Concrete Shear Wall Stiffness Adjustment Factor – Iteration Process Discussion 11

[polskadan]

Hi all, I wanted to inquire about how some of you perform your iterative design process for concrete shear wall crack factors and also discuss my current methodology. I am hopeful that I may be able to create a more efficient process and try to hone down on what may be considered more of a standard “industry practice.” Please note that for this discussion I am discussing the stiffness factors for concrete walls used for design under factored load combinations (not serviceability) as per ACI 318-14 sec 6.6.3.1.1a. Also note that seismic does not control therefore this discussion will strictly pertain to wind loading and linear, pre-yield behavior of the structure.

Scenario: 20 story concrete structure with (3) shear wall “groups” that make up a “shear core.” Each shear wall group consist of (4) walls that form a rectangular shape.

Iteration 1: My first iteration is performed with all walls uncracked using .70Ig -> plot results -> All walls that are ‘cracked’ have their respective cracked factors modified to .35Ig to represent Iteration 1 results (This is done at a per level, per wall basis).
Iteration 2: Using the updated wall crack factors from Iteration 1, I perform a 2nd iteration of the model with crack factors of .35Ig on walls that cracked in Iteration 1, and .70Ig for uncracked walls -> plot results -> Walls whose status match their crack factor remain as is (cracked stays cracked, uncracked stays uncracked, remaining walls have their factors adjusted to match iteration 2 results.
Iteration 3 & beyond: Continue to adjust factors as discussed in iteration 2 until all values converge
At this point I should clarify that the ultimate goal is to have all cracked factors for each individual wall segment at each floor converge with the input factor when checked for all load combinations. This means that if a wall is shown to crack in any of the checked load combinations, then this wall shall have an input of .35Ig and vice versa if the wall is shown to remain uncracked when checking all load combinations, this wall will have a .70Ig.

The issue that I come upon is that I end up chasing my tail when limiting myself to only .35/.70Ig. As you change the stiffness of individual wall groups, you are modifying that load path and subsequently distributing more load to adjacent wall panels. By limiting myself to .35/.70 it seems as if I am trying to say everything is either “white or black” and ultimately consecutive iterations are mere inverses of the previous results. It would appear that in order to accurately reflect conditions, I would need to find “effective” moment of inertia’s for each respective walls segment, but this would be a very time consuming process when one is forced to do this by ‘hand.’ This need for an effective stiffness becomes apparent when one sees the results constantly inversing between 2 sets of walls flashing between “cracked and uncracked” when in reality the wall groups share this load and are somewhere in between.

I have heard from a colleague that "once a wall cracks it is cracked." This is an obvious statement, however it is a more complex issue when we as the engineers are telling the programs which walls are cracked/uncracked and subsequently manipulating where the load is to go. I am under the belief that in a perfect world I would create effective moments of inertia for each individual wall segment (per floor), however I am curious to see how far other engineers/companies take this design approach to get a stiffness model that accurately represents the intent.

I am also curious to find if I am overthinking this and if the general engineering community uses a cracked factor of 0.5Ig for all entities as allowed in ACI 318-14 Section 6.6.3.1.2 .

 

[r13]

I couldn't connect stress-strain curve with this problem. Rather, IMO, the program needs to be able to compare the resulting tensile stress with concrete rupture stress. If the former exceeds the latter, then it shall calculate the revised moment of inertia using next specified depth (say "x inches" negative increment). The program shall stop when the moment of inertia has hitting the goal, say 0.7Ig. When compare tensile stress, it shall also keep an eye on compressive stress, and so on so forth... But this would still be considered "linear analysis", wouldn't it be?! So, no good.

 

[sticksandtriangles]

i maybe in left field here... but I think the 0.7*Ig and 0.35*Ig is a convenient remnant of past analysis techniques for frame type members. For a frame element (stick) it is very easy to access Ig and modify as required.

For shell elements (how i would guesstimate 95% of concrete walls are modeled nowadays)... the concept of Ig becomes a little more fuzzy right ? The elements stitched together inherently make up Ig of a wall. A lot of literature suggests modifying E of concrete to account for the 0.35Ig of 0.7Ig. This inherently is inputting a stress strain curve whether we realize it or not in my opinion.

I think the technique that i have outlined above captures the heart of the 0.35Ig and 0.7Ig requirements for cracked and uncracked walls.
By inputting the explicit stress strain curve into the shell element, ETABs or sap should be able to check whether or not the shell element has cracked and then change the modulus of elasticity accordingly (hopefully in the end somewhat accurately (dripping with sarcasm here) capturing the softening effect of a cracked concrete wall).

Maybe a better stress strain curve would be this:

But this would still be considered "linear analysis", wouldn't it be?! So, no good.

I've come to think of non-linear analysis as synonymous with iterative. I think the process you have outlined above retired is a non-linear analysis at the heart of it.



S&T

 

[Trenno]

KootK, you seem to have ignored my statement "This is all assuming they are doing this innovative work based on sound engineering principles and the latest research."

Horses for courses... buildings that sit in the outlying 1% probably call for the NASA level analysis. Shall we be picking the next pencil-scraper out of a generic structural engineering cookbook? Only 3 outriggers allowed at the 30th, 60th and 90th levels!

I can sympathize with you though, there are many simple things we as a community can't agree on. Look at that steel beam LTB thread from a while back... Perhaps a cookbook is an easy way out?

On the topic of non-linear shells, I'm not privy to those in-house secrets - so would like to explore the topic myself. This thread seems like a good place to discuss such things.

 

[JoshPlumSE]

I've always attributed the meteoric rise of CSI primarily to the innovation that is ETABS. In particular:

1) Early anticipation of, and catering to, the structural engineering community's desperate wish for the ability to handle gravity & lateral design in a single, 3D model and;

2) Not explicitly telling designers how building lateral design ought to be undertaken while simultaneously providing convenient tools for designers to do what their instincts will lead them to want to do naturally.

3) Staying the hell away from light frame construction where the value proposition is much lower while the programming is probably actually trickier.

Keep in mind that I've worked for CSi for less than 2 years. I worked for RISA a lot longer (16 years). So, my insight into CSi isn't as thorough as you would think.

1) I think you're partially correct with item #1. Though I won't point specifically to ETABS. I'll point to SAP80 / SAP90. I think building up an early market share in the industry was very important. STAAD was likely in a similar position. The very early players in a market.

This is my opinion (heavily influenced by my time at RISA): "Momentum" is very important within the structural software industry. What I mean is that it takes time to learn a new software. It's partially learning the interface. But, it's also understanding the peculiarities of the program. How to de-bug the model. How to dig deeper into the results to see what you did right or wrong. Once an engineer (or company) is truly experienced and comfortable with a software (or software company) it is difficult for them to switch.

2) I think your point is essentially true, especially with ETABS. Give the engineering community the software tools they're asking for and which they need. I will amend this slightly.... I think it is also really import to show the engineering community that you respect them and their business. I remember a time (late 90's BEFORE I worked for RISA) where STAAD had real quality control issues. They were releasing features that just didn't work. It felt (to me at the time) like they were concerned about have a list of features that they could show to engineers on a sales call. But, they didn't care whether those features actually worked or not. Who knows what the real cause of their issues was, but to me it felt like a lack of "respect" for their customers.

I'm not aware of the folks at CSi ever doing that. Sure the program has bugs (all programs do). But, my main point is that the company has always been run by TECHNICAL people who are very much concerned about the accuracy and reliability of their program.... People who love and respect the structural engineering profession.

3) Yes, CSi has very much stayed away from light frame wood buildings. My guess is that the reason is they preferred to focus on the higher end / more academic forms of analysis. They have a lot of connections to the folks over at Berkeley (Graham Powell, Ed Wilson, etc). And, that influences what the company is interested in doing. In fact, the get a real head start on the rest of the industry on any of the "new fangled" analysis methods coming from those University researchers.

Contrast that to wood construction. You really need to hang out with engineers who specialize in wood construction to understand the intricacies of that field. And, once you go down the road of wood design, you quickly figure out it's a lot more work to fit it into an analysis program than other materials.
Therefore, avoiding wood (as I see it) is likely related to CSi leaning into its strengths (more advanced analysis) and letting the other companies (Enercalc, etc) focus on the areas they perceived to have lower profitability.

 

[KootK]

KootK, you seem to have ignored my statement "This is all assuming they are doing this innovative work based on sound engineering principles and the latest research."

I didn't ignore your statement at all Trenno. In fact, I'd sued it for source material:

1) As I mentioned, by and large, we all have access to the same research and literature pool.

2) I think that it's dangerous and erroneous to imply that only the folks working at the mega skyscraper firms possess a knowledge of sound engineering principles.

In the past 24 months, I've been involved in peer review assignments for two NY buildings involving WSP and Thornton Tomasetti. In both cases, I've had a look at the wizards behind those curtains and magic being performed has been this:

3) Use ETABs, just like everybody else.

4) Use the latest research papers on coupling beams etc, just like everybody else.

5) Make thumb in the air guesses about effective wall stiffness based on the research and the ACI recommendations, just like everybody else.

6) Be very, very aggressive with #5, not always like everybody else.

And it is the same at the big Canadian firms for which I've worked. If your group is doing something special that is not what I've described then I guess that my comments do not apply to your team and their work. That said, based on my personal experience of this, your team would then be the only one that I'm aware of that is doing something significantly different from that this.

Horses for courses... buildings that sit in the outlying 1% probably call for the NASA level analysis. Shall we be picking the next pencil-scraper out of a generic structural engineering cookbook? Only 3 outriggers allowed at the 30th, 60th and 90th levels!

Now this is you misinterpreting my statements. I do not bemoan the aggressive design methods that firms doing this kind of work are using -- I use them myself. And I have no problem with the results or the use of advanced modelling to get them -- I do the same. If we collectively decide that we want these kinds of aggressive designs, as a profession and as a society, that's just peachy by me. What I do have a beef with is the implication that some groups are entitled to the use of such aggressive methods because they are using top secret, advanced research and computational methods that the rest of us are somehow ignorant of. When I've peaked behind that particular curtain, that simply is not what I have seen.

If we're all going to be out there doing the WAG thing on very important, high dollar design elements, then I think that the standards ought to step into a degree to standardize the practice, at least until the state of knowledge is such that we can calculate effective wall stiffness accurately based on established engineering principles. For now, let's innovate based on things like clever schematic design layout rather than our ability to be brave enough to say that a stiffness factor might 0.55 instead of 0.35.

On the topic of non-linear shells, I'm not privy to those in-house secrets - so would like to explore the topic myself.

So is it then the case that these methods are being used by your firm to design shear wall system?

 

[KootK]

One of the best examples that I know of for a ubiquitous, questionable, aggressive, iterative design approach is the way in which the design of coupling beams is often handled. It goes like this:

1) Decide to couple your shear walls because there's no competitive way to stiffen your lateral system enough without them.

2) Assume an aggressively high stiffness for you coupling beams to give you good drift control.

3) Find that your coupling beams now attract way more shear than you could ever possibly deal with.

4) Start selectively cracking your coupling beams to a larger degree to remove the problems from the hot spot locations.

5) Justify #4 with some sketch arguments like:

a) at high loads, they probably do crack more, don't they?

b) I only need the stiffness for SLS, not ULS.

And again, I'm fine with all this so long as we all know what each other is up to and agree that it is the best path forward. It's the backroom BS that I think is unfair.

 

[KootK]

Here's a personal pet peave that maybe someone can help me with.

Most shear walls have regularly spaced, horizontal construction joints at the floor levels. Are those not flexural cracks present from the outset? Or are they somehow different because they are discretely spaced? I'd actually consider full depth cracks in a 20' long wall at 10' oc vertically to be somewhat distributed flexural cracking.

 

[r13]

KootK,

Don't quite understand your question. How "construction joints" are discretely spaced, or you meant the cracks are?

 

[KootK]

Don't quite understand your question. How "construction joints" are discretely spaced, or you meant the cracks are?

What I mean is that construction joins are flexural cracks in that they represent planes of weakness incapable of transmitting tensile stress perpendicular to the joints from the outset.

 

[sticksandtriangles]

Some testing with layered shells and frame members... set up below:

Concrete shearwall plan view and elevation (100kips applied at the top of the core):

ETABs model with Stick element and shelled wall:

Stress strain curve for non-linear shell (finally took a stab at calc cracking stress at 5*root f`c for 4000psi concrete):

I applied a 0.7 and 0.35 factor to the stick element for Ig

Deflection results:

Stick element moves 1.45in (0.7Ig) 2.86in (0.35Ig), nonlinear shell element moves 1.82in at the top.

Stress results:

Tension maxes out at around 575psi, compression maxes out at around 880psi

S&T

 

[Celt83]

Interesting discussion would like to see how this progresses.

Doing an adjustment on Ig is all fine and dandy but that still ends up applying over the height on an entire story's worth of concrete, I think given the budget and schedule that allowed for the type of analysis we are talking about you'd want software that you could put in a moment-curvature relationship for the wall panel which lets you capture the interaction with the reinforcement. You'd need to do some front end development on panel designs and then as stiffness's and forces change you swap in a new panel design and M-C relationship and re-run or the program does that as part of it's non-linear run.

This is the software area where I think some of the AI stuff could dip it's toe into our realm, when your talking about concrete it's hard to automate this stuff because you can't design the reinforcement until you know the forces and you can't get an accurate estimate of stiffness without the reinforcement, so stuff like our slab software has you already say hey I want you to use #6 bars in design because otherwise it would have to do section designs for every bar size then have criteria to determine how to select a result from those designs.

One thing that seems lost in all of this is these are technically deep beams and the contribution of the shear deformation is significant, how does the amount of flexural tension impact the "shear area", I haven't found much research on this topic which I tried looking into as part of my work on deriving general Timoshenko beam formulas. Most calcs I see on this just use the shear area for a solid rectangle if the fibers are separating under tension not sure this should really be the case.

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[sticksandtriangles]

I will work to post some results with capturing the reinforcing effects as well since that seems to be of interest. Maybe Trenno can give us some pointers on how to handle this.

The example I posted above I think could be used as a "poor mans" non-linear analysis that attempts to capture the 0.35-0.7 effects that ACI spits out.

Most calcs I see on this just use the shear area for a solid rectangle if the fibers are separating under tension not sure this should really be the case.

I've thought about this as well but arrived at feeling OK with utilize the full solid rectangle area. Mind explaining why you feel that this wouldn't be the case?

S&T

 

[r13]

I deleted my previous comment for incorrect strain diagram. Is the stress-strain diagram below non-linear?

 

[Celt83]

If you have a non-zero crack width in my mind you have lost cross section continuity so the shear area should reduce to something other than the full section.

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[sticksandtriangles]

With rebar in the non-linear shells (which I have no idea how to setup correctly)... I get 1.35 inches of deflection at the top of my example.

Concrete Stress strain curve (note that it will drop off any appreciable load carrying capacity in tension):

Steel Stress Strain curve:

Nonlinear shell setup (#6 @ 12"oc ea way ea face):

S&T

 

[r13]

celt is correct. The tension flange will be lifted up, and the stress redistributed on the un-cracked section.

 

[Celt83]

Retired13:

I'm not sold on it either way as in theory for shear the tension steel should still be holding things together so you get the aggregate interlock mechanism across the shear plane, is that interlock enough to justify still using the gross shear area, not sure but nobody has done any different than that and buildings aren't moving crazy amounts.

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

 

[KootK]

Trenno and I discussed the shear flexibility some in this 2016 thread: Link. That included the clip below. This doesn't really provide answers but, rather, just more fuel for the uncertainty fire.

 

[JoshPlumSE]

Sticks and Triangles -

My thoughts about modeling the non-linearity of shear walls in a program like Perform3D (or the version of ETABS that does this):

1) I'm more familiar with the Perform3D version of this. The concepts should be the same. Though the terminology and way it is described might be slightly different.

2) I have no practical experience working on projects like this. My experience comes from seminars, teaching myself the CSi programs and such. So, that is a pretty strong caveat about my level of knowledge.

3) For a performance based analysis, you'd want to define what type of Hysteresis model you want to use for the shear wall. This should be based on research on the type of element you are modeling. To me, this is more clearly defined for moment connections than for shear walls. But, the concept still exists for shear walls. Something like the following:
Pivot Hysteresis model (which involves a pinching in of the curve due to different loading vs unloading stiffness. It starts off with an uncracked stiffness, then cracks and reduces it's stiffness. Unloading follows a stiffness closer to the uncracked stiffness.
There are many other hysteresis models that one could use. What best matches up with FEMA / ASCE recommendations and or test data, I just do not know. Below shows soemthing akin to the "pinched" curve that results from a Pivot Hysteresis model.

 

[sticksandtriangles]

i did a quick pushover test for the layered shell (one directional push only).

Sorta of looks like the first hysteresis image posted by Josh.

Josh, is there a way to set this up to go back and forth like a hysteresis model in ETABs?
I would be interested in seeing what type of loop pops out.

S&T