Strengthening of reinforced concrete shear walls with openings using carbon fiber-reinforced polymers
Abstract
Reinforced concrete shear walls are one of the most widely used lateral load structural resisting elements in high rise buildings. Introducing openings in existing shear walls may be due to remodeling or municipality considerations, such as placement of staircases, windows, doors and elevators. Making openings in existing shear wall decrease the overall structural capacity and integrity of the wall, in addition to stress concentrations around the openings. This necessitates the strengthening of the opening rim with FRP wraps. This paper focuses on developing a 3D high-reliability dynamic nonlinear finite element model on ABAQUS theory manual and users’ manual, version 6.10 (2010) to simulate the behavior of shear walls with openings strengthened with FRP wraps to investigate their seismic response under the monotonic loads. The proposed FE model has been validated using previous experimental data in literature. The FE results indicated that the proposed configuration of CFRP laminates substantially increases the lateral load strength and deformation capacity of the shear wall with openings and also improves the ductility and energy dissipation of the shear wall.
Keywords
Shear wall Openings 3D numerical analysis Strengthening CFRP DuctilityList of symbols
- \(f_{\text{c}}^{{\prime }}\)
Characteristic compressive strength of concrete (MPa)
- E_{c}
Elastic modulus (MPa)
- E_{0}
Initial elastic modulus (MPa)
- σ_{c}
Compressive stress of concrete (MPa)
- ε_{c}
Concrete strain
- ɛ_{cu}
Ultimate strain of concrete
- ε_{0}
Strain at the peak stress
- f_{ctm}
Average tensile strength of concrete (MPa)
- f_{cm}
Average compressive strength of concrete (MPa)
- F_{y}
Yield strength of steel (MPa)
- F_{u}
Ultimate strength of steel (MPa)
- f_{fu}
Ultimate tensile strength of FRP (MPa)
- ʋ
Poisson’s ratio
- R, R_{E,}R_{σ}
Parameters depend on concrete properties
- K_{i}
Secant stiffness (kN/mm)
- F_{i}
Peak load (kN)
- X_{i}
Displacement (mm)
- ɛ_{t}
Total strain
- \(\varepsilon_{t}^{\text{cr}}\)
Cracking strain of concrete
- \(\varepsilon_{t}^{\text{pl}}\)
Plastic strain of concrete
- d_{t}
Tensile damage parameter
- d_{c}
Compression damage parameter
- σ_{t}
Tensile stress of concrete (MPa)
- \(\varepsilon_{t}^{\text{el}}\)
Elastic strain
- k
Ratio of the second stress invariant on the tensile meridian to that of compressive meridian
- f_{b0}/f_{co}
Ratio of initial equibiaxial yield stress to initial uniaxial compressive stress
- ɛ_{fu}
Ultimate strain of FRP
- G
Shear modulus (MPa)
- t
FRP layer thickness (mm)
- P_{u}
Ultimate load (kN)
- Δ_{u}
Ultimate displacement (mm)
- Δ_{y}
Yield displacement (mm)
- n
Number of layers
- E_{b}
Energy absorption capacity (kN mm)
- μ
Ductility index
Introduction
Reinforced concrete shear walls represent a structurally efficient solution to stiffen a building structural system under lateral loads. The main function of a shear wall is to increase the rigidity and strength of the building for lateral resistance. Shear walls have very high in-plane stiffness and strength, which can be used to instantaneously resist large horizontal loads such as wind or seismic forces in addition to resisting gravity loads. RC shear walls must be carefully designed to provide not only adequate strength, but also sufficient ductility to avoid brittle shear failures. Several shear walls all over the world are suffering damages from earthquakes or due to poor design and detailing or have construction faults. As mentioned in Popescu et al. (2015), the description of shear wall openings could be defined as already existing openings, or existing openings that have been enlarged and newly created openings. The introduction of openings in walls due to the architecture and installation’s needs will change the stress distribution within the wall, adversely influencing its strength. Investigations on the behavior of reinforced concrete members strengthened by externally bonded FRP have been mainly focused on either columns or beams, while there are limited experimental and analytical studies exploring the effectiveness of FRP retrofitting and strengthening the structural walls with or without openings.
Experimental investigations on the rehabilitation of shear walls by CFRP strips have been performed by many researchers. According to Lombard et al. (2000), the strengthening of shear walls using carbon fiber-reinforced polymers (CFRP) have been performed to increase its strength and ductility. The study presented shear walls that were strengthened by CFRP strips oriented in the vertical direction to the two faces of the walls. The results showed good improvement of flexural capacity and secant stiffness of the structural wall. Ghobarah and Khalil (2004) have retrofitted RC walls with FRP composites to improve the wall capacity to seismic loads and also to increase ductility. The rehabilitated walls were wrapped with bi-directional sheets in the wall region and uni-directional sheets on the boundary elements. The experimental results showed the improvement of the structural capacity of shear walls under lateral loading and the strip configurations has a major effect on the behavior of the strengthened walls and failure modes.
Antoniades et al. (2003) have retrofitted RC squat shear walls with FRP jackets in combination of FRP strips to increase the strength of heavily damaged walls during earthquake. The results indicated that the repaired wall showed improvement in the original strength with less initial stiffness and energy dissipation capacity. Altin et al. (2013) have constructed and tested five shear walls strengthened with CFRP strips with different configurations under reversed cyclic lateral loading. The experimental results indicated that the best performance has been obtained from the strengthening with lateral strips and showed the improvement of hysteretic behavior and displacement capacity as well.
Mosallam and Nasr (2016) have experimentally investigated the strengthening of reinforced concrete shear walls with openings using CFRP composite laminates under cyclic lateral loading. The experimental results indicated that the average peak loads of the CFRP-strengthened wall specimens with central window opening (R-WO) and eccentric door opening (R-DO) were 1.32, 1.25 times the average peak load of the unstrengthened walls with window opening (C-WO) and door opening (C-DO), respectively. On the other hand, the results showed that the CFRP-strengthened wall with central window opening (R-WO) had the highest toughness and ductility between all wall specimens and the CFRP strip configurations have a significant effect on the performance of the strengthened walls and failure modes. Mohammed et al. (2013) have constructed and tested one-way RC walls with cut out openings subjected to a uniformly distributed axial load with an eccentricity. They have applied two different CFRP patterns for strengthening these opening. The experimental results showed that applying the first and second patterns of CFRP strips around the corners of small openings (5% of the wall area) increased the axial strength of the wall by 49.9%, 75.4%, respectively. The results showed the improvement of the axial strength when applying CFRP inclined at 45° to the small openings.
Behfarnia and Sayah (2012) have developed finite element method to predict the ultimate capacity of concrete shear walls with openings strengthened by FRP and verified with experimental data. The FE results showed the improvement of the ultimate load and displacement capacity of the shear wall. The size and location of openings have a major effect on the wall capacity. Behfarnia and Shirneshana (2017) have developed a nonlinear FE model to investigate the lateral behavior of the squat shear wall with opening strengthened by FRP strips with four different configurations. The FE results showed the improvement of the lateral load capacity and lateral displacement of the shear wall. Briefly, this paper mainly focused on investigating the structural behavior of the RC shear walls with openings strengthened by CFRP composite laminates under monotonic lateral loading using finite element (FE) analysis. The FE models of RC walls with openings were created using (ABAQUS/Explicit) version (6.14) software. Element types, geometric nonlinearity, material nonlinearity, constitutive models and interaction models for CFRP and concrete were proposed. Based on the verified FE model, parametric study was established to predict the performance of the RC shear walls with openings strengthened by CFRP laminates. The effect of CFRP laminates on strengthening of RC beams with openings has been studied by Mahmoud (2012) and has also developed a numerical model using (ANSYS) finite element software.
Mechanical properties of CFRP laminates used in this analysis (Mahmoud 2012)
Nominal thickness (mm) | t | 0.13 |
Elastic modulus (MPa) | E _{1} | 230,000 |
E _{2} | 17,900 | |
Tensile strength (MPa) | f _{fu} | 3500 |
Shear modulus (MPa) | G _{12} | 11,790 |
G _{13} | 11,790 | |
G _{23} | 6880 | |
Poisson’s ratio (V) | v _{12} | 0.22 |
v _{13} | 0.22 | |
v _{23} | 0.3 | |
Ultimate strain (%) | ε _{fu} | 1.5 |
Experimental testing
These specimens have identical geometric dimensions and reinforcement configurations. The wall specimens were 2600 mm in height and had a rectangular cross section of 1250 × 80 mm. The flexure and shear reinforcements consisted of 6-mm-diameter rebar located on both sides of the wall. The height–width ratios of these specimens are all around 2. Specimens consisted of three structural parts, namely, the U steel plate through which the lateral loads were transferred into the wall, the wall panel, and the footing that was used for the anchoring the specimen onto the solid floor as a fixation. The out-of-plane movements were restrained by lateral supports.
Material properties of RC shear wall models
Type | Diameter | Yield strength | Ultimate strength | Modulus of elasticity |
---|---|---|---|---|
Rebars | 6 mm | F_{y} = 386 MPa | F_{u} = 551 MPa | 210,000 MPa |
Average tensile strength (f_{ctm}) | Average compressive strength (f_{cm}) | Compressive strain | Modulus of elasticity | |
---|---|---|---|---|
Concrete | 3 MPa | 50 MPa | 0.0035 | 34,000 MPa |
To avoid the local crushing of the concrete at the application point of the horizontal and vertical loads, a rigid steel plate (with 25 mm thickness) was set on the top surface of the wall models. Specimens SW4 and SW8 were the reference specimen tested without strengthening.
Finite element modeling (FEM)
Concrete
The plasticity parameters used in this analysis
Dilation angle | Eccentricity | f_{bo}/f_{co} | k | Viscosity parameter |
---|---|---|---|---|
37 | 0.1 | 1.16 | 0.67 | 0.001 |
Definition of damage evolution
In ABAQUS, the CDP model requires the definition of damage parameters, namely d_{t} and d_{c}, which are developed to model the degradation of the concrete stiffness when subjected to monotonic loading. In this study, the evolution of the compressive and tensile damage parameters, d_{c} and d_{t}, respectively, which was defined by simplification in a linear damage parameter-strain relationship.
Steel reinforcement
In ABAQUS, longitudinal and transverse steel reinforcements are modeled with three-dimensional, two-node truss elements (T2D3) embedded in a concrete region. Elastic-perfectly plastic behavior is assumed to model the steel reinforcement under both compression and tension. Linear elastic behavior is defined by elastic modulus and Poisson’s ratio.
CFRP composite
CFRP material is usually considered as transversely linear elastic isotropic material until failure. Since the composite is unidirectional, it is clear that the behavior is essentially orthotropic. In ABAQUS, lamina behavior is used to define transversely isotropic material that requires five constitutive constants to define the stress–strain relationship. Hence, in the present study, an isotropic model was considered. Perfect bond is also assumed to define the interaction between Concrete and CFRP laminates. The elastic modulus in the fiber direction of the unidirectional CFRP material considered for the numerical simulation is 230 GPa. The orthotropic mechanical properties of the used laminates are taken according to the values that reported by Mahmoud (2012). CFRP is modeled using three-dimensional reduced integration shell element (S4R). The bond between CFRP and concrete was assumed as perfect to avoid its premature failure.
Element types and meshing
Model validation
Load–displacement response
Numerical results versus Experimental results of wall specimens
Specimens | Experimental | Numerical (FEM) | P_{FEM}/P_{Exp %} | ||
---|---|---|---|---|---|
Ultimate load, P_{u} | Ultimate displacement, ∆_{u} | Ultimate load, P_{u} | Ultimate displacement, ∆_{u} | ||
Control | 113.63 | 14.00 | 106.38 | 18.35 | 93.62 |
SW4 | 88.00 | 13.00 | 86.56 | 15.00 | 98.36 |
SW8 | 71.00 | 11.80 | 69.10 | 13.60 | 97.32 |
Crack patterns and failure modes
The control specimen CW failed in a flexural manner; however, the first crack was observed at a lateral load of 54.4 kN near the base of the wall on the tensile zone. Diagonal cracks along the height of the wall were followed by horizontal flexural cracks. For specimen SW8, the bending cracks appeared at the base of the piers; however, the first crack was observed at 18.50 kN with a lateral drift of (0.02%). The first yield of the horizontal reinforcing steel bar was detected at the extremities of the coupling beam, at a load level of 61 kN. The corresponding displacement at this yield load was 8.62 mm and was followed by yielding the vertical reinforcement (at the base of the piers) at a load level of 58.52 kN and the lateral drift was 8.1 mm (0.33% drift). For specimen SW4, the first crack was observed at the base of wall at a load level of 30.11 kN and followed by inclined shear cracks between the openings. As shown in Fig. 8, it can be noted that in walls with staggered openings, the failure initiated by yielding of vertical steel rebar and followed by concrete crushing at the base of the small piers, after the concrete crushing of previous model, the vertical compressed rebars buckled. The first vertical steel rebar yielding was observed at 73.70 kN lateral load at lateral drift (0.33%) at the base of the small piers.
Parametric analysis
In this section, three different parameters were studied and analyzed as follows: the retrofitting schemes of CFRP laminates, the number of CFRP layers and the concrete strength. These parameters had a major effect on the structural capacity of the RC walls with openings. The same CDP model was developed for all the cases to evaluate the wall behavior. The effects of three parameters on the wall strength are presented in the following sections.
Strengthening schemes methodology
The high tensile strength and performance of fibers used, carbon fiber-reinforced polymers (CFRP) laminates were used to investigate the efficiency of the flexure and shear strengthening of reinforced concrete elements. According to Demeter et al. (2010), the methodology of the retrofit schemes aimed to: (1) offer flexural capacity along the edges, (2) to provide confinement effect and (3) to increase the shear capacity of the wall, especially at the wall base. In this section, ten retrofitted walls were studied [R-SW4 (1-4) and R-SW8 (1-6)]. Wall specimens (R-SW8) were retrofitted using CFRP laminates with six different schemes. In Scheme 1, 1250 mm × 150 mm (length × width) single-ply CFRP laminates oriented in the horizontal direction were applied to the top and bottom of each opening and applied on both wall sides. At the inner edge next to the openings, a 500-mm-long CFRP sheets were applied at each pier with fibers oriented in the vertical direction for flexural strengthening.
In Scheme 2, two different CFRP laminate configurations were used to increase the flexural strength of the left and right piers. For each pier, a 500.0-mm single-ply U-shaped single-ply unidirectional CFRP laminates were applied to the right pier that extended for a distance of 300.0 mm from the opening edge at both wall faces.
A 380.0-mm-wide single-ply U-shaped unidirectional CFRP laminates were applied at each spandrel to increase shear capacity. In Scheme 3, similar to scheme 2 but a 500.0-mm-long single-ply U-shaped unidirectional CFRP laminates were applied on the right pier that extended for a distance of 300.0 mm from wall opening edge at both wall faces. In Scheme 4, a 500.0-mm-length single-ply U-shaped single-ply unidirectional CFRP laminates were applied through the door opening and fully wrapped around wall thickness at both wall sides and a 380.0-mm-wide single-ply U-shaped single-ply unidirectional CFRP laminates were applied at each spandrel beam to increase shear capacity. In Scheme 5, a 500.0-mm-length single-ply U-shaped single-ply unidirectional CFRP laminates were applied through the door opening and fully wrapped around wall thickness on the left pier and a 500.0-mm-length single-ply U-shaped single-ply unidirectional CFRP laminates were applied on the right pier that extended for a distance of 300.0 mm from wall opening edge at both wall faces. In Scheme 6, similar to scheme 4 but a 500.0-mm-length single-ply U-shaped single-ply unidirectional CFRP laminates were applied on the right pier that extended for a distance of 200.0 mm from the wall opening edge at both wall faces.
For wall specimens (R-SW4), four different retrofitting schemes were developed. A 500.0-mm-length single-ply U-shaped single-ply unidirectional CFRP laminates were applied on the right pier that extended for a distance of 240.0 mm from the wall opening edge at both wall faces, 1250 mm × 150 mm (length × width) single-ply CFRP laminates oriented in the horizontal direction were applied to the top and bottom of each opening and applied on both wall faces and a 500-mm-length CFRP sheets were applied at each pier with fibers oriented in the vertical direction for flexural strengthening.
Effect of changing of CFRP schemes around openings
The percent of ultimate load compared to the control wall for retrofitted specimens (R-SW8) & (R-SW4) with one layer of CFRP
Model name | Ultimate load (kN) | Ultimate displacement (mm) | Percentage increase | Model name | Ultimate load (kN) | Ultimate displacement (mm) | Percentage increase |
---|---|---|---|---|---|---|---|
Control | 71.00 | 12.80 | 0 | Control | 88.00 | 13.00 | 0.00 |
R-SW8-1 | 77.74 | 15.60 | 8.67 | R-SW4-1 | 94.85 | 16.19 | 7.20 |
R-SW8-2 | 79.40 | 17.20 | 10.85 | R-SW4-2 | 91.12 | 23.55 | 3.42 |
R-SW8-3 | 77.80 | 18.14 | 8.74 | R-SW4-3 | 93.92 | 17.10 | 6.30 |
R-SW8-4 | 77.17 | 17.71 | 8.00 | R-SW4-4 | 93.82 | 23.55 | 6.20 |
R-SW8-5 | 78.62 | 18.14 | 9.70 | ||||
R-SW8-6 | 76.77 | 17.71 | 7.52 |
Failure modes
Effect of the number of CFRP layers on strength
The percent of ultimate load to the control one for retrofitted specimens (R-SW8) with number of CFRP layers
Specimens | Two layers, n = 2 | Three layers, n = 3 | Percentage increase, n = 2 | Percentage increase, n = 3 | ||
---|---|---|---|---|---|---|
Ultimate load, P_{u} | Ultimate displacement, ∆_{u} | Ultimate load, P_{u} | Ultimate displacement, ∆_{u} | |||
Control | 71.00 | 12.80 | 71.00 | 12.80 | 0 | 0 |
R-SW8-1 | 84.83 | 17.25 | 87.05 | 19.13 | 16.30 | 18.44 |
R-SW8-2 | 84.16 | 17.71 | 91.73 | 19.56 | 15.64 | 22.60 |
R-SW8-3 | 82.10 | 18.51 | 83.96 | 17.71 | 13.52 | 15.44 |
R-SW8-4 | 82.47 | 18.51 | 86.36 | 15.60 | 13.91 | 17.80 |
R-SW8-5 | 83.20 | 18.84 | 86.64 | 18.51 | 14.70 | 18.10 |
R-SW8-6 | 83.65 | 17.71 | 83.32 | 18.51 | 15.12 | 14.78 |
The percent of ultimate load to the control one for retrofitted specimens (R-SW4) with number of CFRP layers
Specimen | Two layers, n = 2 | Three layers, n = 3 | Percentage increase, n = 2 | Percentage increase, n = 3 | ||
---|---|---|---|---|---|---|
Ultimate load, P_{u} | Ultimate displacement, ∆_{u} | Ultimate load, P_{u} | Ultimate displacement, ∆_{u} | |||
Control | 88.00 | 13.00 | 88.00 | 13.00 | 0 | 0 |
R-SW4-1 | 106.00 | 23.10 | 115.25 | 23.55 | 16.98 | 23.64 |
R-SW4-2 | 94.54 | 19.50 | 97.13 | 23.14 | 6.92 | 9.40 |
R-SW4-3 | 97.17 | 24.21 | 105.14 | 21.56 | 9.44 | 16.30 |
R-SW4-4 | 102.83 | 22.67 | 112.06 | 22.67 | 14.42 | 21.47 |
Effect of concrete compressive strength
Stiffness degradation
Ductility
Ductility is considered as a very important property in achieving the acceptance of FRP-reinforced concrete structures in practice [26]. Three parameters, namely yield displacement ∆_{y}, ultimate displacement ∆_{u} and displacement ductility ratio μ, were taken into consideration to evaluate the displacement ductility index. In present study, yield displacement (∆_{y}) corresponding to the load at yielding was evaluated according to the method reported by Park (1989). The ultimate/displacement (∆_{u}) was defined as displacement corresponding to 85% of peak load on descending branch of envelope curve.
The ductility and energy absorption capacity of wall specimens
Wall specimen | Peak load, kN | Peak displacement (∆_{u}), mm | Energy absorption capacity (E_{b}), kN mm | Yield displacement, (∆_{y}), mm | Ultimate displacement (∆_{u}), mm | Ductility index, μ = ∆_{u}/∆_{y} | Failure mode |
---|---|---|---|---|---|---|---|
CW | 113.63 | 26.32 | 2566 | 10.40 | 26.32 | 2.53 | Flexure |
SW4 | 88.00 | 21.81 | 1560 | 8.55 | 21.81 | 2.55 | Flexure |
SW8 | 71.00 | 14.96 | 802 | 8.06 | 14.96 | 1.86 | Shear |
R-SW8-1 | 77.74 | 15.60 | 1258 | 7.82 | 19.98 | 2.55 | Shear |
R-SW8-2 | 79.40 | 17.20 | 1275 | 7.77 | 19.92 | 2.56 | Shear |
R-SW8-3 | 77.80 | 18.14 | 1172 | 8.51 | 19.96 | 2.35 | Shear |
R-SW8-4 | 77.17 | 17.71 | 1247 | 7.71 | 20.00 | 2.60 | Shear |
R-SW8-5 | 78.62 | 18.14 | 1263 | 7.75 | 19.96 | 2.58 | Shear |
R-SW8-6 | 76.77 | 17.71 | 1239 | 7.78 | 19.92 | 2.55 | Shear |
R-SW4-1 | 94.85 | 16.19 | 1953 | 7.76 | 24.87 | 3.20 | Flexure |
R-SW4-2 | 91.12 | 23.55 | 1900 | 8.82 | 24.95 | 2.83 | Flexure |
R-SW4-3 | 93.92 | 17.10 | 1884 | 7.92 | 17.92 | 2.26 | Flexure |
R-SW4-4 | 93.82 | 23.55 | 1952 | 8.82 | 23.55 | 2.67 | Flexure |
Energy dissipation
Park (1989) has investigated the energy dissipation mechanism of slender reinforced concrete structural elements subjected to reversed cyclic lateral loading and reported that the energy dissipation capacity of reinforced concrete member is significantly influenced by different design parameters such as: reinforcement ratio, reinforcement arrangement, magnitude of inelastic deformation and magnitude of axial compressive load. Energy dissipation is described as basic structural property of RC members when subjected to seismic loads. The area under the force–displacement curves can be used as a measure of the energy dissipation capacities (Ghobarah and Khalil 2004). According to Nguyen-Minh et al. (2018), the energy absorption capacity (E_{b}) was estimated by calculating the area under the load–displacement curves until the maximum loads. Table 8 shows that the final dissipated energy absorption capacity of specimens SW8 and R-SW8 (1–6) was 840, 1258, 1275, 1172, 1247, 1263 and 1239 kN.mm, which increased by 50, 52, 40, 48, 50 and 47% when compared with that of reference SW8, respectively. The energy absorption capacity of specimens SW4 and R-SW4 (1–4) was 1630, 1953, 1900, 1884, and 1952 kN.mm, which increased by about 20, 17, 16, and 20% when compared with that of reference SW4, respectively. Energy absorption capacity of the retrofitted specimens was significantly higher than that of the reference specimen SW8 as seen in Fig. 22. As previously mentioned, the benefit of strengthening of the RC walls using CFRP composite laminates was to help RC shear walls sustain further inelastic deformations without collapse.
Summary and conclusions
- 1.
Strengthening of RC shear walls with openings using CFRP laminates was an effective technique. The use of CFRP laminates significantly improved the seismic performance of RC walls under hysteretic and monotonic lateral loads.
- 2.
Hysteretic and monotonic lateral responses of strengthened walls resistance, ductility and dissipated energy were considerably increased as the number of CFRP layers is increased.
- 3.
Walls with staggered openings fail in a different way than those with ordered openings. Walls with regular openings had a brittle failure by crushing the concrete in the coupling beams due to shear forces, followed by yielding of the horizontal reinforcement in these beams. Walls with staggered openings had a ductile failure by the yielding of the vertical reinforcement at the base; however, it followed by concrete crushing.
- 4.
Walls with staggered openings failed at levels of seismic forces and at horizontal displacements higher than the forces and the horizontal displacements recorded in the failure mode of walls with regular openings.
- 5.
Good ductility was not observed in specimens R-SW8-3 and R-SW4-3 as expected, although higher load carrying capacity can be obtained and the widening of the diagonal shear crack could be controlled. The most effective way of improving ductility was to use lateral laminates, which were capable of obtaining good ductility and relative high load carrying capacity at the same time.
- 6.
The strengthened specimens dissipated much more energy than the control wall specimen. The ratio of energy dissipation of strengthened specimens to that of the reference specimen was between 1.16 and 1.57.
- 7.
CFRP laminates are not effective on improving the initial lateral stiffness of the retrofitted specimens.
- 8.
Increasing the number of the CFRP laminates increases the ultimate load by about 17% and 23% when increasing the number of the CFRP laminates from two to three layers, respectively. The failure of strengthened RC shear wall with openings was dependent primarily on the thickness of FRP as well as the location and size of openings. In models with a large opening, increasing the CFRP laminate thickness leads to increasing their resistance.
Notes
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