Torsional instability

Stills from footage of the Tacoma Narrows Bridge wobbling and eventually, collapsing, 7 November, 1940, filmed by Barney Elliot. The cause has been attributed to wind conditions causing torsional instability of the bridge.

Torsional instability is a mechanical phenomenon where a structural element subjected to twisting (torsional) forces undergoes sudden deformation or failure beyond a critical torque threshold. This instability is characterized by a rapid transition from stable twisting to helical buckling, kinking, or collapse, often observed in slender rods, beams, and architectural structures.^[1][2][3]

Examples

The Dee Bridge collapsed in 1847 after adding extra weight to the bridge in the form of rocks and gravel to reduce track vibration, but lead to a critical point of torsional instability.^[1] The Tacoma Narrows Bridge collapsed in 1940 due to specific wind conditions that were exacerbated by torsional oscillations, transitioning from vertical to destructive twisting modes.^[4] In the 1970s, occupants of the top floors of the John Hancock Tower reported feeling motion sickness, which was later revealed to be due to torsional instability of the building.^[1]

This phenomenon is also know to happen to drill strings and pipelines, buckling under rotational loads in oil/gas extraction, as well as aircraft wings, experiencing torsional flutter under aerodynamic forces.^[5]

Mitigation strategies

A way to reduce the chance of torsional instability is by making cross-sections stiffer. This can be done by choosing shapes that naturally resist twisting, like hollow tubes or cross-shaped sections, instead of shapes like flat plates, which twist more easily. Stiffer cross-sections provide more resistance to the twisting force and help the structure remain stable. Another way is by implementing braces, which are structural components that provide extra stability and strength to a building or structure. For example, twisting a scaffold is harder than twisting a ladder because the scaffold has braces that resist twisting, making it much stiffer and more stable than the ladder. Similarly, bracing systems in a building distribute forces and provide resistance against torsion.^[6]

In addition to modifying the shape and bracing, engineers can use materials to make structures stronger and lighter at the same time. These materials include composites like carbon fiber or hybrid materials that are better at resisting twisting forces than traditional steel or concrete. For example, bridges or buildings made with these materials can carry heavy loads and resist twisting without becoming overly bulky or heavy.^[6]

Engineers also rely on mathematical models and computer simulations to predict how a structure will respond to torsional forces under different conditions, such as strong winds, earthquakes, or heavy traffic. These digital tools allow engineers to analyze and optimize their designs before construction begins, ensuring the structure can handle these forces while still being safe, functional, and cost-efficient.^[6]

See also

• Torsion (mechanics)
• Buckling
• Elastic instability
• Shear modulus
• Polar moment of inertia

References

1. Parker, Matt (2019). Humble Pi: A Comedy of Maths Errors. Penguin Books Limited. pp. 39–44. ISBN 978-0-14-198913-6.
2. Zhou, Wei; Jia, Zheng (August 2022). "Pulling actuation enabled by harnessing the torsional instability of hyperelastic soft rods". Extreme Mechanics Letters. 55: 101807. Bibcode:2022ExML...5501807Z. doi:10.1016/j.eml.2022.101807.
3. Pugsley, A.G. (1932). "Torsional Instability in Struts". Aircraft Engineering and Aerospace Technology. 4 (9): 229–230. doi:10.1108/eb029591.
4. Arioli, Gianni; Gazzola, Filippo (2017). "Torsional instability in suspension bridges: The Tacoma Narrows Bridge case". Communications in Nonlinear Science and Numerical Simulation. 42: 342–357. arXiv:1508.03200. Bibcode:2017CNSNS..42..342A. doi:10.1016/j.cnsns.2016.05.028.
5. Antonelli, Richard G.; Meyer, Keith J.; Oppenheim, Irving J. (January 1981). "Torsional instability in structures". Earthquake Engineering & Structural Dynamics. 9 (3): 221–237. Bibcode:1981EESD....9..221A. doi:10.1002/eqe.4290090304.
6. "Torsional Rigidity: Principles, Calculations, and Applications". FirstMold. 2024-09-09. Retrieved 2025-05-02.

Further reading

• Pham, Thang; Oh, Sehoon; Stetz, Patrick; Onishi, Seita; Kisielowski, Christian; Cohen, Marvin L.; Zettl, Alex (20 July 2018). "Torsional instability in the single-chain limit of a transition metal trichalcogenide". Science. 361 (6399): 263–266. arXiv:1803.02866. Bibcode:2018Sci...361..263P. doi:10.1126/science.aat4749. PMID 30026223.
• Ciarletta, P.; Destrade, M. (October 2014). "Torsion instability of soft solid cylinders". IMA Journal of Applied Mathematics. 79 (5): 804–819. doi:10.1093/imamat/hxt052.
• Gent, A.N; Hua, K.-C (April 2004). "Torsional instability of stretched rubber cylinders". International Journal of Non-Linear Mechanics. 39 (3): 483–489. Bibcode:2004IJNLM..39..483G. doi:10.1016/S0020-7462(02)00217-2.
• Vercosa, D. G.; Barros, E. B.; Souza Filho, A. G.; Mendes Filho, J.; Samsonidze, Ge. G.; Saito, R.; Dresselhaus, M. S. (21 April 2010). "Torsional instability of chiral carbon nanotubes". Physical Review B. 81 (16): 165430. Bibcode:2010PhRvB..81p5430V. doi:10.1103/PhysRevB.81.165430. hdl:1721.1/58774.
• Berchio, Elvise; Gazzola, Filippo (July 2015). "A qualitative explanation of the origin of torsional instability in suspension bridges". Nonlinear Analysis: Theory, Methods & Applications. 121: 54–72. arXiv:1404.7351. doi:10.1016/j.na.2014.10.026.
• Bonheure, Denis; Gazzola, Filippo; Dos Santos, Ederson Moreira (January 2019). "Periodic Solutions and Torsional Instability in a Nonlinear Nonlocal Plate Equation". SIAM Journal on Mathematical Analysis. 51 (4): 3052–3091. arXiv:1809.09783. doi:10.1137/18M1221242.
• Wardlaw, R. L. (1994). "Flutter and Torsional Instability". Wind-Excited Vibrations of Structures. pp. 293–319. doi:10.1007/978-3-7091-2708-7_6. ISBN 978-3-211-82516-7.