Pseudo Equivalent Static Analysis (PESA) Forces and Starter bars

[moyseh]

Hi All,

I am new to designing diaphragms and seismic design principles and am wanting some clarity around how starter bar demands and shear wall demands relate to each other.
For non-earthquake loading, typically we just transfer all loads from diaphragms into the lateral load resisting elements with no change in demands. For seismic loading I understand that the NZ code requires diaphragms to be designed for higher forces and hence the starter bars connecting them to the structure. Now, when we get to designing the shear walls for example, we are not expected to design them for the higher, Pesa demands. Where does this difference in force go? Is it taken out of the system through the ductile, energy dissipating shear walls? Is this what capacity design is in a way?

I appreciate this might not make a lot of sense so any help would be much appreciated!

Thanks

 

[Greenalleycat]

Capacity design is the principle/process of designing one item to be a guaranteed weak link so that you can ensure a reliable, controlled, and ductile failure.

In your example, the shear wall would be the ductile element. You then design your other elements e.g. diaphragms to be stronger than this. Overstrength factors etc come into play here to ensure that you cannot accidentally fail your diaphragm before your wall goes ductile.

You don't design a wall for overstrength forces in the diaphragm as the overstrength forces were already derived from the wall's capacity. Basically, you build a model, get some loads on your wall, design your wall to those loads, then say "I'm going to assume that my wall ends up with the strongest steel ever, the strongest concrete ever too, and I will make sure that my diaphragm and the starter bars holding it to the wall will not fail before the wall yields".

I don't have any of my notes in front of me, so I will scratch aeound in my memory for the next bit. For diaphragm design, fancy modelling has found that the forces in the diaphragms have significantly exceeded those expected from typical designs. Look up the thesis by Gardiner out of UC, this set the basis for the pESA provisions in 3101's commentary.

My understanding as to why we don't apply these forces to the walla is that we don't expect concurrency of maximum demands. Any individual floor diaphragm up the building could experience massive peak accelerations, but this is unlikely to coincide with all the other floors experiencing them too, so the net force on the wall itself is not that high - it is more likely to be governed by a different combination of effects.

 

[moyseh]

Thanks for the reply that's cleared a lot of things up for me!

 

[Greenalleycat]

No worries. I don't profess to be an expert on this topic, it is quite complex. Diaphragms in multi storey buildings are hugely critical components so best to find a smart friend or boss to guide you rather than tackle this alone. I am aware that this paper exists and have skimmed parts of it a few times, but have never had to apply it in practice in my own work.

For interest, I just skimmed through Section 5 of that PhD thesis again. It seems pESA is capturing the significant influence of higher mode effects on diaphragm forces, and also significant internal forces (transfer forces) that occur as different lateral elements deform in their own ways relative to each other. These effects are not readily captured by the basic ESA force envelope.

These forces are internal to the diaphragm so you don't design the walls to them. They can develop as the diaphragm tries to force the various lateral load elements to deform in equivalent ways e.g. as per the attached image, the frame and wall structures fundamentally want to deform in different ways but the diaphragm has to hold them together which generates large internal forces. These internal forces are highly sensitive to the imposed displacement, which themselves are highly sensitive to the applied external loads. Hence, if you use ESA you underestimate external forces therefore displacements too therefore internal forces too.

 

[KootK]

1) I agree with Greenalleycat that over strength and temporal non-concurrence of peak diaphragm loads are the main reasons that different force sets are used for diaphragm design and vertical bracing designs. I'm going to attempt to add some additional nuance to the discussion anyhow though. The more voices contributing, the better, right?

2) This is a fine, free article that discusses these same concepts in a very accessible way: Link. The article is written from the US perspective but I believe the concepts to be identical or nearly so.

3) To be extra clear on one point: the best estimate of the peak diaphragm connection forces will come from PESA. Let there be no doubt about that.

4) In addition to over strength and temporal non-concurrence, these factors would also introduce non-conservative inaccuracy in into ESA were it to be used for diaphragm connections:

a) ESA is primarily based on first mode building displacement and does a fairly poor job of capturing the effects of higher displacement modes. Often, higher mode displacements will tend to produce quick motion reversals and higher mass accelerations at lower levels than those predicted by ESA.

b) ESA does a poor job of capturing peak accelerations near the ground, even irrespective of the higher mode stuff. In fact, in a way, ESA predicts no inertial accelerations at the ground level. And that's obviously wrong since we would expect a floor deck very near the ground to experience accelerations at least on the same order as the peak ground accelerations themselves.

5) As engineers, we are trained to enforce equilibrium in all things. When I read you original question, it seems to me that you are fundamentally bothered by the lack of equilibrium between the diaphragm forces and the wall forces. And that's healthy. We've discussed a number of reasons justifying why ESA and PSA are really answer to different questions. However, your concern for the maintenance of fundamental equilibrium still stands. Whatever force is delivered by a diaphragm to a shear wall does need to be able to be resisted by the shear wall. In answer to that, I would say this:

When a peak diaphragm load is delivered to a shear wall, the wall has a high probability of being able to resist that shear load for at least two reasons, even if the wall was not explicitly designed for that load:

a) The temporal non-concurrence of peak diaphragm forces will mean that other levels are contributing less than their peak demand to the wall when demand peaks at the level being considered.

b) One of the benefits of ESA using primarily just the first mode deflection pattern is that the first mode tends to shift more of the base shear demand up higher in the building than is the case for other, higher modes. This tends to result in the shear walls having excess shear capacity available below a particular diaphragm at the moment in time when that diaphragm sees its peak load.

In truth, I'm not sure that 5a + 5b = rigorous proof that a shear wall system will always have enough shear capacity to meet the demand imposed by peak diaphragms forces at all points in time. I do expect that would be the case the overwhelming majority of the time however. And, after all, seismic design is rough stuff by it's very nature.

 

[moyseh]

Thanks KootK. Lots of helpful information there. If you wouldn't mind offering your advice on a specific example I have:
Imagine we have a two storey structure: lower level concrete frame and shear wall and upper level we have concrete columns that extend up through the first level to support steel (pinned) roof framing with vertical cross bracing as the lateral load resisting system for the longitudinal direction.
To find all my demands at the storey levels if first do an ESA and determine the period, and then determine the seismic demand where about 8% of the lower level mass will be kicked up to the roof to account for higher modes. This load I can then apply to the storey levels.
To determine the diaphragm demands I then do the pESA method with appropriate overstrength factors and get a Pesa demand at the top level. Now, the top level is a roof diaphragm which is made of tension only cross bracing. Do these members need to be designed for pESA forces?
Moving on, i then find the difference (?) in the storey forces to apply to the level one concrete diaphragm and then design starters, drag bars etc?

 

[chris3eb]

In terms of being comfortable with the lack of equilibrium and the question of where the load goes, it may help to think about it similarly to live load reduction factors and effective wind areas. For those things, we're comfortable with an overall loading for main elements, but we aren't 100% sure of the distribution of that load, so smaller elements need to designed for more than their "fair share" to account for this.

ELF procedure is set up to maximize the effects on the vertical LFRS elements by putting a lot more of the lateral loading at the top (which means high shear starts further up in the building and overturning moment is maximized). If the distribution is actually a little different (due to higher mode effects), then the vertical LFRS elements will be conservative, but some of the lower-level diaphragms would be unconservative.

 

[Greenalleycat]

Hey mate,

These are good questions that you're asking. If you don't mind me saying though, it seems to me that you do need some senior support on this project.
I have answers to all your questions as I have worked through similar stuff myself, but they are difficult questions to answer concisely as they are big topics. But, I will do my best to give you a head start below.

Now, to answer the questions

1) Let's imagine we had a two storey building with a concrete slab-on-grade, concrete midfloor, and for shits & giggles, a concrete roof too. In this instance, pESA could be appropriate as you have significant seismic mass at each level, and your concrete roof diaphragm will be acting rigidly to distribute loads throughout the building. However, if you look at that paper I recommended, Debra Gardiner investigated 3, 6, and 9 storey buildings. The 3 storey building analysis found very little change in diaphragm forces using the pESA method. So, it would be convention just to roll with typical ESA forces for this height of structure.

Edit to correct myself: Figures 5-28 & 5-29 of that report are what I considered relevant. This shows that ESA & pESA show very similar forces at the TOP floor in the three storey building. At the mid level, pESA is moderately higher than ESA. At the lowest level, pESA is much higher. For 1 or 2 storeys above ground, I don't think pESA is that significant, but for 3 or greater storeys, the effect becomes quite pronounced.

2) Now to your case - one above ground concrete slab, and a lightweight roof. It seems a bit odd to take a bunch of weight that exists at the concrete slab level and whack it up to the steel cross-bracing, doesn't it? This will just lead to ridiculously sized members that don't reflect what engineering judgement would say is reality. So, convention in this situation is to design the lightweight top floor as a separate structure from the RC building below. Use your ESA distribution to get forces on the concrete structure (pretty easy as there is only one above ground floor!) and design it for that. Then, go to Section 8 of 1170.5 and uses parts and components loads to design the steel structure, including steel cross-bracing roof diaphragm, to these loads. Make sure that, when designing the concrete structure below, you lump all the mass of the steel structure, roof, etc at the top concrete level! You don't want to leave this out of your design.

As relevant experience, I recently designed a three-storey RC frame/wall building in Chch. This has two above-ground concrete slabs, and a lightweight steel top floor consisting of steel portals and cross-bracing system. I employed the exact methodology I have outlined above. I lumped the steel mass at the top concrete floor and used an ESA distribution to design my concrete frames and walls. I used parts loads to design the steel portals at the top floor. I looked at pESA and concluded that there would be minimal change for my type of structure, so I designed my diaphragm using my ESA loads instead. Part of my consideration here is that my lateral elements are vertically regular and my diaphragms were similar at first and second floor, meaning that there are minimal transfer forces going through the diaphragm.

Finally, how are you approaching ductility in your design? In the case of my building, I had very tight drift limitations due to a very narrow site. So, I concluded that I could not actually develop ductile mechanisms in my building. If your building doesn't go ductile then you can't really develop overstrength forces. So, pESA methodology with overstrength forces etc is likely quite conservative. The approach I took was to design my beams as nominally ductile, my columns to elastic loads, my BC joints to mild beam overstrength force (I used the relevant code provisions here), and my diaphragms to elastic loads. This gave intelligent looking results (I thought) and my professional reviewers agreed with the aspects I outlined above as this project was part of my submission for CPEng.

Sorry, that's a lot of words, but I hope it helps.

 

[KootK]

...where about 8% of the lower level mass will be kicked up to the roof to account for higher modes.

I understand why you made that statement but, at the same time, it is critical that you understand why that statement is spurious. No mass got kicked up the roof. None, not a single gram. Rather, what happened was this:

1) The center of mass of your single degree of freedom (SDOF) seismic model was lowered to account for the center of mass of the entire building truly being lower.

2) Because your SDOF center of mass was lowered but, simultaneously, retained the same design acceleration, the acceleration of your roof level was amplified per the first mode, shear building model.

In summary: no mass was relocated but the acceleration of the roof mass was increased and, therefore, so were the inertial effects generated by the roof mass. That reflects the truth of the situation and is perfectly reasonable.

In US practice, there are two ways around this:

3) The penthouse clause which relies on the mass of the roof being so small relative to the building as a whole that it doesn't appreciablly affect the vertical center of mass of the building.

4) The dual stage analysis approach which relies on the stiffness of the upper level lateral system being much, much less than the stiffness of the lower level lateral system.

I don't see either of those outs applying to the situation that you've described.

 

[KootK]

Do these members need to be designed for pESA forces?

I would say so, at least conceptually. I don't know the particulars of what NZ code has to say about it though.

Moving on, i then find the difference (?) in the storey forces to apply to the level one concrete diaphragm and then design starters, drag bars etc?

No, I would think that you would simply take the appropriate floor level values from the PESA and apply those to the connections between the floor levels and the shear walls. I've assumed that your diaphragms are not required to be transfer diaphragms in the lateral sense. If they are required to perform that function, then things get a bit more complicated.

 

[Greenalleycat]

NZ code doesn't have a lot to say about this at present, pESA is in its infancy!
I think this situation doesn't sit well within the research today.
That paper I have consistently referenced has this to say (amongst other things) under the Limitations heading
" The pESA method was developed with the intent that it could be used for design of regular structures that are commonly constructed"

This building does not sound commonly constructed (cantilevering concrete columns above the last diaphragm level?
Also, it sounds as if there are significant vertical mass and stiffness irregularities.
Given that this building has frames and walls, horizontal stiffness irregularity seems likely too
So, pESA may not be super applicable, at least not without a healthy dose of engineering judgement.

Regardless though, pESA is for diaphragm design
Not element design
Element forces (walls, frames) should be determined as per code using ESA, or if you are outside the limitations of the ESA method, using modal analysis or other approach

 

[moyseh]

Thanks for your replies. Greenalleycat - Yes I've sought some internal help but just wanted to get some external opinions too to get a headstart.

It is a highly irregular building unfortunately - very difficult to assess. Also compounded by the fact that it has numerous extensions, hence, diaphragms aren't properly connected and seismic design doesn't appear to have been given too much thought.

Kootk - Yep I understand "kick" was not the right word. Thanks for providing the background to that.

 

[Greenalleycat]

Sweet as, good on you for reaching out. I’m also very interested in this topic as I have some experience but certainly have a huge amount left to learn too!

Have you read the John Scarry papers about how to actually model your diaphragms? I have used that method before and found it is quite handy. Though it can be a touch difficult for assessing diaphragms rather than designing new

 

[moyseh]

Yeah I think this is a really good forum and so I keep coming here for questions/discussion.

Yes I have read that paper - really helpful and essential one for diaphragms. I have found new diaphragms which are fairly regular easy to design. It's just when you have transfer diaphragms or irregularities/cutouts etc when it's difficult.

In terms of assessment, I guess it shouldnt be too much different. I suppose I would just use appropriate material stregths/strength reduction factors when assessing capacity. The issue which I think a lot of buildings in NZ have is that the diaphragm is made up of topping with cold drawn mesh. Basically doesnt work for even one-storey structures in lower seismic areas.

 

[Greenalleycat]

The difficulty I found with assessing diaphragms is that you have to buuld your grillage to match the as-built steel layout in order to get accurate comparison... This can then make it difficult to actually match the geometry of the floor.

Yes, the cold drawn wire mesh situation is a pain in the arse. We had a client with a concrete two storey house with mesh in the floors who wanted to know if their house was 100%NBS... Had to basically tell them it was impossible under current guidance to put a number to it but it was effectively <34%

 

[moyseh]

Yep the only solution for the diaphragm I suppose would be FRP? Not sure how you would approach a stengthening scheme if your starters were under capacity? I can see how its a frustrating one for building owners

 

[Greenalleycat]

Yep, they wanted a letter saying it was 100%, only way we could give it was with FRP. So we strengthened it with FRP