Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Dynamic analysis of box girders with tee-stiffening using unconstrained optimization techniques

  • 152 Accesses

  • 8 Citations


The paper presents a numerical procedure for dynamic analysis of box girders with tee-stiffeners utilizing unconstrained optimization techniques. Unlike the finite element or finite strip methods, the procedure does not require discretization to the whole structure, thus resulting in great savings in computational time. The potential and kinetic energy of the assembled structure is expressed in terms generalized functions that describe the longitudinal and transverse displacement profiles. The problem is then converted into uunconstrained optimization problem to determine the magnitude of the lowest natural frequency and the associated mode shape. Results are presented showing the sensitivity the natural frequency to the stiffener depth (d) and the flange width (b). It is shown that the number of longitudinal and transverse stiffeners largely influence the magnitude of the natural frequency (λ) of the box girder. Design guidelines are also provided to optimize the dynamic response of the structure. The procedure is very practical and can be utilized in the industry for the analysis of box girders.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7


  1. Barrette M, Berry A, Beslin O (2000) Vibration of stiffened plates using hierarchical trigonometric functions. J Sound Vib 235:727–747

  2. Bedair O (2006) Limit state design procedures for static and dynamic analysis of stiffened box girders. Technical report submitted for Bechtel Corporation

  3. Bedair O (2009) Analysis and limit state design of stiffened plates and shells: a world view. J Appl Mech Rev 62:76–92

  4. Cheung YK, Fan SC (1983) Static analysis of right box girder bridges by spline finite strip method. Proc Inst Civ Eng Part 2 75:311–323

  5. Ghavami K, Khedmati R (2006) Numerical and experimental investigations on the compression behaviour of stiffened plates. J Constr Steel Res 62:1087–1100

  6. Ghosh A, Biswal K (1996) Free-vibration analysis of stiffened laminated plates using higher-order shear deformation theory. Finite Elem Anal Des 22:143–161

  7. Harik IE, Guo M (1993) Finite element analysis of eccentrically stiffened plates in free vibration. Comput Struct 49:1007–1015

  8. Harik I, Salamoun G (1988) The analytical strip method of solution for stiffened rectangular plates. Comput Struct 29:283–291

  9. Koko TS (1990) Super finite elements for non-linear static and dynamic analysis of stiffened plate structures. PhD dissertation, University of British Columbia

  10. Koko TS, Olson MD (1991) Non-linear analysis of stiffened plates using super element. Int J Numer Methods Eng 31:319–343

  11. Kumar Y, Mukhopadhyay M (2002) Transient response analysis of laminated stiffened plates. Compos Struct 58:97–107

  12. Madhavan M, Davidson J (2005) Buckling of centerline-stiffened plates subjected to uniaxial eccentric compression. Thin-Walled Struct 43:1264–1276

  13. Mukherjee A, Mukhopadhyay M (1989) Finite element free vibration of eccentrically stiffened plates. Comput Struct 33:295–305

  14. Mukhopadhyay M (1989) Vibration and stability of stiffened plates by semi-analytic finite difference method. Part I: consideration of bending displacement only. J Sound Vib 130:27–39

  15. Murray NW, Thierauf G (1983) Tables for the design and analysis of stiffened steel plates. Birkhauser, Basel

  16. Patel S, Datta P, Sheikh A (2006) Buckling and dynamic instability analysis of stiffened shell panels. Thin-Walled Struct 44:321–333

  17. Park B, Cho S (2006) Simple design formulae for predicting the residual damage of unstiffened and stiffened plates under explosion loadings. Int J Impact Eng 32:1721–1736

  18. Peng L, Kitipornchai S (2006) Buckling and free vibration analyses of stiffened plates using the FSDT mesh-free method. J Sound Vib 289:421–449

  19. Peng-Cheng S, Dade H, Zongmu W (1987) Static, vibration and stability analysis of stiffened plates using B spline functions. Comput Struct 27:73–78

  20. Qing G, Qiu J, Liu Y (2006) Free vibration analysis of stiffened laminated plates. Int J Solids Struct 43:1357–1371

  21. Rikards R, Chate A, Ozolinsh O (2001) Analysis for buckling and vibrations of composite stiffened shells and plates. Compos Struct 51:361–370

  22. Shen PC, Dade H, Wang Z (1987) Static, vibration and stability analysis of stiffened plates using B-spline functions. Comput Struct 27:73–78

  23. Siddiqi Z, Kukreti A (1998) Analysis of eccentrically stiffened plates with mixed boundary conditions using differential quadrature method. Appl Math Model 22:251–275

  24. Wittrick WH (1968) General sinusoidal stiffness matrices for buckling and vibration analysis of thin flat-walled structures. Int J Mech Sci 10:949–966

  25. Zhang W, Wang A, Vlahopoulos N, Wu K (2005) Vibration analysis of stiffened plates under heavy fluid loading by an energy finite element analysis formulation. Finite Elem Anal Des 41:1056–1078

Download references

Author information

Correspondence to Osama Bedair.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bedair, O. Dynamic analysis of box girders with tee-stiffening using unconstrained optimization techniques. Struct Multidisc Optim 42, 547–558 (2010). https://doi.org/10.1007/s00158-010-0499-5

Download citation


  • Unconstrained optimization
  • Steel structures
  • Dynamic analysis