Moment-curvature and strain energy of beams with external fiber-reinforced polymer reinforcement

M. Achintha, C.J. Burgoyne

Research output: Contribution to journalArticlepeer-review


To calculate the load at which fiber-reinforced polymer (FRP) plates will debond from a reinforced concrete (RC) beam using fracture mechanics principles based on energy release rates, it is necessary to accurately determine the strain energy in the beam. This study presents a moment-curvature model for an RC beam with the presence of a net axial force that is due to the force in the FRP plate. The classical Branson analysis only covers the case of a cracked-elastic concrete beam with no axial force. The paper shows how the model can be extended into the inelastic regime and can be used to determine the moment-curvature relations on loading. Comparisons with the available test data have shown good correlation. The model is then extended into an unloading regime for the strain energy determinations of RC beams with external reinforcement, which may be bonded or partially debonded.
Original languageEnglish
Pages (from-to)20-29
Number of pages10
JournalACI Structural Journal
Issue number1
Publication statusPublished - 1 Jan 2009


  • Branson’s model
  • elastic stiffness
  • moment-curvature
  • strain energy


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