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    Suspension Bridge Analysis: Melan & Moisseiff's Insights

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    The Question

     

    We have structural analysis programs. Can we make the model (like other conventional bridges) and perform the analysis (as usual)?

     

     

    The Answer

     

    The short answer is yes, we can! 


    But the results may be useless. The scary parts of FEM are it gives results without any warning/error message, but the output may not be correct or useless.

     

    Fig1 Girder moments due to live load from linear

    Fig1 Girder moments due to live load from linear/conventional analysis

     

    Fig1 shows girder moments due to live loads for a medium-span suspension bridge. The main span is around 2600 ft (now the longest one was built by Turkish engineers, and the main span, between pylon to pylon, is 6600ft, much more than a mile!). This example bridge is not a real one and was proposed by Dr. Hirai for comparison (Steel Bridge III, by Hiral Atsushi).

     

    We can analyze suspension bridges in a conventional way. However, the output moment is too big, and we cannot design the section. From conventional linear analysis (dashed line), we got a moment around 29,000 t-m at the center of the side span. Moment 29,000 t-m is huge and not easy to design for this moment. This is one of the main reasons why we couldn’t design a long-span suspension bridge in the 19th century, and the span limit was around 2,000 ft.

     

    Fig2 John A. Roebling suspension bridge, opened 1867, main span 1057 ft

    Fig2 John A. Roebling suspension bridge, opened 1867, main span 1057 ft (https://en.wikipedia.org/wiki/John_A._Roebling_Suspension_Bridge)

     

    If you have hawk’s eyes, you can see that the girders are somewhat stocky for these traditional suspension bridges in the 19th century.

     

    Fig3. Historic longest bridge spans

    Fig3. Historic longest bridge spans (https://aiimpacts.org/historic-trends-in-bridge-span-length/)

     

    As can be seen from Fig3, somewhere in the 1930s, the bridge span went up dramatically, approximately twice. What has happened in these eras?

     

    Fig4 Girder moments due to live load from linear

    Fig4 Girder moments due to live load from linear/conventional and linearized finite displacement analysis

     

    If we consider some kinds of non-linearity (red solid line), even a very simple one like linearized finite displacement methods, the moment will drop down to 4,300 t-m, and we are much more comfortable designing the girder section.

     

    Content visible until here

     

    You can check more of these details in the download file.

     

    How is this possible?

     

    An example

     

     

    About the Editor
    Seungwoo Lee PhD, P.E., S.E.
    Senior Supervising Engineer at WSP USAs (Tampa, FL)

    He is a Senior Supervising Engineer with a high level of expertise in the design and analysis of suspension bridges. He has a solid fundamental understanding of structures and can apply his knowledge exceptionally well to the design and analysis of highly complex structures. He is also a strong communicator, able to identify and distill the key information that is relevant to the task at hand and present it in a clear and quickly understandable manner.

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