Skip to main content
SpringerLink
Log in
Book cover

International Conference on Arch Bridges

ARCH 2019: Proceedings of ARCH 2019 pp 145–152Cite as

Closed-Form Solution for In-plane Nonlinear Elastic Buckling of Parabolic Three-Pinned Arches

  • Conference paper
  • First Online:

Part of the book series: Structural Integrity ((STIN,volume 11))

Abstract

The parabolic three-pinned arches are commonly used in structural engineering; however, its in-plane nonlinear buckling is not explored in the available publications. This paper investigates the closed-form solutions of in-plane nonlinear elastic buckling of the parabolic three-pinned arches. The equilibrium differential equations of in-plane nonlinear elastic buckling are derived based on the membrane and bending strain in the Cartesian coordinate system and the virtual work principle, and the equilibrium equation of nonlinear buckling are obtained by the integration of the membrane strain along the span. Comparisons with finite element results show that the nonlinear elastic buckling predictions of proposed method have sufficient accuracy in a large parameter range.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Wang, T., Bradford, M.A., Gilbert, R.I.: Creep buckling of shallow parabolic concrete arches. J. Struct. Eng. ASCE 132, 1641–1649 (2006)

    Article  Google Scholar 

  2. Moon, J., Yoon, K.Y., Lee, T.H., Lee, H.E.: In-plane elastic buckling of pin-ended shallow parabolic arches. Eng. Struct. 29, 2611–2617 (2007)

    Article  Google Scholar 

  3. Moon, J., Yoon, K.Y., Lee, T.H., Lee, H.E.: In-plane strength and design of parabolic arches. Eng. Struct. 31, 444–454 (2009)

    Article  Google Scholar 

  4. Bradford, M.A., Wang, T., Pi, Y.-L., Gilbert, R.I.: In-plane stability of parabolic arches with horizontal spring supports, I: theory. J. Struct. Eng. ASCE 133, 1130–1137 (2007)

    Article  Google Scholar 

  5. Wang, T., Bradford, M.A., Gilbert, R.I., Pi, Y.-L.: In-plane stability of parabolic arches with horizontal spring supports, II: experiments. J. Struct. Eng. ASCE 133, 1138–1145 (2007)

    Article  Google Scholar 

  6. Chen, Y., Feng, J.: Elastic stability of shallow pin-ended parabolic arches subjected to step loads. J. Central South Univ. (English Edition) 17, 156–162 (2010)

    Article  Google Scholar 

  7. Cai, J.G., Feng, J.: Effect of support stiffness on stability of shallow arches. Int. J. Struct. Stab. Dyn. 10, 1099–1110 (2010)

    Article  MathSciNet  Google Scholar 

  8. Cai, J.G., Feng, J.: Buckling of parabolic shallow arches when support stiffens under compression. Mech. Res. Commun. 37, 467–471 (2010)

    Article  Google Scholar 

  9. Cai, J.G., Xu, Y.X., Feng, J., Zhang, J.: Effects of temperature variations on the in-plane stability of steel arch bridges. J. Bridge Eng. ASCE 17, 232–240 (2012)

    Article  Google Scholar 

  10. Cai, J.G., Xu, Y.X., Feng, J., Zhang, J.: In-plane elastic buckling of shallow parabolic arches under an external load and temperature changes. J. Struct. Eng. ASCE 138, 1300–1309 (2012)

    Article  Google Scholar 

  11. Wu, X.R., Liu, C.Y., Wang, W., Wang, Y.Y.: In-plane strength and design of fixed concrete-filled steel tubular parabolic arches. J. Bridge Eng. ASCE 20, 04015016 (2015)

    Article  Google Scholar 

  12. Cai, J.G., Feng, J., Chen, Y., Huang, L.F.: In-plane elastic stability of fixed parabolic shallow arches. Sci. China Ser. E-Technol. Sci. 53, 596–602 (2009)

    Article  Google Scholar 

  13. Cai, J.G., Zhou, Y., Feng, J.: Post-buckling behavior of a fixed arch for variable geometry structures. Mech. Res. Commun. 52, 74–80 (2013)

    Article  Google Scholar 

  14. Attard, M.M., Zhu, J., Kellermann, D.C.: In-plane buckling of prismatic funicular arches with shear deformations. Arch. Appl. Mech. 84, 693–713 (2014)

    Article  Google Scholar 

  15. Zhu, J., Attard, M.M., Kellermann, D.C.: In-plane nonlinear buckling of funicular arches. Int. J. Struct. Stab. Dyn. 15, 1450073 (2015)

    Article  MathSciNet  Google Scholar 

  16. Sabale, A., Gopal, K.V.N.: Nonlinear in-plane stability of deep parabolic arches using geometrically exact beam theory. Int. J. Struct. Stab. Dyn. 18, 1850006 (2018)

    Article  MathSciNet  Google Scholar 

  17. Bradford, M.A., Pi, Y.-L., Yang, G.T., Fan, X.C.: Effects of approximations on non-linear in-plane elastic buckling and postbuckling analyses of shallow parabolic arches. Eng. Struct. 101, 58–67 (2015)

    Article  Google Scholar 

  18. Hu, C.-F., Pi, Y.-L., Gao, W., Li, L.: In-plane non-linear elastic stability of parabolic arches with differential rise-to-span ratios. Thin-Walled Struct. 129, 74–84 (2018)

    Article  Google Scholar 

Download references

Acknowledgments

This work was financially supported by National Natural Science Foundation of China (No. 51568020, No. 11772129) and Science and Technology Plan in Jiangxi Province (20141BBG70089).

Author information

Authors and Affiliations

  1. East China Jiaotong University, Nanchang, China

    Chang-Fu Hu & Xiao-Qian Liu

  2. Transport and Municipal Engineering Visualizing Simulation Laboratory of Nanchang, Nanchang, China

    Chang-Fu Hu

Authors
  1. Chang-Fu Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiao-Qian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chang-Fu Hu .

Editor information

Editors and Affiliations

  1. Faculdade de Engenharia, University of Porto, Porto, Portugal

    António Arêde

  2. School of Technology, Department of Engineering, Polytechnic Institute of Tomar, Tomar, Portugal

    Cristina Costa

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Hu, CF., Liu, XQ. (2020). Closed-Form Solution for In-plane Nonlinear Elastic Buckling of Parabolic Three-Pinned Arches. In: Arêde, A., Costa, C. (eds) Proceedings of ARCH 2019. ARCH 2019. Structural Integrity, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-030-29227-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-29227-0_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-29226-3

  • Online ISBN: 978-3-030-29227-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation