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Assa Auerbach’s course was the most maddening course I’ve ever taken. I was a master’s student in the Perimeter Scholars International program at the Perimeter Institute for Theoretical Physics. Perimeter trotted in world experts to lecture about modern physics. Many … Continue reading →
At a time in American history when even the most intelligent Black women were expected to become, at most, teachers or nurses, Willie Hobbs Moore broke with societal expectations to become a noted physicist and engineer. Moore probably is best known for being the first Black woman to earn a Ph.D. in science (physics) in the United States, in 1972. She also is renowned for being an unwavering advocate for getting more Black people into science, technology, engineering, and mathematics. Her achievements have inspired generations of Black students, and women especially, to believe that they could pursue a STEM career. Moore, who died in her Ann Arbor, Mich., home on 14 March 1994, two months shy of her 60th birthday, is the subject of the new book Willie Hobbs Moore—You’ve Got to Be Excellent! The biography, published by IEEE-USA, is the seventh in the organization’s Famous Women Engineers in History series. Moore attended the University of Michigan in Ann Arbor, where she earned bachelor’s and master’s degrees in electrical engineering and, in 1972, her barrier-breaking doctorate in physics. In 2013, the University of Michigan Women in Science and Engineering unit created the Willie Hobbs Moore Awards to honor students, staff, and faculty members who “demonstrate excellence promoting equity” in STEM fields. The university held a symposium in 2022 to honor Moore’s work and celebrate the 50th anniversary of her achievement. Physicist Donnell Walton, former director of the Corning West Technology Center in Silicon Valley and a National Society of Black Physicists board member, praised Moore, saying she indicated that what’s possible is not limited to what’s expected. Walton befriended Moore while he was pursuing his doctorate in applied physics at the university, he says, adding that he admired the strength and perseverance it took for her to thrive in academic and professional arenas where she was the only Black woman. Despite ingrained social norms that tended to push women and minorities into lower-status occupations, Moore refused to be dissuaded from her career. She conducted physics research at the University of Michigan and held several positions in industry before joining Ford Motor Co. in Dearborn, Mich., in 1977. She became a U.S. expert in Japanese quality systems and engineering design, improving Ford’s production processes. She rose through the ranks at the automaker and served as an executive who oversaw the warranty department within the company’s automobile assembly operation. An early trailblazer Moore was born in 1934 in Atlantic City, N.J. According to a Physics Today article that delved into her background, her father was a plumber and her mother worked part time as a hotel chambermaid. An A student throughout high school, Moore displayed a talent for science and mathematics. She became the first person in her family to earn a college degree. She began her studies at the Michigan engineering college in 1954—the same year that the U.S. Supreme Court ruled against legally mandated segregation in public schools. Moore was the only Black female undergraduate in the electrical engineering program. Her academic success makes it clear that being one of one was not an impediment. But race was occasionally an issue. In that same 2022 Physics Today article, Ronald E. Mickens, a physics professor at Clark Atlanta University, told a story about an incident from Moore’s undergraduate days that illustrates the point. One day she encountered the chairman of another engineering college department, and completely unprompted, he told her, “You don’t belong here. Even if you manage to finish, there is no place for you in the professional world you seek.” “There will always be prejudiced people; you’ve got to be prepared to survive in spite of their attitudes.” —Willie Hobbs Moore But she persevered, maintaining her standard of excellence in her academic pursuits. She earned a bachelor’s degree in EE in 1958, followed by an EE master’s degree in 1961. She was the first Black woman to earn those degrees at Michigan. She worked as an engineer at several companies before returning to the university in 1966 to begin working toward a doctorate. She conducted her graduate research under the direction of Samuel Krimm, a noted infrared spectroscopist. Krimm’s work focused on analyzing materials using infrared so he could study their molecular structures. Moore’s dissertation was a theoretical analysis of secondary chlorides for polyvinyl chloride polymers. PVC, a type of plastic, is widely used in construction, health care, and packaging. Moore’s work led to the development of additives that gave PVC pipes greater thermal and mechanical stability and improved their durability. Moore paid for her doctoral studies by working part time at the university, KMS Industries, and Datamax Corp., all in Ann Arbor. Joining KMS as a systems analyst, she supported the optics design staff and established computer requirements for the optics division. She left KMS in 1968 to become a senior analyst at Datamax. In that role, she headed the analytics group, which evaluated the company’s products. After earning her Ph.D. in 1972, for the next five years she was a postdoctoral Fellow and lecturer with the university’s Macromolecular Research Center. She authored more than a dozen papers on protein spectroscopy—the science of analyzing proteins’ structure, composition, and activity by measuring how they interact with electromagnetic radiation. Her work appeared in several prestigious publications including the Journal of Applied Physics, The Journal of Chemical Physics, and the Journal of Molecular Spectroscopy. Despite a promising career in academia, Moore left to work in industry. Ford’s quality control queen Moore joined Ford in 1977 as an assembly engineer. In an interview with The Ann Arbor News, she recalled contending with racial hostility and overt accusations that she was underqualified and had been hired only to fill a quota that was part of the company’s affirmative action program. She demonstrated her value to the organization and became an expert in Japanese methods of quality engineering and manufacturing, particularly those invented by Genichi Taguchi, a renowned engineer and statistician. The Taguchi method emphasized continuous improvement, waste reduction, and employee involvement in projects. Moore pushed Ford to use the approach, which led to higher-quality products and better efficiency. The changes proved critical to boosting the company’s competitiveness against Japanese automakers, which had begun to dominate the automobile market in the late 1970s and early 1980s. Eventually, Moore rose to the company’s executive ranks, overseeing the warranty department of Ford’s assembly operation. In 1985 Moore co-wrote the book Quality Engineering Products and Process Design Optimization with Yuin Wu, vice president of Taguchi Methods Training at ASI Consulting Group in Bingham Farms, Mich. ASI helps businesses develop strategies for improving productivity, engineering, and product quality. In their book, Moore and Wu wrote, “Philosophically, the Taguchi approach is technology rather than theory. It is inductive rather than deductive. It is an engineering tool. The Taguchi approach is concerned with productivity enhancement and cost-effectiveness.” Encouraging more Blacks to study STEM Moore was active in STEM education for minorities, as explored in an article about her published by the American Physical Society. She brought her skills and experience to volunteer activities, intending to produce more STEM professionals who looked like her. She was involved in community science and math programs in Ann Arbor, sponsored by The Links, a service organization for Black women. She also was active with Delta Sigma Theta, a historically Black, service-oriented sorority. She volunteered with the Saturday Academy, a community mentoring program that focuses on developing college-bound students’ life skills. Volunteers also provide subject matter instruction. She advised minority engineering students: “There will always be prejudiced people; you’ve got to be prepared to survive in spite of their attitudes.” Black students she encountered recall her oft-repeated mantra: “You’ve got to be excellent!” In a posthumous tribute essay about Moore, Walton recalled befriending her at the Saturday Academy while tutoring middle and high school students in science and mathematics. “Don Coleman, the former associate provost at Howard University and a good friend of mine,” Walton wrote, “noted that Dr. Hobbs Moore had tutored him when he was an engineering student at the University of Michigan. [Coleman] recalled that she taught the fundamentals and always made him feel as though she was merely reminding him of what he already knew rather than teaching him unfamiliar things.” Walton recalled how dedicated Moore was to ensuring Black students were prepared to follow in her footsteps. He said she was a mainstay at the Saturday Academy until her 24-year battle with cancer made it impossible for her to continue. She was posthumously honored with the Bouchet Award at the National Conference of Black Physics Students in 1995. Edward A. Bouchet was the first Black person to earn a Ph.D. in a science (physics) in the United States. Walton, who said he admired Moore for her determination to light the way for succeeding generations, says the programs that helped him as a young student are no longer being pursued with the fervor they once were. “Particularly right now,” he told the American Institute of Physics in 2024, “we’re seeing a retrenchment, a backlash against programs and initiatives that deal with the historical underrepresentation of women and other people who we know have a history in the United States of being excluded. And if we don’t have interventions in place, there’s nothing to say that it won’t continue.” In the interview, Walton said he is concerned that instead of there being more STEM professionals like Moore, there might be fewer. A lasting legacy Moore’s life is a testament to perseverance, excellence, and the power of mentorship. Her achievements prove that it’s possible to overcome the inertia of low societal expectations and improve the world. Willie Hobbs Moore—You’ve Got to Be Excellent! Biography is available for free to members. The non-member price is US $2.99
[Note that this article is a transcript of the video embedded above.] I’m Grady, and this is Practical Engineering. You know, every once in a while, all the science, technology, economic factors, and stylistic tastes converge into a singular, beautiful idea of absolute perfection. Am I being superfluous? I don’t think so. Destin’s got laminar flow. Grey thinks hexagons are the bestagons. Matt loves the number 3, for whatever reason. Vi prefers 6. Alec loves the refrigeration cycle. I am not going to mince words here; they’re just wrong. I’m not trying to say that cable-stayed bridges are the best kind of bridge. I’m saying they’re the best, period. So, on this day dedicated to the people and things we love, let me tell you why I adore cable-stayed bridges. Spanning a gap is a hard thing to do, in general - to provide support with nothing underneath. Even kids recognize there’s some inherent mystery and intrigue to the idea. Almost all bridges rely, to some extent, on girders - beams running along their length - to gather structural forces from the deck and move them to the supports. This action results in bending, known as moments to engineers, and those moments create internal stress. Too much stress and the material fails. You can increase the size of the beam to reduce the stress, but that creates more weight that creates a higher moment that results in more stress, and you’re back to where you started. For any material you choose as a girder, there is a practical limit in span because the self-weight of the beam grows faster than its ability to withstand the internal stress that weight causes. The easiest way to deal with a moment that might stress a beam too much is to simply support it from below; build another column or pier there. And in old-fashioned viaducts, this is precisely what you’ll see. But there are a lot of places we want to cross where it’s just not that simple. Putting piers in areas where the water is deep or the soil is crummy can be cost-prohibitive. And sometimes, we just don’t want more supports to ruin the view. Fortunately, “push” has an opposite. Cables can be used to pull a bridge upward toward tall towers, supporting the deck from above. There was a time when a suspension bridge was practically the only way to cross a long span. Huge main cables drape across the towers, and suspenders attach them to the deck below. You get that continuous support, reducing the demand on the girders and allowing for a much lighter, more efficient structure. But you get some other stuff too. All those forces transfer to the cables and to the tops of the towers. But the cables don’t just pull on the towers vertically. There’s some horizontal pulling too, and I’m sure you know what happens when you put a horizontal force at the top of something very tall. So the cables have to continue to the other side, balancing the lateral component. And that’s just kicking the force-can down the road; ultimately they have to go SOMEWHERE. In most suspension bridges, it’s the anchorage - a usually enormous concrete behemoth that attaches the main cables to the ground. The anchorages on the Golden Gate Bridge weigh 60,000 tons each. Compare that to a cable-stayed span. Get rid of the main cables and just run the suspenders - now called stays - diagonally straight to the tower. You have balanced horizontal forces on the tower without the need for a massive anchorage that can be expensive or, in places with poor soils, completely infeasible. Instead, those horizontal forces transfer into the bridge deck and girders, but because they’re balanced, there’s no net horizontal force on the deck either. Of course, with traffic and wind loads, you can get slight imbalances in forces, but those can be taken care of with the stiffness of the tower and the anchor piers at the end of each backspan, which are much simpler than massive anchorages. I should note that some suspension bridges do this too. So-called self-anchored suspension bridges also put the deck in compression in lieu of anchorages. In that case, the entire bridge deck has to withstand the full compression force from the main cables attached at its ends. In a cable-stayed bridge, the maximum compressive force in the deck is localized near the towers and diminishes as you get further from them, allowing you to be more efficient with materials. This tension management also means cable-stayed bridges work well in multi-span arrangements. Consider the Western side of the Bay Bridge, an admittedly impressive multi-span bridge connecting traffic from San Francisco to Oakland. This is two suspension spans connected to one another, but look what’s in between them. This manmade mountain of a concrete anchorage is an unavoidable cost of this kind of construction. Compare that to the sleek multi-span wonder of the French Millau(MEE-oh) Viaduct with eight spans, six of which are longer than a thousand feet or three hundred meters. While there certainly is a significant volume of concrete in the viaduct, it’s all in the deck and eight elegant pylons. No hulking anchorages to be seen; just gently curving spans above the French countryside. It also happens to be the tallest bridge in the world, with its tallest pylon surpassing the Eiffel tower! If that doesn’t make your heart flutter, nothing will. And speaking of flutter, suspension bridges have another downside. You’ve probably seen this video before. Gravity loads aren’t the only forces for long-span bridges to withstand. The lightness of a suspension bridge is actually a disadvantage when it comes to the wind. Because of the droopy, parabolic shape of the main cables, suspension bridges are susceptible to relatively small forces causing outsized deflections of the structure. This is true laterally. But it’s also true for vertical forces. Since the main cables reach very shallow angles, even horizontal in the center of the span, huge tensions are required just to withstand moderate vertical loads, and those tensions come with large deflections as the cables straighten. Put another way, it’s a lot easier to straighten a sagging cable than to stretch one that’s taut. For a cable-stayed bridge, they’re already straight. There’s very little sag in the stays, so any deflections require the actual steel to stretch along its length. That makes cable-stayed bridges generally much stiffer than suspension bridges, giving them aerodynamic stability and allowing the decks to be lighter. The thing about a bridge is that you can design pretty much anything on paper, or in CAD, but at some point, it has to be built. You have to get the structure into place above the area it spans, and that can be a tricky thing. Consider an arch bridge. That arch can’t do its arch thing until it’s a continuous structure member. Before that, forces have to be diverted through some other temporary structure or falsework, usually something underneath. For one, that requires engineers to design, essentially, several different versions of the same bridge, where (in some cases) the construction loads actually govern the size and shape members rather than the final configuration. For two, if building extra vertical supports was easy, then we would just design the bridge that way in the first place. Check out this timelapse of the construction of the I-11 bridge over the Colorado River downstream of the Hoover Dam. If you look carefully, you can see that before the arch is complete, it is supported by cable stays! And this is where you see the huge advantage that cable-stayed bridges have: constructability. The flow of forces during construction is the same as when the bridge is complete. But it’s not just that; the construction itself also is much simpler. Look at a conventionally anchored suspension bridge. You have to build the towers and anchorages first. Only when they’re complete can you hang the main cables. That’s a process in itself. Main cables are too heavy and unwieldy to be prefabricated and hoisted across the span, so they are generally built in place, wire by wire, in a process called spinning. Then you have to attach the suspenders, and only then can you start building the road deck. It’s an intricate process where each major step can’t start until the one before it is totally finished. Self-anchored suspension bridges are even more complicated, because you have to have the entire deck built before the cable can be anchored, but you have to have the cable to suspend the deck. It’s a chicken and egg problem that you have to solve with temporary supports. None of this is true with cable-stayed bridges. You can have your chicken and egg, and eat it too! You start with the pylons, and then as you build out the bridge deck, you add cable stays along the way, slowly cantilevering out from the towers. Since they’re usually symmetrical, the forces balance out the whole time. The loading is the same during construction and after, and there’s no need for falsework or temporary supports, dramatically lowering the cost to build them. Some bridges can even begin work on the deck before the tower is even finished, speeding up the construction timeline and reducing costs even more. This constructability also has a positive feedback loop when it comes to contractors and manufacturers as well. As the popularity of cable-stayed bridges has exploded since the second half of the twentieth century, more and more contractors have recent and relevant experience, and more and more manufacturers can produce the necessary materials, reducing the costs even further and making them more and more likely to be chosen for new projects. But once you put up a bridge, you also have to keep it up. Maintenance is another place cable-stayed bridges shine. Besides the stays themselves, most of their parts are easily accessible for inspection. Most structures don’t rely heavily on coatings to protect the steel, so you don’t have to contract with specialized, high-access professionals for maintenance. And just using more concrete instead of steel means fewer problems with corrosion. With more rigidity, you get less fatigue on materials. And they’re redundant. Suspension bridges rely on the two massive main cables for all their structural support. You can’t take one cable out of service for repair or replacement without very complicated structural retrofits. With cable-stayed bridges, it’s no problem. The stays are designed to be highly redundant, so if one breaks or you need to replace them, the remaining cables can still effectively support the bridge's load. And each cable can be tensioned individually, so the structure can be “tuned” to match the design requirements just like a piano, and adjusted later if needed. You might be looking at all these examples and thinking, this is kind of obvious. But there are a lot of reasons why cable-stayed bridges only started becoming popular in the last few decades. Part of that is in the field of engineering itself. Where the deck, tower, and main cables of a suspension bridge behave fairly independently, a cable-stayed structure is much more interdependent. Each stay is tensioned independently, meaning you have lots of different forces on the deck and towers that depend on each other, and they have to be calculated for each loading condition. Solving for all the forces in the bridge is a complicated task to do by hand, so it took the advent of modern structural analysis software before engineers could gain enough confidence in designs to push the envelope. And that brings me to a deeper point about structural elements resisting forces. Cable-stayed bridges just make such efficient use of materials, many of which have existed for centuries, but have been refined and improved over time. A lot of engineering sometimes feels like designing around the weaknesses of various materials, but cable-stayed bridges take full advantage of materials’ strengths. We put the towers and deck in compression and make them out of high-strength concrete, a material that loves compressive stress. We put the stays in tension and make them out of high-strength steel. They love tension. We’ve slowly gained confidence in the innovations that make these bridges possible, like parallel wire strands, concrete-to-cable anchoring systems, segmental construction, and prestressed concrete. And all these gradual improvements in various aspects of construction and material science added up to create the pinnacle of engineering technology. You want to know the other reason why cable-stayed bridges are becoming more popular? It’s taste. Bridges are highly visible structures. They are tremendous investments of public resources, and the public has a say in how they look. I hate to even say the word outloud, but oftentimes, there are architects involved in their design. The swooping shapes of suspension structures were in vogue during the heyday of long-span bridge design, but no more! One of the huge benefits of cable-stayed bridges is that they’re flexible. Not structurally flexible of course, but architecturally. Most bridges do have a few rules of thumb - the tower height is usually about a fifth of the main span length, and the side spans about two fifths of the main span. However the number of variations on the theme is practically endless. Let me show you some examples. For short spans, you’ll typically see single cable planes. Each of the masts of the Millau viaduct has a single cable plane, connecting the cables along a central line of the bridge deck. Go a little bigger and you’ll see double cable planes. This is the Russky Bridge in Russia, the current world record holder with a main span of 1,100 meters or 3,600 feet. The two cable planes give the structure extra stiffness. Double planes can be parallel like you see in the Øresund bridge in Denmark. Or, cable planes can be inclined towards one another, like in the Charilaos Trikoupis bridge in Greece. They can use the radial or “fan” style, where the stays originate from the pylons near a single point at the top, like the Pasco Kennewick bridge. Or they can use the harp style, where the stays are more or less parallel. Lots of structures use a style somewhere between the two. If the pylons get tall enough, they might get connected by a cross member, giving H pylons. Continuing in the alphabetical trend, another option is A-frames with inclined cable planes. If an A-frame gets too tall, though, you end up requiring two foundations per pylon, which can quickly get pricey or just too challenging to construct. In that case, tuck the legs back in towards each other, and you’ve got stunning diamond frames. You might see asymmetrical designs like Malaysia’s famous Seri Wawasan bridge or Spain’s Puente del Alamillo. You’ve got Sao Paolo’s Octávio Frias de Oliveira Bridge with its iconic X-shaped pylon holding two curved roadways, each with double cable planes inclined and crossing each other. Even my home state of Texas boasts some impressive cable-stayed bridges. Corpus Christi’s Harbor Bridge will be finished soon, now that they got the construction issues worked out. Houston has the double diamond-framed Fred Hartman bridge. And Dallas has the iconic Margaret Hunt Hill Bridge with its high arched single pylon gracefully twisting its single cable plane through the third dimension. You can see how these simple structural principles work together to allow architects to really get creative while still allowing the engineers and contractors to bring it into reality. I mean, just look at this. There’s nothing extraneous. Nothing extravagant. This is the highest form of utility meets beauty. Have you ever seen something like this? I hope you can see why we’re in the heyday of cable-stayed bridge construction. This is my opinion, and maybe I’m a little bit biased, but I don’t think there’s a better example in history where all the various factors of a technical problem converged into a singular solution in this way. Many consider the Strömsund Bridge in Sweden, completed in 1956, to be the first modern cable-stayed bridge. But it’s only been over the past three or four decades that things really took off. Now, there are more than 15 with spans greater than 800 meters or 2600 feet, not including the Gordie Howe Bridge, which will soon be the longest cable-stayed bridge in North America. Even the famously hard-hearted US Federal Highway Administration declared their affection for the design, stating, “Today, cable-stayed bridges have firmly established their unrivaled position as the most efficient and cost-effective structural form in the 150-m to 460-m span range.” And that range is only growing. We humans built a lot of long bridges in the 20th century, and a lot of them are reaching the end of their design lives. I can tell you what kind of bridge most of them are going to be replaced with. And I can tell you that any time a new bridge that needs a span less than 1000 meters or 3,300 feet goes into the alternatives analysis phase, it’s going to get harder and harder not to choose a cable-stayed structure. They’re structurally efficient, cost-effective, easy to build, easy to take care of, and easy to love. The very longest spans in the world are still suspension bridges, but I would argue: we don’t really need to connect such long distances anyway. Doctors don’t tell you this, but engineers don’t actually have heartstrings; they have pre-fabricated parallel wire heart strands, and nothing tugs on them quite like a cable-stayed bridge. Happy Valentine's Day!
A new proof reveals the answer to the decades-old “moving sofa” problem. It highlights how even the simplest optimization problems can have counterintuitive answers. The post The Largest Sofa You Can Move Around a Corner first appeared on Quanta Magazine