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Bridge collapse: Structural issue or plain old resonance?

The Bridge in Minneapolis collapsed yesterday evening, It was built in 1967 and was undergoing some repairs. And it just collapsed like a house of cars. So, 7 people died. Now, what could lead to the collapse of a very "healthy" bridge – as it was given a "clean bill of health". Here is what I think may have some explanation to its collapse. Two theories – Resonance and Flutter (or Aeroelasticity). This could be a work of aerodynamics or wind resonance. We know that there were some jack hammers plodding and the weather was about to take a turn as rain was expected – so maybe there was some wind? I think they need to look at it in a more scientific as in aerodynamics and torsion basics probably.

Shortly after construction finished at the end of June (opened to traffic on July 1, 1940), it was discovered that the bridge would sway and buckle dangerously in relatively mild windy conditions for the area. This resonance was longitudinal, meaning the bridge buckled along its length, with the roadbed alternately raised and depressed in certain locations-one half of the central span would rise while the other lowered. Drivers would see cars approaching from the other direction disappear into valleys which were dynamically appearing and disappearing. From this behavior the bridge gained the nickname "Galloping Gertie" from a local humorist. However, the mass of the bridge was considered sufficient to keep it structurally sound.

The failure of the bridge occurred when a never-before-seen twisting mode occurred, from winds at a mild 40MPH. This is called a torsional, rather than longitudinal, mode (see also torque) whereby when the left side of the roadway went down, the right side would rise, and vice-versa, with the centerline of the road remaining still. Specifically, it was the second torsional mode, in which the midpoint of the bridge remained motionless while the two halves of the bridge twisted in opposite directions. A physics professor proved this point by walking along the centre line, unaffected by the flapping of the roadway rising and falling to each side. This vibration was due to aeroelastic flutter. Flutter occurs when a torsional disturbance in the structure increases the angle of attack of the bridge (that is, the angle between the wind and the bridge). The structure responds by twisting further. Eventually, the angle of attack increases to the point of stall, and the bridge begins to twist in the opposite direction. In the case of the Tacoma Narrows Bridge, this mode was negatively damped (or had positive feedback), meaning it increased in amplitude with each cycle because the wind pumped in more energy than the flexing of the structure dissipated. Eventually, the amplitude of the motion increased beyond the strength of a vital part, in this case the suspender cables. Once several cables failed, the weight of the deck transferred to the adjacent cables which broke in turn until almost all of the central deck fell into the water below the span.

The bridge’s spectacular self-destruction is often used as an object lesson in the necessity to consider both aerodynamics and resonance effects in structural and civil engineering. However the effect that caused the destruction of the bridge should not be confused with forced resonance (as from the periodic motion induced by a group of soldiers marching in step across a bridge).[8] In the case of the Tacoma Narrows Bridge, there was no periodic disturbance. The wind was steady at 42 mph (67 km/h). The frequency of the destructive mode, 0.2 Hz, was neither a natural mode of the isolated structure nor the frequency of blunt-body vortex shedding of the bridge at that wind speed. The event can only be understood while considering the coupled structural and aerodynamic system which requires rigorous mathematical analysis to reveal all the degrees of freedom of the particular structure and the set of design loads imposed.

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Desh Kapoor

The panache of a writer is proven by the creative pen he uses to transform the most mundane topic into a thrilling story. Desh - the author, critic and analyst uses the power of his pen to create thought-provoking pieces from ordinary topics of discussion. He writes on myriad interesting themes. Read the articles to know more about his views and "drishtikone".

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