In this blog post, we’ll examine the Tacoma Narrows Bridge collapse to understand what resonance is and how an object’s natural frequency relates to vibrations caused by wind.
On November 7, 1940, the Tacoma Narrows Bridge, built across the Tacoma Narrows in Washington State on the U.S. West Coast, collapsed. Although the bridge was designed to withstand strong winds of approximately 120 mph (about 53 m/s), the wind speed at the time of the collapse was only about 42 mph (about 19 m/s). So, was the wind that caused the bridge to collapse blowing at a speed far exceeding the design standards? The answer is no. The bridge began to vibrate violently even in relatively light winds and eventually collapsed. Consequently, this incident came as a major shock to builders and engineers alike, leaving an important lesson: when designing long-span bridges, one must consider not only the simple static loads that wind imposes on the structure but also its dynamic behavior and aerodynamic instability. So why was a wind much weaker than the design wind speed able to cause the bridge to collapse? To understand this, we need to examine the phenomenon of resonance, natural frequencies, and aerodynamic vibrations caused by wind.
Resonance is a phenomenon in which a small external force applied at a specific frequency greatly amplifies an object’s vibrations. Here, frequency refers to the number of back-and-forth movements per second and is measured in Hz (hertz). For example, if a child on a swing completes five back-and-forth movements in one second, the vibration frequency is 5 Hz. Similarly, when a repeated external force is applied to an object at a specific frequency, and that frequency is close to the object’s natural vibration characteristics, the amplitude of the object’s vibration can increase significantly. Therefore, even if a small external force acts repeatedly, it can lead to considerable movement if that force aligns with the object’s vibration characteristics. However, it is inaccurate to explain the collapse of the Tacoma Narrows Bridge solely as a typical resonance phenomenon in which the wind’s frequency exactly matched the bridge’s natural frequency. In the actual collapse process, aeroelastic instability—in which the periodic aerodynamic forces generated by the wind and the structure’s vibrations interacted to amplify the vibrations—played a significant role.
To understand the principle behind this resonance phenomenon, one must grasp the concept of natural frequency. For example, fix one end of a 30-cm ruler in place and gently flick the other end. The ruler will then vibrate up and down while one end remains stationary. At first, the vibration appears rapidly due to the externally applied force, but as time passes, various vibration components diminish, and the object’s inherent vibration characteristics become prominent. The representative frequency that the object naturally exhibits at this point is called the natural frequency. The natural frequency is determined by the object’s mass and stiffness, among other factors. Stiffness refers to an object’s resistance to deformation. Therefore, all structures possess mass and stiffness, and accordingly, each structure has its own unique vibration characteristics.
Now, let’s examine the collapse of the Tacoma Narrows Bridge from the perspective of the concept of natural frequency and the phenomenon of resonance. Just like the 30-cm ruler described earlier, the Tacoma Narrows Bridge also had unique vibration characteristics based on its mass and stiffness. When wind acts on the bridge, the bridge does not simply move as it is pushed by the wind; rather, the wind flow and the structure’s motion influence each other, causing the bridge to vibrate. In particular, periodic vortices generated by the airflow around the bridge can exert repetitive forces on it, and if these forces align with the bridge’s vibration characteristics, the vibrations can be significantly amplified. On the Tacoma Narrows Bridge, significant torsional vibrations followed the initial vertical oscillations; during this process, aeroelastic flutter occurred—in which aerodynamic forces and the structure’s motion exchanged energy—causing the vibrations to grow in an unstable manner. Therefore, one should not conclude that the bridge could not withstand winds of that magnitude simply by looking at the wind speed at the time, which was approximately 19 m/s. What is important is not only the wind’s intensity itself but also how that wind interacted with the structure’s natural vibration characteristics.
To summarize, the Tacoma Narrows Bridge was a structure with specific natural vibration characteristics. As the wind blew, repetitive aerodynamic forces acted on the structure, and under specific wind speed and flow conditions, the bridge’s vibrations gradually amplified. This process is more accurately understood as a phenomenon in which the periodic forces generated by the wind interacted with the bridge’s vibrations, continuously supplying energy to the structure, rather than simply being explained by the wind blowing at a constant frequency that exactly matched the bridge’s natural frequency. In the case of the Tacoma Narrows Bridge, in particular, torsional motion was significantly amplified, destabilizing the structure’s behavior. This ultimately led to a progressive failure in which the central span collapsed following damage to major members and suspension cables. This is why the Tacoma Narrows Bridge collapse has long been cited as a prime example for understanding resonance, vibration, and the aerodynamic stability of structures.
As demonstrated, the phenomenon of resonance can cause even a small force to result in high-amplitude vibrations under specific conditions, which can lead to the transfer of significant energy to the structure. As seen in the previous example, resonance and aerodynamic instability can cause extremely dangerous damage to structures. Not only the Tacoma Narrows Bridge but all buildings and bridges possess mass and stiffness; therefore, they each have unique vibration characteristics and are susceptible to interacting with externally transmitted vibrations or wind. Therefore, when designing a structure, one must not simply consider how much wind or load it can withstand; instead, one must comprehensively consider the structure’s stiffness, mass, damping characteristics, and natural vibration characteristics, along with its aerodynamic behavior induced by wind. The collapse of the Tacoma Narrows Bridge serves as a prime example illustrating just how crucial it is for structural safety to identify and prepare for the risks of such vibrations and aerodynamic instability in advance.
