Abstract
Navier’s 1823 Memoire (C. L. Navier. 1823. Rapport à Monsieur Becquey, Conseiller d’État, Directeur Général des Ponts et Chaussées et des Mines; et mémoire sur les ponts suspendus. Paris: L’Imprimerie Royale) is the seminal analytical study on displacements, stiffness, and vibration of suspension bridges. Navier derived a linearized formula for the vertical displacement at midspan of an unstiffened cable caused by a small change in cable length or span length. He predicted the vertical displacement caused by a concentrated midspan load on a cable with a dominant, uniformly distributed load on its horizontal projection. He thus quantified the geometric stiffness of a cable with a large axial force. Navier also examined the effects of different bearings on displacements of multispan suspension cables subject to unequal vertical loads on adjacent spans. To assess the accuracy of Navier’s quantitative results and to provide insights on structural behavior, geometrically nonlinear models were defined and solved. Navier’s analyses of the vibration of cables and the later contributions of Edward Routh, Hans Reissner, and David Steinman were assessed by geometrically nonlinear OpenSees models of unstiffened and deck-stiffened suspension cables. The influence of Navier’s work on the designs of Charles Ellet and John Roebling was revealed.
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Acknowledgments
We thank William Barrow, Special Collections Librarian at Cleveland State University, for allowing us to study their original copies of the Navier (1823) Memoire, his 1830 second edition, and Corti’s 1840 translation.
References
Ammann, O. H., T. von Karman, and G. Woodruff. 1941. The failure of the Tacoma Narrows Bridge. Rep. to the Honorable John M. Carmody Administrator. Washington, DC: Federal Works Agency.
Bakis, K. N., D. J. N. Limebeer, M. S. Williams, and J. M. R. Graham. 2016. “Passive aeroelastic control of a suspension bridge during erection.” J. Fluids Struct. 66: 543–570. https://doi.org/10.1016/j.jfluidstructs.2016.08.008.
Balog, L. 1945. “Discussion of Steinman.” Trans. Am. Soc. Civ. Eng. 110: 522–532.
Beliveau, J. G., R. Vaicaitis, and M. Shinozuka. 1972. “Motion of suspension bridge subject to wind loads.” J. Struct. Div. 103 (6): 1189–1205.
Brown, W. C., and M. F. Parsons. 1975. “Bosporus bridge. Part I: History of design.” Proc. Inst. Civ. Eng. 58 (4): 505–532. https://doi.org/10.1680/iicep.1975.3556.
Buonopane, S. G. 2006. “The technical writings of John A. Roebling and his contributions to suspension bridge design.” In Proc., Roebling Project Symp., 37–61. Reston, VA: ASCE.
Buonopane, S. G. 2012. “A historical perspective on suspension bridges: Design vs. analysis and the work of John A. Roebling.” Festschrift Billington, Int. Network of Structural Art, 38–76. Princeton, NJ: Int. Network of Structural Art.
Buonopane, S. G., and D. P. Billington. 1993. “Theory and history of suspension bridge design from 1823 to 1940.” J. Struct. Eng. 119 (3): 954–977. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:3(954).
Corti, G. 1840. Rapporto e memoria sui ponti pensili di L. Navier. Milano, Italy: Presso Angelo Monti.
Dana, A., A. Andersen, and G. M. Rapp. 1933. “George Washington Bridge: Design of superstructure.” Trans. Am. Soc. Civ. Eng. 97 (1): 97–163.
Dietlein, J. 1825. Auszug aus Navier’s abhandlung uber die hangebrucken. Berlin: Reimer.
Dumanoglu, A. A., J. M. W. Brownjohn, and R. T. Severn. 1992. “Seismic analysis of the Fatih Sultan Mehmet (second Bosporus) suspension bridge.” Earthquake Eng. Struct. Dyn. 21 (10): 881–906. https://doi.org/10.1002/eqe.4290211004.
Ellet, C. 1840. Report and plan for a wire suspension bridge across the Mississippi River at Saint Louis. Philadelphia: W. Stavely & Co. Printer.
ENR (Engineering News-Record). 1941. “Why the Tacoma Narrows Bridge failed.” ENR, 75–79.
Gasparini, D. A., and V. Gautam. 2002. “Geometrically nonlinear behavior of cable structures.” J. Struct. Eng. 128 (10): 1317–1329. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:10(1317).
Günaydin, M., A. Süleyman, A. C. Altunisik, and B. Sevim, 2012. “Construction stage analysis of Fatih Sultan Mehmet suspension bridge.” Struct. Eng. Mech. 42 (4): 489–505. https://doi.org/10.12989/sem.2012.42.4.489.
Irvine, H. M., and T. K. Caughey. 1974. “The linear theory of free vibrations of a suspended cable.” Proc. R. Soc. A 341 (1626): 299–315. https://doi.org/10.1098/rspa.1974.0189.
Jakkula, A. A. 1936. “Theory of the suspension bridge.” Publ. Int. Assoc. Bridge Struct. Eng. 4: 33–58.
Jennings, A. 1983. “Gravity stiffness of classical suspension bridges.” J. Struct. Eng. 109 (1): 16–36. https://doi.org/10.1061/(ASCE)0733-9445(1983)109:1(16).
Johnson, J. B., C. W. Bryan, and F. E. Turneaure. 1911. The theory and practice of modern framed structures, Part II. New York: Wiley.
Jurado, J. A., S. Hernández, F. Nieto, and A. Mosquera. 2011. Bridge aeroelasticity. Southampton, UK: WIT Press.
Kranakis, E. 1997. Constructing a bridge. Cambridge, MA: MIT Press.
Kutschera, J. G. 1829. Abhandlung uber die hangebrucken von Herren Navier. Lemberg: Piller.
Lin, Y. K., and S. T. Ariaratnam. 1980. “Stability of bridge motion in turbulent winds.” J. Struct. Mech. 8 (1): 1–15. https://doi.org/10.1080/03601218008907350.
McKenna, F. 2017. “OpenSees: The open system for earthquake engineering simulation.” Accessed September 21, 2018. http://opensees.berkeley.edu.
Mehrtens, G. C. 1908. Vorlesungen uber ingenieur-wissenschaften, zweiter teil: Eisenbruckenbau. Leipzig: Verlag von Wilhelm Engelmann.
Melan, J. 1888. “Theorie des eisernen bogenbrucken und der hangebrucken.” Handbuch der ingenieurwissenschaften. 2nd ed. Leipzig: Verlag von Wilhelm Engelmann.
Moisseiff, L. S. 1925. “The towers, cables and stiffening trusses of the bridge over the Delaware River between Philadelphia and Camden.” J. Franklin Inst. 200 (4): 436–466. https://doi.org/10.1016/S0016-0032(25)90148-2.
Moisseiff, L. S. 1927. The deflection theory as applied to suspension bridges with suspended spans. Final Rep.: The Bridge over the Delaware River Connecting Philadelphia, PA and Camden, NJ, Appendix D, 96–105.Camden, NJ: Delaware River Bridge Joint Commission.
Navier, C. L. 1823. Rapport à Monsieur Becquey, Conseiller d’État, Directeur Général des Ponts et Chaussées et des Mines; et mémoire sur les ponts suspendus. Paris: L’Imprimerie Royale.
Navier, C. L. 1826. Resume des leçons donnes a l’Ecole des Ponts et Chaussees sur l‘application de la mecanique a l’etablissement des constructions et des machines. Paris: Chez Carilian-Goeury.
Navier, C. L. 1830. Rapport a Monsieur Becquey, Conseiller d’État, Directeur Général des Ponts et Chaussées et des Mines; et memoire sur les ponts suspendus, deuxième édition. Paris: L’Imprimerie Royale.
O’Connor, C. 1971. Design of bridge superstructures. New York: Wiley.
Pasley, C. 1840. “Description of the state of the suspension bridge at Montrose after it had been rendered impassable by the hurricane of the 11th of October, 1838; with remarks on the construction of that and other suspension bridges, in reference to the action of violent gales of wind. (including plate).” Trans. Inst. Civ. Eng. 3 (3): 219–227. https://doi.org/10.1680/itrcs.1840.24366.
Pugsley, A. G. 1949. “On the natural frequencies of suspension chains.” Q. J. Mech. Appl. Math. 2 (4): 412–418. https://doi.org/10.1093/qjmam/2.4.412.
Pugsley, A. G. 1957. The theory of suspension bridges. London: Edward Arnold Publishers Ltd.
Rannie, W. D. 1941. The vibrations of suspension bridges. The failure of the Tacoma Narrows Bridge. Rep. to the Honorable John M. Carmody Administrator, Appendix VI, 1–28. Washington, DC: Federal Works Agency.
Reissner, H. 1943. “Oscillations of suspension bridges.” J. Appl. Mech. March: A23–A32.
Roebling, J. 1841a. “Some remarks on suspension bridges, and on the comparative merits of cable and chain bridges.” Am. Railroad J. Mech. Mag. 6 (6): 161–166.
Roebling, J. 1841b. “Some remarks on suspension bridges, and on the comparative merits of cable and chain bridges.” Am. Railroad J. Mech. Mag. 6 (7): 193–196.
Roebling, J. 1855. Final report of John A. Roebling, civil engineer, to the presidents and directors of the Niagara Falls Suspension and Niagara Falls International Bridge Companies. Rochester, NY: Lee, Mann & Co.
Rohrs, J. H. 1851. “On the oscillations of a suspension chain.” Trans. Cam. Phil. Soc. 9 (3): 379–398.
Routh, E. J. 1905. Dynamics of a system of rigid bodies. 6th ed. London: MacMillan and Co. Ltd.
Saxon, D. S., and A. S. Cahn. 1953. “Modes of vibration of a suspended chain.” Q. J. Mech. Appl. Math. 6 (3): 273–285. https://doi.org/10.1093/qjmam/6.3.273.
Scanlan, R. H. 1984. “Role of indicial functions in buffeting analysis of bridges.” J. Struct. Eng. 110 (7): 1433–1446. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:7(1433).
Scanlan, R. H., and J. T. Tomko. 1971. “Airfoil and bridge deck flutter derivatives.” J. Eng. Mech. Div. 97 (6): 1717–1737.
Steinman, D. B. 1913. Theory of arches and suspension bridges. Chicago: Myron C. Clark Publishing Co.
Steinman, D. B. 1929. A practical treatise on suspension bridges. 2nd ed. New York: John Wiley & Sons.
Steinman, D. B. 1945. “Rigidity and aerodynamic stability of suspension bridges.” Trans. Am. Soc. Civ. Eng. 110: 439–475.
Tsiatas, G., and D. A. Gasparini. 1987. “Torsional response of long span bridges in presence of turbulence.” J. Eng. Mech. 113 (3): 303–314. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:3(303).
Veletsos, A. S., and G. R. Darbre. 1983. “Free vibration of parabolic cables.” J. Struct. Eng. 109 (2): 503–519. https://doi.org/10.1061/(ASCE)0733-9445(1983)109:2(503).
West, H. H., L. F. Geschwindner, and J. E. Suhoski. 1975. “Natural vibrations of suspension cables.” J. Struct. Div. 101 (11): 2277–2291.
West, H. H., J. E. Suhoski, and L. F. Geschwindner. 1984. “Natural frequencies and modes of suspension bridges.” J. Struct. Eng. 110 (10): 2471–2486. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:10(2471).
Westergaard, H. M. 1941. “On the method of complementary energy and its application to structures stressed beyond the proportional limit, to buckling and vibrations, and to suspension bridges.” Proc. Am. Soc. Civ. Eng. 67 (2): 199–227.
Information & Authors
Information
Published In
Journal of Bridge Engineering
Volume 24 • Issue 7 • July 2019
Copyright
© 2019 American Society of Civil Engineers.
History
Received: Sep 26, 2018
Accepted: Feb 8, 2019
Published online: Apr 24, 2019
Published in print: Jul 1, 2019
Discussion open until: Sep 24, 2019
ASCE Technical Topics:
- Bridge engineering
- Bridges
- Bridges (by type)
- Cables
- Continuum mechanics
- Design (by type)
- Displacement (mechanics)
- Distinguished engineers
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Equipment and machinery
- Geometrics
- Highway and road design
- History and Heritage
- Motion (dynamics)
- Practice and Profession
- Solid mechanics
- Static loads
- Statics (mechanics)
- Stiffening
- Structural behavior
- Structural engineering
- Structural mechanics
- Suspension bridges
- Vertical loads
- Vibration
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