Finite difference equation of Volterra integral equation for estimating the time-dependent prestress loss of a prestressed concrete beam

Hyun Woo Park, Nur Indah Mukharromah, Jin Ho Hwang, Seong Cheol Lee

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A new finite difference equation is proposed to estimate the time-dependent prestress loss of a prestressed concrete (PSC) beam. The finite difference equation is derived by discretizing the Volterra integral equation in the time domain which provides a rigorous physical insight into the interactions of the prestress loss with concrete creep, shrinkage, tendon relaxation, and the change in concrete elastic modulus. The effect of the beam's self-weight on the concrete stress has been rigorously accounted for by using the time-varying transformed section of the PSC beam. The tendon relaxation is adequately considered by employing the equivalent creep coefficient of linear viscoelasticity. The proposed method was verified by comparing the numerical results from the finite element analysis for various cross-sections of PSC beams. The comparison of the proposed method with the design provisions of Eurocode 2 and AASHTO for examples with straight or parabolic tendon profiles revealed that both Eurocode 2 and AASHTO generally underestimate the effective prestress force when concrete creep, shrinkage, and tendon relaxation are considered simultaneously. In addition, the proposed analysis method has been validated through comparison with the effective prestress force measured in the literature. The proposed analysis method is expected to aid in the rational design of PSC beams, particularly because of its effective prestress evaluation and camber control during construction.

Original languageEnglish
Article number107437
JournalStructures
Volume69
DOIs
StatePublished - Nov 2024

Keywords

  • Concrete creep
  • Concrete shrinkage
  • Finite difference equation
  • Prestress loss
  • Prestressed concrete (PSC) beam
  • Tendon relaxation
  • Volterra integral equation

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