Footbridges are particularly susceptible to dynamic excitation from pedestrians due to their flexibility and lightweight construction. Steel footbridges are particularly susceptible; composite footbridges are less likely to be affected.
A structure's natural frequency depends on its span, mass, and bending stiffness. For bridges that can be idealised as a beam, it is possible to do a very quick calculation to determine the natural frequency, which will tell you if your design is susceptible or not. The equations provided are from the Structural Engineer's Pocketbook; they are derived from first principles and are not code specific.
Although you should focus your time on sizing for strength first (bending / shear / foundation design), I had just enough time in the exam to complete this calculation. The Eurocode requires a full dynamic analysis if the natural frequency is < 5Hz for vertical modes.
If, like me, you find that the natural frequency is < 5Hz, then conclude that "full dynamic analysis will be required at detailed design, if deck acceleration is unacceptable then the structure's mass or bending stiffness could be changed, or mass dampers could be provided if necessary". If the natural frequency is > 5Hz then you can conclude that "initial calculations indicate that the structure is not susceptible to dynamic excitation by pedestrians".
If you don't have enough time to do the calculation, just make a note saying something like "The structure may be excited by pedestrian loading. An assessment of the structure's natural frequency will be required at detailed design, to determine if a full dynamic analysis is required" - this shows you understand it's a key requirement.
Context
Although the Eurocodes require a full dynamic analysis if the natural frequency is < 5Hz, not every bridge with a natural frequency under this value will have problems in reality - the acceptance criteria are based on peak deck acceleration derived from the analysis (which depends on the natural frequency and the applied load, which in turn depends on the bridge type and location). The "pedestrian combined factor" (k(fv), Figure NA.8 on the cheat sheet) is essentially a measure of how likely it is that pedestrians will walk or jog at a given frequency; in the analysis it is a factor that reduces the applied loading depending on natural frequency. You can see from the graph that the highest likelihood is between 1 and 3Hz, so in some cases issues can be resolved by reducing the natural frequency rather than trying to push it up over the 5Hz limit where a full analysis is no longer required. Adding additional mass will reduce the natural frequency, and making the structure stiffer in bending will increase it. Mass damping can also be used to resolve dynamic issues.
Add new comment