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Construction and design

Describe about the Case Study Topic for Tacoma Narrows Bridge.

Tacoma Narrows Bridge connects Kitsap Peninsula and Tacoma and Washington State Department of Transportation maintains this bridge. Tacoma Narrows Bridge has exhibited a large oscillation in vertical manner and total length of this particular bridge is 5000 feet. However, Tacoma Narrows Bridge was opened on 1940, July 1 and it was collapsed just after four moths because of aero elastic flutter, which is caused by a wind of 42 mph. The major reason of collapsing Tacoma Narrows Bridge was the failure of engineering and science. Arioli and Gazzola (2015) have mentioned that the use of plate girders and the main length of the span should be decided with a proper consultation of the potential civil engineer. Tacoma Narrows Bridge was narrow and long in unusual manner and was severely compared with the other existing suspension bridges of previous era. The design of Tacoma Narrows Bridge was not suitable as cheaper stiffening used for girders, which are 8 foot tall. Even the stiffening was not in adequate manner and aerodynamic stability theory of suspension bridges had not worked out in the case of Tacoma Narrows Bridge (McKenna 2014).

The facilities and possibilities of wind tunnel were not available for Tacoma Narrows Bridge because of the military effort of pre-war. As opined by König and Weig (2012), suspension bridges require wind tunnel, which can move a large quantity of air instead of slow velocity and it should be controlled in careful way. Tacoma Narrows Bridge collapsed because of desirability of three-dimensional dynamic model and the partial use of this model. Gander and Kwok (2012) have stated that the issue of stability includes aerodynamic lift, which is very much sensitive towards the profile of deck.

In today’s great era of suspension bridge the concept of using rope for the cables is an old one and with the constant advancement of technologies, there are drastic transformation in the designing and construction of suspension bridge (Fernandes and Armandei 2014). Mostly the chains, wrought-iron bars and iron bars are used instead of cables and ropes in order to build a perfect and durable suspension bridge. However, the collapsing of suspension bridge is not as abnormal as it mainly collapses only because of windstorms or after suffering various damages. Therefore, people generally avoids suspension bridges during 19th century as it was unreliable and risk, with the advancement of modern technology and bridge architecture, the suspension bridges are built in reliable manner by the civil engineer. McRobie et al. (2013) have suggested that deflection theory is considered as best way o build suspension bridges as following this particular theory, suspension bridges do not require cable stays or stiffening trusses. This is the reason that suspender cable, main cables, weight of the deck provides the structural strength alone against the fundamental effects of traffic and wind in sufficient manner. Tacoma Narrows Bridge represents a perfect culmination of the contemporary trend for building a longer bridge with low stiffening and narrower road width.

Reasons behind the Collapse of Tacoma Narrows Bridge

The civil engineers encountered first problem of building Tacoma Narrows Bridge involves the geographical location of the bridge itself, as the water is more than 200 feet deep and treacherous and swift tides move 8.9 miles per hour. Even the basic lengths of crossing of Tacoma Narrows Bridge posed difficulties with the combination of water depth. If the incident of collapsing would not happen, then Tacoma Narrows Bridge would be third longest suspension bridge, holding its position just after Golden Gate Bridge and George Washington Bridge (Malík 2013).

The major reason of collapsing of the Tacoma Narrows Bridge is the traffic surveys, which is imposed by the challenge of final engineering, as there is no justification of making a bridge of more than two lanes. Clark Eldridge developed the original design of the Tacoma Narrows Bridge and this particular design suggested two traffic lanes and towers of completely different heights, 2 side spans, stiffening trusses of 25 feet deep and a centre span. However, this primary design was changed after the force of federal authorities and Moisseif has made the new design of this particular ridge. Koo et al. (2013) have suggested that a suspension bridge should be most appropriate choice for the decided site. However, only because of the critical design just after four months, Tacoma Narrows Bridge collapsed during a windstorm as the attached cables were anchored into the ground and later the cables were replaced and because of it was scary, notorious and risky of travelling through this particular suspension bridge during high winds. As the mathematics of oscillations were difficult to understand in the era of 1940, therefore, the design of Tacoma Narrows Bridge was not appropriately made and it collapsed after oscillating and twisting in violent manner because of a windstorm of 60 kph. However, there were also advantages of Tacoma Narrows Bridge.

As opined by Olson et al. (2015), Tacoma Narrows Bridge was more flexible than the Golden Gate Bridge and George Washington Bridge. The other bridges of its time are more stiff and less prone to the accelerations of wind induction. The Federal Works Agency (FWA) identified and investigated the major reasons behind the collapse of Tacoma Narrows Bridge. Although this bridge was well built and well designed, it failed to face the static forces like windstorm (Pipinato 2013). The exceptional flexibility of Tacoma Narrows Bridge is another reason of the collapse as it was unable to absorb the dynamic forces that can handle wild oscillations. Wind causes a vertical oscillation and it caused structural damage before collapsing. North end’s cable band failed to prevent the sudden twist motion on the bridge. As opposed by Arioli and Gazzola (2016), any kind of twisting motion can cause a high stress into the bridge that is responsible for leading a failure of collapsing of central span and suspenders. Although the workmanship and supervision of Tacoma Narrows Bridge was exceptional, still it collapsed just after four months of its inauguration because of technical fault and wrong mathematical design of suspension bridge. Another major reason of collapsing Tacoma Narrows Bridge involves its rigidity against the existing dynamic forces and static forces, which can be calculated by employing the same mathematical methods of civil engineering (Bulleit 2013). However, there were efforts for handling ad controlling the primary amplitude of oscillation of the bridge during windstorm.

Theories of Collapsing the Bridge

Carpinteri and Paggi (2013) have stated that relevant experiments and studies are required for determining the necessity of aerodynamic forces that has a serious impact upon suspension bridge. Only because of the narrowness, lightness and extreme flexibility, Tacoma Narrows Bridge failed to face the random environmental forces. There was a resonance on the bridge because of structural difficulties and the natural frequencies approached the oscillation, which was induced by the wind (Wuand Kareem 2013). An aeronautical engineer, named von Karman, has provided another explanation of the collapse of Tacoma Narrows Bridge. According to this individual, the attributed motion of this particular bridge creates a periodic shedding of large air vortices and then there was structural oscillation. Oh (2014) has argued with this proposed theory and mentioned that this theory cannot be considered to be appropriate in the case of Tacoma Narrows Bridge because of critical and wrong mathematical calculation. Tacoma Narrows Bridge collapses because of the general proportions of this particular bridge and the type of floor and stiffening girders. The basic ration of width of this bridge to the length of central span was smaller. Even its vertical stiffness was less than the previously constructed bridges (Zhao et al. 2014).

As bridges are all about appropriate structures, therefore, all the features should be added according to the stiffness and strength of it. The consequences of a bridge failure are immense as the society begins to question to the structure and type of the bridge. Even during the planning of next design of suspension bridges, the civil engineers should follow the modern law of physics for actual life span of the bridges. The theories of aerodynamics have been proved as essential while making the design of suspension bridge. According to Meador (2014), the present bridge architecture is solely based on the appropriate and cumulative experiences of the bridge planners, builders, designers and fabricators. Even the bridge designer should have made a thorough research on the existing forces that can damage the structure of bridge and its ultimate collapsing (Rogers et al. 2013).  The associated engineers, who have investigated the collapse of Tacoma Narrows Bridge has found that it caused because of high level of flexibility, lightness and narrowness, which is completely against the theories of physics of making a stable and strong bridge. Yu et al. (2012) have suggested that resonance can be considered as an essential process and the frequency of the object should be matched with the natural frequency level, that has the potentiality to cause a dramatic enhance in the amplitude. Robert H. Scanlan and K Yusuf Billah have come up with another theory of collapsing of the Tacoma Narrows Bridge (Brownjohn et al. 2014). They suggested that because of aerodynamic flutter, the bridge collapsed.  The physics theory can be applied here as the rotation of the deck of Tacoma Narrows Bridge became faster during the action of wind force and because of this; there was a failure in centre stay. The constant enhances in the rotation and negative damping effects lead up a terminal oscillation, which caused the collapse of this particular bridge (Tang and Bittner 2013).

Zhan and Fang (2012) have mentioned the collapse of Tacoma Narrows Bridge clearly reveals the failure of engineering education. Static forces like wind with high velocity have destroyed most of the suspension bridges. In this era of new technologies, there should be a perfect and adequate balance in between the progress and public welfare. If Moisseif followed the same design of the existing suspension bridge that sustained and is stable, therefore, Tacoma Narrows Bridge would not collapsed for the costs of endangering lives and dollars. Even if the engineers had not adapted innovative techniques of building suspension bridges, then there would be no such disaster (Seely 2015). The engineers should not push the ultimate limits of the present modern technologies, for making the most flexible suspension bridge and there was very little consideration of the research that it could hold the weight of rail traffic. The actual failure was the structural design of the Tacoma Narrows Bridge, which was sleeker, longer and less expensive bridge. As opined by Hook and Olson (2015), the pushing of the modern technologies by the civil engineer caused such disasters like the collapse of Tacoma Narrows Bridge and offer with the cost of the loss of life. However, with the advancement in modern technology, the bridge architecture is constantly improving and it can be expected from the potential and efficient civil engineers not to make same faults of building the Tacoma Narrows Bridge during their new ventures. The civil engineers should learn more about the physics of oscillation while making the suspension bridge and avoid the cases like Tacoma Narrows Bridge (Olson 2015). Even the implementation of the dumping devices ether being planned and installed in the bridge.

Conclusion

Tacoma Narrows Bridge was not the first suspension bridge that collapses because of technical faults or the wrong measurement in the structural design of the bridge. In fact, from the history of bridge architecture, it can be seen that there are several cases of destruction of suspension bridges only because of their failure to prevent the static and aerodynamic forces in proper manner. Tacoma Narrows Bridge was the most expensive suspension bridge, which collapsed after interaction with the windstorm. The civil engineers should remember the safety of human beings before designing and innovating structures of the new suspension bridges. The collapse of Tacoma Narrows Bridges reveals the necessity of vertical rigidity, torsion resistance and damping in the suspension bridges. This disaster should be avoided during the basic design of the bridge.

References

Arioli, G. and Gazzola, F., 2015. A new mathematical explanation of what triggered the catastrophic torsional mode of the Tacoma Narrows Bridge.Applied Mathematical Modelling, 39(2), pp.901-912.

Arioli, G. and Gazzola, F., 2016. Torsional instability in suspension bridges: the Tacoma Narrows Bridge case. Communications in Nonlinear Science and Numerical Simulation.

Brownjohn, J.M.W., Koo, K.Y. and De Battista, N., 2014. Sensing solutions for assessing and monitoring bridges. Sensing technologies for civil infrastructures, 2, pp.207-233.

Bulleit, W.M., 2013. Uncertainty in the design of non-prototypical engineered systems. In Philosophy and Engineering: Reflections on Practice, Principles and Process (pp. 317-327). Springer Netherlands.

Carpinteri, A. and Paggi, M., 2013. A theoretical approach to the interaction between buckling and resonance instabilities. Journal of Engineering Mathematics, 78(1), pp.19-35.

Fernandes, A.C. and Armandei, M., 2014. Phenomenological model for torsional galloping of an elastic flat plate due to hydrodynamic loads. Journal of Hydrodynamics, Ser. B, 26(1), pp.57-65.

Gander, M.J. and Kwok, F., 2012. Chladni figures and the Tacoma bridge: motivating PDE eigenvalue problems via vibrating plates. SIAM Review,54(3), pp.573-596.

Hook, J. and Olson, D., 2015. Analyzing the Tacoma Narrows Bridge Collapse Using the Physics of Free Fall. Bulletin of the American Physical Society, 60.

König, D.R. and Weig, E.M., 2012. Voltage-sustained self-oscillation of a nano-mechanical electron shuttle. Applied Physics Letters, 101(21), p.213111.

Koo, K.Y., Brownjohn, J.M.W., List, D.I. and Cole, R., 2013. Structural health monitoring of the Tamar suspension bridge. Structural Control and Health Monitoring, 20(4), pp.609-625.

Malík, J., 2013. Sudden lateral asymmetry and torsional oscillations in the original Tacoma suspension bridge. Journal of Sound and Vibration, 332(15), pp.3772-3789.

McKenna, P.J., 2014. OSCILLATIONS IN SUSPENSION BRIDGES, VERTICAL AND TORSIONAL. Discrete & Continuous Dynamical Systems-Series S, 7(4).

McRobie, A., Morgenthal, G., Abrams, D. and Prendergast, J., 2013. Parallels between wind and crowd loading of bridges. Phil. Trans. R. Soc. A,371(1993), p.20120430.

Meador, G., 2014. Failure by Design. Source: https://www. bps-ok. org/physics/faildes/failure_by_design. pdf, Accessed on, 10.

Oh, H., 2014. Motion in a hanging cable with various different periodic forcing. The Pure and Applied Mathematics, 21(4), pp.281-293.

Olson, D., 2015. The 75th Anniversary of the Tacoma Narrows Bridge Collapse. Bulletin of the American Physical Society, 60.

Olson, D., Hook, J., Doescher, R. and Wolf, S., 2015. The Tacoma Narrows Bridge collapse on film and video. The Physics Teacher, 53(8), pp.461-465.

Pipinato, A., 2013. Moving load and fatigue analysis of a long span high speed railway bridge. In Advanced Materials Research (Vol. 629, pp. 403-408). Trans Tech Publications.

Rogers, M., Pfaff, T., Hamilton, J. and Erkan, A., 2013. Incorporating Sustainability and 21st-Century Problem Solving into Physics Courses. The Physics Teacher, 51(6), pp.372-374.

Seely, B., 2015. Wind Wizard: Alan G. Davenport and the Art of Wind Engineering. by Siobhan Roberts (review). Technology and Culture, 56(1), pp.281-283.

Tang, P. and Bittner, R.B., 2013. Use of value engineering to develop creative design solutions for marine construction projects. Practice Periodical on Structural Design and Construction, 19(1), pp.129-136.

Wu, T. and Kareem, A., 2013. A nonlinear convolution scheme to simulate bridge aerodynamics. Computers & Structures, 128, pp.259-271.

Yu, Y., Wang, J., Mao, X., Liu, H. and Zhou, L., 2012. Design of a wireless multi-radio-frequency channels inspection system for bridges. International Journal of Distributed Sensor Networks, 2012.

Zhan, H. and Fang, T., 2012. Flutter stability studies of Great Belt East Bridge and Tacoma Narrows Bridge by CFD numerical simulation.

Zhao, X., Gouder, K., Limebeer, D.J. and Graham, J.M.R., 2014, December. Experimental flutter and buffet suppression of a sectional suspended-bridge. In 53rd IEEE Conference on Decision and Control (pp. 3197-3202). IEEE.

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