Tacoma Bridge Collapse Resonance

The Tacoma Narrows Bridge Collapse: A Resonant Disaster

The collapse of the Tacoma Narrows Bridge on November 7, 1940, remains a chilling example of the devastating consequences of resonance, a phenomenon where a system vibrates with increasing amplitude when subjected to external forces matching its natural frequency. This article will explore the intricate interplay of wind, bridge design, and resonance that led to this catastrophic event, examining the scientific principles involved and the lessons learned from this tragic incident. We will dissect the factors contributing to the collapse, analyze the subsequent investigations, and highlight the enduring impact on engineering design and safety protocols.

Understanding Resonance: A Simple Analogy

Before delving into the specifics of the Tacoma Narrows Bridge, let's understand the basic concept of resonance. Imagine pushing a child on a swing. You don't push randomly; you time your pushes to match the swing's natural rhythm. Each push adds energy, increasing the swing's amplitude until it reaches a considerable height. This is resonance: the amplification of vibrations when an external force matches a system's natural frequency. The Tacoma Narrows Bridge, unfortunately, experienced a similar effect, but with far more dramatic consequences.

The Design Flaws of the Tacoma Narrows Bridge

The original Tacoma Narrows Bridge was a suspension bridge with a relatively long and slender deck. This design, while aesthetically pleasing, possessed inherent weaknesses concerning aerodynamic stability. Its shallow deck, only 8 feet deep, offered little resistance to wind forces. Furthermore, the stiffening girders – designed to counteract vertical oscillations – were insufficient to handle the torsional (twisting) forces generated by the wind. This lack of torsional stiffness proved to be a crucial factor in the bridge's demise.

The Role of Wind and Aerodynamic Flutter

The collapse wasn't caused by a single, powerful gust of wind, but rather by a complex interaction between the wind and the bridge's structure. A phenomenon called "aerodynamic flutter" played a critical role. Flutter occurs when the wind's force interacts with the bridge's flexible structure, creating a feedback loop. Slight oscillations, initially induced by the wind, are amplified by the wind itself, leading to progressively larger and faster oscillations. Think of it like a leaf caught in a vortex – the swirling wind increases the leaf's spinning motion. This process continued until the oscillations exceeded the bridge's structural limits, leading to the catastrophic failure.

The Collapse and its Aftermath

On that fateful day, a relatively moderate wind of around 40 mph triggered the fatal oscillations. The bridge began to undulate, first in a vertical motion, then increasingly in a torsional motion – twisting back and forth. These oscillations intensified rapidly, exceeding the bridge's elastic limit and ultimately leading to its collapse. The bridge's failure generated a significant amount of debris, but remarkably, only one car was on the bridge at the time, whose driver escaped unharmed. This disaster prompted extensive research into bridge aerodynamics and led to significant improvements in bridge design and construction techniques.

Lessons Learned and Modern Bridge Design

The Tacoma Narrows Bridge collapse served as a stark lesson in the importance of understanding and mitigating the effects of wind and resonance in bridge design. Subsequent investigations identified the critical role of aerodynamic stability, leading to the development of more robust design principles. Modern bridges incorporate features such as deeper decks, increased torsional stiffness, and sophisticated aerodynamic analysis to prevent similar catastrophes. Wind tunnel testing is now a standard procedure in bridge design, allowing engineers to assess a bridge's response to various wind conditions and prevent resonance-induced failures.

Conclusion

The Tacoma Narrows Bridge collapse remains a pivotal moment in engineering history, highlighting the potentially devastating consequences of neglecting the principles of resonance and aerodynamic stability. The disaster spurred significant advancements in bridge design and construction, leading to safer and more resilient structures. The legacy of this event continues to shape engineering practices, reminding us of the critical importance of rigorous analysis and a deep understanding of the forces acting upon structures.

FAQs

1. What is the primary cause of the Tacoma Narrows Bridge collapse? The collapse was primarily caused by aerodynamic flutter, a self-sustaining oscillation induced by the interaction between wind and the bridge's flexible, shallow deck.

2. Could this happen to modern bridges? While modern bridges are designed with significantly improved aerodynamic stability and incorporate wind tunnel testing, the possibility of resonance-induced failure, though greatly reduced, remains a concern that engineers actively address.

3. What is the difference between vertical and torsional oscillations? Vertical oscillations are up-and-down movements, while torsional oscillations involve twisting or rotating motions. The Tacoma Narrows Bridge experienced both types.

4. What safety measures are now in place to prevent similar incidents? Modern bridge design incorporates advanced aerodynamic analysis, wind tunnel testing, increased torsional stiffness, and deeper decks to enhance stability and resist wind-induced oscillations.

5. What materials are used in modern bridges to enhance resilience? Modern bridges often utilize high-strength steel, composite materials, and advanced concrete formulations to increase their strength and resistance to various environmental stresses, including wind.

Search Results:

A new mathematical explanation of the Tacoma Narrows Bridge collapse The purpose of the present paper is to suggest a new mathematical model for the study of the dy-namical behavior of suspension bridges which provides a realistic explanation of the Tacoma collapse.

A MATHEMATICAL MODEL OF A SUSPENSION BRIDGE CASE STUDY: ADOMI BRIDGE … The collapse of the Tacoma Suspension Bridge in 1940 stimulated interest in mathematical modeling of suspension bridges. The reason of collapse was originally attributed to resonance and this was generally accepted for fifty years until it was challenged by mathematicians Lazer and McKenna (Lazer and McKenna, 1990).

A Comprehensive Review of the Aeroelastic Collapse of the Tacoma … Four crucial aspects have been synthesized in order to fully understand the difficulties underlying the Tacoma Bridge collapse. All these elements work together to provide a more complex picture of the Tacoma Bridge's unique collapse mechanism.

A new detailed explanation of the Tacoma collapse and some … Abstract: We give a new full explanation of the Tacoma Narrows Bridge collapse, occurred on November 7, 1940. Our explanation involves both structural phenomena, such as parametric resonances, and sophisticated mathematical tools, such as the Floquet theory.

A new detailed explanation of the Tacoma collapse and some … We give a new full explanation of the Tacoma Narrows Bridge collapse, occurred on November 7, 1940. Our explanation involves both structural phenomena, such as parametric resonances, and...

the Tacoma Narrows Bridge case - arXiv.org We suggest a new nonlinear model for a suspension bridge and we perform numerical experiments with the parameters corresponding to the collapsed Tacoma Narrows Bridge. We show that the thresholds of instability are in line with those observed the day of the collapse. Our analysis enables

arXiv:physics/0408101v1 [physics.flu-dyn] 22 Aug 2004 The Tacoma Narrows Bridge opened on July 1, 1940 and collapsed on November 7, 1940 under winds of approxi-mately 40 mph. During that brief period, it became an attraction as it oscillated, at a relatively low amplitude (a few feet) in a number of diﬀerent modes, in all of which the bridge deck remained horizontal. Low mechanical damping

The Tacoma Narrows bridge - MIT Mathematics central span of the bridge collapsed and fell into the water below. One car and a dog were lost. Why did this collapse occur? Were the earlier oscillations a warning sign? Many di erential equations textbooks announce that this is an example of resonance: the gusts of wind just happened to match the natural frequency of the bridge.

Old and new explanations of the Tacoma Narrows Bridge collapse … collapse with resonance. History may explain why the TNB collapse was attributed to resonance. Built in 1826, the Broughton Suspension Bridge collapsed in 1831 due to mechanical resonance induced by troops marching over the bridge in step. Since then, all troops “break step” when crossing a bridge. The

The Tacoma Narrows Bridge collapse - Harvard University O n 7 November 1940 the Tacoma Narrows Bridge in Washington State collapsed during a gale. The remarkable oscillations of its long and slender center span in the months leading up to the catastrophe earned the bridge the moniker “Galloping Gertie.” The disaster is especially well known because of dramatic film footage taken the day of the collapse.

Resonance, Tacoma Narrows bridge failure, and undergraduate physics ... Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks K. Yusuf Billah and Robert H. Scanlan Citation: Am. J. Phys. 59, 118 (1991); doi: 10.1119/1.16590 View online: http://dx.doi.org/10.1119/1.16590 View Table of Contents: http://ajp.aapt.org/resource/1/AJPIAS/v59/i2 Published by the American Association of Physics …

The failure of the Tacoma Bridge: A physical model - University of … The Tacoma Narrows Bridge opened on July 1, 1940 and collapsed on November 7, 1940 under winds of approxi-mately 40 mph. During this brief period of existence, the bridge became an attraction as it oscillated at a relatively low amplitude a few feet at the very most in a number of dif-ferent modes, in all of which the bridge deck remained hori ...

Figure 2a. Failure of the Tacoma Narrows Bridge - Vibrationdata 7 Apr 2009 · Tacoma Narrows Bridge, Strouhal Calculation The original Tacoma Narrows Bridge collapsed in 1940. It experienced severe torsional oscillations driven by a 42 mile per hour wind. The fundamental weakness of the Tacoma Narrows Bridge was its extreme flexibility, both vertically and in torsion.

The Collapse of the Tacoma Narrows Suspension Bridge Recent research provides an alternative explanation for the collapse of the Tacoma Narrows Bridge. Lazer and McKenna [4] contend that nonlinear effects, and not linear resonance, were the main factors leading to the large oscillations of the bridge (see [5] for a good review article). The theory involves partial differential equations.

THE TACOMA NARROWS BRIDGE FAILURE Revision A 29 Dec 1999 · Strong winds caused the bridge to collapse on November 7, 1940. Initially, 35 mile per hour winds excited the bridge's transverse vibration mode, with an amplitude of 1.5 feet. This motion lasted 3 hours. The wind then increased to 42 miles per hour. In addition, a support cable at mid-span snapped, resulting in an unbalanced loading condition.

Chapter Eii: Suspension Bridges – Tacoma Narrows Case Study There are lots of videos showing the movement and collapse, search Tacoma Narrows Bridge collapse on the internet.

Ethical Issues from the Tacoma Narrows Bridge Collapse - CED … blame for the bridge’s collapse, but other early investigations tended to conclude that the probable cause was self-induced vibrations driven by vortex shedding as the wind passed around the solid plate girders.

A new mathematical explanation of what triggered the … We suggest a mathematical model for the study of the dynamical behavior of suspension bridges which provides a new explanation for the appearance of torsional oscillations during the Tacoma collapse. We show that internal resonances, which depend on the bridge structure only, are the source of torsional oscillations.

Vertical and torsional vibrations before the collapse of the Tacoma ... We perform a three-dimensional direct numerical simulation of flow over the Tacoma Narrows Bridge to understand the vertical and torsional vibrations that occurred before its collapse in 1940. Real-scale structural parameters of the bridge are used for the simulation.

Twin Views of the TACOMA NARROWS BRIDGE COLLAPSE After the various studies of the collapse, a new suspension bridge was constructed at the same location . The new bridge is four lanes wide and has open grid sides instead of solid I-beams . It was opened on October 14, 1950, and has not displayed any of the interesting oscillatory properties of the first bridge . Tacoma Narrows Bridge History