At the entrance of puente Albert Bridge In London there is a sign that reads: ‘All troops must break step when marching over this bridge’. A legend that recalls the tendency of the structure, inaugurated in 1873, to vibrate when a large number of people walked on it. A singularity that motivated her to be nicknamed from the beginning as ‘trembling lady’ (trembling lady).
The vertical rocking caused by the march of the troops on the platform of a bridge was already a known fact. In the year 1831 the seventy-four men of a company of the rifle corps of the British army -on returning from military maneuvers- noticed a slight rocking when they walked on the broughton bridge, in Manchester. In seconds they increased in intensity and a few minutes later one of the four pillars that supported the chain that supported the weight of the bridge gave way and the structure collapsed.
Physics has taught us that an action with a similar frequency to the structure may be able to collapse it, even though the value of the action is much smaller compared to the action with which it was designed. We know this phenomenon as resonance.
It was the fault of the flame
The same luck befell the angers bridge on French soil. The event occurred in 1850 while a battalion of French soldiers were crossing it, despite the fact that they had broken the pass and increased the distance between them. In this case, it was the action of the wind that caused a strong oscillation of the deck, preventing the soldiers from maintaining verticality.
To avoid falling into the river, the Gauls continuously moved from the lowest to the highest area of the board, which, having more weight, descended abruptly causing the soldiers to have to run again to the opposite side. With these swings, the only thing they managed to do was increase the resonance of the board. The collapse of the bridge caused the death of more than two hundred people.
The cause of the collapse was due to a phenomenon known as flutter, a self-induced vibration that is generated when an airfoil bends under aerodynamic load.
Perhaps the flutter is better understood by recalling a sensation that we have all experienced at some time when driving. If we put our left hand out the window when the car is moving and place it parallel to the ground, we cut the air, but if we turn the wrist a few degrees, raising the thumb area, we feel that an invisible force pulls our arm up. If we then turn the wrist in the opposite direction, the effect will be the reverse, the hand feels attracted to the ground. This phenomenon is precisely the flutter.
Synchronous Side Excitation
In the year 2000, the millennium bridge, a steel suspension bridge for pedestrian use and linking Bankside with the City of London. An unexpected and excessive lateral vibration due to a resonant structural response caused its closure two days after its opening.
After many diagnostic tests, the experts concluded that it had suffered a “synchronous lateral excitation”, in Roman Paladino, the deck had swayed slightly as pedestrians passed, but the oscillations increased when the daunted pedestrians adjusted their pace to the movements of the bridge. That ‘corrective’ maneuver not only fed back the effect, but also intensified it. The problem was solved after installing a series of additional shock absorbers to the structure.
The collapse of the Tacoma Narrows Bridge
Under normal conditions when the load is reduced the deflection is subdued and the original shape of the structure is restored. In the most harmless cases there may be a slight buzzing in the structure, but in the most violent cases it may suffer irreparable damage. One of the best-known extreme cases was that of the Tacoma Narrows Bridge.
In the summer of 1940, the Tacoma Narrows Bridge in Washington State opened to traffic, becoming the third longest suspension bridge in the world, behind the Golden Gate Bridge and the George Washington Bridge. From the very beginning the platform moved vertically when there was wind, so the workers soon nicknamed it ‘Galloping Gertie’. Despite the fact that several damping measures were carried out, the bridge collapsed the same year of its inauguration, after being hit by winds of up to 64 km/h. At that speed the bridge stopped oscillating vertically and began to wriggle crosswise, like a drying towel.
A swarm of onlookers came by to watch the spectacle, including Barney Elliott, a local photographer who videotaped the sequence of movements. In the film, which can be seen today on the Internet, oscillations of an amplitude close to seven and a half meters are observed.