Loads: 4a. Seismic Loads

Okay so let's talk a little bit about seismic loads earthquakes uh let's start here in the middle on this sheet it says just like wind it is very important to make sure that the building stays together, it doesn't shear off in an earthquake, or that it bends too much, that it either overturns or it breaks on the tension side if it bent too much, or the stiffness. Stiffness is dictated by drift in the case of lateral forces, which is movement of one floor with respect to the other, or total over the overall height of the building, there is a limit specified in the code. And it's around L over 400 to L over 600, which is, let's say, an average of L over 500. Compared to deflection in gravity loads, L over 240, L over 360, this one is much more strict compared to gravitational deflection. And again, we need to be sure that the building does not overturn by securing, by calculating the anticipated overturning moment and increasing it by a certain factor of safety in the code and making sure that the stabilizing moment is significantly larger than the overturning moment. Then there is a matter of the diaphragm. The diaphragm wants to be symmetrical as much as possible in order to minimize torsion. Now, in a hurricane, the code says try to minimize damage and, of course, save lives. Now, in an earthquake, the code says nothing about damage. It's all about life safety because it's a much more stringent phenomenon. Very good. So here's some scales, the Richter magnitude scale. And probably I need to say here that the highest recorded one thus far has been a magnitude 9.5. It was in Chile in 1960. Okay, so there's acceleration, there's velocity, there's displacement, the ground is moving. And then there's shaking in addition to lateral translation. The duration of an earthquake is a significant factor also. Clearly, the longer the earthquake lasts, the more the shaking, the more the damage caused. Okay, so there's a magnitude measured by the Richter scale that is now defined as the moment magnitude scale replaced the Richter scale. And then there's an intensity scale, which is basically how did it feel? Take a look at this. Not that important on the ARE or what have you. It's just there's two scales. One is magnitude. It's a logarithmic scale. The other one is how did it feel? Very good. Important to understand is the quality of the soil underneath a building during an earthquake. So if we have, there is something called the building period versus the soil period. So hard rock vibrates very quickly. It has a short period of vibration versus slushy clay will take a long time, a longer time. So it's period, the time it takes from one position, then reverse is coming back to that same position. That is the building period. Careful down here, it says liquefiable soils. What is liquefiable soils? This is an important discussion for the ARE. When you have wet sand, that's when you get liquefaction. The ground starts shaking. The sand has a reasonable grain size, and so it packs, and it settles. And now you had friction with the soil in your foundation, and now that is gone, and you have water. And so the building might lean over and get out of plum, and then the building might crush the supports underneath it. So liquefaction. Very good. So we're trying to compare the building period to the soil period. A tall building will have a long period versus a short building. A concrete structure will have a shorter period than a comparable same number of floors, area, etc. Of a steel frame, steel will have a longer period of vibration. So the period of a building depends on its height, its weight, its ductility. Very good. We're going to talk about ductility in a minute. So the problem here is if you have resonance. And resonance is essentially if the period of the building is similar to the period of the soil shaking, then you will have resonance and the damage will be amplified or called amplification of damage. That happens when the periods are similar. I'm going to discuss this a little bit further on the next page. So there are ways of reducing the amount of vibration that goes from the ground up to the structure. And I have a little video I'm going to prepare on that. But basically, the ways to dampen the impact of an earthquake on a building are a reduced beam section. I'll talk about it. Bates isolation, fluid viscous dampers, tuned mass dampers. There's a lot more. It's just you're not studying to be an engineer. The whole earthquake thing is for engineers. It's not for architects, but you want to be able to understand the concept in order to speak with an engineer about certain things and understand what they're saying and why they're making the moves they are. Excellent. Very important here is the concept of ductility. Ductility is how well can you shake with the earthquake without breaking. Sounds like concrete is not very good. Sounds like steel is awesome. So there is a rating system that I will talk about in the next page, on the next page. But basically, a moment frame is very ductile. It'll dance with the earthquake. It'll vibrate like crazy. But everything on the inside is subject to damage. The water pipes, the ceiling tiles, all the electrical equipment. But the structure is good, and it's dancing with the earthquake, it's just the interiors are not doing too well. So that a moment frame is not a very good solution to a hospital because the cost of the structure in a hospital is minor compared to the HVAC system. So for example, if you have a server area or a server farm rather, well then the structure is less important than the servers in there. So we need to make sure that a moment frame may not be the best answer to that because it'll shake a lot and maybe things will fall on the servers. So going down the line, this is the most, this one is the most, where's purple, here's purple. This one is the most ductile. Ductility gets a symbol R because it represents the response modification coefficient R in an equation that we're going to see on the next page without any numbers, so don't panic. So this one has the most ductility, but because it has the most ductility, it has very low rigidity. So it's not going to get a lot of base shear. It's not fighting the earthquake. So the next step up is an eccentrically braced frame. This one has some ductility, but then it has pin connections. What happens with ductility is this guy is going to bend. Bending brings me ductility. This guy is going to bend. The vertical is going to bend. Everybody's bending without breaking. Bending is ductility. Bending, reverse bending, bending, reverse bending without breaking. Now, in an eccentrically braced frame, there is a link beam, this one. that is there in order to bend. And the longer that link beam is, the closer you are to moment frame and the more ductility you have. Versus a concentrically braced frame. A concentrically braced frame is going to be more rigid than an eccentrically braced frame that is more rigid than a moment frame. So a concentrically braced frame has pin connections everywhere and a diagonal going in between, and it's got less rigidity. Please notice the size of the R here. It's getting smaller as we travel this way versus the rigidity and the base shear is increasing towards the shear wall. So the next option is a shear wall, and a shear wall is very stiff, very rigid. It's going to attract a lot of base shear. It has low rigidity, if at all. So we're going to see a table on the next page that explains this stuff. But the greater ductility is the moment frame. The brace frame and the shear wall have very low ductility. The eccentrically brace frame has a link beam that provides some ductility. But the greater rigidity that results in a greater base shear is increasing in this direction. And the shear wall has a lot more rigidity and attracts a lot more base shear than a moment frame that doesn't have much rigidity and doesn't attract as much base shear. Another factor to consider, which is really architectural, which is important to us, is basically discontinuities and irregularities. The design of a building for seismic forces needs to be a simple building with, most importantly, a direct load path. Send the lateral load directly to the components without zigzag or coming down to the foundation without detours. So a simple rectangle, a simple square, something like that is very easy. Not very easy, but easier to handle than a funky shape. So it's important, please, to recognize that the code breaks down the irregularities into two categories, a plan irregularity and an elevational or vertical irregularity. We must be familiar with what these things are. so torsional irregularities I'm going to have a video on diaphragms and you'll understand that one but if there's a very stiff member on this side and less stiff on the other side as far as lateral system then this diaphragm is going to twist because it's not going to rotate much here and it it's a little bit looser on this side so it'll do that and then the earthquake reverses and it'll do that. So this one is going to rotate, but not as much as the rest. The other side is a lot looser. So torsional irregularities. The other one is re-entrant corners, these inside corners. This is not a problem, not a problem, not a problem, not a problem. This inside corner is a problem. And so the typical solution is to put a seismic joint. So to break it down into smaller buildings. Let me erase a little bit. To break it down into, sorry, not smaller, but independent wings or independent buildings. So in this case, we might put a seismic joint here, which would make this one block and this another block. And so they can vibrate independently. but of course we need something soft in between them, and that's what the seismic joint is providing. So we can break them down in different ways, but basically separate the wings so that they vibrate independent of each other. Very good. Another one is a discontinuous diaphragm where you have a big old opening in a diaphragm. That is a big irregularity that will cause a lot of problems here and here. Another one is out-of-plane offsets. Let's say this column is going down for nine floors and then on the ground floor, it used to be here, now it's here, it shifted. That is not a direct load path. Non-parallel offsets, same thing, it's a shape that is not regular, is going to twist. Therefore, these irregularities are going to cause torsion and some other things that are dangerous in an earthquake. Looking at vertical irregularities, we have the first one is a weight or a mass irregularity. Imagine you have a steel frame and then over there you put just on that one floor, you put a lot of masonry or something like that. So that becomes a weight or a mass irregularity. Geometric irregularities or setbacks, fine. You break it down into three blocks with a seismic joint. A soft story and a weak story have been asked on the ARE before and we need to know the difference. This one is about strength failure versus stiffness failure. So what does that mean? I have columns that are not going all the way down to the ground. You get an earthquake going this way. Well, then the block wants to go the other way. And that ground floor is not as strong as the other floors. It's taller and it has some discontinuities. Same thing happens with columns that don't continue down to the ground. The ground floor is different than the other floors. Earthquake is going to come here. The block wants to go that way. It's going to butcher these columns in no time. Another vertical discontinuity is discontinuous bracing. But when we look at a weak story or a discontinuous shear wall, imagine a massive concrete or CMU shear wall, and then you put a beam at the bottom in columns. This is not as strong. This one is about strength. This is very strong. This is very weak. The soft story may not collapse right away, but it'll tilt and it'll become out of plumb and then the mass will break it. And therefore, there is something called the P-delta effect. And that is when the building used to be here and it was a soft story. And then an earthquake came in and this thing shifted a little bit and the columns did that. And now this guy will crush that right away. That's the P-delta effect. Excellent. So we have these discontinuities and much like wind, there is building components that need to be designed independently, such as chimneys, mechanical parapets, suspended ceilings. These are secondary damage, secondary meaning non-structural. Very good. This is an overview of some of the issues that we might encounter in the design of buildings for earthquakes. But what I would like to do is spend a minute with this equation because it's extremely important. It says your base shear, the amount of force between the foundation and the building, base shear, sorry, between the soil and the foundation, depends entirely on dead load. So this is a factor. It's just a factor. How much percent of the dead load are we going to encounter based on our risk? Are we going to estimate based on our risk? Are we in a seismic zone? Do we have discontinuities? All these things go into factoring how much percent of dead load. Please notice we're not talking live load, just dead load, the weight of the structure plus permanent attachments. Okay, so let me go to my next sheet and let's detail this equation a little bit more. So the base shear is a certain factor, CS, or the spectral response acceleration. Sorry, the spectral response acceleration, CS, depends entirely. Sorry, the base shear depends entirely on the dead load. If you have a heavy building, that sounds like concrete. then you are going to attract a lot more base shear than if you had a steel frame. The base shear is directly proportional to the dead load. Very important to understand this relationship. Dead load in a hurricane is very good because the building will not overturn. But here, base shear depends entirely on dead load. so dead load in wind is in the stabilizing moment here it's on the attack the other one it's on the defense very good so greater dead load means greater base shear lighter buildings will attract less base shear very good that's the first thing now let's see what's in this cs factor it's a factor. It says there's a map of the United States in the code book and it says what's your seismic history? What's your seismic location? How much risk do you have? How near to a frequent source of earthquakes are you? So we see that there is three areas here. Area one is Charleston, South Carolina. There was an earthquake in 1886 with a magnitude of 7.0. That's it. You have a seismic history. Then there is New Madrid in Missouri. There was an earthquake in 1811, and the magnitude was 7.8. These are significant earthquakes above 7.0 Richter scale or moment magnitude scale. Then, of course, there was San Francisco, 1906, and the magnitude there was 8.3. Not on this map, which should have been on the map. I'm sorry, I didn't copy it. It's Alaska, 1964. That one was a 9.2 magnitude earthquake. It's the highest in the United States. This is the San Andreas Fault over here. It goes up to Alaska, it goes down to Chile and South America. And the Chilean engineers are top-notch as far as earthquakes because they've developed some excellent codes to prevent collapse and minimize casualties. Okay, so seismic history and seismic risk, that is going to increase the percentage of the dead load that you have to design for. That's the first thing. So I'm going to write them here. Seismic risk. Seismic risk. That's the first thing under that spectral response acceleration factor. Okay. The second thing is what used to be called, now it's changed, it used to be called the importance factor. And it is based on the building occupancy. Like we said, under wind, it's the same factor. Police station, fire station, et cetera, are more important than residential. So this is the old code, frankly. The equation is the same, but the current code combines these two and gives different maps for different occupancies. That's the only difference. So we need to understand big picture. Again, you are studying or you're practicing in architecture, not in engineering. So looking at the importance factor, the old importance factor, it said there's four categories. Category three, and it says it applies to seismic, to snow, and to wind. And you can see it's just basically adding 25% or 10% or 15% to the design based on seismic snow or wind. And based for the category, this category looks like it's nastier than the previous one. So let's look at category three. Here's a definition. Buildings and other structures that represent a substantial hazard to human life in the event of failure. And then it lists a bunch of them. They are places where people congregate in a disaster. Okay, take shelter. Category four says buildings and other structures designed as essential facilities. So hospitals, fire, rescue, designated earthquake, hurricane, emergency shelters. You're going to beef up your design for seismic by 50%, for snow by 20%, and for wind by 15%. I don't need you to remember any of the numbers. Just understand that these occupancies need to be designed to higher standards so that people don't suffer. And search and rescue can continue. So left with three is substantial hazard to human life. Four is essential facilities. Two is buildings and other structures, not in one, three, and four. Category one is low hazard to human life, agricultural facilities, etc. So four categories of importance. Importance factor, there is a category four. That one is essential facilities. There's a category three, substantial hazard to human life. There is a category one, agricultural, and then other, category two. Very good. Like I said, the current code, I'm talking about 2021, the 2021 IBC code publishes wind speed maps and seismic maps that give us the CS coefficient based on occupancy and seismic risk. Okay, number three, important. Number three says building has a period. The soil has a period. And it's basically how long does it take for this building to start in this location, swing one way, then swing the other way, then come back to the starting position. The time it takes in seconds is called period. and 1 over period is called frequency. How many oscillations did it do in one second? That is the frequency versus how many seconds did it take to complete one oscillation is the period. Very good. Let me erase this because I need to talk about this diagram a little bit differently. So soil also has a period and bedrock is going to vibrate very quickly versus with a short period versus clay might be a longer period and sand might be somewhere in the middle. So let's go in there and change colors. This one has a long period. This one has a short period. And looking at the buildings, a lower building, fewer number of floors versus a tall building. A tall building is going to have a long period versus lower rises will have a short period. Please, there's a lot of factors in here that affect the period of a building. It's a good rule of thumb to say every 10 floors has a period of one second, 20 floors, 2 seconds, 30 floors, 3 seconds. That's just a rule of thumb. Because it really depends. Is it made of concrete? Is it made of wood? Is it made of steel? And what is the lateral resisting system that we saw on the previous page? Is it a moment frame? Is it a brace frame? Is it a shear wall? All of that enters into the period. A shear wall is not going to vibrate, and it's not going to move as much as a moment frame. Very good. So this factor in the seismic response coefficient is basically addressing the fear of resonance. Resonance happens when the period of the soil is similar to the period of the building. So you get an earthquake going this way. This building is at rest. It wants to go the opposite way. Then there's some base shear. I want to go this way, the ground is moving this way, there is base shear. But it looks like this one doesn't have much of a dead load compared to the tall one. So a short period on a long period soil is probably going to avoid resonance because the periods are dissimilar. Clay has a long period and our building is short and is probably a steel frame that makes it, Sorry, and probably a concrete frame that makes it a short period. The problem comes in when you have similar periods. That causes resonance. So if I have a tall building on clay, that's nasty. If I have a short building on bedrock, that's nasty. A short building on clay is a short period building on a long period soil is okay. So resonance causes amplification of damage. Amplification of damage. So that is the danger of resonance. And when you look at the images and the video I'm going to prepare for earthquake, there is a demonstration of what resonance is. excellent so the fear here is base shear because it could for example this earthquake could take the basement with it because this force is greater than the inertia of the basement then we get base shear right here if we didn't make a good connection between the building and its basement wall then is vulnerable to shear right here. But this is where it's initiated. The ground is moving to the left. The building is at rest. It reacts by going to the right due to inertia. Okay, so let's put number three in here. Building versus soil period. Resonance. and amplification that we need to be careful of. Amplification. Okay. Number four. We talked about number four. It's right here. And it's the discontinuities and the need for a direct load path. Okay? Any indirect load path is going to jack up that percentage of the dead load, which is the base shear that we have to design for. So I'm just going to call it discontinuities and irregularities. Irregularities. And the objective here is to have a direct load path. That's what we aspire to, direct load path. Very good. Now, number five said my lateral systems, my vertical lateral systems are a moment frame, an eccentrically braced frame. This is a moment frame. This is an eccentrically braced frame. Let's say we take it up to here. This is an EBF. it has a link beam, this one. It's there to bend because this is very strong. The triangle is very strong. It's not going anywhere. But that beam there is there to bend. Bending gives me ductility. Then there is the next option is a concentrically braced frame. And this one is going concentric versus eccentric. So a concentrically braced frame. And then finally, a shear wall. So let's make this masonry, for example. So this one is going to have the greatest base shear for the same earthquake and the same properties of a building. This one's going to have the least base shear. But this one has the greatest ductility. This one has the least ductility, and it's in order. Now, this R factor, or the ductility factor, is basically from 1 to 8. It's just a number. 8 is very ductile, and 1 is not very ductile at all. So you might expect a shear wall to be here, a moment frame to be here. Very good. So there is a table in the code. Where is this table? Right here. Did I not copy it? It's right here. There is a table in the code that says, okay, based on the detailing of the structural frame, we're going to assign a certain, sorry, based on the detailing and the material, we're going to assign a certain coefficient for ductility. Okay? It's called the response modification coefficient. R is the response modification coefficient. I call it the ductility coefficient. Fine. Here is a high, the maximum is 8, a high ductility factor, which is a special steel moment-resisting frame. Special is the detailing level. Steel is much more ductile than concrete or wood. And then moment frame is more ductile than eccentrically braced or braced or sheer wall. Very good. So you get an 8. Who's next? Special. That means good detailing. Steel, truss, moment frame. Versus ordinary. Ordinary means that's it. The R value is going down. It is going to be reduced. Let's see. Is there a 1 here somewhere? 1 1⁄2. Who's 1 1⁄2? Ordinary. Not detailed for ductility. plain, masonry, sheer wall, everything is against it. So I think it's easier. I've come up with this other way of explaining this table because this is just one page out of five pages. So anyway, I thought this is an easier way of explaining it. Here is the detailing level. Here is the material. Here is the lateral force resisting system. If you are a moment frame, you're close to 8. If you're a shear wall, you're close to 1. If you are in steel, you're close to 8. If you are unreinforced, forget it. That's the plain value. It's going down, way down. Unreinforced, terrible in an earthquake. Reinforced is good. Reinforced concrete, detailed for ductility with special. Reinforced concrete moment frame will go up to an eight. Reinforced masonry is a little bit less ductile than reinforced concrete, depending on where you place your rebars. There's more restrictions with masonry. In reinforced concrete, the formwork is open. You can put the rebar wherever you want to get more ductility. So detailing is one of the spinners. The material is the other spinner. And the lateral force system is the third spinner. We have special detailing versus ordinary. Intermediate is in the middle. Steel versus unreinforced concrete. And then moment frame, eccentrically braced, and concentrically braced, and finally shear wall. So the highest you can get is a value of 8. So that is going to reduce the amount of base shear you have to design for. Okay, I'm going to stop here and then prepare the video.