Torsional instability in suspension bridges: The Tacoma Narrows Bridge case

• Thresholds of torsional instability of suspension bridges.
• Periodic solutions for a nonlinear model of a suspension bridge.
• Application of Floquet theory to the stability of nonlinear modes.
• Structural explanation of the Tacoma collapse.

All attempts of aeroelastic explanations for the torsional instability of suspension bridges have been somehow criticised and none of them is unanimously accepted by the scientific community. We suggest a new nonlinear model for a suspension bridge and we perform numerical experiments with the parameters corresponding to the collapsed Tacoma Narrows Bridge. We show that the thresholds of instability are in line with those observed the day of the collapse. Our analysis enables us to give a new explanation for the torsional instability, only based on the nonlinear behavior of the structure.