Abstract
An efficient formulation is developed for the elastic analysis of thin-walled beams curved in plan. Using a second-order rotation tensor, the strain values of the deformed configuration are calculated in terms of the displacement values and the initial curvature by adopting the right extensional strain measure. The principle of virtual work is then used to obtain the nonlinear equilibrium equations, based on which a finite element beam formulation is developed. The accuracy of the method is confirmed through comparison with test results, shell finite element formulations and other curved beam formulations from the literature. It is also shown that the results of the developed formulation are very accurate for the cases where initial curvature is large.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Akhtar, M. N. (1987). “Element stiffness of circular member”, Journal of structural engineering New York, N.Y., 113 (4), pp. 867–872.
Basler, K. and Kollbrunner, C. F. (1969). “Torsion in structures-An engineering approach (Book on torsion emphasizing beam stressed state calculation and civil engineering problems)”, Torsion in structures-An engineering approach (Book on torsion emphasizing beam stressed state calculation and civil engineering problems).
Batoz, J. L. and Tahar, M. B. (1982). “Evaluation of a new quadrilateral thin plate bending element”, Int J Numer Methods Eng, 18 (11), pp. 1655–1677.
Brookhart, G. C. (1967). “Circular-arc I-type girders”, American Socienty for Civil Engineers, vol. 93.
Crisfield, M. A. (1990). “A consistent co-rotational formulation for non-linear, three-dimensional, beam-elements”, Computer Methods in Applied Mechanics and Engineering, 81 (2), pp. 131–150.
de Veubeke, B. F. (1972). “A new variational principle for finite elastic displacements”, International Journal of Engineering Science, 10 (9), pp. 745–763.
El-Amin, F. M. and Brotton, D. M. (1976). “Horizontally curved beam finite element including warping”, International Journal for Numerical Methods in Engineering, 10 (6), pp. 1397–1406.
El-Amin, F. M. and Kasem, M. A. (1978). “Higher-order horizontally-curved beam finite element including warping for steel bridges”, International Journal for Numerical Methods in Engineering, 12 (1), pp. 159–167.
Erkmen, R. E. and Bradford, M. A. (2009). “Nonlinear elasto-dynamic analysis of I-beams curved in-plan”, International Journal of Structural Stability and Dynamics, 9 (2), pp. 213–241.
Fukumoto, Y. and Nishida, S. (1981). “Ultimate load behavior of curved I-beams”, ASCE J Eng Mech Div, 107 (2), pp. 367–385.
Ibrahimbegovic, A., Taylor, R. L., and Wilson, E. L. (1990). “Robust quadrilateral membrane finite element with drilling degrees of freedom”, International Journal for Numerical Methods in Engineering, 30 (3), pp. 445–457.
Iura, M. and Atluri, S. N. (1988). “On a consistent theory, and variational formulation of finitely stretched and rotated 3-D space-curved beams”, Computational Mechanics, 4 (2), pp. 73–88.
Koiter, W. T. (1984). “Complementary energy, neutral equilibrium and buckling”, Meccanica, 19 (1) Supplement, pp. 52–56.
Krenk, S. (1994). “A general format for curved and nonhomogeneous beam elements”, Computers and Structures, 50 (4), pp. 449–454.
Love, A. E. H. (1944). A Treatise on the Mathematical Theory of Elasticity, 4th edn, Dover Publications Inc., New York.
Pai, P. F. and Palazotto, A. N. (1995). “Polar decomposition theory in nonlinear analyses of solids and structures”, Journal of Engineering Mechanics, 121 (4), pp. 568–581.
Pai, P. F., Palazotto, A. N., and Greer Jr, J. M. (1998). “Polar decomposition and appropriate strains and stresses for nonlinear structural analyses”, Computers and Structures, 66 (6), pp. 823–40.
Pi, Y.-L., Bradford, M. A., and Uy, B. (2005). “Nonlinear analysis of members curved in space with warping and Wagner effects”, International Journal of Solids and Structures, 42 (11-12), pp. 3147–3169.
Pi, Y. L., Bradford, M. A., and Uy, B. (2003). Nonlinear analysis of members with open thin-walled cross-section curved in space, University of New South Wales, School of Civil and Environmental Engineering, Sydney.
Pi, Y. L. and Trahair, N. S. (1997). “Nonlinear elastic behavior of I-beams curved in plan”, Journal of Structural Engineering, 123 (9), pp. 1201–1209.
Richard Liew, J. Y., Thevendran, V., Shanmugam, N. E., and Tan, L. O. (1995). “Behaviour and design of horizontally curved steel beams”, Journal of Constructional Steel Research, 32 (1), pp. 37–67.
Sandhu, J. S., Stevens, K. A., and Davies, G. A. O. (1990). “A 3-D, co-rotational, curved and twisted beam element”, Computers and Structures, 35 (1), pp. 69–79.
Sawko, F. (1967). “Computer analysis of grillages curved in plan”, International Association for Bridge and Structural Engineering, vol. 8, pp. 151–170.
Shanmugam, N. E., Thevendran, V., Liew, J. Y. R., and Tan, L. O. (1995). “Experimental Study on Steel Beams Curved in Plan”, Journal of Structural Engineering, 121 (2), pp. 249–259.
Simo, J. C. (1985). “A finite strain beam formulation. The three-dimensional dynamic problem. Part I”, Computer Methods in Applied Mechanics and Engineering, 49 (1), pp. 55–70.
Simo, J. C. and Vu-Quoc, L. (1987). “The role of non-linear theories in transient dynamic analysis of flexible structures”, Journal of Sound and Vibration, 119 (3), pp. 487–508.
Simo, J. C. and Vu-Quoc, L. (1991). “A Geometrically-exact rod model incorporating shear and torsion-warping deformation”, International Journal of Solids and Structures, 27 (3), pp. 371–393.
Vlasov, V. Z. (1961). Thin-walled elastic beams, 2nd edn, Israel Program for Scientific Translations, Jerusalem, Israel.
Yoo, C. H., Kang, Y. J., and Davidson, J. S. (1996). “Buckling analysis of curved beams by finite-element discretization”, Journal of Engineering Mechanics, 122 (8), pp. 762–770.
Yoshida, H. and Maegawa, K. (1983). “Ultimate strength analysis of curved I-beams”, Journal of Engineering Mechanics, 109 (1), pp. 192–214.
Young, M. C. (1969). “Flexibility influence functions for curved beams”, American Society of Civil Engineers, vol. 94.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Afnani, A., Erkmen, R.E. & Niki, V. An efficient formulation for thin-walled beams curved in plan. Int J Steel Struct 17, 1087–1102 (2017). https://doi.org/10.1007/s13296-017-9018-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13296-017-9018-5