Why don't bridges and skyscrapers
collapse when they sway in the wind?
On a windy day, the upper floors of a skyscraper sway slowly. That sway is built into the design. Yet in 1940, a bridge in the United States collapsed in wind that wasn't even especially strong. And the explanation textbooks gave for decades was wrong.
When you push a child on a swing, pushing hard doesn't make it swing higher. Only when the timing matches does a light push, repeated, build the swing bigger and bigger.
Every swing has a "speed it wants to swing at." A long swing goes slowly, a short swing goes fast. Push in time with that speed, and small pushes stack up into a big swing.
Bridges and buildings have exactly the same property. Each one has its own "speed it wants to sway at." Taller buildings sway more slowly; shorter ones sway faster.
So the first question an engineer asks is: "Is there anything nearby that pushes at that exact speed?"
This is resonance. A crowd walking in step across a bridge, or an earthquake wave whose period matches a building's — once they match, the sway stacks up.
A steady wind doesn't push periodically. Yet the bridge twisted more and more on its own. It wasn't pushed — it grew the motion itself.
These two look alike but are different mechanisms. And they stayed confused in textbooks for a long time. Let's go through them in order.
First, what is resonance?
Every object has its own "speed it likes to sway at." Push a swing once and let go, and it keeps swinging at a fixed tempo, set by its length — you can't change that by pushing differently.
Push in time with that tempo, and each push adds force in the same direction. Even small pushes, repeated, add up to a big sway. That's resonance.
You can find examples everywhere.
- Rubbing a wine glass makes it sing — only the vibration that matches the glass's own tempo grows
- A washing machine shakes violently only at certain spin speeds — that speed matches the machine's own sway tempo
- Tuning a radio — you're matching the receiver circuit's own tempo to the frequency of the station you want
- Soldiers break step crossing a bridge — marching in step risks matching the bridge's own tempo. A 19th-century collapse in Britain during a marching column's crossing is a well-known case
How do bridges and buildings deal with this?
In design, engineers check "is there anything nearby that pushes at this building's own tempo?" Then they take steps such as:
- Shift the tempo — change stiffness or mass so the natural sway speed sits outside the dangerous range
- Soak up the sway — fit dampers (devices that turn vibration into heat) inside the building
- Cancel it with a weight — hang a large mass near the top of a skyscraper that moves opposite to the building, cancelling the sway. The giant ball visible at Taipei 101's observation deck is this device, made visible on purpose. Tokyo Skytree uses the same idea, built around its central pillar
Modern design doesn't try to "stop the sway" — it tries to "let it escape safely." Making a structure rigid to contain the sway just passes the force straight into the frame.
a design failure — it's by design.
So what actually happened at Tacoma Narrows?
In 1940, a suspension bridge completed in Washington State, USA, collapsed just four months after opening. Footage of the deck twisting violently and undulating apart is still used as science teaching material today.
The wind that day was around 20 metres per second — nowhere near a typhoon, just a strong breeze. The bridge had been designed to withstand far stronger winds.
For decades, this accident was explained as "a textbook case of resonance" — the idea that the period of wind-generated vortices matched the bridge's own sway speed. But this is wrong.
A study published in the 1990s showed the vortex-shedding period and the bridge's twisting speed did not match. And the wind that day blew steadily from one direction — there was no periodic push, like a hand timed to a swing, at all.
What really happened — a sway that grew itself
What actually occurred was a loop like this (bottom of Figure 1):
- Something makes the bridge deck twist slightly
- The tilted shape changes how the wind strikes it
- As a result, a force acts that increases the twist
- The twist grows further, and the cycle returns to step 2
The key point: there was no periodic push from outside. The bridge itself drew energy from a steady wind and grew its own sway. This is called self-excited vibration.
The difference from resonance is decisive. Resonance happens "when pushed at the matching timing," so it stops if the pushing stops. Self-excited vibration grows on its own, as long as the wind exceeds a certain speed. And the bigger the sway gets, the more force it draws in.
This bridge's deck was a flat, I-beam cross-section. It was a shape prone to twisting when hit by wind. Today's suspension bridge decks use smooth cross-sections like an aircraft wing, or shapes with gaps that let wind pass through. That's a direct lesson learned from this accident.
This accident stayed in textbooks as "an example of resonance" because, it's been argued, the explanation was simple and the footage was striking. Resonance is taught in secondary school; self-excited vibration is a university specialist topic. The easier explanation to teach was chosen, and it stuck.
Even after papers pointing out the error were published, it took a long time for the correction to spread. It's still cited today as an example of how "the easy explanation" can crowd out "the correct explanation."
In 2000, a new footbridge opened in London. On its first day, once large crowds began crossing, the bridge started swaying sideways. It was closed after two days, and it took over a year of fixes before it reopened.
The cause, again, wasn't simple resonance. When the bridge swayed slightly sideways, people unconsciously adjusted their balance and fell into step with the sway. Their footsteps then landed in unison, and the sway grew further. An unintended synchronization arose between people and bridge.
This wasn't "pushed periodically from outside" either — the system itself grew the sway — putting it in the same family as Tacoma Narrows.
Something you can check at home
- Hang three strings of different lengths from a horizontal cord or curtain rail, and tie a weight (like an eraser) to each
- Hold the ends of the horizontal support and move it side to side at a slow, steady tempo
- Only the longest weight swings widely. The others barely move
- Speed up the tempo, and the weight that swings widely changes in turn
You're shaking with the same force each time, but which one responds changes. You can see with your own eyes that each has a different "speed it likes to sway at." This is the same reason different buildings suffer different amounts of damage from the same earthquake.
Summary
Bridges and buildings survive wind because engineers identify each structure's "own sway speed" and design so nothing pushes it there. And the Tacoma Narrows collapse wasn't resonance — the bridge itself drew energy from a steady wind and grew its own sway.
It wasn't pushed into swaying.
It grew the sway itself.
Flow generating its own rhythm also happens in the kitchen. In Why does water glug out in bursts when you turn a bottle upside down?, you can see how water and air trading places produces a regular rhythm.
Want to go deeper? — terms, formulas, and textbook connectionsRanges from junior-high science to active research, each labeled by level
- JHSCovered in junior high school science
- HSCovered in high school physics ("Physics Basics"/"Physics")
- HS+High school "Physics," or advanced/column content in textbooks
- UnivNot taught in high school — university-level specialist courses (vibration engineering, wind engineering)
- ResearchNot settled fact even at university — an active research question
JHSTerms: words for talking about sway
- Natural frequency (natural period): this article's "speed it likes to sway at." Natural frequency is how many sways per second; natural period is how many seconds per sway.
- Resonance: when an external force's period matches the natural period, and the sway grows.
- Damping: the natural shrinking of a sway over time. Friction or a material's internal resistance turns the sway's energy into heat.
- Self-excited vibration: a phenomenon where a system draws in energy and grows its own sway without any periodic external push. This is what happened at Tacoma Narrows.
- Flutter: self-excited vibration that occurs in a structure sitting in a flow. It's also a serious problem for aircraft wings.
HSChecking with a formula: how often should you push a swing?
Resonance is "matched timing makes it swing big." So what exactly is the timing you need to match, in seconds? That can be calculated.
T = 2π √(L ÷ g)
| T time for one full swing | unit: seconds |
| L length of the string | unit: m |
| g strength of gravity | 9.8 m/s² |
| √ square root | the value that, squared, gives that number |
Notice something odd here. The weight of whoever's riding doesn't appear in the formula. That means the swing's period doesn't change no matter who's on it. An adult or a child — same period. And that's exactly what happens in practice.
A formula like this tells you not only "what matters" but also "what doesn't".
| Swing rope length | L = 2.5 m |
| First, work out inside the brackets | 2.5 ÷ 9.8 ≒ 0.255 |
| Find its square root | 0.505 × 0.505 ≒ 0.255, so the answer is about 0.505 |
| Multiply by 2π (≒ 6.28) | 2 × 3.14 × 0.505 ≒ 3.2 |
| Answer | T ≒ 3.2 seconds |
Push once every 3.2 seconds and it swings highest. Push faster or slower and the pushes start cancelling each other out. Anyone who's ever pushed a swing already knows this rhythm in their body. Here it is, as a number.
Buildings, too, swing back at a fixed speed when pushed. The exact calculation is complex, but as a rough rule of thumb, for steel-frame buildings, "number of floors × about 0.1 seconds" is sometimes used.
| 10-storey building | 10 × 0.1 = 1.0 sec |
| 50-storey building | 50 × 0.1 = 5.0 sec |
| Wooden house | roughly 0.2–0.5 sec |
This tells us something about damage patterns. A direct-hit earthquake carries strong short-period shaking, which matches wooden houses at 0.2–0.5 sec. Meanwhile, a large, distant earthquake carries slow, long-period shaking, which matches super-tall buildings at around 5 seconds. Buildings hundreds of kilometres from the epicentre swaying violently is attributed to this match.
※ These are rough figures. They vary with structure, shape, and ground conditions. Actual design calculations are done individually.
Look closely at the formula: T is proportional not to L itself but to its square root. That means you'd need to cut the length to a quarter to halve the period. Let's check.
| Cut length to a quarter | 2.5 ÷ 4 = 0.625 m |
| Inside the brackets | 0.625 ÷ 9.8 ≒ 0.0638 |
| Its square root | 0.253 × 0.253 ≒ 0.0640, so about 0.253 |
| Period | 2 × 3.14 × 0.253 ≒ 1.6 sec (exactly half of 3.2 sec) |
Just as predicted. Plugging in numbers makes clear what "proportional to the square root" actually means. That's why a short pendulum swings so much more frantically than you'd expect.
HS+How sharp resonance is, and the role of damping
How large a sway resonance produces depends on the amount of damping. With zero damping, the amplitude would in theory grow without limit. Real structures always have some damping, so it settles at a finite value.
The quantity describing "how sharply something resonates" is the Q factor. A higher Q means a stronger response over a narrower range of periods. A wine glass sings well because it has a high Q; conversely, lowering Q (increasing damping) is a design goal for buildings.
A tuned mass damper's job is exactly to artificially add this damping. It attaches an "extra pendulum" tuned to the building's natural period, and swings out of phase with the building, soaking up the sway's energy.
UnivWhy self-excited vibration is fundamentally different from resonance
The forced-vibration equation is written m ẍ + c ẋ + k x = F₀ cos(ωt), with a periodic external force on the right-hand side. Resonance is when the response grows large as ω approaches the natural frequency.
In self-excited vibration, however, there's no periodic force on the right-hand side. Instead, the force appears as a function of the system's own motion, x and ẋ. In a structure sitting in a flow, this force can effectively act in the direction that cancels damping. If the overall damping coefficient turns negative, the amplitude grows exponentially.
What happened at Tacoma Narrows is understood as single-degree-of-freedom torsional flutter. Above a certain wind speed (the flutter onset speed), the system's effective damping turns negative, and it enters a state where the sway grows on its own. "Staying below this wind speed" is a design condition — simply making a structure strong enough to withstand high wind isn't enough.
Modern long-span bridges evaluate the flutter onset speed through wind-tunnel testing and numerical analysis, and address it by refining the cross-section — adding a central slot, fitting fairings, and similar measures.
ResearchWhat's still hard
- Damping still can't be predicted theoretically. Even though it's a critically important quantity for design, it's tangled up with material internal friction, slippage at joints, interaction with the ground, and many other factors — in practice, it can only be measured by shaking real buildings. Design relies on empirically derived values, and this remains one of the most uncertain inputs.
- Synchronization between crowds and structures also isn't fully solved. The London footbridge incident spurred research into models of how pedestrian walking synchronizes with bridge sway. But accurately predicting in advance "how many people trigger it" remains hard, and design standards still lean partly on measured data. The problem involves unconscious human behaviour, which is part of what makes it difficult.
- Predicting flutter still can't do without wind-tunnel testing. Computational fluid dynamics has advanced, but computing flow around complex, full-scale cross-sections with sufficient accuracy remains far from easy, and model experiments are still indispensable in long-span bridge design.
- Predicting long-period ground motion is still developing. How slow shaking propagates to distant locations from an epicentre depends heavily on underground structure. Sedimentary basins are known to amplify shaking, but our knowledge of underground structure is limited, leaving uncertainty in predictions.
Connections to textbooks, by level
| Level | Subject / unit | Where in this article |
|---|---|---|
| JHS | Science - Pendulums / Properties of sound / Earthquakes | Natural sway speed, string-and-weight observation |
| HS | Physics - Simple harmonic motion and resonance | Natural period formula, rough building period figures |
| HS+ | Physics - Damped and forced vibration (advanced topic in many textbooks) | Q factor, how dampers work |
| Univ | Vibration engineering, wind engineering, earthquake engineering | Self-excited vibration, negative damping, flutter onset speed |
| Research | Structural engineering (unresolved) | Predicting damping, crowd synchronization, long-period ground motion |
- Billah, K. Y. & Scanlan, R. H., Resonance, Tacoma Narrows Bridge Failure, and Undergraduate Physics Textbooks, American Journal of Physics 59(2), 118–124, 1991 (the paper pointing out the error in the resonance explanation).
- Dallard, P. et al., The London Millennium Footbridge, The Structural Engineer 79(22), 17–33, 2001 (pedestrian-induced lateral sway).
- Simiu, E. & Scanlan, R. H., Wind Effects on Structures (a standard textbook of wind engineering).
- Explanatory materials on long-period ground motion from the Japan Meteorological Agency (気象庁) and the Building Research Institute (建築研究所).
- Guidelines on damping and vibration-control structures in buildings from the Architectural Institute of Japan (日本建築学会).
※ Figures such as natural period and wind speed vary greatly with structure and conditions. This article presents commonly used rules of thumb.
※ This article is a general-audience science explainer. The figures given are meant to aid understanding of the underlying mechanisms and are not actual design standards. For questions about a building's earthquake resistance or safety, please consult experts and your local authority.