Geometric Non-linear Form-Finding Design for Optimal Tied Arch Bridge

  • Esko JärvenpääEmail author
  • Rauno Heikkilä
  • Matti-Esko Järvenpää
Conference paper
Part of the Structural Integrity book series (STIN, volume 11)


The article discusses the overall optimization of the tied arch bridge. The parabolic arch is hardly never the best shape of arch. The optimum height which gives the minimum volume of the load-bearing structure is solved mathematically in the article. The span length relation to arch height l/h = 2,309 gives the minimum load bearing material amount. Practical examples are calculated numerically by using iteration, based on geometric vector algebra solution in finding the arch thrust line. The iteration is performed so that the weight of the arch is in the correct position and has the correct size during each iteration round. The geometry changes after each calculation round. The area of the cross-section is determined by the axial force along the arch. The comparison calculations are made for the selected tied arch bridge for four different heights.

The arch structure is a concrete filled steel tube. The assumption is that the concrete is cast into the tube when the arch is still supported by the temporary structures. The optimum rise relation l/h, for the example bridge is 2,55. The bridge has a span of 250 m, and the weight of superstructure is 200 kN/m. Calculations are based on permanent loads, selected stress level and unit prices. The calculation takes into account the weights of the tie member and the hangers. The cost increase related to the arch height is estimated. An example calculation produces an optimal rise relation of l/h = 3,2.

The calculations are prepared only for permanent gravity loading. Stability of the arch in lateral direction is not discussed in the paper. Stability in the plane of tied arch will not be decisive problem. It is not handled in the paper. The article does not take opinion on the bridge aesthetics.


Tied arch Form-finding Composite arch Optimum rise relation 


  1. 1.
    Nettleton, D.: Arch Bridges. Bridge Division. Department of Transportation, pp. 9–14 (1977)Google Scholar
  2. 2.
    Petersen, C.: Statik und Stabilität der Baukonstructionen, Elasto- und plasto-statische Berechnungsverfahren druckbeanspurchter Tragweke: Nachweisformen gegen Knicken, Kippen, Beulen, Friedr. Vieweg & Shon, pp. 598–663 (1980)Google Scholar
  3. 3.
    Järvenpää, E., Tung, Q.: Simple innovative cost comparison between tied-arch bridge and cable-stayed bridge. In: MATEC Web of Conferences SCECSM 2018, p. 258 (2019)Google Scholar
  4. 4.
    Tyas, A., Pichugin, A.V., Gilbert, M.: Optimum structure to carry a uniform load between pinned supports: exact analytical solution. Proc. Roy. Soc. (2010)Google Scholar
  5. 5.
    Rozwany, G., Wang, C.-M.: On plane parger –structures. Int. J. Mech. Sci. 25(7), 519–527 (1983)Google Scholar
  6. 6.
    Pournaghshband, A.: Contribution of form-find shape of pin-ended arch 15(4), 406–413 (2017).
  7. 7.
    Lewis, W.: Mathematical model of a moment-less arch. Proc. Roy. Soc. A. Scholar
  8. 8.
    Marano, G., Trendatue, F., Petrone,F.: Optimal arch shape solution under static vertical loads. Achta Mech. (2014).
  9. 9.
    Heikkilä, R., Jaakkola, M.: 3-D real-time accuracy control of automated road construction machines. In: 21st International Symposium on Automation and Robotics in Construction ISARC 2004, Jeju, Korea, pp. 49–52, 21–25 September 2004. 013-0985-0Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Esko Järvenpää
    • 1
    Email author
  • Rauno Heikkilä
    • 2
  • Matti-Esko Järvenpää
    • 3
  1. 1.WSP Finland and University of OuluOuluFinland
  2. 2.University of OuluOuluFinland
  3. 3.WSP FinlandHelsinkiFinland

Personalised recommendations