Strand Debonding for Prestressed Concrete Girders to Control End Horizontal Web Cracks Based on a Modified G-S Model
Publication: Journal of Bridge Engineering
Volume 27, Issue 2
Abstract
Horizontal web cracks are frequently observed at the ends of pretensioned concrete members (I girders or Bulb Tee girders) at the time of prestress transfer. Using a modified Gergely–Sozen (mG-S) model to calculate the spalling forces of prestressed concrete girder ends was illustrated step by step. A new design procedure based on the mG-S model was proposed with the aim to control horizontal web cracks by debonding a number of strands. Three different criteria were introduced to determine the suitable debonding ratios and debonding patterns of the girder ends. Prestressed Standard Wisconsin Wide-Flange girders (WF54) and Standard Nebraska I girders (NU1100) were chosen for case studies, in which several debonding ratios and debonding patterns were analyzed to check the reasonability and effectiveness of the current limits in the standards. The analysis results obtained from the mG-S model were validated by the finite-element analysis (FEA) method, which proved that 25% debonding can greatly reduce the concrete tension strains in the web but cannot eliminate the web crack, and it can satisfy the code requirements on the vertical reinforcement stresses and crack width. Four percent of the total prestressing force is enough to be used to design the vertical reinforcement at the girder ends. The recommendations on debonding patterns are also presented.
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Acknowledgments
This research project was made possible by generous support from the National Natural Science Foundation of China (Grant No. 51878250). The financial support is greatly appreciated.
Notation
The following symbols are used in this paper:
- A0
- equivalent cross-sectional area;
- As
- area of vertical reinforcements within the distance of h/4 from the girder end;
- b
- width of the web;
- e
- Pb’s eccentricity from the junction;
- eh
- distance from the vertical central axis to the acting point of the resultant of half-strand forces;
- em
- Pb’s eccentricity from the bottom fiber;
- design concrete compressive strength at transfer time;
- fcskj
- characteristic tensile strength of the concrete;
- Eci
- concrete modulus;
- Ec1
- secant modulus from the origin to the peak compressive stress;
- GF
- fracture energy of concrete;
- h
- height of the girder;
- h1
- height of the compression zone;
- h1eq
- equivalent height of the compression zone;
- I0
- equivalent moment of inertia;
- L
- distance from the girder end to the section where the stresses become linear distribution;
- lm
- arm length of the horizontal moment at the junction;
- Mj
- unbalanced horizontal moment at the junction section;
- Pb
- resultant of strand forces;
- Pcb
- resultant force of concrete stresses of the bottom flange;
- T
- spalling force;
- w
- crack opening;
- yjun
- location of the junction;
- equivalent location of the junction;
- ɛc1
- strain at maximum compressive stress;
- σjun
- stress at the junction concrete;
- σs
- stress of vertical reinforcement; and
- σt-spalling
- vertical stress of concrete of the bh/8 area of the member end.
References
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Published In
Journal of Bridge Engineering
Volume 27 • Issue 2 • February 2022
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jul 21, 2021
Accepted: Oct 20, 2021
Published online: Dec 13, 2021
Published in print: Feb 1, 2022
Discussion open until: May 13, 2022
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