§1. Factor of safety: definition and historical origins [00:51]
Rather than talking about Harvard and MIT and things like that, we could talk about factors of safety. How many of you are mechanical engineers? Three out of five. So what do you understand a factor of safety to be?
Student: [Offers a definition in terms of capacity over operating stress.]
Right. So it's capacity or capability — Dr. Belmar, being more of a mechanical engineer, calls it the capacity — divided by operating stress. If the capacity is the stress, that's how much it takes to break it, or fail it. Remember that in some cases failure is not breaking something. A lot of times we think of breaking as the failure stress, but you can have failure if something starts to deform, which means it would be the yield stress. The operating stress is what you would calculate from mechanics as your nominal stress, and it's often defined by some code or standard that's been around for a while.
The oldest factor of safety I've seen — some books on the history of engineering written by civil engineers go through this. The first engineering school was West Point, in the United States. It was military engineering. The next engineering school — I've learned since then it's not Rensselaer, it's actually Norwich in Vermont — had an engineering program in 1820. RPI was 1823. RPI is obviously a more well-known engineering school than Norwich now; Norwich is still a good school, just smaller. So in the 1820s both came along with something they called civil engineering to distinguish it from military engineering. Originally engineering was military — building works and dams and bridges for catapults and things like that. Then with the Erie Canal, Norwich and Rensselaer being near upstate New York, started producing students who could help build the Erie Canal. Civil engineering was really the only main type of engineering. It was MIT in the 1860s that started breaking things up. Number one at MIT, course one, is civil engineering.
The bridge designers, around 1850, were just beginning to be able to calculate the strength of a beam. If you go back, Galileo has a picture of a weight hanging off a beam — Galileo Galilei's way of doing things — trying to understand the strength of a beam. They started developing those equations in the mid-1800s, so they could calculate the strength of a bridge kind of like a sophomore mechanical engineer, and they found a factor of safety around six. About that time there was actually a commission in 1850 in Britain that determined they should have a factor of safety of six. Before that it was all, well, I built one like this and it didn't fall down for the last fifty years, so I'll build one similar. Then someone would come along with a different material or a different design to try to save some money or some time, and the factor of safety would go down and things would get worse.
History has a way of repeating itself. You've all seen the Tacoma Narrows Bridge failure — I'm getting nods from most of you. The Tacoma Narrows failure in 1940 [1940, not 1942] was an example of making things too slender, and the winds came down. They called it Galloping Gertie. I saw it in my freshman physics class here at MIT, when they were teaching waves — you'd see the waves on this bridge.
§2. Codes and the boiler and pressure vessel tradition [06:04]
About a hundred and ten years ago, the American Society of Mechanical Engineers came up with the granddaddy code, the boiler and pressure vessel code. The whole set takes up about this much shelf space and costs fifteen thousand dollars. Every three years you get all the updates.
It was a shoe factory down here in Brockton, Massachusetts — a boiler blew up, kapow, around 1905 or so — and the ASME decided we're getting tired of this. The first research contract ever led by the US government was in 1836 or so. Some steamboat on the Ohio River blew up, and Congress actually appropriated some money for someone to go and figure out why these boilers were blowing up and killing people. So pressurized boilers — the Barlow formula, sigma equals PR over T, pressure radius over thickness — those types of equations were around. The boiler and pressure vessel code is the world code today. Mainland China doesn't use it because they don't want to spend sixteen thousand dollars to purchase a code; they basically have their own codes that copy it, and they don't care about copyrights.
You can't make a boiler or pressure vessel out of grey cast iron, because grey cast iron has lousy fracture toughness. You can make it out of ductile iron, which is almost like steel, but even so, ductile iron being a casting can have larger flaws, and the code requires a safety factor of five even today. For steel — and there are different safety factors throughout the code for different nozzles and connections — but generally for steel it's about a factor of two. Is that based on yield or on tensile? Well, sort of on tensile. For an A36 steel of 36 ksi yield, it turns out to be about 18 or 19. There's a table, it depends on the specific steel — lots of experience over the years — but it's basically 55 or 60 percent of tensile. When you get to higher strength steels things change a little, but in general a safety factor of two is good for steels.
Why? You mechanical engineers, what do you know about fatigue of steels? If you look at the old-fashioned S-N curve — stress versus number of cycles — you'll find for steel it comes down and tends to level out, and we sometimes call it the fatigue limit, at forty-five to fifty percent of yield stress. Aluminum doesn't have a fatigue limit; aluminum keeps on going down, and they've gone out to ten to the eight cycles. At one cycle a second on a fatigue machine, that's a year-long test. They've gone ten to the — well, they didn't do a hundred-year test, they go to higher frequencies. At 100 Hertz you can have machines that do it, but you have to start worrying about heating of the sample. You're putting enough work in that it'll heat up on you, so you have to be careful when you go to such long tests.
Usually we're talking way out at ten to the eighth, and the plots only go out to ten to the seventh. The break between low cycle and high cycle fatigue is usually around ten to the third, ten to the fourth, ten to the fifth — 10,000 cycles or so. You have a factor of safety and you're good. You shouldn't have a fatigue problem unless you have stress concentrations. That's why we have safety factors of two for steel in the boiler and pressure vessel code. They have all kinds of provisions for stress concentrations — reinforcements around nozzles and so on.
Virtually all these codes, in the very beginning, have a scope. The first paragraph might be the first three pages of the boiler and pressure vessel code. It doesn't apply if you're less than 15 psi and one and a half cubic feet, or 15 psi and a thousand cubic feet — basically it's pressure times volume. How much energy did you store in this pressure vessel? If it doesn't have much energy we don't care, the ASME says, the explosion won't be that big. If it's got a lot of pressure or a lot of volume — there are a couple of different thresholds — basically with a certain amount of energy you've got a big enough bomb that you don't want to be there if it goes off.
§3. Other structural codes: AWS, OSHA, tree stands [13:10]
The American Welding Society structural welding code has a static and a dynamic side. Static for buildings is 5/3. The World Trade Center was 5/3. I gave you an article I wrote, and I used that 5/3. That building would have been built to the AWS structural welding code. The AWS structural welding code is a companion to the boiler code — something for bridges dynamic, something for buildings static. Bridges are dynamic with trucks going over them — dynamic why? Because you've got fatigue. Buildings, it's not really fatigue, not at the high level of stress. So those things make sense.
OSHA for ladders and scaffolding — if it's man-rated, meaning a cherry picker with someone in the basket — factor of four. Someone could die. In OSHA, if it's more than six feet off the ground you've got to follow the code, because if you start figuring out the energy of a fall, you can break your back from a six-foot fall. You won't break your back from a two-foot fall — not enough energy, unless you have health problems ahead of time. So man-rated equipment — ladders, scaffolding, lifts — everything will be 4.0. An extra factor of two, an extra factor of safety. It's still the same steel.
Tree stands don't come under the boiler and pressure vessel code — it's not a pressure vessel. They have their own Tree Stand Manufacturers Association, only in the last fifteen years or so. People are dying or being maimed by tree stands falling out of the tree with them on it all the time. If you were in Pennsylvania or Colorado or certain places where the deer run wild, people will go to the store and buy a little tree stand. There are lots of mom-and-pop shops — some guy's a hunter, he says he's got a better design, doesn't know anything about design, and he starts making it and selling it at Cabela's or Bass Pro Shops. You carry the thing in — you don't want it too heavy, usually made out of aluminum — you climb the tree, wrap it up there, sit and wait for Bambi to come by. Some of them have canopies, they get very elaborate. If you don't have anything else to do with your life, you go out there and wait for Bambi to come by in the fall. The deer know when hunting season's come, so they're more skittish in the fall anyway. Some people sit out there eight hours a day in the cold waiting.
§4. X-33 and how safety factors get fudged [17:22]
The X-33 spaceplane was supposed to replace the space shuttle. They designed it for a 2.0. It was a 1.3 billion dollar program. The vessels that held the liquid hydrogen were about the size of a house — I have a piece of the composite material — very lightweight, size of a house, the basic structure weighed about 12,000 pounds. Very few houses are that lightweight, but this had to go in space. They had some problems with bonding of the carbon fiber and the Nomex honeycomb with the adhesive. They didn't want to cancel the program — it was a rush program in the early 90s to demonstrate rapid prototyping. So they just recalculated their safety factor and found out a 5 percent safety factor's good enough.
They put it in tests in Alabama. The only place you can get 50,000 gallons of liquid hydrogen is Huntsville, Alabama, where they're testing rockets. They put it in testing, and everything was fine until they started to warm it back up. They were giving everybody high fives because they had passed the test, and they were going to use it in a prototype and go from Edwards Air Force Base to Dugway Proving Grounds in Utah and get up above 100 miles so they actually got to space. Then they heard a pop. All the frost on this thing is on the video because no one's going to be near it — this is a bomb, 50,000 gallons. It's the size of a two-story house. It split open. Nothing exploded, but they went back and found they didn't really have their 5 percent safety factor. This thing was a disaster from the initial fabrication, and they were just hoping they could get it to pass so they could keep their 1.3 billion dollar program. NASA cancelled the program.
1880, the New Orleans levees had a safety factor of 1.3. One of the civil engineers designing those in 1880 was my grandfather. You needed a bigger safety factor, but back then they were lucky if they could even calculate the safety factors. So a safety factor — it's hard to decide what you want to call your capacity, your operating stress will be defined historically by codes and standards, and then it's really a question of what risk you're willing to take. If it's man-rated, you want a bigger safety factor.
I used to think, until I started working on them, I never wanted to get in a helicopter. They're sometimes called flying fatigue machines. But as I started doing some helicopter failures, it turns out helicopters tend to have a safety factor of about ten on most parts. They have to be weight critical, but they have had enough failures over the years that they do a lot of work. If you get in and actually look at the designs and calculate safety factors, you find helicopters have tremendous safety factors, which is why most helicopter accidents are pilot error.
§5. Bolting in offshore structures: BSEE and the National Academies [22:07]
I served on a committee about a year and a half, two years ago, commissioned by a part of the Department of the Interior called BC [BSEE], Bureau of Safety and Environmental Enforcement. [BSEE] is basically the part of Interior that regulates things like offshore structures in the Gulf of Mexico. They were the predecessor — they changed their name after the BP [Deepwater] Horizon failure in the Gulf, the big oil well blowout. They had a different name before that, trying to hide afterwards.
We've had three other near-misses since 2000 — all public knowledge, they're not hiding anything. They just didn't end up with big oil losses like the BP disaster. A number of the other failures had to do with bolting. So we just finished this report.
Does anybody know what the National Academies, the National Research Council, is? In 1863, Abraham Lincoln chartered the National Academy of Sciences. It's not a government agency, but it has a charter from the President to advise the government — or governments, including state governments — on matters of science and technology. It was sort of an old boys club. Now they're trying to get women and minorities, and they are slowly. In 1964 [1964] the National Academy of Engineering was formed — some people in the National Academy of Sciences felt it should have something separate for engineers — sixteen people, of which two or three were MIT professors, one from this department, was it Phil de Bruyne, I think.
You can only be nominated by people who are already members. When I say it's an old boys club — started out with sixteen men, and for years it was almost all men. Now it's about 15% female and like 1 or 2% minority. The average age of election is about 69. It's considered the highest honor an engineer can have. There are about 2,000 members of the National Academy of Sciences, about 2,000 in the National Academy of Engineering. A few years later, around 1970, they started the Institute of Medicine — about 2,000 members, mostly MDs or PhD researchers. So you've got about 6,000 people who advise the government on different matters of science and technology.
They formed around 1910 the National Research Council. The National Academies building is right on the mall near the Lincoln Memorial, a couple blocks down from the White House. It's not a government agency — sometimes called a quasi-governmental body, a private institution. It works very hard to have objective studies. On a committee of 15 or 16, about a third might be members of the National Academy, the elected old boys, and the other people will be put on because of their expertise — not as old and senior but with particular expertise.
I've served on a number of these — for the Army Ballistics Lab down in Aberdeen Proving Ground, Maryland; for the Alvin submarine, on whether we could afford to build a new Alvin. So I served on this one about bolting technology in a marine environment. Risk equals hazard times consequences — there's a book from Harvard School of Public Health, not unique to Harvard, on the risk and benefits of hamburgers and cheeseburgers. It's the probability of an event times the severity or consequences. There are standards on this stuff now, many of them starting with the military, who have had some pretty major disasters at times.
§6. Bolting mechanics: tension, shear, and the springs model [28:43]
Bolts can be in tension or shear, typically. They get more complex, and they're all over bridges and buildings. If you look at some books on bolting, this is typical fractures for shear-tension ratios. This is 100% shear, just slicing it. And this is pure tension. Square root of 3 over 3 is an important parameter out of mechanics. If you get to tension equal to square root of 3 over 3, and the shear is square root of 3 over 3 and the tension is 1, you start seeing a 45-degree shear plane, and then you get a pure tensile load. So the type of failure in a ductile joint can vary depending on the shear-tension ratio.
For undersea drilling, bolting is getting more and more important. The first undersea platforms in a sense were off the coast of Bakersfield, California, in around 1908. They were just going from the land into the ocean where it was 10 or 20 feet deep — not very deep. Then they kept getting deeper, and they have designs for up to 10,000 feet deep now. The Macondo well, the BP Horizon well — these things now can cost five billion dollars for the production platform.
They have blowout preventers. That's what failed in the BP system. These can be four or five stories tall. Great big valves that are going to shut off the flow if all goes well. That'll be at the bottom of the ocean, maybe in 10,000 feet of water. One, two, three, four, five, six valves in this thing, different types. Shear rams — that was one of the things that failed on the BP [Deepwater] Horizon. Basically if all else fails, they have big shears that are supposed to squeeze the pipe off and cut it in two and seal it. Big hydraulic rams.
You can analyze bolts in terms of springs — the spring model. The bolt is a spring, and you have compression between your two things. A fairly small spring force here can generate significant spring force here. You have lots of stress concentrations in bolts — tensile stress, and a higher stress down near the threads and the nuts where the section is reduced. There are all kinds of high-strength bolts. Some of these critical structures have bolting you wouldn't even recognize as a bolt.
§7. Torque control, stretch control, and the limits of operator feel [33:00]
Has anybody ever used a torque wrench on a bolt? What do you think the accuracy of that is? Pretty bad — plus or minus 30 percent in some cases. But that's what people use when they're trying to be precise. To get good fatigue strength in the bolt, you want the bolt tensioned to 70 to 90% of its yield strength. And you've got plus or minus 30% as your ability to do it. So in really critical applications — I first saw it on the crankshaft of an airplane engine — they actually grind the tip and the bottom of the bolt to an exact dimension, and someone takes a micrometer, and the bolt is 2.62 inches before they tension it and 2.68 inches after — stretched six tenths of an inch. Young's modulus is pretty well known, and you can get down to plus or minus 10% of your stress in your bolt, which is what you really need.
They sometimes have holes down the center of bolts where you can put a little gauge. For those small piston engines for prop aircraft, you just need a three-inch micrometer — but that's what people use. There's a guy who is a graduate of mechanical engineering at MIT — I think he may have passed away now — John Bickford, wrote a book on bolting, about 1,200 pages long. John Bickford knows more about bolting than anybody else in the world. When people are putting bolts in a nuclear reactor you hire John Bickford, because he knows how to bolt things together properly. Why do you use bolts? Why don't you just weld things? You have to take it apart, right. Exactly. It's harder to take welds apart — you can do it, but it's harder.
Here's something Bickford did for the Nuclear Regulatory Commission. Bolt plant variation: calibrated torque wrench plus or minus 23%; hard joint, soft joints, which is the compliance of the joint, plus or minus 20 to 40 — that's the plus or minus 30 I mentioned. You can use torque wrenches, impact wrenches, hydraulic tensioner stretch control. Stretch control is measuring the elongation of the bolt with the micrometer. Now they actually use ultrasonics to measure the stretch — you can measure the length of the bolt fairly precisely before and after tensioning. Even stretch control, plus or minus 10 to 20 percent. Turn of the nut, plus or minus 10 to 20 percent. Operator feel, plus or minus a hundred to two hundred percent. A lot of times people are using plus or minus a hundred to two hundred percent. On the offshore structures, torque wrenches plus or minus thirty percent — and they wonder why they have failures when they put these things down in the ocean.
So what can you do? You have to plan for this. With big bolts you can use hydraulic tensioners. You're measuring a pressure on a hydraulic cylinder, and you can get that within 1 or 2 percent, which gives you in some cases plus or minus 10%. But that's when you get a bolt bigger than about 2 or 3 inches and it's no longer somebody's arm anymore. You've got bolts out there where the nuts can be this big around.
What's in between? Unless you're in a critical application like the nuclear business or the aerospace business, most people still use torque control. The guys in the oil and gas industry — we had a three-day workshop, and they didn't want to do anything other than torque control because it's easy. You get a number, they're happy with the number. The number is garbage, but they're happy with it because they have a number — they can write it down in a little log and say we checked it. Still garbage. We've known about ultrasonics for four decades, fifty years, seventy years, but people still use the same old technology.
Cut threads versus rolled threads. With a smaller bolt you can machine it and cut it. But most bolts up to a couple of inches in size, they actually cold-roll the threads. There are some hard dies at an angle, and you roll the bolt and make a thread by crushing things. So at the bottom of the V you have compressive residual stresses, which gives you much better fatigue resistance. So you like rolled threads.
One of the big problems with the torque wrench is lube control. If it's lubricated, you'll get the same normal distribution, but the torque will be much less than if it's not lubricated and you've got dry friction. There's your plus or minus 30%. So if all you have is a torque wrench, lube it — put grease on it — and you'll get a more consistent result. Bickford has a little couplet, something about if uniform torque is what you want — I don't remember it exactly — but basically lubricated bolts give you more consistent torque. If you want to know anything about bolting, go to Bickford's book. He's got hundreds of references to the mechanical engineering literature. People have studied this over and over, they just don't follow it. It's not that we don't know what to do. Lubrication is a good thing. Torque-turn — you torque it and then do another quarter turn at the end — that can give you a little variation, but you still get a histogram.
§8. Reading fractures: bolt failure analysis cases [40:49]
There are some critical applications. This was actually a whole lecture once. Variable-pitch propellers — if you want more efficiency and you drive your ship at different speeds, particularly in some military ships, you actually have your propeller blade twist depending on the rotation speed, and you have a gearbox that changes the pitch. You lose one of those bolts, you lose the ship. The thing's severely out of balance, going to bend the shaft, you're dead in the water. If you're a military ship, that's not good. Here are some of the internal mechanisms — a gearing mechanism. These bolts have holes down the middle so you put a long micrometer in to measure the stretch — you don't torque those.
You can do fracture analysis on bolts. This is fatigue. Tom Eagar looks at this and says, well, I have a fatigue crack that grows this deep, and this is the final fracture. This little serrated stuff over here is part of the final fracture. Metallurgists have been using these types of fatigue analysis diagrams for different types of stress — high nominal stress, low nominal stress. High nominal stress: the final fracture area is the dark area, high area. Low nominal stress: small area. Different amounts of stress concentration, tension or tension-compression.
With experience you can tell a lot about the fracture of broken bolts. Back thirty years ago a nuclear reactor had a problem on some of its bolts, and I was working for a test lab — early 80s — and they said, we're going to send you a bolt, and we're not going to tell you anything about it. We want to know what you can tell us just from looking at it. They sent it, I looked at it, and I said: low cycle fatigue, moderate nominal stress, variable amplitude loading — because some of the fatigue cracks had different widths, telling you how fast it was growing. And it was operating at 600 degrees Fahrenheit. They were all surprised. You get blue coloring where the temperature was not uniform with time. Blue coloring in steel — they sometimes call it blue brittleness in carbon steels, but the temper colors. The steel forms a blue oxide around 600 degrees Fahrenheit; you can look it up on the internet. So I knew the temperature, in some cases I could see the different striations and the variability, I could tell the size of the high nominal stress, and I told them it didn't have a stress concentration — just by looking at the fracture. Sort of like reading tea leaves, except it's knowledgeable tea leaves.
A building fell down at a sports complex at a university south of here. Here are some of the fractures: fatigue fracture right here, final fracture, high nominal load, ductile all the way. Fatigue fracture nearly half of the way before it broke. The reason this thing broke down while they were erecting it was that some of the anchor bolts were broken. I don't remember whether it was fatigue or heat-treating defects. Another one was on a turntable — you can see at the crack T, A, B and C: low cycle fatigue, high cycle fatigue, low cycle fatigue, final fracture, has a different appearance.
This is one where obviously the nut wasn't tight — it was peening itself apart. And another one with some really big bolts — this was a 50,000-ton forging press. There are only like half a dozen of these in the world. The posts are basically four bolts, four big bolts about a meter across. Stress concentration, there's the fatigue crack, there's the final fracture. They changed the steel and they thought they were going to a higher strength steel and everything would be wonderful. The fatigue crack is this big, there's the final fracture area. Yeah, it was higher strength, but it still broke through fracture mechanics. We won't get into the fracture mechanics right now.
Lots of things you can tell if you get into the details. One time they taught you about fatigue, one time about fracture mechanics, one time about heat treatment of steels. They all actually fit together, and if you want to solve the real problem, you've got to know something about all of them. Next Monday Dr. Belmar will be here; I'll be in Henderson, Kentucky. Then I'll be here the Monday after that. So bring your questions, or email them to me or to Dr. Belmar, anything you come up with, and we will try to say something intelligent about your questions. This time I was just making up my own.