Excessive long-time deflections of prestressed box girders. II: Numerical analysis and lessons learned

Zdeněk P. Bažant*, Qiang Yu, Guang Hua Li

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

124 Scopus citations


As a sequel to Part I, which clarified the causes of the unexpectedly large deflections of the Koror-Babeldaob Bridge in the Pacific island nation of Palau, Part II presents the numerical procedure and reviews the lessons learned. The box girder represents a thick shell that is discretized by eight-node, three-dimensional (3D) finite elements. Except for corrections due to cracking, concrete creep is assumed to follow aging linear viscoelasticity and is modeled by a rate-type law based on the Kelvin chain, the properties of which are adjusted for humidity conditions and temperature. In each time step and at each integration point, Widder's formula is used to convert the aging compliance function to a continuous retardation spectrum for the current age of concrete, and discretization of the spectrum yields the current elastic moduli of the Kelvin units. The shrinkage strains depend on the environmental humidity and the thickness of each plate in the cross section. The computations proceed according to Baant's exponential algorithm, which is unconditionally stable and reduces the problem to a sequence of elasticity problems with an orthotropic effective stiffness of material and nonisotropic inelastic strains, different for each integration point in each time step. These problems are solved by commercial software ABAQUS. The segmental construction sequence is also modeled. The computer results reported in Part I explain the excessive deflections and compare the performance of various material models for creep and shrinkage. Part II formulates the lessons learned and makes recommendations for implementation.

Original languageEnglish (US)
Pages (from-to)687-696
Number of pages10
JournalJournal of Structural Engineering (United States)
Issue number6
StatePublished - Jun 2012


  • Bridges
  • Design standards
  • Kelvin chain
  • Prestressed concrete
  • Relaxation
  • Segmental erection
  • Shear lag

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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