CS_F2012_12

It wasn't, it's not really relevant to the course. It's true, but it's not really relevant. Okay so we've talked a couple of times about this ASTM A106, and I finally have the sample to discuss some of the hydrostatic testing, not for the one that occurred at the oil refinery where they bought six hundred lengths of pipe. But if you remember, ASTM A106 for a piece of pipe allows hydrostatic testing okay. You can just pressurize the pipe with water to fifty, sixty, seventy percent of the yield strength of the material. That doesn't burst open, it's good. And that's actually called proof testing. And if you do it on every piece of pipe, which they do according to ASTM A106, you have to do it according to the standard unless you say as the purchaser you don't want it, and then they have to mark it that it hasn't been done okay. Well, most of the pipe gets done.

And so the alternative to hydrostatic testing is the standard approach. You can specify the pressure you want, and typically you might specify a pressure that's 25 or 50 percent above your expected operating pressure. So if you're going to operate it at a thousand psi of whatever it is, gas, oil, whatever, you might test it at 1,500 psi. And so if it survives 1,500 psi, it's unlikely that it's going to fail at a thousand psi, right? Because it took, you over-stressed at fifty percent. And if you go through fracture mechanics, a fifty percent over-stress is basically, it's used kind of square that, and it's about a factor of two of safety in terms of those, who goes as a square root of the crack length. So if there is a flaw there, you should have detected the flaw within a factor of two of stress, not stressed but of safety factor so far as that goes.

Anyway, this is a story about a pipe. This pipe that went through an American steel mill. It's a seamless pipe, so it could have been sold under ASTM A106. I don't remember if it was or not. It could have been sold as an API pipe because they have standards for pipe. In fact, I think it was sold as an API pipe. Fact, I now as I think about it, I know it was. But it's actually the same pipe, comes out of the same mill, could be they make it the same way, but it's just a question of which standard they measure it to. And the standards are uniform enough between API and ASTM that the mill basically, whatever they got out there in the yard, it will probably meet both specs, and so they can sell it to either one. And sometimes people say they wanted to meet both specs, if you want to pay extra okay.

In any case, what they do, they have the mill, this is seamless pipe, and so they basically take a big piece of steel that they made and they heat it up to about 2,200 degrees Fahrenheit. It melts at 25, 2,600, so it's really getting not quite white hot but very yellow. And they basically take a cold mandrel and they just push it right through there. It's pretty interesting to see. The mandrel is about 60 feet long, and you end up making a piece of pipe that eventually, after you cut off the ends and throw them away, is about a 40-foot length of pipe okay. And you can get pipe — this was I think six inch or 8 inch in diameter or something. You can get them 20, 30 inches — well, probably 20 inches probably the largest for a seamless pipe. If you start getting much above 10 inches, it becomes cheaper to roll it and weld it okay, make welded pipe.

In any case, to test it, they go in and they grab it with these automatic jaws at each end. They fill it with water first, and they actually do both the non-destructive electric test and the hydro test on all these pipes. It's just easier to manufacture that way. They fill it up, and except for the last 18 inches where they grab it, they have an automatic ultrasonic test. So you know, there's no one, even — I mean there has to be an operator to set it up, but it's basically just automated. And they do an ultrasonic test through the water to see if there's any defect in the pipe. Since they couldn't measure the last 18 inches of pipe, they have a bunch of lowly paid, most of them people can't speak English as a first language, employees that are doing magnetic particle testing by hand, where you've got basically got an ultraviolet light, and you magnetize the pipe by putting some electric current through it. If there's a flaw or defect, it'll have a magnetic anomaly, and you put some magnetized iron oxide powder, magnetite, in there, and see, it fluoresces in the black light, and you see if you have a flaw. And so these guys have these little, actually they're just plastic tubes that have some of the powder on there, and they pour some in there and they look in there with their light, and they do all this for, they look for a second a half okay, but they're used to doing this all day. It's pretty boring work, it's not automated, and sometimes people will miss something okay. But they're checking the last 18 inches of pipe.

Student: [inaudible question about magnafluxing]

Great. Oh no, magnaflux, they magnaflux the outside. They also magnaflux the inside. The outside is easy to magnaflux.

Student: [inaudible follow-up]

Oh, you're right. Through the thickness there can be flaws, but they're going to later hydrostatic test this and see. Keeps on going down the line, and they do a hydrostatic test at whatever the pressure they want to do. But still the ends are kind of the problem, because even in the hydrostatic test you have to grab it by the ends and make the seal. Now sometimes people will cut off the ends, but most of the time they don't after they've done all this testing. Sometimes the problems occur at the end, and this oil refinery, the pipe that had the leak, it was on the leak they found was on the end. Because all this other testing — you've got a stress test, the hydrostatic test, you got magnetic particle on the end, you got ultrasonic in the middle — all this testing has a high probability of finding something, but the probability is never one. There's always something that might get through. So out of these 600 pipes at this oil refinery they were building, they found one pipe and they condemned all the rest, all the 599 brothers and sisters, and they said we want our money back okay, which was not the appropriate way to handle that problem.

But this other pipe, this one got through the mill, and it went through — first of all, they took off all the identification okay, because they wanted to coat it. This was going to be buried in the Gulf of Mexico, so they coated it for corrosion resistance, and to do that they had to sandblast it and apply this epoxy paint and stuff coating on the outside. Then they buried it in the Gulf of Mexico. This was going to be a pipe to bring the oil from a production platform onshore, so they didn't have to have ships shuttling back and forth full of oil right. And when they pressure tested it when it was in service, they were actually pressure testing like 3,400 psi rather than the 3,500 that they had done at the mill. Well, it turns out it started to leak. And now the problem is, it costs a lot more to repair it when it's down buried a couple hundred feet in the Gulf of Mexico, or a couple of thousand feet in the Gulf of Mexico. So in which case it might have been cheaper just to abandon the whole pipeline that you just built at a cost of fifty million dollars or something. This one only cost five million dollars to recover the pipe and replace it after it had already been buried in the ground okay. So people weren't happy and they sued each other and whatnot.

Anyway, when they got it up, here's the defect, I'll pass it around. [Tom passes around the pipe defect sample.] You can see this gouge in here. And if you look at it and think about it, how could you form something like that? Well, what happened is, the mandrel, the steel mandrel that pushed to make the tube, probably had a fatigue crack on the end, and a piece broke off inside this thing as it's piercing it, and just rolled that piece of cold steel into the hot steel. And in fact, we confirmed that. We cut out a little section, did some metallography, found it was decarburized on the surface okay, which means it had to have been hot at some point in its life. And the only time it would've been hot at some point in its life, the last time it would have been hot, was when it was being pierced. And that was, you get decarburization at high temperatures because you're burning the carbon out of the steel. And so we knew it was a steel defect.

However, that actually goes through more than eighty percent through the wall, and some people said it couldn't have been there present at the steel mill, because how could it support the stress? Because 3,500 psi was like 50 or 60 percent of the maximum capability of that pipe. Well, it turns out it's not oriented in the proper orientation okay. It's not infinitely long. The calculation these people were doing assumes that you have an infinitely long axial, perfectly axial crack. If you actually do a finite element analysis on that flaw, you'd find that it would take right around 3,500 psi to fracture it okay. So a more sophisticated stress analysis says it was right on the edge. If it'd been a little bit, you know, a little bit bigger defect, the hydrostatic test would have found it at the mill, it never would have been shipped. If it had been a little bit smaller, it'd be in service in the Gulf of Mexico today. It just happened to be just the right size to fail at just the wrong time in the second hydro test okay.

So in any case, however, the company that had manufactured it is doing everything to say, well, it's not our pipe, you can't prove it's our pipe. You eliminated all the identification on the pipe when you coated it down in Houston okay. You took off all our markings. If it was our pipe, and you can't prove it's our pipe — a piece of steel's a piece of steel, no one can tell the difference. Well, not exactly as they say it. It turns out even in carbon steel, there are probably about 10 different elements that are markers. What are the elements in steel? Carbon, manganese, iron is probably not the easiest one to tell the difference because there's a lot of iron in all steel okay. Carbon, manganese, silicon, sulfur, phosphorus, which are impurities. There might be some residual nickel or copper. It's a whole bunch of things, probably eight or ten. And so what we did there is — it's amazing if you go looking.

And now that we have, I mean, I had these, actually, this is a 1984 issue from the American Iron and Steel Institute. [Tom holds up the AISI report.] Not that you need to read this, but it started out in September '74, and in 1984 they updated it. "The variation of product analysis and tensile properties, carbon steel plates and wide flange shapes." Well, this wasn't a plate or wide flange shape, but it is carbon steel, and product analysis is how much variation you have in different things like the carbon content. So the steel companies looking at different levels of carbon, different thicknesses of product, hundreds and thousands of tests, looked at the statistics, here's the standard deviation, and it's point one five percent carbon plus or minus five to seven thousandths okay on the carbon. So there's a distribution for the carbon content.

And so if you look at that Gaussian distribution for carbon, and you look at another one for manganese, another one for phosphorus and sulfur and silicon on the next page, and keep on going — and we didn't just use this one source — but the steel composition is actually a fingerprint. And we knew what the heat analysis was at the steel mill, as reported by the steel mill, for this amount of pipe they purchased. And we compared that, and we showed that within one chance in a hundred million, this had been made at this plant okay and conformed to this heat that had been purchased by the oil company from the steel company. So that argument kind of went away. When you start getting down to statistics of one in a hundred million, most people say that's pretty good insurance that it really was the same piece of pipe.

But then we got into the argument of how could it have passed the hydro test and everything else? Well, it passes the hydro test because it was just the right size. This was the mama bear crack or defect okay. If it had been a daddy bear or papa bear, baby bear, it would have been okay. So that's just sort of another case study of hydro testing and what can go wrong and what can go right. You never have one hundred percent assurance on anything. When you're manufacturing, you try to do the best you can, but there's still going to be mistakes that get through.

So let me spend a little bit of time just talking about safety factors. Dr. Belmar has been talking about it, but I wanted to kind of go over some of the typical types of safety factors and where they come from. If we look at structural welding code AWS D1.1, which is bridges and buildings, turns out for buildings the safety factor's 1.67. That's historical safety factor. People found for statically loaded steel structures 1.67 is a good number okay. For bridges, it's a different chapter in the code because the bridges are fatigue loaded, it's 2.0. And we mentioned the other day, when Dr. Belmar at the end of Dr. Belmar's lecture, he put up this stress-strain curve for fatigue. This is stress versus log of cycles, and you come down like this. When you get to about fifty percent of your yield stress, essentially the fatigue life in steel goes out, and we call the fatigue limit, and the life is infinite in fatigue. And that's why if you have a 2.0 safety factor and you never go to more than half of your allowable stress, or not your allowable stress but your capacity stress, your yield strength, you shouldn't get fatigue cracks, all other things being equal.

Turns out for welds, most welds the safety factor is 3.3, and that's again it's historical. But people, again you're going to produce defects in welds, you're going to have, welds are located at the most highly stressed locations, the corners, they create notches, toe of the weld, and things like that. And people just found that safety factor on the weld is usually sufficient that you won't get failures of the weld okay, unless you have really big defects in the welds. So this is experience. This one you actually can look at some scientific stress-strain curve, and this is sort of experience, and that's where they come from.

Now the problem with these buildings, and I think I mentioned it briefly before, that's what the code says. And you remember Dr. Belmar was talking about the tongue on his trailer, and he said he wanted to make it 15 feet long rather than 12 foot long beam, but he wanted to keep the weight way down. So he actually shaved it down and made it a smaller beam in the last 3 feet and take some weight out of it. He also mentioned, just in passing, he put a doubler plate back where the beam is welded to the crossbar okay. That's 'cause you need more stress there. He had more stress there. That stress concentration where the beam connects to the crossbar, you have higher stress. It's the maximum bending moment. And so you put a doubler plate on top and you strengthen it there.

Well, back in the early to mid '80s, the people who made prefabricated buildings decided that computers were getting good enough that these civil engineers could design beams and put doubler plates on beams. So if they got a roof joist, and a roof joist looks something like this, and it has stiffeners in between like this, that you actually need a lot, out here where you have your maximum bending moments you need more thickness here than you do out here at the ends where it's right on a support. In fact, you can tell you don't need the same thickness — this is where it's going to be supported on some column, and you don't even have to have the big depth that you get for the stiffness of these supports out here when you're right next to the thing. The big bending moments right in the middle. If you put weight on this, you'd see it sagging most in the middle, but that's where you need an extra metal there. You don't need as much metal here. But for years we've just been making beams uniform thickness and length because that's the way they come off the rolling mill. And even when they built these beams up, that's the way they did it. But with automated cutting technology, we could cut all kinds of shapes in the computer without a lot of labor. With improved welding procedures, we could weld it together, and they decided they could start designing these beams for minimum weight and meet the 1.67 safety factor.

So the real safety factor in the past was not really 1.67 that we developed our experience on. In most cases it was more like a 2.0 safety factor even for buildings, because we're always using more material than we really needed to. But these guys decided, okay, we're going to be able to calculate exactly how much steel we need and we'll put it where we want, and we can get thirty percent of the weight out of these things. And that's a huge profit to get a lot of your steel out of that. So that's what they started doing. Now the problem with computers in the mid-'80s, you know, an IBM PC might have a twenty megabyte hard drive, you know, it was this big right? Now we talked about, you know, a terabyte. The cost, I just want, bought a terabyte for 100 bucks right? But I remember my original 10 megabyte hard drive on, in the late '70s, it was this big around okay, 10 megabytes. This is a DEC, Digital Equipment, PDP-11/23. So things had improved quite a bit, but by the mid-'80s they still couldn't, didn't have enough capacity to do things that weren't symmetric. So they designed everything as if the building was perfectly erected.

And everything was fine until the big snowstorm of 1988 I think it was okay. '79 was here. This one, they had a huge snowstorm, it was the storm of the century, and it came right up through Princeton, New Jersey and stuff. And it just, buildings were collapsing all over New Jersey and eastern Pennsylvania okay, because they had bigger snow loads than they were used to having. Now so far as the snow loads had been built up from historical experience, in one little township might have a 28 pound per square foot snow load, another one might have 35. It depends on how much snow they got in their local region. And so those standards are actually by township almost okay, what the snow load is. And then people start getting in arguments about, well we exceeded the snow load, oh no we didn't, you know. But what it really turned out in a lot of cases is these things had been designed to 1.67, which was what the code said. But the code had been built up at a time when you couldn't do all this optimization, and the real standard was actually significantly greater than 1.67. So today with computer technology instead, water, but has also shaved the safety factors down to the bare minimum. In many cases the bare minimum that was built up, where it was just sort of a guideline before, and we always exceeded it like twenty, thirty percent. And so what's happened is we've been shaving the guideline all along.

What happened with AWS D1.2, which is the aluminum code, it turns out the metallurgy of aluminum is much more complex, and they have heat treated alloys. Steel has heat treated alloys, but mostly we're not heat treating fancy steels for structures. But the aluminum structural welding code has safety factors of 2 to 4 depending on the alloy. You'll have a different safety factor in the code. And that's why that Aluminum Design Manual, like someone asked me one day, and I had just happened to have the old 1997 AWS D1.2 and I had the smaller 2003 version. But in between there was the 2000 Aluminum Design Manual okay, and it's that thick. [Tom indicates thickness.] Well, what happened is, because of all these changes, they used to have big safety factors. Now they're getting down so specific that there's a different safety factor for each alloy or each group of alloys. So this is one of the reasons codes and standards are proliferating in size.

The fatigue strength okay, there is no fatigue limit for aluminum alloys. In aluminum alloys, this thing doesn't become horizontal, it just starts, keeps going down. And they've measured it out to 10 to the 8 cycles. I think I've seen some data going out close to, two, several times 10 to the 8th cycles. You start figuring out what 10 to the 8 cycles is in seconds — there's about, was it, there's 8,000 hours in a year, so there's about 10 to the 7 seconds in a year. So if you go 10 to the 8 cycles, that would be a 10-year fatigue test at one cycle per second. Now in fact when they do a lot of these tests they actually do it in a very high speed vibrating machine, and they might do it at a hundred Hertz. A problem with doing a fatigue test at 100 Hertz: you're actually putting enough elastic energy in there that you have to be careful that you don't overheat your sample, and you're now doing a hot test okay, rather than a room temperature test. But nonetheless, there is no fatigue limit.

And this is a problem for aircraft and other things. Typical lifetime on a commercial aircraft is a hundred thousand hours. You just, you go park it in Arizona after a hundred thousand hours okay. It's full of cracks. Hopefully none of them have propagated to crash it, but you don't want to keep flying it, and you can't afford to repair it. But you leave it there for spare parts or for whatever reason okay. You don't do that with ships. What do you do with ships? We used to sink them, but there's too many PCBs down in there with all the other stuff. What do we do with ships? They take them to Bangladesh and they run them aground okay. They do, they literally run them aground on the beach, and all these little Bangladeshis go out there with acetylene torches and start cutting them up. And why do we do that? Because they're full of the asbestos, and we're, good, we're not, we wouldn't, we couldn't even begin to cut up and recycle that ship in the United States because of the asbestos standards. But in Bangladesh they have no asbestos standards, and frankly it's almost a crime what's going on.

I've read some things that a lot of people who work on those things live for three years, because it's not just asbestos. They're cutting through steel, and first of all they might get crushed because they don't have a lot of safety, and there's, you know, somebody else cutting something over here and all of a sudden you have 20 tons fall on top of you. But the other thing is they're cutting into old pipes that have chemicals and you know all kinds of things in them that had been carried in those ships for 30 years before the ship's ready to recycle. But we tend to export our problems, our environmental problems, and that's one. And actually there's a National Geographic thing about this, but I knew about it before. But literally they just find a beach in Bangladesh, it's not any old beach, but they just put the motors on and head it toward shore, and it just beaches there. And people come out with all their little acetylene torches and cut it up into little pieces, and they recycle the steel and the asbestos and the sickness okay.

So the boiler pressure vessel code has fatigue limits. It also has, it's on alloy, but typically there 2.25. Most of these are statically loaded structures. Why do they have a higher safety factor than the AWS D1.1?

Student: [response — consequences of failure]

Yes, the consequences of failure of a pressure vessel are usually much more severe than the cost of a crack in a bridge or a building. And in fact, I can remember when I first started, young faculty member here, there was a big brouhaha in the Federal Highway Administration because some tugboat captain who's going up and down the Allegheny River in Pittsburgh noticed that, he went down the river, the crack in that interstate highway bridge that he was going under okay, was shorter than when he came back up. It was getting longer, noticeably longer. And when they got to it, it was like nine feet long okay. I mean he could see it from, you know, 20, 30 feet away. This was not a small crack. They ended up closing the interstate highway until they got out there to fix this thing. But it created a lot of consternation. But fortunately bridges tend to be redundant structures.

I had one in New York City once. It was the underpinning of a 20-story high-rise that, if you come into New York City on the George Washington Bridge, you go underneath some buildings. Well, I got to be right up there above the highway, because they found, maybe this was the nine-foot crack, they found the nine-foot crack in an 8-foot beam. The bottom flange of the beam had cracked, the whole web at flat crack, it was only basically the top flange that was holding this together. And it was sort of an interesting area of New York City. I remember being dropped off there by the cabbie, and he just buzzes away, and I'm sitting there with my camera bag with five thousand dollars worth of equipment, and I look down and see all these little capsules, empty capsules, on the sidewalk. And I decided that's why the cab driver got out of that area so quickly. And here I am, you know, not looking like one of the natives, and carrying five thousand dollars with the camera.

And anyway, so they take me down to look at this crack underneath the building, and they were banging things as we went. The guy was leading. I said, what's that for? He said, scare away the rats. Oh, this is good. I mean okay, that's who lived down there. Anyway, so we got to the crack, and then they told me the story that when they discovered it, they had a meeting of all the tenants — this was an apartment building — and they discussed that there was no danger but they were going to close off the highway in that particular area and those lanes right underneath there until they could fix the crack. And the only question they got after the tenants' meeting is, where could they go get some of that crack in the basement okay.

So there's some interesting things when you go on these inspections. Nonetheless, the boiler pressure vessel code, if something blows up, it can be serious, and depending on the amount of energy stored, the alloy, this factor of five safety on the pressure design is for ductile cast iron. Castings tend to have larger flaws than other things, so bigger safety factor is a safety, just like the welds have more defects, larger defects than the base steel. This is for a cast vessel okay. This is for a welded vessel with certain levels of inspection. Sometimes your safety factor, if you want to save on inspection cost and only do ten percent of the vessel, you have to design to a different safety factor than if you do one hundred percent inspection okay. So it's a question of what's the variability, what's your knowledge of the population of defects in that thing okay.

The other safety factors: OSHA, for man-rated equipment like scaffolding, ladders, it's a safety factor of four. Why do you need a safety factor of four? Well, you don't, you only need a safety factor of two, but if someone falls — the consequence — if someone falls from four stories, it's not a good day. And so OSHA basically requires that anything that's man-rated, like the scaffolding, see the scaffolding going up the Great Dome behind there right now, that's got a factor of four safety on whatever loads are going to be placed on there. Why? Because if you go through — actually that stuff's in pretty good shape, I walk by it every morning. That's, I've seen scaffolding that, you know, they dropped an I-beam on it, and so the beams are bent like this before they even put them up there. And there's a lot of wear and tear on scaffolding that gets taken down and put up and stuff. And so they have bigger safety factors. But even the ladder, why do you need a bigger safety factor on a ladder? Because people don't mount the ladder on a flat surface, you know, they kind of tilt it, and therefore the stresses are higher than what they designed it for. You have to assume that people are going to do things that are not that smart.

The New Orleans levees, I think someone may have mentioned that, because I pointed that out. Did he tell you what the safety factor on the levees is? It's 1.3 okay. And frankly the levees didn't fail in New Orleans because the safety factor wasn't, you know, they weren't strong enough. They got breached over and they got washed away from the top okay. My grandfather in the 1880s was building levees in New Orleans okay.

The X-33 spaceplane, I didn't bring the piece but some of the other lectures you'll see it. That's one of mine. It's a piece of composite material. They originally designed it for a 2.0 safety factor. Well, turns out they had a manufacturing problem and they knew they had some flaws that were not, half an inch in size, they could have been three or four inches in size. So they go through and they sharpen their pencils, because they have this 50 million dollar — actually they have $225 million vessels, or maybe it was $250 million vessels, don't remember. I just remember the 15 million number. And they didn't want to declare them junk. That would not be politically a good move okay. So they sharpen their pencils and they said, oh well, we don't have a factor of two safety, we have a factor of 1.05 safety, so we can put them in test. This is for the liquid hydrogen tank for the X-33 spaceplane. And as long as we pass the test, it'll be fine and we can fly the father thing. Well, unfortunately they put them in test, and it probably wasn't 1.05, maybe was 0.95. Anyway, they failed in tests in Huntsville, Alabama. And so people will play games with safety factors. That sort of an example of a political game: oh yeah, we still got a safety factor. I've never known anyone who designed something with a 1.05 safety factor.

Student: [inaudible question, ~30 seconds]

Not necessarily the safety factor, but the design rules. For example, the Twin Towers would have been built to a safety factor 1.67. They were designed to survive an airplane impact, and they did. It was the fire afterwards. They weren't designed, they were designed to survive fires, small fires like the combustibles in the room. They weren't designed to survive 20,000 gallons of fuel on one floor all at once. And you can see some pictures where the whole floor is glowing red, and all the beams everywhere were getting weak, and eventually just started pancaking and going down. What happened after the World Trade Center is, what they tightened up was not, then I gotta start putting more steel in buildings — you can barely afford to build the buildings anyway, right? If you start doubling the steel, you're going to, if you double the steel, you've got to make not just the steel but the windows, everything else goes up in price.

And I remember those were some of the arguments right after World Trade Center. I said, look, no — everybody said, oh, we got to build stronger buildings. I said, yeah, and if you only want one percent of your population to live in a building because they're the only ones who can afford it okay, then that's one choice. But maybe the choice would be something else. So what they did is they improved the standards for design of egress and public announcements to tell people to get out of the building okay. A lot of people stayed in the building for an hour waiting to see what was going to happen, and it was a little late to get out at that point okay. If they had called the alarm and said get out now, they would have lost fewer people. Although most of the people they lost were on the floors above. And why did they lose those people? Because they had a no-fly zone, and no helicopters could go and get those people off the roof. And so when they, for national security, they said nothing's going to go in the sky and fly, that meant the rescue vehicles couldn't rescue those people off the top of the World Trade Center. And most of the people who died were up above the floors that were burning.

Now another example of buildings: the Northridge earthquake, which I think was early '80s in Los Angeles. They had a fairly major earthquake out there. It turns out they didn't increase the strength safety factor. What they increased was the toughness safety factor. Because buildings that were supposed to be statically loaded structures, right, but in the Northridge earthquake, they all of a sudden became dynamically loaded structures, as the building swaying in the breeze. I don't know if any of you've been in a tall building and felt the building swaying in the breeze.

Student: [response — surprise/skepticism]

Just from wind — go up to Pru, yeah I've been on top of the Pru, and you can, well that's the elevator swaying back and forth. But I went to the Sears Tower once and you could sort of, if you stood there on the observation deck on the 100th floor or whatever it was of the Sears Tower in Chicago, if you just stood still, you could slowly feel the building has a natural frequency that's only a few seconds, it's like three or four seconds. And then I went into the restroom on the top floor, and you could see in the toilet, you can see the water sloshing in the toilet okay. So, you know, it's moving right? And if you ever been through an earthquake, it actually has a frequency a little higher than the swaying of the building in the breeze. And at those frequencies, sometimes the foundation, the soil, can turn to jello. I mean basically if there's enough moisture in the right type of soil, it can just turn to something that's like jello, and things can come collapsing down.

But people have designed things for this. I got an email, was just yesterday or the day before, from some guy in Seattle who wanted to know what he should do if an earthquake struck. He's in a high-rise building in Seattle, he wanted to know if it was safe and things. I said, well in Seattle it probably is. In certain other parts of the world it may not be, because they don't have the same types of building codes. And you know, there were earthquakes in Chile — was it Chile? They lost a lot of people with the magnitude nine earthquake. And Japan had another big one, and Japanese didn't lose anywhere near as many people. But they did earlier than that. And though there's a 1907 earthquake or something in Tokyo, that was a big firestorm. We had one in San Francisco in 1912 or whatever, and it wiped out San Francisco okay. They had fires afterwards, and that's when we started our building codes for earthquake protection.

What happened in Northridge in Southern California in the early '80s is they had fractures. No one died, because — well, I wouldn't say no one, there might have been some home or something, or concrete structure, that fell down on a couple of people, but the number of people who died in the Northridge earthquake you could probably, less than 100, probably less than a couple of dozen, because of anything collapsing. In San Francisco, the Oakland Bay Bridge, actually a section of it collapsed, but there, I don't remember any deaths from that okay. It's a question of how we know how to design for an earthquake. What we didn't realize in San Francisco — not in Los Angeles, in Northridge — is that when these things start swaying as rapidly as they were, not as rapidly but as far as they were, they started getting brittle fractures because of impact loading okay. And so they have realized the building codes dramatically — if, well actually it hasn't gotten bigger, the civil engineering construction building code. Now they went through kind of two iterations since Northridge, and so now it's, Dr. Belmar was here, he could tell me, it's instead of the old beam formulas, which is what we did for a hundred years, they now have load factor resistance design, LRFD. It's a whole new way of doing calculations for things, and it's nice if you have a computer to do the calculations for you, but it's a more sophisticated way of calculating loads.

And it was because, things, they had whole buildings that they had to condemn, big buildings, not because anyone got hurt and not because anything collapsed, but they had some of the connections that had completely broke, and some of them they could fix and some of them, it was cheaper to tear the building down. So we do improve things, but it's not always the safety factor that we're improving. Against, just to answer your question, we look at what the real cause is, and we figure out what the least expensive way to fix it is okay. Hopefully.

Student: [extended question, ~45 seconds, likely about probabilistic methods / uncertainty]

Well, it is uncertainty. And what we're having — he was giving you some stuff because I saw his overheads before he did, it from a book on safety factors in design or something like that, goes through a big probabilistic thing. Remember he had kind of three-dimensional Gaussian picture and stuff. So people are now trying to apply statistics to safety factors when, right after World War II in the Liberty ships, we knew about fracture mechanics. But the big thing in the early '50s was probabilistic fracture mechanics okay. So you took your deterministic — you can calculate, you know, the fracture mechanics, you've got the fracture toughness has to be greater than the stress times the square root of pi times crack length. Well, they had known since 1925 okay, and that's a deterministic formula okay. You can plug the numbers in and you get, you know, is this greater than that.

But people started thinking about, while designing things and having a whole fleet of aircraft is really a situation of probabilities. And so now people when they look at safety factors, they're saying, well, we should do some probabilistic design. The thing is, now you're taking something that was very simple — do I have a safety factor of 2 or 1.67 that, you know, even you and I can calculate — and now they give in to, you now have to hire a higher PhD in statistics to tell you what your safety factor is okay. Well, it's good for the statisticians okay, full employment for the statisticians. And it is useful for calculating, estimating what your reliability, probability of failure is. But it's still the problem of, I would say, you know, we can talk about the probability of being hit by a car crossing Mass Ave, and that's fine to talk about probabilities, but if you're the one hit by the car, it's a hundred percent right? And so a lot of this probabilistic safety factors to me is just taking something that's simple enough to be understood and used and turning into something that's too hard to use. I mean, that's a personal opinion about that stuff.

We do get more sophisticated about it. Turns out that my best friend when I was, you know, five and six years old living in Atlanta, Georgia, was from Norway. And he showed up in my office about 15 years ago, because, you know, I have an unusual spelling of the last name, and somehow he had come across me, and he was in Boston, and he showed up. I hadn't had contact with him since I was 10 years old. But so we started talking. I knew his father worked at Martin Marietta where they made the C-5A and did all this Air Force stuff. But his father was brought from Norway about 1950 because he was one of the world's experts in the new field of probabilistic fracture mechanics. And when he was working on it in the early 1950s at Lockheed Martin — and Georgia, Lockheed Corporation in Georgia — it was all classified work okay. This is something the Air Force was trying to figure out, the probability of whether the planes could fly okay. Well, I'm not sure if most of the pilots would feel good about knowing that they have a probable chance of flying, unless you're a test pilot. Those guys, that's what they are, that's what it's all about, is the probability of whether you're going to, you know, whether you're going to have the same number of takeoffs and landings okay, or controlled landings or whatever you want to call it. That's what test pilots are all about okay.

So I tend to lowball, if that really answers your question. Tells you my cynical view about trying to complicate a simple concept and making it so complex that few people can understand it. It's sort of like the tax code. I mean, you know, who understands the tax code? It's so complex.

In any case, the couple points I wanted to make though, just — oh let me say, well actually, maybe we will. I was — Dr. Belmar's going to give his last lecture on Tuesday, and I got enough things I didn't talk about today that we go ahead and have class on Monday and Tuesday. Those would be the last two classes okay. That would be the simplest way to do it. And if you haven't told me what you're going to, which modules you're going to take, or what — I think Marissa, I'm not sure you gave me that okay. And Steve, I'm not sure you've given me. Okay, well there's two things I need to know: which modules of the next two modules that you're going to study for the class.

Student: [response]

Yeah, you give one presentation in—