Cable bridges are a type of bridge which are capable of achieving long spans. Like any relatively new system, cable bridges have a lot of unknown problems and behaviors. Since the time this type of bridge was invented (1784), a lot of failures took place and became educational cases for new design projects. Construction of cable bridges are very expensive, therefore each failure wastes lots of money. In addition, failure of a bridge, even a performance failure, can cause life loss. Therefore, we should study past failure events to improve our design criteria and construction methods.
There are different types of cable bridges which can be categorized in two main groups. These two group are called are "Cable Stay Bridges" and "Suspension Bridges". In addition to common problems and failures among cable bridges, in general, each type of cable bridge also has its own range of problems. Some of these failure causes are related to structural elements of the bridge and some are related to characteristic behaviors of these long span bridges. In this article different major problems of cable bridges are discussed and different case study examples of each type are presented.
Differences Between Cable Stayed Bridges and Suspension Bridges
The main difference between cable stayed bridges and suspension bridges is in the way that they transfer loads from deck to pylon. As depicted in Figure 1, in cable stayed bridges straight cables transfer deck loads directly to the pylon (Walther et al., 2003, P19-39). But as shown in Figure 2, in suspension bridges, there are main cables (suspension cables) that carry vertical cables. These vertical cables behave as restraints for the deck and transfer deck loads to the main cables.
Usually main spans of suspension bridges are longer than cable stay bridges; therefore, decks of the suspension bridges have less stiffness in comparison with cable stay bridges. As a result, suspension bridges have more vibration concerns. In addition, design and construction of suspension bridges are more complicated rather than cable stay bridges; and that's the reason why most of the failures of the cable bridges happened in suspension bridges.
Deck Vibration
Due to the low stiffness, light weight, and long spans of cable bridges, the lateral and torsional stiffness of these bridges are low in comparison with regular non-cable bridges . Usually, cable bridges are built in vast areas such as rivers, coasts, and valleys. Therefore, they are exposed to wind loads. The speed of the wind through a bridges varies frequently; in some moments it decreases and in some moments it increases. If the wind speed variations follows a regular pattern, then the time distance between tow adjacent peeks of wind speed graph can be called as period of the wind loads. Usually wind loads have long periods. Because of high stiffness and short natural vibration period of the regular bridges (non-cable bridges), wind resonance usually cannot happen on them. But, cable bridges have long periods in both lateral and torsional vibration; therefore, resonance is a design concern in this type of bridge (Miyata, 2003, P1407 and Plaut, 2008, P613-5). Due to the above mentioned difference between cable bridges and regular bridges (non-cable bridges), a lot of collapses and performance failures have happened since the cable bridge invention. Tacoma Narrows Bridge (Wiki Failures) and Silver Bridge over Ohio River are two examples of cable bridge failures which led to complete collapse of structures. In Figure 3 and 4 the Tacoma Narrows bridge is shown during the fluttering and at the moment of collapse, respectively.
Figure 3: Tacoma Narrows Bridge with severe viberation (Credit by: YouTube)
Figure 4: Tacoma Narrows Bridge after collapse due to wind fluttering (Credit by: Wikipedia)
At the earlier time of use of cable bridge systems, due to the lack of information about the behavior of this type of bridge, designers didn't pay enough attention to the deck stiffness of the bridges. As a result, a lot of bridges were faced with wind-fluttering problems. In bridges with this problem, when the period of wind impact loads becomes close to the period of deck vibration, they begin to oscillate. This oscillation can continue to the point of damage or collapse of the bridges.
There are two major solutions for fluttering problems of cable bridges (Miyata, 2003, P1403-5). a) Modification of the Deck: In this solution the shape and configuration of the bridge deck become modified to create a more stiff deck (with respect to the length of the span). In addition, the shape of the deck can be modified to a more aerodynamic shape resulting in less wind load on the deck. b) Use of Dampers: By use of damper the induced energy to the deck and cables can be damped. In addition, dampers limit deformation of the deck and by this means keep the deck away from large deformation.
Low lateral, torsional ,and vertical stiffness of the cable bridges can cause performance failure of the bridges in some cases. A good example of this type of failure is Millennium Pedestrian Bridge in London which became closed a few days after opening for fixing its problem. The problem was side vibration of the bridge deck due to pedestrian walking synchronous lateral excitation. Two main reasons of this vibration was low lateral stiffness of the deck and low damping potential of the bridge for lateral movements and deformations. The problem of the Millennium bridge was solved by installation of lateral dampers (Newland, Cambridge University website). In Figure 5 a view of this bridge is shown. In the following YouTube link a movie of vibration of this bridge is shown: YouTube Link
Figure 5: Millennium Bridge in London (Credit by: Wikipedia)
Ship Collision with Pylon
Generally, cable bridges have long-spanned deck and high-rise pylons which results in a high distance of the free-board. With these characteristics, passing of huge vessels is possible through the spans. Unfortunately, the redundancy of this type of bridge is low; as a result, if one of the pylons fails, all parts of the bridge will fail. Therefore, soundness of the pylons is an essential factor in stability of the cable bridges. As we can see in the history of bridges, collision of vessels with piers is one of the most common reasons of failures. Fortunately, pier collocation evidences before and after the invention of cable bridges made designers aware to prevent collision with pylons (Svensson, 2009, P21-31). There are two main solutions to prevent collisions with pylons which are listed in the following:
a) Pier barriers: In this solution, some barriers, which are in fact short columns, become installed around the pylon. By this means, if a ship mislead through the pylon, it will collide with the barrier instead of pylon. In Figure 6, the Sunshine Skyway Bridge is shown which is protected by barriers. The old Sunshine Skyway Bridge collapsed in 1980 due to collision of a vessel with one of the piers of the bridge (Sayers, 2007, P1) and it cost $244 million to reconstruct a new bridge. b) Decreasing the number of collision-exposed pylons: Characteristic of cable bridges makes it possible to have longe spans. Therefore, designers prefer to place pylons out of water, have longer spans, and by this means prevent collision of vessels with pylons
Figure 6: Pylon protection against collision in Sunshine Skyway Bridge (Credit by: Wikipedia)
Tendon System Problems
Like each relatively new material, a tendon has its unknown problems. In addition, long tendons have different behavior in comparison with short tendons. Fortunately, due to use of multiple-tendon cables, and high redundancy cable systems, failure of tendons often only results in temporary performance issues with the bridge. Therefore, by regular control and maintenance of the cables, we can prevent failures, when without a frequent maintenance procedure we can expect the collapse of the bridge.
One of these failures is rain/wind-induced vibration of cables. If some of the cables become loose or if the pretension loads in the cables be non-compatible with the dead load distribution, then under the combination of light wind and rain loads, they began to vibrate like strings (FHWA, 2007, P13-14). In the following link a movie of Sabo Pedestrian Bridge vibration is shown: Youtube Link
There is three solution for this type of failure (FHWA, 2007, P14-36): a) Special surface shape: Specially roughed surface of the cables ducts efficiently increases aerodynamic stability of the cables. In Figure 7 different common shapes of the ducts are depicted. b) Use of Dampers: By use of dampers, the movement of the cables become limited and the vibration energy of the cables become damped. Usually, these dampers are install between deck and cables (perpendicular to the cables direction). In figure 8, use of dampers in Ravenel Bridge is shown. c) Tie of the cables together: By installing the cross-tie on the cables, internal restraints for the cables become established, and as a result, transverse stiffness of the cables increases. In Figure 9, a sample cross-tie is shown.
Figure 7: Common types of cable duct surface in cable stayed bridges (Credit by: FHWA)
Figure 8: Dampers on Ravenel Bridge cables (Credit by: Wikipedia)
Figure 9: Cross-tie on cables (Credit by: FHWA)
Another type of failure in the cable systems is cable anchorage failure. Transfer and distribution of concentrated load in the cables are two main duties of cable anchorages. Due to the changes in the magnitude of the cable load, fatigue can easily happens in anchorages. Therefore, a regular inspection is necessary to avoid fracture in in the anchorages. In Figure 10, tearing out of one of the of Sabo Bridge anchorages is shown (Wiss, 2012, P35).
Figure 10: Fracture in anchorage of Sabo Bridge (Credit by: WJE Associates Inc.)
Failure During Construction
Due to the different job site conditions, varying construction procedures, and heavy construction loads, the construction of cable bridges is very complicated. Many failures occur during the construction phase and the design group must maintain constant communication with contractors during in this period. The reasons of the failures during construction can be categorize in the following three major groups: a) Mistake in evaluation of load of construction: Due to very complex load path and presence of very concentrated loads in different part of the structure, construction methods of this type of bridges are very complicated and should be studied by the design group. Some times, design group makes mistake on evaluation of the construction loads or select a risky method for construction, and these can lead to collapse of the whole structure. b) Mistake in selection of suitable construction machinery and mistake of workers: Generally, due to special construction situations such as high elevation job site, heavy weight of bridge parts, and using gigantic machinery like cranes, workers feel high pressure on themselves and are stressful during construction of cable bridges, In these situations, workmen mistakes are more likely to happen. This type of mistake can cause small failures or total collapse of structures. c) Natural disasters during construction: Construction period of the cable bridges are long in comparison with regular bridges. Before installation of all parts of the bridge, the bridge has not too much redundancy and most of the times decks are hanged like cantilever beams; therefore, if a sever load such as high wind pressure or earthquake load, which is not considered in the design of the stages of construction, is induced on the bridge, the structure may have not enough reserved resistance for the additional load and in this situation the bridge is very susceptible to collapse.
Collapse of Kukar Bridge in Indonesia is one of the most recent cable bridge collapses during construction. As depicted in Figure 11, the deck of this bridge totally collapsed. The main reason of this failure was detachment of hanger cables from main cable which was due to mistake in design phase and overloading of deck during construction (Matsuno, 2007, P3-5).
Figure 11: Kukar Bridge in Indonesia (Credit by: YouTube)
On October 1970, West Gate Bridge at Melbourne, with 112 meter main span, collapsed during construction and killed 35 people. Many factors are mentioned as the causes of the collapse of this bridge. Most important of them were the unusual erection method used by the contractor, insufficient study on construction loads and temporary structures, and high work pressure on construction team due to tight time schedule which increased the risk of human mistakes (Charret et al., 2008, P7-10).
Another example of the failures in construction period happened when an earthquake occurred during construction of Akashi-Kaikyo Bridge in Japan. The main span of this bridge which is depicted in Figure 12 was 1990 meter. At the time of the earthquake the pylons were built; and due to earth movement the main span (distance between pylons) increased about 1.3 meter; but, as the result of good cooperation between design and construction groups, construction continued to the end without any problem (Nasu et al., 1999, P312).
Due to relatively short age of the cable bridges and the use of high tech materials and machinery in the construction phase, we should do more study to have thorough understanding of the cable bridges behaviors .Construction of cable stayed bridges are very expensive, and due to dimensions of the structure, failure of them can endanger too many people's lives; therefore, existing bridges are very valuable investments in our hand for more study. In addition, as discussed in different parts of this article, a lot of failures of the bridges are due to a lack of regular inspection and maintenance; therefore, by doing of more study on existing bridges, we can learn more about the characteristics of the cable bridges and prevent failures of the under-study bridges.
Due to using high tech in both design and construction of cable bridges, design and construction group prefer to keep their information and do not publish their experiences; that's why there are just a few published books about cable bridges. I think by more information sharing, the number of cable bridge failures will decrease and future cable bridges will have better performances.
This article discusses about aerodynamic behavior of cable bridge due to their long spans and low stiffness of deck.
Nasu, Seigo ; Tatsumi , Masaaki, (1995). “Effect of The Southern Hyogo Earthquake on the Akashi-Kaikyo Bridge.” Honshu-Shikoku Bridge Authority, Tokyo, Japan.
An analysis report about increment of main span length of one of the longest bridge in the world because of earthquake during construction.
Newland, David E. “Vibration of the London Millennium Foot Bridge”, Website of Department of Engineering, University of Cambridge. <http://www2.eng.cam.ac.uk/~den/ICSV9_04.htm>
This paper studied causes of the vibration of the Millennium Bridge in London and discussed the remedial works for solving its problem.
The study contains a complete modeling and study of the Tacoma Narrows Bridges failure due to oscillation which caused by resonance.
Sayers, Adam T. (May 4, 2007). “Critical Analysis of Sunshine Skyway Bridge.”Proceedings of Bridge Engineering 2 Conference. <www.skywaybridge.com/splash/070504.pdf>
This article includes maintenance history of Sunshine Skyway Bridge.
Issa J.Ramaji, Penn State University, 2013, ramaji@psu.edu
Table of Contents
Key words
Bridge, Cable Stay Bridge, Suspension Bridge, Collapse, Failure, Wind, Vibration, CableIntroduction
Cable bridges are a type of bridge which are capable of achieving long spans. Like any relatively new system, cable bridges have a lot of unknown problems and behaviors. Since the time this type of bridge was invented (1784), a lot of failures took place and became educational cases for new design projects. Construction of cable bridges are very expensive, therefore each failure wastes lots of money. In addition, failure of a bridge, even a performance failure, can cause life loss. Therefore, we should study past failure events to improve our design criteria and construction methods.There are different types of cable bridges which can be categorized in two main groups. These two group are called are "Cable Stay Bridges" and "Suspension Bridges". In addition to common problems and failures among cable bridges, in general, each type of cable bridge also has its own range of problems. Some of these failure causes are related to structural elements of the bridge and some are related to characteristic behaviors of these long span bridges. In this article different major problems of cable bridges are discussed and different case study examples of each type are presented.
Differences Between Cable Stayed Bridges and Suspension Bridges
The main difference between cable stayed bridges and suspension bridges is in the way that they transfer loads from deck to pylon. As depicted in Figure 1, in cable stayed bridges straight cables transfer deck loads directly to the pylon (Walther et al., 2003, P19-39). But as shown in Figure 2, in suspension bridges, there are main cables (suspension cables) that carry vertical cables. These vertical cables behave as restraints for the deck and transfer deck loads to the main cables.
Usually main spans of suspension bridges are longer than cable stay bridges; therefore, decks of the suspension bridges have less stiffness in comparison with cable stay bridges. As a result, suspension bridges have more vibration concerns. In addition, design and construction of suspension bridges are more complicated rather than cable stay bridges; and that's the reason why most of the failures of the cable bridges happened in suspension bridges.
Deck Vibration
Due to the low stiffness, light weight, and long spans of cable bridges, the lateral and torsional stiffness of these bridges are low in comparison with regular non-cable bridges . Usually, cable bridges are built in vast areas such as rivers, coasts, and valleys. Therefore, they are exposed to wind loads. The speed of the wind through a bridges varies frequently; in some moments it decreases and in some moments it increases. If the wind speed variations follows a regular pattern, then the time distance between tow adjacent peeks of wind speed graph can be called as period of the wind loads. Usually wind loads have long periods. Because of high stiffness and short natural vibration period of the regular bridges (non-cable bridges), wind resonance usually cannot happen on them. But, cable bridges have long periods in both lateral and torsional vibration; therefore, resonance is a design concern in this type of bridge (Miyata, 2003, P1407 and Plaut, 2008, P613-5). Due to the above mentioned difference between cable bridges and regular bridges (non-cable bridges), a lot of collapses and performance failures have happened since the cable bridge invention. Tacoma Narrows Bridge (Wiki Failures) and Silver Bridge over Ohio River are two examples of cable bridge failures which led to complete collapse of structures. In Figure 3 and 4 the Tacoma Narrows bridge is shown during the fluttering and at the moment of collapse, respectively.At the earlier time of use of cable bridge systems, due to the lack of information about the behavior of this type of bridge, designers didn't pay enough attention to the deck stiffness of the bridges. As a result, a lot of bridges were faced with wind-fluttering problems. In bridges with this problem, when the period of wind impact loads becomes close to the period of deck vibration, they begin to oscillate. This oscillation can continue to the point of damage or collapse of the bridges.
There are two major solutions for fluttering problems of cable bridges (Miyata, 2003, P1403-5).
a) Modification of the Deck: In this solution the shape and configuration of the bridge deck become modified to create a more stiff deck (with respect to the length of the span). In addition, the shape of the deck can be modified to a more aerodynamic shape resulting in less wind load on the deck.
b) Use of Dampers: By use of damper the induced energy to the deck and cables can be damped. In addition, dampers limit deformation of the deck and by this means keep the deck away from large deformation.
Low lateral, torsional ,and vertical stiffness of the cable bridges can cause performance failure of the bridges in some cases. A good example of this type of failure is Millennium Pedestrian Bridge in London which became closed a few days after opening for fixing its problem. The problem was side vibration of the bridge deck due to pedestrian walking synchronous lateral excitation. Two main reasons of this vibration was low lateral stiffness of the deck and low damping potential of the bridge for lateral movements and deformations. The problem of the Millennium bridge was solved by installation of lateral dampers (Newland, Cambridge University website). In Figure 5 a view of this bridge is shown. In the following YouTube link a movie of vibration of this bridge is shown:
YouTube Link
Ship Collision with Pylon
Generally, cable bridges have long-spanned deck and high-rise pylons which results in a high distance of the free-board. With these characteristics, passing of huge vessels is possible through the spans. Unfortunately, the redundancy of this type of bridge is low; as a result, if one of the pylons fails, all parts of the bridge will fail. Therefore, soundness of the pylons is an essential factor in stability of the cable bridges. As we can see in the history of bridges, collision of vessels with piers is one of the most common reasons of failures. Fortunately, pier collocation evidences before and after the invention of cable bridges made designers aware to prevent collision with pylons (Svensson, 2009, P21-31). There are two main solutions to prevent collisions with pylons which are listed in the following:a) Pier barriers: In this solution, some barriers, which are in fact short columns, become installed around the pylon. By this means, if a ship mislead through the pylon, it will collide with the barrier instead of pylon. In Figure 6, the Sunshine Skyway Bridge is shown which is protected by barriers. The old Sunshine Skyway Bridge collapsed in 1980 due to collision of a vessel with one of the piers of the bridge (Sayers, 2007, P1) and it cost $244 million to reconstruct a new bridge.
b) Decreasing the number of collision-exposed pylons: Characteristic of cable bridges makes it possible to have longe spans. Therefore, designers prefer to place pylons out of water, have longer spans, and by this means prevent collision of vessels with pylons
Tendon System Problems
Like each relatively new material, a tendon has its unknown problems. In addition, long tendons have different behavior in comparison with short tendons. Fortunately, due to use of multiple-tendon cables, and high redundancy cable systems, failure of tendons often only results in temporary performance issues with the bridge. Therefore, by regular control and maintenance of the cables, we can prevent failures, when without a frequent maintenance procedure we can expect the collapse of the bridge.One of these failures is rain/wind-induced vibration of cables. If some of the cables become loose or if the pretension loads in the cables be non-compatible with the dead load distribution, then under the combination of light wind and rain loads, they began to vibrate like strings (FHWA, 2007, P13-14). In the following link a movie of Sabo Pedestrian Bridge vibration is shown:
Youtube Link
There is three solution for this type of failure (FHWA, 2007, P14-36):
a) Special surface shape: Specially roughed surface of the cables ducts efficiently increases aerodynamic stability of the cables. In Figure 7 different common shapes of the ducts are depicted.
b) Use of Dampers: By use of dampers, the movement of the cables become limited and the vibration energy of the cables become damped. Usually, these dampers are install between deck and cables (perpendicular to the cables direction). In figure 8, use of dampers in Ravenel Bridge is shown.
c) Tie of the cables together: By installing the cross-tie on the cables, internal restraints for the cables become established, and as a result, transverse stiffness of the cables increases. In Figure 9, a sample cross-tie is shown.
Another type of failure in the cable systems is cable anchorage failure. Transfer and distribution of concentrated load in the cables are two main duties of cable anchorages. Due to the changes in the magnitude of the cable load, fatigue can easily happens in anchorages. Therefore, a regular inspection is necessary to avoid fracture in in the anchorages. In Figure 10, tearing out of one of the of Sabo Bridge anchorages is shown (Wiss, 2012, P35).
Failure During Construction
Due to the different job site conditions, varying construction procedures, and heavy construction loads, the construction of cable bridges is very complicated. Many failures occur during the construction phase and the design group must maintain constant communication with contractors during in this period. The reasons of the failures during construction can be categorize in the following three major groups:a) Mistake in evaluation of load of construction: Due to very complex load path and presence of very concentrated loads in different part of the structure, construction methods of this type of bridges are very complicated and should be studied by the design group. Some times, design group makes mistake on evaluation of the construction loads or select a risky method for construction, and these can lead to collapse of the whole structure.
b) Mistake in selection of suitable construction machinery and mistake of workers: Generally, due to special construction situations such as high elevation job site, heavy weight of bridge parts, and using gigantic machinery like cranes, workers feel high pressure on themselves and are stressful during construction of cable bridges, In these situations, workmen mistakes are more likely to happen. This type of mistake can cause small failures or total collapse of structures.
c) Natural disasters during construction: Construction period of the cable bridges are long in comparison with regular bridges. Before installation of all parts of the bridge, the bridge has not too much redundancy and most of the times decks are hanged like cantilever beams; therefore, if a sever load such as high wind pressure or earthquake load, which is not considered in the design of the stages of construction, is induced on the bridge, the structure may have not enough reserved resistance for the additional load and in this situation the bridge is very susceptible to collapse.
Collapse of Kukar Bridge in Indonesia is one of the most recent cable bridge collapses during construction. As depicted in Figure 11, the deck of this bridge totally collapsed. The main reason of this failure was detachment of hanger cables from main cable which was due to mistake in design phase and overloading of deck during construction (Matsuno, 2007, P3-5).
On October 1970, West Gate Bridge at Melbourne, with 112 meter main span, collapsed during construction and killed 35 people. Many factors are mentioned as the causes of the collapse of this bridge. Most important of them were the unusual erection method used by the contractor, insufficient study on construction loads and temporary structures, and high work pressure on construction team due to tight time schedule which increased the risk of human mistakes (Charret et al., 2008, P7-10).
Another example of the failures in construction period happened when an earthquake occurred during construction of Akashi-Kaikyo Bridge in Japan. The main span of this bridge which is depicted in Figure 12 was 1990 meter. At the time of the earthquake the pylons were built; and due to earth movement the main span (distance between pylons) increased about 1.3 meter; but, as the result of good cooperation between design and construction groups, construction continued to the end without any problem (Nasu et al., 1999, P312).
Conclusion
Due to relatively short age of the cable bridges and the use of high tech materials and machinery in the construction phase, we should do more study to have thorough understanding of the cable bridges behaviors .Construction of cable stayed bridges are very expensive, and due to dimensions of the structure, failure of them can endanger too many people's lives; therefore, existing bridges are very valuable investments in our hand for more study. In addition, as discussed in different parts of this article, a lot of failures of the bridges are due to a lack of regular inspection and maintenance; therefore, by doing of more study on existing bridges, we can learn more about the characteristics of the cable bridges and prevent failures of the under-study bridges.Due to using high tech in both design and construction of cable bridges, design and construction group prefer to keep their information and do not publish their experiences; that's why there are just a few published books about cable bridges. I think by more information sharing, the number of cable bridge failures will decrease and future cable bridges will have better performances.
Bibliography
Charrett, Donald E; Barrister; Bar, Victorian. (2008). “Lessons From Failures-West Gate Bridge.” Melbourne TEC Chambers.
<http://www.mtecc.com.au/uploads//papers/Dr_Donald_Charrett_(2008)_Lessons_from_failures_-_Westgate.pdf>
Failures Wiki. "Tacoma Narrows Collapse (Nov. 7, 1940)." "Failures Wiki" website
<http://failures.wikispaces.com/Tacoma+Narrows+Collapse>
Federal Highway Administration (FHWA). (August, 2007). "Wind-Induced Vibration of Stay Cables.".
<http://www.fhwa.dot.gov/publications/research/infrastructure/bridge/05083/05083.pdf>
Walther, Rene; Houriet, Bernard; Klein, Jean-Francois; Isler, Walmar; Moia, Pierre. (June 1, 2003). “Cable Stayed Bridges.” Thomas Telford Publishing, 2nd edition.
Matsuno, Sohei. (May 4, 2007). “A Study on The Cause of Kukar Bridge collapse.” IBA University, Palembang, Indonesia.
<http://www.iba.ac.id/documents/52/Study%20on%20the%20cause%20of%20KuKar%20bridge%20collapse_Prof%20Matsuno%20-%20V.2.pdf>
Miyata, Toshio. (December, 2003). "Historical view of long-span bridge aerodynamics." Journal of Wind Engineering and Industrial Aerodynamics, Volume 91, Pages 1393–1410.
<http://www.sciencedirect.com/science/article/pii/S0167610503001211>
Nasu, Seigo ; Tatsumi , Masaaki, (1995). “Effect of The Southern Hyogo Earthquake on the Akashi-Kaikyo Bridge.” Honshu-Shikoku Bridge Authority, Tokyo, Japan.
Newland, David E. “Vibration of the London Millennium Foot Bridge”, Website of Department of Engineering, University of Cambridge.
<http://www2.eng.cam.ac.uk/~den/ICSV9_04.htm>
Plaut, Raymond H. (January, 2008). "Snap loads and torsional oscillations of the original Tacoma Narrows Bridge." Journal of Sound and Vibration, Volume 309, Pages 613–636.
<http://www.sciencedirect.com/science/article/pii/S0022460X07005792>
Sayers, Adam T. (May 4, 2007). “Critical Analysis of Sunshine Skyway Bridge.” Proceedings of Bridge Engineering 2 Conference.
<www.skywaybridge.com/splash/070504.pdf>
Svensson, Holger. (March, 2009). “Protection of bridge piers against ship collision.” Steel Construction, Vol.2, No.1, pp.21-32.
<http://onlinelibrary.wiley.com/doi/10.1002/stco.200910004/pdf>
Wiss, Janney. (June 28, 2012). “MARTIN OLAV SABO PEDESTRIAN BRIDGE Cable Diaphragm Plate Fracture Investigation.” WJE, Report No. 2012.0901.
<http://www.scribd.com/doc/98690035/Sabo-Bridge-report>