Journal of Marine Science and Technology

, Volume 20, Issue 4, pp 703–710 | Cite as

Buckling phenomenon for imperfect pipe under pure bending

  • Hartono YudoEmail author
  • Takao Yoshikawa
Original article


The buckling phenomenon for imperfect pipe under bending has been investigated by nonlinear FEA, considering the effect of a cross sectional oval deformation by changing the variables of pipes, that is, L/D varying from 2.5 to 20, D/t varying from 50 to 200, and imperfection (δ o/t) varying from 0.05 to 0.5. As well as the elastic buckling, the elasto-plastic buckling was investigated. From the calculation results, the followings were found. The reduction of buckling moment due to imperfection is larger in short pipe than in long pipe. The effect of imperfection for pipes with large values of D/t is larger than those with small values of D/t if L/D of both pipes is same. The effects of imperfection for elastic analysis are larger than elasto-plastic analysis. The buckling moment reduces more by the imperfection of buckling mode than by that of oval mode.


Imperfect pipe Buckling moment Oval deformation Elastic buckling Elasto-plastic buckling 



Diameter of cylinder


Young’s modulus


Length of pipe


Applied moment


Buckling moment obtained by nonlinear calculation in elastic analysis


Critical bending moment


Critical bending moment, when the critical buckling stress of a cylinder under bending is same as the buckling stress of a cylinder under axial compression


Critical bending moment by Timoshenko


Maximum buckling moment in elastic analysis without imperfection


Ultimate moment in elasto-plastic analysis


Initial yield moment


Parameter β = (D/t)(σ Y/E)


Amplitude of oval deformation


Maximum amplitude of imperfection


Poisson’s ratio


Critical buckling stress under axial compression


Yield stress


Non-dimensional buckling moment in elastic analysis


Non-dimensional buckling moment in elasto-plastic analysis


  1. 1.
    Timoshenko S, Gere J (1961) Theory of elastic stability, 2nd edn. McGraw-Hill International Book CompanyGoogle Scholar
  2. 2.
    Yudo H, Yoshikawa T (2012) Mechanical behaviour of pipe under pure bending load. In: Proceedings of the 26th Asian technical exchange and advisory meeting on marine structures, pp 359–364Google Scholar
  3. 3.
    Seide P, Weingarten VI (1961) On The buckling of circular cylindrical shells under pure bending. Trans ASME J Appl Mech 28:112–116MathSciNetCrossRefGoogle Scholar
  4. 4.
    Odland J (1978) Buckling resistance of unstiffened and stiffened circular cylindrical shell structures. Nor Marit Res 6(3):2–21Google Scholar
  5. 5.
    Ju GT, Kyriakides S (1992) Bifurcation and localization instabilities in cylindrical shells under bending: part II predictions. Int J Solids Struct 29:1143–1171CrossRefGoogle Scholar
  6. 6.
    Yudo H, Yoshikawa T (2014) Buckling phenomenon for straight and curved pipe under pure bending. J Mar Sci Technol 20(1):94–103CrossRefGoogle Scholar
  7. 7.
    SUPERB (1996) Buckling and collapse limit state, December 1996Google Scholar

Copyright information

© JASNAOE 2015

Authors and Affiliations

  1. 1.Department of Maritime Engineering, Graduate School of EngineeringKyushu UniversityFukuokaJapan
  2. 2.Naval Architecture, Faculty of EngineeringDiponegoro UniversitySemarangIndonesia
  3. 3.Department of Marine System Engineering, Faculty of EngineeringKyushu UniversityFukuokaJapan

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