Theoretical Analysis of Behavior of FRP-Strengthened Reinforced Concrete Members Subjected to Combined Torsion and Biaxial Bending
Publication: Journal of Composites for Construction
Volume 28, Issue 3
Abstract
Reinforced concrete (RC) structural members, such as bridge girders and columns, flanged and spandrel beams, and edge frame beams, may be subjected to combined actions in the general case of loading. Despite extensive research on the behavior of RC members strengthened with fiber-reinforced polymer (FRP) composites under pure actions, questions have been raised about the strengthened RC members subjected to combined actions, particularly actions including torsion. As a contribution to this demanding field of research, the first theoretical model capable of predicting the full load–deformation response of RC members strengthened with conventional FRP-strengthening configurations, and subjected to torsion combined with biaxial bending, was developed based on the principles of the well-known combined-actions softened truss model (CA-STM). The proposed model considered the influence of various parameters, such as FRP stiffness, on the constitutive laws of materials. In addition, the computational operations and duration were significantly reduced, and the numerical stability of the solution procedure was enhanced by extending the refined efficient solution algorithm for FRP-strengthened RC members for the first time. Furthermore, the efficiency and contribution of the FRP system and the governing failure mode was accurately predicted. Three categories of equations, including equilibrium equations, compatibility equations, and the constitutive relationships of materials, were incorporated into the proposed model, then a system of 16 nonlinear equations, containing 16 unknown variables, was solved to obtain the full load–deformation response of an FRP-strengthened member subjected to combined actions, including torsion. A detailed comparison conducted between the test results of a database with various strengthening patterns collected from the literature and the predictions of the proposed model showed that the model was able to estimate the ultimate strength, with a mean value and coefficient of variation of 1.11% and 13%, respectively, in addition to predicting the overall load–displacement response well.
Practical Applications
This research highlights the importance of considering the combined effects of bending and torsion on the capacity of fiber-reinforced polymer (FRP)-strengthened reinforced concrete (RC) members, particularly in members where torsion is critical. The addition of flexural moment in certain situations can lead to a reduction in the torsional capacity of the member’s cross-section. While in specific situations, where the strengthening system is asymmetrically applied or the internal steel arrangement of the section is asymmetrical, the torsional capacity can even increase compared to the case when subjected to pure torsion. Therefore, the arrangement of the strengthening system plays a crucial role in determining the failure mode and strength of the member. The model proposed in this study, along with its resulting findings, will provide valuable assistance to engineers in determining the optimal percentage of an FRP system and its pattern in these situations. This will allow them to achieve the highest possible effectiveness of the strengthening system in cases involving combined actions, including torsion and flexure.
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Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Notation
The following symbols are used in this paper:
- Acp
- cross-sectional area of the member;
- Afl,i
- cross-sectional area of the FRP materials on side (i) in the l direction;
- Aft,i
- cross-sectional area of the FRP materials on side (i) in the t direction;
- Al,i
- total cross-sectional area of the longitudinal steel reinforcement on side (i);
- At
- cross-sectional area of one stirrup;
- A0
- area enclosed by the centerline of the shear flow;
- b
- cross-sectional width;
- b0
- width of area enclosed by the shear flow;
- c
- bond characteristic factor for the constitutive law of concrete in the tensile direction;
- Df
- stress distribution factor of the FRP;
- Ec,i
- precracking elasticity modulus of the concrete in tension on side (i);
- Ef
- elasticity modulus of the FRP material;
- Es
- elasticity modulus of the bare rebar;
- fc
- peak cylindrical compressive strength of the concrete;
- fcr,i
- cracking strength of the concrete on side (i);
- ffe
- effective FRP strength;
- ffl,i
- average stress of the FRP materials on side (i) in the l direction;
- fft,i
- average stress of the FRP materials on side (i) in the t direction;
- ffu
- ultimate FRP strength;
- fl,i
- average stress of the internal reinforcement on side (i) in the l direction;
- fs,i
- average stress of the internal reinforcement on side (i);
- ft,i
- average stress of the internal reinforcement on side (i) in the t direction;
- fy
- yielding stress of the bare rebar;
- fyl
- yielding stress of the longitudinal rebar;
- fyt
- yielding stress of the transverse rebar;
- h
- cross-sectional height;
- h0
- height of the area enclosed by the shear flow;
- Kf/s
- FRP:steel stiffness ratio coefficient;
- Kw
- strengthening scheme coefficient;
- kc,i
- ratio of the average stress to the peak stress of the compressed concrete on side (i);
- kf
- confinement coefficient;
- kt,i
- ratio of the average stress to the peak stress of the tensile concrete on side (i);
- Le
- effective length of the FRP;
- Lmax
- defined as 0.9 min (b, h);
- li
- length of the segment corresponding to side (i);
- My
- flexural moment about the y-axis;
- Mz
- flexural moment about the z-axis;
- Nx
- normal force along the x-axis;
- nft,i
- number of transverse FRP layers on side (i);
- pcp
- cross-section of the perimeter;
- p0
- enclosed perimeter of the circulating shear flow;
- qi
- shear flow on side (i);
- s
- centerline-to-centerline spacing of the stirrups;
- sf,i
- centerline-to-centerline spacing of the FRP strips on side (i);
- Tcr
- torsional moment at the cracking stage;
- Tx
- externally applied torsional moment;
- td,i
- effective thickness of the segment corresponding to side (i);
- tf
- thickness of the FRP sheet;
- ti
- thickness of the hollow tube section corresponding to side (i);
- Vy
- shear force along the y-axis;
- Vz
- shear force along the z-axis;
- wf
- FRP strip width;
- zi
- index for the shear flow zone describing the location at which the strain distribution is zero or intersects the inside surface of the wall panel;
- αi
- rotating angle of the principal coordinate of the concrete struts with respect to the longitudinal axis of the member on side (i);
- αn
- in-section confinement coefficient;
- αs
- in-height confinement coefficient;
- βw
- coefficient used to calculate the FRP effective strain;
- γFRP
- coefficient taking into account the type of FRP;
- γlt,i
- average shear strain in the l−t coordinate on side (i);
- average longitudinal strain of the elements;
- cracking strain of the concrete on side (i);
- ultimate strain of the concrete on side (i);
- average strain of the concrete struts in the d direction on side (i);
- strain of the extreme compression concrete fiber in the d direction on side (i);
- effective strain of the FRP material;
- ultimate strain of the FRP material;
- average strain of the concrete on side (i);
- average strain in the l direction on side (i);
- peak compressive strain of the softened concrete on side (i);
- average strain of the concrete struts in the r direction on side (i);
- strain of the extreme tensile concrete fiber on side (i);
- average strain of the internal reinforcement on side (i);
- average strain in the t direction on side (i);
- yielding strain of the internal reinforcement;
- concrete strain corresponding to the peak cylindrical compressive strength of the concrete;
- η
- coefficient used to calculate the FRP effective strain;
- θ
- angle of twist per unit length;
- ξi
- softening coefficient of the concrete on side (i);
- ρfl,i
- ratio of the FRP materials with respect to the effective thickness of element (i) in the l direction;
- ρft,i
- ratio of the FRP materials with respect to the effective thickness of element (i) in the t direction;
- ρl,i
- reinforcing steel ratio in the l direction;
- ρt
- reinforcing steel ratio in the t direction;
- σd,i
- principal compressive stress of the concrete struts on side (i);
- σf,max
- maximum FRP stress factor;
- σl,i
- longitudinal stress of the cross-section on side (i);
- σp,i
- peak cylindrical compressive stress of the softened concrete on side (i);
- σr,i
- principal tensile stress of the concrete struts on side (i);
- σt,i
- transverse stress of the cross-section on side (i);
- average stress of the concrete struts;
- τlt,i
- applied shear stress on side (i);
- ϕl,13
- curvature of Panels (1) and (3) in the longitudinal direction;
- ϕl,24
- curvature of Panels (2) and (4) in the longitudinal direction;
- ϕt,13
- curvature of Panels (1) and (3) in the transverse direction;
- ϕt,24
- curvature of Panels (2) and (4) in the transverse direction;
- ψc,i
- curvature of the compression concrete strut on side (i);
- ψi
- total curvature of the concrete strut on side (i);
- ψt,i
- curvature of the tensile concrete strut on side (i); and
- ωw
- volumetric mechanical ratio of the FRP.
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Published In
Journal of Composites for Construction
Volume 28 • Issue 3 • June 2024
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© 2024 American Society of Civil Engineers.
History
Received: May 26, 2023
Accepted: Jan 5, 2024
Published online: Mar 19, 2024
Published in print: Jun 1, 2024
Discussion open until: Aug 19, 2024
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