces and deliver them to the braced frame.

There is a line of thinking that utilizes different regions of diaphragms as collectors, and as chords, however I think its is most commonly applied in all concrete construction.

Seems like if you follow the normal convention, then most of your questions become easy to answer. If you are dead set on going down this path of using the floor to collect loads and what now then your are going to have to apply additional judgement to your design.

Your steel drag connections shouldn't be that massive. Generally collectors I see use shear tabs with multiple rows of bolts (not had at all). Or perhaps some welded plate splices, still not the end of the world.

 

[Futzin]

Thanks @DL - No, as a rule I make no decisions based on the results of analysis model alone. I learned too much about FEA during grad school to ever trust it blindly. As mentioned, I was fully onboard with the collector strategy until I started see the size of the connections and I got some reviewer pushback questioning why the collector elements were necessary to consider. The plates are compatibly and consistently meshed with the beams throughout the model. I was slightly embellishing in the "single point" statement - the shear generally begins building up at chevron beams but dumps a disproportionate amount of load right into the brace intersection nodes. There's virtually no long being picked up by the "collectors". I'm of the opinion that this is simply a limitation of a structural modeling with beam elements and plates. The program doesn't know the plate forces need to be transferred through concrete bearing on shear studs welded to the top flange etc... it's all modeled at the steel CL. Again, the diaphragm was modeled w/ a rigid nodal restraint, no nodes can move relative to one another in the plane so no axial loads should develop in the collect beams.

The subject structure is very large (the attached image was for illustrative purposes only, not representative of the full structure) and functionality/architectural considerations have led us to try to limit the number of braces both along the perimeter and at the interior of the building. When considering the diaphragm shear evenly distributed along the full length of the beams in line with the braces, the maximum collector axial force (omega nought = 3.0) was on the order of 600 kips. Feels like an awfully large connection (25 - 7/8" A325s) to design if I could instead say that we are not relying on collectors and therefore aren't subject to the ASCE overstrength design requirement. That is if the chevron beams aren't considered collectors, like I was questioning at the end of my post.

BTW, it's not lost on me that this could be a sign to add more braces. I think ASCE slyly admits this in the seismic commentary that the overstrength collector forces requirement "unintentionally" causes engineers to produce more redundant designs because the axial loads get so onerous.

Hope that clarifies my motivations.

 

[driftLimiter]

600 kips. How big is this structure in plan? Recently finished a 500,000 sqft warehouse with 40' concrete tilt walls. 1 line of braced frame and the collector force was 700 kips. Granted this was not the overstrength load but instead the capacity limited design.

Something I feel aught to be considered about this proposal is whether or not there is a variation in stiffness of the slab for compression vs tension loads. If you want it to be a collector it will need to resist both. In compression you have a big effective block of concrete, for tension you have a few bars. I cannot believe that a few pieces of rebar would end up being more stiff then the steel beams in your collector line.

I think like you say, these are all subtle signs from ASCE that your system is perhaps not well proportioned. Also with this level of load, I would definitely be a bit more concerned about ductility. Switching over to a detailed system with a higher R factor may benefit other parts of the structure as well. At the very least I would investigate the inherent ductility of the system, protect the non-yielding elements etc.

This reference you posted is for elevated slabs with no dropped beams. I think that is a pretty significant difference.

 

[sandman21]

This is a case of GIGO with regards to the model, which we have no idea what program is being or the assumptions. The beam at the chevon is a collector and the forces would need to use overstrength, same as shown in your example. You will then need to design for the moment at the chevon beams. Overstrength is not ASCE trying to produce more redundant, as it does not make for a redundant system.

 

[driftLimiter]

Perhaps there is a basis for your approach. Reading through this nehrp document
This approach is discussed in lieu of full depth collectors and even specially referenced as a means to reduce collector demand forces.

However there is a ductility demand in the collectors that is not easy to establish. Furthermore there is an eccentricity from the collector to the braced frame line that must be resolved. I would think if you want to take this approach you will want to understand these and concepts well.

Perhaps this nehrp document could be of use to you. And perhaps due to my unfamiliarity with the approach I spoke out against it too quickly.

 

[Futzin]

@DL - I was actually giving that nerhrp document a thorough read through last night. While it does give credence to the limited-depth collector conapt, it also gives a few reasons why you may not want to do that (like you and @sandman mentioned in your replies), and I'm inclined to heed that advice. On some of your other points:
-My structure is similarly on the order of 500k sqft.
-I agree with respect to the slab properties in tension/compression. The analysis was linear and the plate elements presenting the diaphragm were modeled linear elastic which would of course not capture that stiffness variation. Furthermore, nehrp recommends to reduce the stiffness of the diaphragm elements to ensure the collector beams actually pick up load if you're running a semi-rigid diaphragm analysis. Why do a semi-rigid analysis at all if you're not trying to accurately (albeit approximately) characterize the properties of the diaphragm?
-I'm strongly considering going to a seismically-detailed ordinary concentrically braced frame. The slight R-value increase and significant Omega-naught decrease would both be beneficial. The additional analysis and detailing requirements don't appear too onerous. Plus I would no longer feel like I was designing collectors to overstrength for no appreciable benefit...

More rant on the end of the final point which prompted the questions at the end of my initial post. I think the code is lacking in providing guidance on what it considers to be a collector. Even the design examples in the AISC Seismic Design Manual are inconsistent. They provide a design example for an SDC C structure with R=3 (i.e., they just design to the Specification) but they do not consider the beams in the braced bay as collectors or brace connection subject to the ASCE overstrength requirement. In their seismically-detailed examples, they do consider the braced-frame beams as collectors and appropriately consider overstrength. A strict reading of Section 12.10.2.1 of ASCE 7-16 ("In structures assigned to Seismic Design Category C, D, E, or F, collector elements and their connections, including connections to vertical elements, shall be designed to resist the maximum of the following:") suggests to me that the braced-frame beam is a collector, therefore if you are SDC C and select R=3 as permitted by Table 12.2-1, the brace to beam and/or column gusset connection must be designed considering loads amplified by the overstrength factor. At that point, why not just design per 341 and attempt to take advantage of the exceptions to considering overstrength in your brace connection design (e.g., in Section F1.6a of 341)? Alternatively, if you don't consider a beam in a braced-frame bay to be a collector but do consider all other beams along the braced-frame column line to be collectors, then what's the benefit of only designing the beams you consider as collectors for overstrength? I don't think the code-writers are intending to allow the braced-frame beam connections or the gusset plate connections to see inelastic deformation anymore the collectors.

Does something seem half-baked here or is it just me?

 

[Futzin]

Out of curiosity I looked at ASCE 7-22 and confirmed the subject provision remains unchanged, but the whole section on diaphragms, chords, and collectors looks to have increased in length and complexity. BUT so long as the system for determining Site Class hasn't changed, I would be in SDC B. Started the project 5 years too early!

 

[Deker]

Braced frame beams collect load from adjacent collector bays in addition to the diaphragm shear along their length and deliver it to discrete points at brace connections, therefore they are collectors.

You could design the diaphragm with partial length collectors, but you'd need to pay close attention to the load path and provide primary / secondary collectors and chords as outlined in the documents posted above. A few thoughts:

1. In my area it's uncommon to design steel beams beneath a composite deck as non-composite, so every beam is going to have shear studs anyway. Once the studs are there, I've found that it's generally more efficient to use the beams as collectors. I usually don't need to provide any additional studs for diaphragm shear than I've already provided for gravity (Link). With the reduced gravity demand under seismic load combinations, beam sizes and connections often work as-is. If not, upsizing the beam one or two sizes and adding a second column of bolts at the connection usually covers it. For really large loads, use 1" A490 bolts or a welded connection. There are plenty of ways to move large forces through steel...

2. Steel beam collectors are generally sized for compression whereas rebar is sized for tension. As a result, the beams will be oversized for tension and the building behavior will benefit from the reduced tensile strain along the collector lines.

3. A diaphragm with partial depth collectors and primary / secondary chords will experience more chord strain at the edges compared to a traditional approach. This results in more damage to the diaphragm during an earthquake and requires consideration over whether deformation compatibility will be a concern.

 

[driftLimiter]

Futzin, They have included the new Alternative Design Provisions for diaphragm which is worth a couple of pages, I think thats probably what you have noticed.

 

[Deker]

As far as ASCE 7 is concerned, where does a collector end and the SFRS begin?

In your case, the SFRS is the brace. All beams that collect load and deliver it to the brace, including beams in the braced bays, are collectors.

Is the chevron beam itself a “collector”?

Yes.

If so, does the gusset plate to beam weld need to consider overstrength forces? Does the bolted connection between the gusset plate and a brace need to consider overstrength forces?

For an R=3 system there are no design requirements beyond the specification and the basic seismic load combinations, so no. That is the benefit of using an R=3 system. The tradeoff is that there's no telling how the lateral system is going to behave since there are no requirements for proportioning the system. That's why it's only permitted in lower seismic design categories.

If that’s the case, then why aren’t the column base brace connections required to be designed for overstrength forces? (It’s acknowledged that ACI 318 anchorage ductility requirements require consideration of overstrength in certain situations.) It doesn’t seem to make much sense for one end connection of a brace to have 3x the capacity of the other end.

Because an R=3 system in SDC C exists in the gray area where AISC requires nothing but the specific requirements of ASCE 7 and ACI 318 for collectors and anchorage still apply.

 

[Futzin]

@Deker - Thanks for your insight and answers to my question. I agree with your answers, generally, and maybe you hadn't gotten to my rant in my last post, but let me ask a more pointed question. I apologize in advance for being such a stickler on code language.

Does Section 12.10.2.1 of ASCE 7-16 apply to an SDC C, R = 3 structure?

The awkward way they qualified the title of the section ("Collector Elements Requiring Load Combinations Including Overstrength for...") is the only potential "out" I see. As you said, your position is that the beam/brace gusset connection has no additional design requirements aside from design to the spec and the basic seismic load combinations (overstrength LCs not invoked). But if this section does apply to SDC C R=3, then "collector elements and their connections, including connections to vertical elements, shall be..." requires that the gusset connection shall consider overstrength.

 

[Deker]

I don't see "Requiring Load Combinations Including Overstrength" as a qualifier, but rather as a description of what's in the section. So 12.10.2.1 does apply.

But if this section does apply to SDC C R=3, then "collector elements and their connections, including connections to vertical elements, shall be..." requires that the gusset connection shall consider overstrength.

That's an interesting point that I hadn't considered since I'm used to using designing in SDC D or higher where R=3 isn't an option. Yes, in this case I agree that the gusset-beam connection should be designed for overstrength. The brace forces would be adjusted to be in static equilibrium with the collector force. This results in no net vertical component acting on the gusset-beam weld and a horizontal component equal to the amplified collector force.

Starting to get a bit off-topic, but here's a great presentation for coming up with a rational way to combine diaphragm and braced frame forces in case you haven't already seen it: Link.

 

[sandman21]

Does Section 12.10.2.1 of ASCE 7-16 apply to an SDC C, R = 3 structure?

Yes, you have elected to not detail your SFRS with special seismic detailing but your building is still required to comply with ASCE. All you have done is remove the requirements in AISC 341 and the requirements for overstregnth does not apply. Your sketch show a chevon brace so your gusset is not even attached to the vertical elements, but if you configurated in such a way that it transferred loading them it would need overstrength.

 

[Futzin]

@sandman In Section 12.10.2.1, I'm interpreting "vertical elements" as shorthand for "vertical elements of the SFRS" (i.e., the braces not gravity columns). Doing a CTRL+F through Ch. 11 and 12, this is consistent with how the term "vertical elements" is used throughout the chapters and makes the most sense in the context of the section.

 

[driftLimiter]

If you think about your seismic system here, you have two chevron braces as your ductile element.

Lets say you design the gusset for the same force as the braces with no omega.

The braces are supposed to have ductile capacity to provide R=3.

But the gusset ductility is not known because there is no attention to it's detailing.

If there is strain hardening, or other overstrength effects that develop as the braces go ductile, then the gusset should be designed to accommodate those additional loads without undergoing ductile deformation and definitely without rupture.

IMHO you should design the gusset at top and bottom of the brace for omega. I know that it isn't required with seismic system. but man you have a lot of seismic load, a pretty large sized structure. Ductility is important!!!

 

[sandman21]

Not sure how your gusset transfers vertical loads but maybe you are designing the braces to take vertical loads.

IMHO you should design the gusset at top and bottom of the brace for omega. I know that it isn't required with seismic system. but man you have a lot of seismic load, a pretty large sized structure. Ductility is important!!!

Why only the top and bottom gussets? Why not connection of the braces, anchor bolts, columns? Why try to create it in only parts of the system? Selecting an R of 3 means you are not concerned with ductility for your system.

 

[driftLimiter]

I guess when I say gusset I do mean the brace connections as well at the top and bottom. These could be proportioned to have a brittle limit state as its first failure mode and that is not good for ductility.

If you are not worried about ductility then have it. What I am saying is that I would be. The OP has a large seismic load going into a substantially long diagonal brace.

If you think that just following the cookbook and getting out of AISC 341 detailing requirements is sufficient then go for it. But what I am saying is that for this structure I would not do that.

Maybe its because I'm living in SDC D and up, but I am always a bit concerned with ductility. I very much dislike this exception to AISC 341.

 

[Deker]

Vertical elements are members of the SFRS that exist in the vertical plane. Braces are considered vertical elements. From AISC 341:

 

[sandman21]

I guess when I say gusset I do mean the brace connections as well at the top and bottom. These could be proportioned to have a brittle limit state as its first failure mode and that is not good for ductility.

If you are not worried about ductility then have it. What I am saying is that I would be. The OP has a large seismic load going into a substantially long diagonal brace.

If you think that just following the cookbook and getting out of AISC 341 detailing requirements is sufficient then go for it. But what I am saying is that for this structure I would not do that.

Maybe its because I'm living in SDC D and up, but I am always a bit concerned with ductility. I very much dislike this exception to AISC 341.

Anchor bolts and columns dont factor in for ductile behavior? The chevon brace beam behavior? Again why only the gussets? There is more to ductility then just designing the gusset and brace connections for overstrength, which is not an indicator of ductility. OP has already selected an R of 3 for not detailing for seismic systems. Why now try to add only some elements back into the picture? AISC SDM covers R=3 systems and braces, gussets, connections, columns, etc. are not designed for overstrength.