Softened Membrane Torsional Model for GFRP–Reinforced Concrete Bridge Box Girders
Publication: Journal of Bridge Engineering
Volume 29, Issue 3
Abstract
This study investigates the experimental and analytical torsional behavior of reinforced concrete (RC) bridge box girders reinforced with glass fiber–reinforced polymer (GFRP) bars and continuous spiral stirrups, representing a first in literature. Reinforced concrete box girders were constructed and examined until failure to assess the influence of the spiral pitch and web reinforcement configuration on torsional behavior and strength. The test specimens had continuous GFRP spirals and tie stirrups; the control specimen did not have web reinforcement. The specimens were 4,000 mm long, 380 mm wide, and 380 mm high, and had a wall thickness of 100 mm. The test results demonstrate that the box girder with spiral GFRP reinforcement achieved higher torsional strength and lower twist than its counterpart specimen reinforced with individual GFRP tie stirrups by approximately 6% and 11%, respectively. The specimen with a narrow spiral pitch performed better than the specimens with a wide spiral pitch. An analytical iterative softened membrane model for torsion (SMMT) was used to estimate the entire torsional behavior of box girders with spiral GFRP reinforcement. The analytical results were compared with the experimental results of four bridge box girders with spiral GFRP reinforcement to validate the model's accuracy. The comparison indicates that the model could reasonably predict the cracking and ultimate torsional strength as well as the associated twists.
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Data Availability Statement
All data, models, and codes generated or used during the study appear in the published paper.
Acknowledgments
This research was conducted with funding from the Natural Science and Engineering Research Council of Canada (NSERC). The authors are grateful to the GFRP bar manufacturer, Pultrall Inc., Thetford Mines, QC, Canada, for their effective involvement in the project, and the technical staff of the structural lab in the Department of Civil Engineering at the University of Sherbrooke.
Notation
The following symbols are used in this paper:
- Ao
- area enclosed by the centerline of the shear flow path; ;
- Al
- total cross-sectional area of the longitudinal GFRP bars;
- At
- cross-sectional area of one transverse GFRP bar;
- Ac
- cross-sectional area enclosed by the outer perimeter of the concrete;
- d
- vertical distance of the spiral link;
- Ec
- elastic modulus of concrete;
- Eft
- elastic modulus of transverse GFRP bars;
- Efl
- elastic modulus of the longitudinal GFRP bars;
- cylinder compressive strength of concrete;
- cracking stress and strain of concrete;
- ffl
- tensile strength of the longitudinal GFRP bars;
- fft
- tensile strength of the transverse GFRP bars;
- fftu
- ultimate tensile strength of the GFRP stirrup's straight portion;
- fft,(bend)
- tensile strength of the GFRP stirrup at the bent portion;
- fftu,(bend)
- ultimate tensile strength of the GFRP stirrup at the bent portion;
- k1c
- ratio of the average compressive stress to the peak compressive stress in the concrete strut, considering the tensile stress of concrete;
- k1t
- ratio of the average tensile stress to the peak tensile stress in the concrete struts;
- pc
- perimeter of the outer concrete cross section;
- ph
- perimeter of the centerline of stirrups;
- po
- perimeter of the centerline of shear flow; po = pc − 4td;
- Q
- variable as defined in Eq. (9);
- q
- shear flow;
- s
- spacing of the GFRP web reinforcement;
- T
- torsional moment;
- Tu
- ultimate torsional moment;
- Tcr
- cracking torsional moment;
- t
- wall thickness of the hollow section;
- td
- thickness of the shear flow zone;
- α2
- angle of applied principal compressive stress (two-axis) with respect to the longitudinal GFRP bars (l-axis);
- β
- deviation angle; ;
- concrete cylinder strain corresponding to the peak cylinder strength ;
- average biaxial strain in one direction and two directions, respectively;
- average uniaxial strain in the one-direction and the two-direction, respectively;
- uniaxial surface strain in the one-direction and the two-direction, respectively;
- average biaxial strain in the l-direction and the t-direction of the GFRP reinforcement, respectively;
- average uniaxial strain in the l-direction and the t-direction of the GFRP reinforcement, respectively;
- average uniaxial strain of the GFRP stirrups;
- average uniaxial strain of the longitudinal GFRP bars;
- average uniaxial strain in the GFRP spiral direction;
- ultimate strain of the GFRP stirrups;
- ultimate strain of the longitudinal GFRP bars;
- average strain of the GFRP bars, considering Hsu/Zhu ratios;
- γ21
- average shear strain in the 2–1 coordinate;
- γlt
- average shear strain in the l−t coordinate of GFRP reinforcement;
- average normal stresses of concrete in the one-direction and two-direction, respectively;
- σl, σt
- applied normal stresses in the l-direction and t-direction of the GFRP reinforcement, respectively;
- average shear stress of concrete in the 2–1 coordinate;
- τlt
- applied shear stresses in the l−t coordinate of the GFRP reinforcement;
- ρl, ρt
- longitudinal and transverse GFRP reinforcement ratios, respectively. ρl = Al/potdand ρt = At/std;
- (ν12)GFRP
- modified Hsu/Zhu ratio used in the SMMT-H-GFRP model;
- θ
- angle of twist per unit length;
- θcr
- cracking angle of twist per unit length;
- θu
- ultimate angle of twist per unit length;
- ϕ
- curvature of the concrete struts along the two-direction;
- ζ
- softened coefficient of concrete in compression; and
- φ
- inclination angle of the spiral link.
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© 2023 American Society of Civil Engineers.
History
Received: Nov 11, 2022
Accepted: Oct 16, 2023
Published online: Dec 20, 2023
Published in print: Mar 1, 2024
Discussion open until: May 20, 2024
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