Hi everyone, I'm Kiara McKenna on behalf of the Apply Technology Council. I'd like to welcome you to this webinar on FEMA P. 2,012. Assessing seismic performance of buildings with configuration irregularities. This webinar is brought to you by the Apply Technology Council under our contract with FEMA, the Federal Emergency Management Agency. If you have already, you can download the handouts using the link in the chat if you if you don't see the link yet, it will be provided again in a couple of minutes. We know that many of you are interested in receiving professional development hours for your attendance today. For those who registered and attend the webinar, a certificate documenting professional development hours. Will be sent by email within 4 weeks automatically. If at, anytime during the webinar you have questions, please type them into the Q&A window that you can open from the Zoom control panel.
We're planning to have a live question and answer session at the end of the webinar. So please submit your questions as you have them rather than waiting until the very end to submit them. Will answer as many questions as we can time permitting. If there are any questions that we aren't able to answer live, we do plan to provide written responses for as many as is practically feasible. I'd now like to turn it over to Christina Aronson from Fema's Earthquake and Wind Programs branch.
He will provide a brief introduction to today's webinar. Christina, please go ahead. Hello. My name is Christina Aronson. I'm a structural engineer at the Federal Emergency Management Agency's Earthquake and Wind Programs Branch. It's my pleasure to welcome you to today's webinar and assessing performance, seismic performance of buildings with configuration irregularities.
A little bit of background. Fema has the goal of reducing the ever-increasing costs that disasters inflict on our country, addressing the risk. Presented by our population of existing buildings is of course the most effective way of reducing the cost of future disasters. As part of its responsibilities under the national earthquake hazard reduction program, FEMA is charged with supporting the investigation of seismic technical design issues, the development, publication, and dissemination of technical design and construction guidance products. And the support of training and related outreach efforts. A significant concern for the program is the risk presented by buildings with vulnerabilities due to configuration irregularities. So FEMA and ERP sponsored a problem-focused study to assess the seismic performance of buildings with structurally irregularities and the effectiveness of design requirements in ASEE 7 on regularities. The resulting, publication, VP, 2,01220 12 report was to inform and improve codes and standards.
So that structures with configuration irregularities have a similar level of safety against collapse. During an earthquake as regular structures. Many of the findings in the report have been used and adopted by the 20,000, and 20, NIH, her recommended seismic provisions for new buildings and other structures. And ASE, 7 22. We hope you will find this webinar useful and we encourage you to let us know if you have questions. We want also wanna thank Apply Technology and Council and, Mike Valley for helping us deliver this. Session. Back to you, Kiara. Thank you so much, Christina. So now let me tell you about your incredibly accomplished presenter today.
Mike Valley is a principal at Magnus and Clemensik associates. He was project technical director for the development of FEMA P. 2,012, the report on which this webinar is based. Mike has over 30 years of experience managing complex projects involving new construction and renovation. He brings special expertise in seismic and foundation analysis and design, and he has been a key participant in the US development of performance-based seismic design approaches. Mike, frequently serves on committees and advisory panels to develop and write national engineering code standards and guidelines. Mike was named Engineer of the Year by the Seattle Chapter of the Structural Engineers Association of Washington in 2,007.
And you received the National Council of Structural Engineers Association's James M. Delahi Award in 2,008. I'd now like to turn the webinar over to Mike. Mike, please go ahead. It's my pleasure to speak with you today. Configuration irregularities. We're gonna talk about to manage your expectations. We're gonna talk about what configuration and regularities are in the first place. Why is there a concern to us how they affect size and performance, how they're treated in the US codes the standards. And as we consider that you'll see that there triggers or definitions of these irregularities. So that we all understand what we're speaking of. There are design consequences maybe analysis design and detail requirements associated with the existence of various irregularities.
And there are ways that we can mitigate some of those irregularities that we'll talk about specific to each type. As we're doing so, you've already heard that the FEMA P. 2012 project. Was addressing irregularities. So we're gonna give you a little bit of background about that project. The way that we'll lay out our webinar here. We're gonna have some background information on the subject. We'll talk about that FEMA P. 2,012 project as in an overview since. Will then get into the meat and potatoes of this. We're gonna talk about modeling and analysis requirements because they're key to understanding and resolving structural irregularities.
And we'll have specific examples on horizontal regularities and vertical irregularities. To start though, we wanna. Get on the same page with you about. What an irregularity is at least as defined in in this project. We really needed to focus our effort. There have been lots of observations in the past about how structural configuration can affect.
Performance in earthquakes. So the definition that we settled on After careful consideration by the project team. Regularity is an aspect of configuration. That if unaddressed. Detrimentally affects the structures performance during an earthquake. Leading to an unacceptable reduction in collapse safety or increase in damage. We're gonna talk about some of those specific words that we crafted in order to manage. The way that the products would go forward. There are concerns with configuration and the performance concerns that we could have. In order of priority being the highest priority is that there could be an increased potential for collapse.
And we know that collapse of buildings. Leads to loss of life. And of course there are economic considerations but loss of life is one of our key societal concerns with. Perfect. Configuration challenges can also. Produce increased damage in a building. And. And as we want to understand the configuration of a building and it's expected performance. We need to have the right kind of analysis. To capture the behaviors. So that we understand the problem well. And so configuration can affect our choice of analysis methods. Just to set the table on this idea, this is not simply an academic issue. Irregularities can cause collapse in buildings.
In fact, about half of the deaths in US earthquakes. Since 1970 are due to the collapse of buildings. There are other causes of death, but collapse is the primary cause. And that could be due to unreinforced masonry buildings. Or non ductile concrete buildings, those are not the subject of today's discussion. But irregular buildings often have problems that lead to collapse and loss of life.
That's not just a US problem, it's a global problem. Of the deaths in the COVID are quick in 2,005. Most of the deaths were due to the collapse of buildings. And when we dig in and look at those collapse statistics and the performance that's associated with it. Most often those collapses are associated with either soft or weak story irregularities. Which may include the, we call them strong beam, variant we'll talk about in more detail. And, regularities. So those regularity types. Are most often associated with collapse.
So the project looked at the horizontal regularities, that are defined. And rank them in order of importance as they might relate to collapse. And on the right side, you'll see just some little plan view. Cartoons you'll see similar cartoons later so that we can make sure that we understand what we're talking about. But in the case of horizontal regularities, Each of these is a plan. And if there is some twisting response in the building, Do through torsional stiffness or strength. Characteristic, there is a greater chance of collapse. For the out of plane offset irregularity. Where the vertical elements of the seismic force resistant system Don't extend from the top of the building all the way to the foundation. But there's some offset at one or more levels. That also can cause collapse. Because the fuse between those vertical elements can fail and perhaps that was not anticipated by the designer.
What the way the diaphragms of a building are laid out. And configured, can cause problems, local failures usually usually not a global collapse. But those local failures can also be dangerous. Reentent corners so where there's diaphragms where there are separate wings in the diaphragm they can respond dynamically out of sync with each other and there can be increased damage. The other, type of horse on the regularity that has been defined in in ASC 7 for a long time is a non-parallel system. The idea is that, the system, the lateral systems. Cannot be readily. Transformed into 2 orthogonal systems.
And if that's the case, you need to consider 3 dimensional analysis. You can't separate the response in one direction from the other. That's really just an analysis problem, not a performance. And we'll talk about that some more. The vertical regularities of now in this case because we're looking at vertical regularities these are elevations or sections of buildings.
In each of the cartoons. And so we could have a week story. So with respect to the stories above it and below it, that story has a much reduced strength. And we could get concentrated damage in that week story and that could lead to collapse as it has in many earthquakes in the past. A soft story, a regularity. Is not a question of how much strength there is there. It's a stiffness issue. And the softer or more flexible story. I can deform more, especially under dynamic loading. And that could produce collapse. For an in plain discontinuity, the challenge is that vertical elements of the size and force resisting system.
Don't go from top of building to the foundation. There's some transfer of that load. Some concentration of that load as it works its way down. And in the concentrated areas, they can have. Excessive damage that could lead to collapse again. The week column strong beam issue is a moment frame. Irregularity. The idea being that when you look at the joint of a moment frame, the beams and columns that frame into it. If the, if the system prefers to have hinging in the columns. There's a greater chance that all of the columns in a single story could hinge. And if that's the case, then the story could collapse. And so that's a concern.
Vertical geometric irregularity. The idea is a little qualitative, it's not so much quantitative. It's You can see it when you look at it and you can see that there's some. Change in the dimensions of the size and force existing system. That would make it have a non uniform stiffness or strength. They're maybe a heavy story in the building, a heavy floor. And that's a weight or mass irregularity. The concern being you could concentrate in elastic response because of that. Non-uniform performance. Walls and buildings can have discontinuities in them for a number of reasons. That we'll speak of in detail a little later.
But the idea is if there are those discontinuities. They tend to be areas where the performance of the building is worse where there's a concentration of damage. And that can cause problems. And we'll talk about a gravity induced lateral demand. This is not a not characterized in US codes, but the idea is important and should be on your radar. Especially given modern trends in architecture. The idea is that if the gravity loads cause lateral response that needs to be considered in the design of the building. For the So with that background on what are horizontal and vertical regularities and some cartoons to maybe help you understand.
Let's talk a little bit about the. ATC 1 23 project. That led to the publication of FEMA. . 2012 so this was, funded by the federal emergency management agency. And the project was. Managed by the Apply Technology Council. Who's hosting this webinar today? We did the work primarily in 2,015 through 18. You'll see on the next slide. Some key participants, as most. Apply Technology Council projects. This was laid out with a. Project technical committee with a large supporting cast of other researchers and, engineers and And then there was a product review panel. So the findings, were well vetted. And so that even the course of the project was directed so that it could be most useful.
So the objective of this project that FEMA sponsored was to look at. Hey, regularity related design requirements in US codes and standards. As specifically as they appear in. The Nerve recommended seismic provisions, which then make their way into ASE, 7 sizing provisions. In some cases, the US codes and standards we have with for existing buildings, ASC, 41 addresses existing buildings. And some of our material standards. Like ACI 3, 18 and AISC 3, 41. Address aspects of configuration that are specific to their material. Of interest. So the notion is that configuration is important to all of us.
The way that is dealt with is across these family of products. And the goal of this project was to compare the performance of buildings with regularities to the performance of buildings that don't have those irregularities. And see what we could do to level the playing field of performance. What can we do so that Configuration of regularities, which can't always be avoided. What can we do so that those configuration and regularities don't lead to poor performance? And rather than simply qualitatively discussing the issue. The project was specific in that we wanted to quantitatively evaluate. These aspects so that although our past observations of performance have been qualitative in many cases. If we could actually quantify the issues.
We could do a better job of getting consistency and the level of performance. And that meant that the quantitative consideration was looking at current building code triggers. And then thinking about how irregularities effect size and performance and specifically collapse. And then we can measure code provisions to see how effective they are in. Fixing the problem or in improving performance. That really was the goal. The way that the project approached this. Was to, do a literature review first, understand what, has gone before.
How the US and international codes and standards. And guidelines address configuration. Look at the research that's available. Consider the observations in past earthquakes. And think about what the greater structural community has considered to be irregularities. What are the metrics and triggers? That have been used. What kind of analysis methods can be used in order to do the quantification that the project aims for.
So we did some literature. Then we chose the irregularities that we wanted to study. We'll talk about why we chose the ones we did. And then we had to embark on this quantification of irregularities and their effects in size. And we'll give you just a little background on how the project did just that. So this live represents the irregularities that the project had on our radar. And the ones that are in gray.
H 6 and V 6 through V 8. Are not in ASC 7 they're in some other documents so they may be in another US code or standard like ASE, 41. They may not even be in US codes at all like the gravity and use lateral demand. It's treated in the Canadian building code, but not in the US code. So this was casting our net wide. The range of configuration issues that we. Decided to approach. And then we needed to choose, what we were going to focus on. I mentioned that there was a desire not just to have a room full of experts chatting about what they think is the case or what's important but to look for opportunities to quantify The triggers and the the metrics that Describe them and to quantify how we can address irregularities. And so that made us focus on some. Irregularities that already had a way to be quantified. For instance, you see on the screen. Torsional stiffness of regularities. Can be quantified and they're the way that we understand whether we do or don't have that irregularity.
Similarly with week story irregularities. There are strength metrics that can be used in order to help us identify and then perhaps address the irregularity. So what our project focus was, yes, quantifying things, but going back to our definition of irregularity. We wanted to look at aspects of configuration that could detrimentally affect the structure performance. So it's not just an interesting aspect of its behavior, but something that could cause the behavior to be worsened. With a particular focus on collapse safety. We do include increasing damage as a concern. That's a reality.
That's practical. But the higher priority is to try to address collapse safety. And so that meant that the ATC 1 23 project that led to FEMA P 2012 now had our focus of issues. An example of some of the things that didn't get. Considerable study. Include the non parallel system regularity because there's no reason to think that a structure that behaves poorly simply because the lateral system is complex. Or it's not orthogonal. Frankly, earthquakes always shake buildings. In in all 3 dimensions.
And so the fact that the that the systems are not laid out so that So North South and East West response. Or somehow, definable separately doesn't mean that the building will form badly. Similarly, things like Can cause increased damage. And should be addressed as a result. But they rarely cause collapse. And so we could take off the table. Detailed assessments of. Those kinds of irregularity. So then the way that we approached our work. With a focus on collapse was. Do I identify the structural irregularities that we wanted to focus on?
We talked about how we selected those. 2 pick size and 4 existing systems that we could use to specifically analyze those configuration issues. Then to design those baseline systems. Without irregularities. So to design regular systems. And then introduced irregularities. And redesign and analyze those irregular structures. And understand the degree of irregularity. And for all of those studies, we used the FEMA piece, 6 95 method to assess the collapse safety.
Of the building. Will give you that you could have a day, days worth of, seminar on the P 6 95 method. We don't have time. We have one slide. So I'll try to describe to you the way that the system works. The goal of this method is to simulate collapse using nonlinear dynamic response history analysis. And so you'd have to come up with a characterization of the building, a model, and include in that modeling the nonlinear.
Behavior of the system. That's used to determine. Post your displacement capacities. And then you perform incremental dynamic analysis. In a in a in a sense you are shaking the this model with larger and larger earthquakes. To understand when it collapses, what causes collapse. And to determine. What its margin against collapse is when it's been designed properly because the reality is you can always shake something hard enough to cause collapse.
It's just a question of when and how much that deviate from the design target. So that method is used. In order to better understand. Collapse. The, project wanted to have broad application across the US. And of course to that same degree, it could have application worldwide to the degree that the types of construction are similar. So we looked at high seismic demands. Sided design category D and we looked at lower sized demands. So not 0. That would be a trivial exercise, but, We wanted to think about size and force existing systems that had either special or ordinary.
So that we can understand the differences, the sensitivities of those. Systems. To the configuration changes. We looked at load to mid rise. Structures for the horizontal irregularities. We looked at mid to high rise structures for the vertical regularities. We thought about the range of analysis methods. At at our disposal in ASE. Specifically, the equivalent water of force, procedure. Which is a static. A method with linear modeling. We looked at the mobile response spectrum analysis procedure. And we looked at we used nonlinear response history analysis for our assessments. You are permitted to use nonlinear response history analysis and design. That wasn't the way that we approach the design because that's not the most common usually the linear methods are used for design and nonlinear analysis may be used to.
Pro. We looked at high low gravity loading. And for the degree of irregularity, as I mentioned, we selected first. Regular baselines and then we looked at making them more and more irregular with a certain classification of irregularity until they were highly irregular so that we go understand the range of response. So what we have here is. Again, it's a listing of the horizontal. Configuration issues that were considered in the project. And what you see highlighted in yellow. Our metrics. That were later modified as a result of this project. And most of the requirements that we see here appear in ASC 7, which is used for new buildings.
Some of the requirements appear in ASC, 41, 17. Then for the vertical regularities, we did the same thing. We've got this whole suite of configuration issues that we. The ones in yellow are areas where this project resulted in specific quantitative changes in ASE. The ones highlighted in We're also changed in ASC 7 22 But as a result of other studies, we'll mention it as we consider.
Continue. And so then the way that these irregularities were considered in the ATC 1 23 project that led to FEMA P. Twenty- You see here, you see the We of course we focused on certain irregularities. And we had a number of different building types in terms of material. And building heights. That we addressed. All the details there are in the document. So this brings us to our first poll. Great. So I'm launching it. So this poll is which irregularity or irregularities are associated with the increased risk of collapse.
Non-parallel system, reentering corner, soft story, torsional stiffness or strength, weak story. And then there are a couple options that allow you to pick multiple. So just Be aware that the first few options or you're saying just that irregularity. So then we have non parallel system. Reentering corner and wait irregularity. You can also choose soft story, torsional stiffness or strength and weak story. There's also the option to say that all of the above or none of the above. And this is, I know this is a bit of a long pull, so we'll give you some time to. To think about it and get your responses in.
It looks like so far about half of the people have. Responded. Alright, I'm gonna go ahead and close the pull in a few seconds. So. Do your best to get a response in. And it looks like. About 3 quarters of people have responded. So Mike, I'm gonna go ahead and end the poll and share the results. Are you able to see them? Yes. Great. So it looks like most people have responded all of the above. Or they've selected the option with Soft Story, Tor, and A and Week story. Right, so since our focus here is on an increased risk of collapse, most of you selected the correct option.
I, 39%. That it is soft story week story or to original regularities that tend to lead to collapse. The other things may matter and some of them are still defined in our document. But non-parallel system and re-infant corner. Irregularities don't cause buildings to class generally. And the mass or stiffness regularity also does not cause buildings to collapse. We'll talk about that more as we go on. Great, Mike. I'll go ahead and close the poll. So this final slide sort of summarizes what we learned from the. Fema P. 2012 project.
Borne out by other studies as well. And it's interesting finding is that If you use the mobile response spectrum analysis method. Which we have traditionally thought of as a superior method a more precise or more accurate method than ELF. Your buildings actually have a higher probability of collapse. And you might think of it that way because if the ELF Design is more conservative. If it has greater strength and stiffness than the response spectrum analysis designed building. You should expect that it has. Better performance. Gravity induced lateral demands are important in system. But as long as you consider the effect that the gravity.
Demands have on your performance. You'll not have worse performance. If you ignore the fact that you have sloping columns. Or that you have sustained lateral effects, you will end up with a port design. For, we found that it is good to consider strength A/C 7 previously had not considered strength. Only stiffness. We found that considering strength. Was important. If we use the orthogonal combinations. They can help us if they're towards more regularities. Because the ELF method is more conservative than mobile response spectrum analysis.
We found that we could allow the use of ELF. It didn't need to be prohibited. And in fact, with mobile response spectrum analysis, there are some options that you could use that would actually cause problems. In your assessment of accidental, we'll talk about that, but the project found that. We also suggested that the P Delta. Requirements in ASE. 7 should also, be related to some P theta requirements that may be a new term to you. We'll talk about it in detail. Because the ELF is conservative. And already we're required to accurately model. Mouse?
We really don't need to have a defined irregularity for mass irregularity or weight irregularity. The design can as long as it considers the real weights and masses. And the real strength and stiffness. The design can be adequate. We found places where the diaphragm design requirements needed to be clarified because the scope of the mitigation far exceeded the scope of the irregularity. And we made some minor adjustments to the triggering dimensions. For re-entering corner and diaphragm discontinuity. Based not on new studies, but by looking back at. At the considerations that were made when they were codified in the first place. That's gonna take us into this next section where we're gonna start to think in more detail.
About the technical aspects of our designs. So the idea here is that we have modeling and analysis requirements set forth in ASC. 7 22. As we have in earlier editions of the document. Oh, we're gonna talk about some of the, requirements that were removed in ASC. And we're gonna discuss the significance of the modeling requirements. So why is it it's so important to be careful in your modeling of your structures? Where are the places to focus? And so that you don't get into trouble or so that you can find problems before they.
Occur in the field. And then related to that there are specific requirements in ASE, 7 22 that we're going to step through. So the we can understand how they help us to understand structural configuration. And to make sure the structural configuration is treated properly. So just as a piece of background for ASE, 7 22, it outlines 4 methods. To perform structural analysis. In increasing degrees of complexity the simplest method is the equivalent lateral force procedure ELF We use a linear analysis. And we have by static lateral loads. And those loads have been historically defined. So that we can try to get not necessarily the true set of loads in a building. But a reasonable envelope of demands in a building that are suitable for use in design. That analysis method can be used 2 dimensionally for 3 dimensionally.
But it's our simplest tool. Motor response spectrum analysis takes that same model or model perhaps. And does something different. We still consider the structure to behave linearly. So So you're using linear elastic analysis. But then we think about some dynamic response in a mortal sense. That method can only be done 3 dimensionally. So we can't use 2 dimensional, characterizations. Of our structure to use this method. The next step up would be to use linear response history analysis where we actually select suites of ground motions.
The idea is that we're trying to even better understand the dynamic response. So instead of characterizing the demands with a simple response spectrum. We actually think about specific crown motions. It's still a linear analysis though and it's 3 dimensional. And sort of the greatest tool, strongest tool at our disposal for. Practical structural engineering is nonlinear response history analysis method. So that method uses ground notions to characterize demands. And considers the inelastic response of a building.
So nonlinear modeling, again, this is a 3 dimensional. Method. To understand the ideas here, we want to remember the reality that we're just trying to quantify. We're trying to take a mathematical look at some realities. And the reality is that earthquakes are always dynamic. The response is always dynamic. Our approach to design in the US and in most countries. Uses our factors or some other similar method. To say that, effectively we can't afford to design everything to remain. Perfectly linearly elastic. For the greatest magnitude of earthquake that could possibly occur. Instead, we accept societally and then professionally. That we could have some inelastic performance, some inelastic behavior. As long as we don't have collapse and as long as we don't have too great an impact on life safety.
Perhaps we think about. Level of damage as well. But we use a shorthand method to get there. Instead of, you know, typical designs instead of using explicit nonlinear characterizations. We use our factors for systems that have been qualified. For a certain degree of inelastic response. We know that not many response history analysis is always permitted. It probably gives us the best shot at understanding the true nonlinear dynamic behavior. But it's not practical in 2023 to use that method for every building design. Now you could expect.
The linear dynamic methods. Are better than the equivalent lateral force procedure. Because they're more complex, they include a explicit characterization of the dynamic response. Of the building. But in fact, that proves not to be true. It's possible in fact, and you notice what the, NERP provisions, 2020 report says that the ELF provides more consistent stories, shear, overturning moment, and story drift results than mobile response back from analysis. So, when you compare the gold standard, let's say a nonlinear response history analysis. Story forces and overturning moments and drifts. To mobile response spectrum analysis and then you compare it to the ELF.
The ELF envelope results. Probably do a better job of capturing that nonlinear response. And so that means that in ASC, 7 22, a change was made. That allows the equivalent lateral force procedure without limitations. For structures that don't have seismic isolation or damping systems. And where there are those other systems there are some limitations but ELF is still permitted. The caveat here is This study and other studies do find that ELF to be conservative. But you probably could somehow dream up a building where mobile response back from analysis. Good idea, and so, there's just that caveat kinda hanging out there.
We're not suggesting that you stop using mobile response vector analysis. But know that it is less conservative than ELA. So irregularity requirements that were changed in ASC, 7 22. Based on the findings of the project that we're discussing today. The weight or master regularity was removed. It's no longer in a regularity as defined in the code. And ELF is permitted for systems with torsional irregularity. Since we studied that very carefully and we found that the ELF designs behave at least as well as the mobile response background analysis designs. And so the consequence that was in the code previously requiring that you use mobile analysis. Was counterproductive. So we, took away that. Prohibition. The building size and safety council PUC issue team 3, which develops.
The Nerd recommended provisions which feed into ASC 7. They did some of their own studies in parallel with what we were doing on our study. And they found that EOF could be permitted for systems with a soft story or vertical geometrical regularity. So the prohibitions on the left will remove there as well. Primarily due to the conservatism of the ELF method.
So now let's talk about the significance of the modeling requirements that you do find in ASC, 700, and 22. There's a reason that each of those requirements exist. Frankly, there's a reason that each word in each of those requirements exists. We're not gonna read it together carefully word by word. But we will draw your attention to some important considerations. We do have to think about story displacements and drifts. We need to identify design forces for members. That's just part of our design process. And that means that we don't just build buildings and then.
Put them on a shake table and test them. The reality is that we need some mathematical models in order to understand what we can anticipate. We already mentioned that the most accurate analytical model would be 3 dimensional. It would include all the sources of stiffness in both the structure and the foundation system. It would include p delta effects. It will allow nonlinear in elastic behavior. In the entire system.
So that you could best to the best of our knowledge today identify exactly how this would perform for a given ground motion and then maybe consider in a very wide range of ground motions. But the reality is that, we have to design not just one building in our career, but we need to be able to design many. And as a society, we need to be able to. Accommodate construction and growth, but do so safely. And so there are some simplifications that we can make. We'll talk about those as we go. So there's a requirement, ASC. You have to think about the spatial distribution of mass and stiffness.
Now this is true whether you're thinking about it horizontally and plan on the left side of the page. You do need to think about where the center of mass is. You need to think about the resistance. You need to think about the flexibility of the system and then also vertically in elevation. So for instance, you see that you have to think about where masses are greater at one story than others.
Maybe where stories are taller. Where the system changes so it's not in uniform. Perhaps there's weaknesses introduced because of the reality of having door openings or something like that. But the code requires that we our mathematical model has to consider these aspects. Of the configuration. Another aspect of that that you I hope are familiar with if you're a structural engineer. It is still common practice that we may have. Models, mathematical models of our building. Where the lateral response of that. Building is assessed separately from the gravity response of the building.
And if that's the case. We need to make sure that we have an appropriate characterization. Of the gravity effects as they impact lateral system. So this is the classic P Delta effect. You see a frame at the top. And then if you wanted to analyze that frame only using the lateral elements, which are shown in red. You would need to consider. How the rest of the system leans on that, lateral system. So that as the building leans over. And there's a gravity, the total gravity effect, let's call it P. And it acts through a displacement delta that tends to soften the building. It's a geometric. Reduction in the stiffness of the building. If you ignore that, your results are unconservative and you can have.
Problems with behavior. So this is one that you probably have heard about. Maybe you consider it carefully in your designs already. A related issue. Can be called the P theta effect. And in this image, imagine that this building. Has not transformed translated laterally. But it has some torsional response and of course buildings have real torsional response to the to the way that earthquake motions hit the building. So even if the center of mass of the building hasn't moved. In plan. The perimeter of the building. And the loads, the gravity loads at the parameter. Are being displaced. And that can cause the twist to be amplified.
So that's a PP effect, a gravity effect on the system. Going through an angle theta. And that's the name of this. So that's the idea that we can get lateral twisting response. Out of a system even if it didn't. Move translationally. Another aspect of the distribution of mass and stiffness and perhaps of forces. Is the idea of a gravity induced, so I will say that the project, the P 2012 project suggested that a change be made to ASE.
22 to specifically identify this issue. The A/C 7 committee chose not to make that change. I will see if they make it in 2028. But the, idea embodied in this. Is related to the distribution of mass and stiffness and of loads. So in the cartoon, you see the idea that if we have a bunch of columns at one story that all slope in the same direction. When you apply the gravity loads on the structure above. You get a net shear in that story. And that shear is exists whether there's an earthquake. Or not whether the wind is blowing or not. There's a preference a preferred direction of move mode movement in this building. And it's already under a lateral load.
Even when nothing else is happening. And we find that it's important to consider that effect. Because on the one hand you could say that it uses up some of the lateral capacity of your system. It also would tend to make the system want to move in a preferred direction. And so that's a, an important issue of distribution of mass and stiffness.
Aseu 7 22 identifies where 3 dimensional analysis is required and the big idea is if in plan you could get coupling in the 2 directions, then you need to consider a 3D analysis or else you'll miss that coupling. So that's true for torsional systems. I have a plane offsets and non-parallel systems. There are detailed requirements related to diaphragm modeling. Asc, 7, 22, the big idea is the first bullet. The structural analysis shall consider the relative stiffnesses of diaphragms and the vertical elements of the sizing, So we can't think about the vertical elements in isolation. We need to think about how the diaphragms. Tie them together and how those various differences interact. But we mentioned before that although structural analysis and seismic response may be a complex problem. There are ways that we can simplify it at times.
So there are some rules that you can apply. Without supporting calculations to decide that the diaphragm is. Flexible, infinitely flexible. And so load should be distributed on a tributary area basis. There are some other rules that say you can consider this diaphragm to be rigid without any calculations. Infinitely rigid for the sake of your design. You also could do some calculations of the diaphragm condition to understand whether it seems relatively rigid.
The code identifies that. If you can't put it into one of these categories. You have to actually consider the diagram stiffness explicitly because it has an impact on the way that the system performs. So some examples of that. If we've got part of one level has effectively a rigid diaphragm and another part of that same level has a flexible diaphragm. There's no simple mathematical way to describe those. Differences and we would need to think about the. Actual stiffness of the diaphragm explicitly. If you have very large openings in a diaphragm, it can lead to diaphragm performance that could be mischaracterized. If you treated it as rigid. Where you have out of plane offsets. As you see in the bottom left, the diaphragm at that level where the wall above and the wall below.
Connect to the same diaphragm, that diaphragm is subject to greatly increased forces. And so you need to understand the stiffness and strength of the diaphragm to characterize the problem correctly. And then if you have what the code identifies as a re-ent corner. Condition where it's got some triggers. It doesn't have to be just a tiny corner but If it's big enough that you end up with wings of a building that could behave. Dynamically independently of one another. You'd need to think about the diagram stiffness. And where you have a non-parallel system, you're counting on the diaphragm to get the 3 dimensional behavior to work. And so you need to think about that. Diaphragm stiffness as it relates.
So then for dynamic analysis. I mentioned before that the prohibition of ELF was removed. Because we find that more conservative. ELF analysis actually produces results that are more consistent with the True dynamic inelastic response, then the model method would suggest. And so we're allowed without limitation to use ELF. Unless we have seismic isolation or damping systems and those systems allow ELF with some additional requirements.
I again note the caveat although mobile response spectrum analysis. Is generally less conservative than ELF. It may be possible that there's some strange a distribution and so the commentary cheats a little bit and says You may still need to think about that mobile response. Because earthquakes happen not just in one direction or 2 directions, they happen across. All directions, it's important to think about those 2 directions or multiple directions. Again, the basic statement is that you have to think about an earthquake coming from any direction. But we've got some simple methods to get us there. If we're doing ground motions we use 2 dimensional ground motions that's automatic if we're doing other linear methods like ELF and modal response vector analysis. We have some, rules that allow us to combine the 2 directions. The idea is, well, first.
Although earthquakes happen in all directions for all earthquakes. For lower sized design categories, the consequences are not so great. And for size and signing category B, you're allowed to still consider the systems independently in the 2 directions. For higher size and design categories. If the SISS, VITAL system elements are intersecting so they get loaded from both directions. We need to think about that.
So for instance, orthogonal directional combinations are required in ASC. 7 22 if we've got torsional regularities or non-parallel system irregularity. It's also important that we think about where the displacements might happen. If we have a twisting building. The displacement of the perimeter of the building is not the same as the displacement at the middle of the building. If there's not much twist in the system, it's probably okay to think about story dress.
Just at the center of mass. But where there's great twisting. There could be greater deformation demands and you'd need to understand that to make sure that your system is proportioned properly. And so, we'd have to think about the drift at the perimeter. There is, an interesting finding from the project. We found that using one method that you might think is, is precise, would help. It makes the problem worse. The big idea with accidental, is that we can't predict perfectly how our system is laid out. So there could be some twisting in a system that is nominally doubly symmetric, it could still twist. And so the long used code rule is that we need to consider a 5% offset. Of the lateral force from the center of mass.
You could do that explicitly in a mobile analysis by moving the mass around and performing additional mobile response spectrum analyses. That sounds like it's more precise. But in fact, what we find and it wasn't just this project, past products have founded as well. That you can actually for some highly irregular torsional towards my sensitive systems. That method can actually de-amplify the torsional demand. And produce collapse potential. So there are some limits that you say you actually have to use a static characterization. In some instances. And I won't go through all the detailed modeling requirements for nonlinear response history analysis. They're in chapter 16. But for time we'll We'll move on to our next poll question.
Great. So our next poll. Is which linear analysis method produces story shears, overturning moments, and story drifts that are more consistent with anticipated nonlinear dynamic response at the design earthquake level. And I'll tell you, Mike, this has been a popular. Topic in the QA so far. Okay. Okay, looks like almost half of those, half of the people in the audience have already voted. I will give everyone a few more.
Seconds to consider their responses and get them in. Alright, looks like they're starting to level off. So Mike, I'm gonna go ahead and close the poll. I'm sharing the results so everyone can see it and up 2 thirds of Those in the audience voted for the equivalent lateral force procedure. And a third voted for modal response spectrum analysis.
Yes. And so it may fly in the face of your past expectations, but ELF. Produces results that are more consistent with the envelope demands from a non-linear dynamic analysis. So I mean, on one hand, I guess you could say that the framers of that method who developed it initially. Did a good job when they were trying to do some enveloping. And perhaps, we fool ourselves by doing more complicated analysis with more response spectrum analysis. Thinking that the answers were more. Accurate and that's not necessarily the case. The reason being in part Moller response spectrum analysis is still linear. And when you have an art factor of 5 or 8. The response is definitely not linear. And so the strength matters a lot in a way that, the method can't pick up. So, does a better job of characterizing the results. It doesn't mean you can't use mobile response spectrum analysis.
It does give you some insights into the dynamic performance of a building. But the, procedure is both more conservative and generally. Better matches the envelope of results from non-linear analysis. Alright, thanks, Mike. I'll go ahead and close the poll. Great. So now we'll move on to. Some horizontal regularity design examples. And I will tell you that there are 5. Detailed step by step design example handiles.
We're not going to go step by step through them, but I hope you will find them useful in your practice. So that you can better understand the specific requirements. In ASC 7 or other documents as you'll see. So that you can understand. How to do your work. So we're gonna talk about design examples. We're gonna walk through all of the horizontal regularities. In varying levels of sophistication and in each case we're gonna try to understand what the trigger is why we're concerned and how to mitigate it.
So this table summarizes the requirements related to horizontal irregularity in ASE, 7, 12. Oh, it identifies the the metrics that we have, how do we quantify it? And then as a result of quantifying it. What do we do for the analysis? What could we do for design and what did we do for detail? So our first irregularity is a torsional stiffness irregularity. The method is unchanged in essence. From what has been in previous editions of A/C 7 that we apply a static force.
We compute how much twist there is in the building. Asc 7 22 defines a new term. So instead of carrying around Delta max over Delta average. We've defined that itself as a torsional regularity ratio. And that TIR is compared to various. Triggers that allow the provide for additional requirements whether you're greater than 1.2 or 1.4 or 1.6. Indicating that you're more and more irregular, torsionally. The reason that we're concerned about torsional response here. Is that we could get collapse potential at the perimeter because there's so much twisting. And the 3 dimensional orthogonal effects are significant.
And if we ignore those effects, we'll have a port design. What can we do to fix the problem if we identify it? Well, first we need to make sure we have the right kind of analysis method to find the problem. We need to make sure that we're checking the drift at the perimeter of the building. We need to amplify those torsional responses. Make sure that our design our design. Which is remember within our factor are greater than one. That means the problems could get worse as it deforms inelastically. So let's amplify the results. Maybe we need to have places where the collectors and diaphragms. Need to have greater strength in order not to perform badly.
We also have, a redundancy factor in our document ASC 7. And there are places where the twisting performance is so severe that we need to think about using that redundancy factor. And of course we can mitigate this by reprocessing our lateral system. Within the bounds of what works for the building program, let's say. Tortial strength of regularity is a new one to ASC 7 22. The definition of this is if 75% or more of the strength.
In one direction is on or to one side of the center of mass. When the system behaves inelastically, you could get an unanticipated twisting in the system. And that could again lead to a collapse problem. Hey, it again is an issue where. 3 dimensional orthogonal effects matter. So you've got to have the right kind of analysis to find it. Think about the performance of the perimeter and then amplify loads as you need in order to come up with a safe design. So this is our first detail design example. I think it's 4 or 5 pages in the in the handout. We're just gonna go over a summary of the results. This is a 5 story steel moment frame building. In a high seismic area. You see in elevation, the layout of the system.
And then in plan you see the layout of the system. You'll notice that the lateral system is offset. In the building so it's not the center of the lairal system is not at the center of the building. So there is in the y direction up down on the page there is eccentricity which you should expect could cause twisting. In the x direction, there is no access, so you wouldn't expect to see twisting there. So in the design example, we go through and we. Calculate the torsional regularity ratio.
It's worth noting that We're looking for problems a story at a time. And so we're characterizing this TIR based on story drift. Not on the displacement of the building. And so we go through in the example. And we identify the we have we apply static loads. And we include after accidental, either positive or negative. We have to consider both of those. Because there's some inherent in the negative direction applying the accidental, in the same sense. Is a, is the more, is, is the worst consideration. So in X direction, we see that things are regular.
But in the y direction. When we have a counterclockwise accidental, that amplifies along with the. Inherent, and we see that we have irregularity in the top 4 stories of the building. With the worst regularity being. In the third story. Because we have an irregularity, we have to do some amplification of the accidental version. When we do this calculation, it's based on story displacements, not story drifts.
And the idea here is that if you get twisting. In an upper story of the bill. If the upper story twists. That twist carries down. And so you'll notice in this case that The third story. Had the worst performance expected. The system's above it. Go on, go along for the ride and they twist as well. And so they get amplification. Factors, even though those stories aren't as bad. So then when we find this irregularity in the design example, what we had to do nonlinear to related to three-dimensional analysis, we have to do orthogonal combinations.
We have to amplify the torsion in one direction and the other direction it's regular and torsion does not need to be amplified. We do have to think about drifts up the perimeter of the building. Because the, the, the, regularity ratio is greater than 1.4. We have to consider the redundancy factor in the Y direction. But not in the extra direction because it's not irregular in that direction. When we have this type of irregularity, it triggers some increased. Design forces for collectors and diaphragms and so those are invoked as well. So that detailed example is for the torsional stiffness or regularity. Let's go on to the.
Strength the regularity. We're not gonna have a detailed example here. The idea is if more than 75% of the strength in one direction is app or on one side of the center of mass. There's a twisting potential when the system performs. Inelastically. So you see that in in all of these cases the top left case. There's, it's a U-shaped system. All the resistance is on one side of the building for the left right direction. And so we would expect that we could get some twisting if we get yielding. In the bottom case.
All of the resistances at the center of the building in the left right direction. So again, when the real Chrome motion that it's experiencing is not perfectly concentric. We could get twisting that we would not have anticipated. So these would be irregular and we'd have to think about the requirements as outlined in ASC, 7 22. Moving on to the out of plane offset irregularity. This is something that you know it when you see it so you have to look at your system.
When you know that you have a system where the vertical elements from a story above do not align with the vertical elements in the story below You have this irregularity. Concern is that we could get a greater collapse potential because of demands in the diaphragm. How do we fix it? Well, first we need to understand the problem well, so we have to use 3 dimensional analysis. We need to think about stiffness of the diaphragm explicitly. And then there are requirements to amplify with overstream. Factors. The demands in those key. Transitions so that we don't precipitate collapse there. And that includes requirements for the. Diaphragms and connectors at that level. So the the requirements are that we amplify the demands in that diaphragm. And that we have collectors and drive structures, let's say that make the connections work.
The A/C, 7 22 clarifies this requirement because in the prior editions, if you found this condition at one story of a 20 story building. You would have amplified all of the diaphragm forces at every level. And of course that doesn't address the problem at hand. So A/C, 7 22 clarifies the scope that it's where the irregularity occurs.
Hey, Diafram forces have to be amplified. For the diaphragm discontinuity, regularity, consider a large opening, let's say, the concern is that we could get something that we didn't anticipate there. We wouldn't understand correctly the distribution of and we could get concentrations of demands. At the opening. How do we fix that? Well, we have to think about explicitly the diaphragm stiffness.
And then we need to increase in demand demands. Where necessary. The diaphragm discontinuity regularity. Also occurs where we've got flexible versus rigid systems and abrupt changes in the behavior. That we need to think about those. Diffnesses explicitly or we'll miss. The real issue. And then we've got. If we change the stiffness of the system. Say a very flexible system over a very stiff system. That could produce dynamic results that we would have missed. So we need to think about those explicitly. Similarly with the re if the behavior of this re-enter corner is all the action is in the diaphragm. We would miss that if we, model the diaphragm rigidly. We'd have to think about that.
Explicity in order to understand the problem. And then as a result, we probably end up with some collectors. And cords in the diaphragm to resolve those increased demands. The non parallel system really we mentioned before it's not a structural performance issue. We just have to use a 3 dimensional analysis to understand it and that really is the issue. And Mike, I'm just gonna jump in to say we have about 15 min left until we're planning to start the QA session. Okay, thank you. So we're gonna step into the vertical irregularity design examples.
And we'll need to focus a little more quickly on some things. The big idea again is there triggers in ASC 7 22. With resulting requirements for design and detailing. And other prohibitions for instance. In addition to the ASC, 7 22 configuration items that are addressed. There are configuration irregularities that actually occur in other documents. The Moment frame, we call them strong beam requirements actually occur. In the material standards, not in ASC 7. We mentioned that the wait irregularity was removed.
Wall discontinuities for concrete walls are addressed in ACI 3 18. Not an A. So. And we talked about how thinking about gravity and use lateral demands. That's something we need to do on our analysis. Or else the results are suspect. Before we can consider these vertical issues though, we need to get on the same page on how to calculate story stiffness and story strength. It sounds simple. Those words are simple words, perhaps. But there's a lot of, disparity in the way that people might think about those calculations. And ASC 7 doesn't entirely tell you how to calcula
2023-08-02