An Engineer’s Love Letter to Cable-Stayed Bridges
[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!