A Strut-and-Tie Model for Predicting the Shear Strength of Exterior Beam–Column Joints Strengthened with Fiber-Reinforced Polymers
Publication: Journal of Composites for Construction
Volume 27, Issue 1
Abstract
This paper presents a new strut-and-tie model (STM) based on provisions of ACI 318-19 and ACI 440.2R-17 for estimating the shear strength of fiber-reinforced polymer (FRP)-strengthened exterior joints. Beam–column joints are vulnerable elements in reinforced-concrete structures subjected to seismic loadings and similar extreme demands. The FRP strengthening technique offers numerous advantages for retrofitting joints in existing structures with inadequate reinforcement or confinement. The design of FRP-strengthened joints requires the development of reliable procedures, including equations to predict the shear strength of the joint. Existing literature and research on STM warrant the development of simple, reliable, and practical specifications applied to a wide range of design criteria. The proposed method involves an STM model containing horizontal and vertical mechanisms. The methodology compares predicted joint shear strength results with existing experimental results to obtain a reliable design approach. This comparison, along with verification of alternative analytical results, indicates the appropriateness of the presented model for predicting the shear strength of FRP-strengthened joints. Results contribute to the enhancement and efficiency of the practical design of these joints.
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Data Availability Statement
All data, models, and codes generated or used during the study appear in the submitted article.
Notation
The following symbols are used in this paper:
- Afh
- area of horizontal FRP (mm2);
- Afv
- area of vertical FRP (mm2);
- Ajh
- area of transverse reinforcement (stirrup) in the joint region (mm2);
- Ajv
- area of the column intermediate reinforcement (mm2);
- Asb
- area of the top and bottom reinforcement of the beam (mm2);
- Ast
- cross-sectional area of tensile beam reinforcement (mm2);
- Astrut
- effective area of the diagonal strut (mm2);
- bb
- beam width (mm);
- bc
- column width (mm);
- bj
- effective joint width (mm);
- Cstrut
- compression force in the diagonal strut (N);
- db
- beam internal lever arm (mm);
- Ef
- tensile modulus of elasticity of FRP (MPa);
- f1
- principal tensile stress at the mid-depth of the joint (MPa);
- fce
- effective compressive strength of the concrete in a strut (MPa);
- fyb
- yield strength of beam reinforcement (MPa);
- fyh
- yield strength of transverse reinforcement (stirrup) in the joint region (MPa);
- fyv
- yield strength of the column intermediate reinforcement (MPa);
- specified compressive strength of concrete (MPa);
- Hb
- beam depth (mm);
- Hc
- column depth (mm);
- k
- nondimensional function;
- Lb
- beam length (mm);
- Lc
- total column height (mm);
- Nc
- axial force acting on the column (N);
- nfh
- number of FRP layers;
- np
- number of joint panel sides strengthened in shear with FRP systems in the plane of the load;
- nstr
- number of strips on the joint panel;
- Rd
- ratio of the joint shears resisted by the diagonal mechanism;
- Rh
- ratio of the joint shears resisted by the horizontal mechanism;
- Rv
- ratio of the joint shears resisted by the vertical mechanism;
- T
- tensile force resulting from the beam longitudinal (N);
- tf
- thickness of the FRP reinforcement (mm);
- Vb
- maximum recorded shear force on the beam (N);
- Vh,strut
- contribution of the concrete diagonal strut mechanism to horizontal joint shear strength (N);
- Vjh
- horizontal joint shear strength (N);
- Vjh,EXP
- experimental horizontal joint shear strength (N);
- Vjh,STM
- strut-and-tie model horizontal joint shear strength (N);
- Vjv
- vertical joint shear strength (N);
- Vth
- contribution of horizontal mechanism to the joint shear strength (N);
- Vtv
- contribution of vertical mechanism to the joint shear strength (N);
- Vu
- design shear force (N);
- Wb
- depth of the compression zone in the beam (mm);
- Wc
- depth of the compression zone in column (mm);
- Ws
- diagonal strut width (mm);
- Wfh
- horizontal FRP width (mm);
- Wfv
- vertical FRP width (mm);
- Wstr
- strip width (mm);
- x
- distance of the column edge beyond the edge of the beam (mm);
- yf
- FRP strength reduction factor;
- α1
- angle of direction of horizontal FRP relative to the horizon;
- α2
- angle of direction of vertical FRP relative to the horizon;
- βc
- strut-and-node confinement modification factor;
- βs
- strut coefficient or concrete softening coefficient;
- γ
- bond factor;
- γh
- fraction of horizontal shear transferred by the horizontal tie with the absence of the vertical tie;
- γv
- fraction of vertical shear carried by the vertical tie with the absence of the horizontal tie;
- Δf1
- principal tensile stress corresponding to the FRP contribution to the shear strength (MPa);
- δc
- correction factor for the diagonal mechanism;
- δh
- correction factor for the horizontal mechanism;
- δv
- correction factor for the vertical mechanism;
- correction factor for the horizontal mechanism for FRP-strengthened joints;
- correction factor for the diagonal mechanism for FRP-strengthened joints;
- correction factor for the vertical mechanism for FRP-strengthened joints;
- ɛfe
- effective strain in FRP reinforcement;
- θ
- inclination angle of the diagonal compression strut;
- θ1
- inclination angle of the flat strut;
- θ2
- inclination angle of the steep strut;
- λ
- bond factor which depends on the bond behavior of beam reinforcement;
- νjh
- net horizontal shear stress at mid-depth of the joint core (MPa);
- σc
- column axial stress (MPa);
- ϕv
- shear strength reduction factor;
- Ψ
- nondimensional function;
- ωb
- beam reinforcement index;
- ωh
- horizontal reinforcement index; and
- ωv
- vertical reinforcement index.
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© 2022 American Society of Civil Engineers.
History
Received: Aug 4, 2021
Accepted: Sep 6, 2022
Published online: Nov 8, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 8, 2023
ASCE Technical Topics:
- Continuum mechanics
- Design (by type)
- Dynamic loads
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering materials (by type)
- Engineering mechanics
- Fiber reinforced polymer
- Joints
- Material mechanics
- Material properties
- Materials engineering
- Polymer
- Seismic loads
- Shear strength
- Solid mechanics
- Strength of materials
- Structural behavior
- Structural design
- Structural dynamics
- Structural engineering
- Structural members
- Structural strength
- Structural systems
- Structure reinforcement
- Struts
- Synthetic materials
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