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44Magazine of Civil Engineering. 2019. 92(8). Pp. 48-62 Инженерно-строительный журнал. 2019. № 8(92). С. 48-62
Magazine of Civil Engineering
journal homepage: http://engstroy.spbstu.ru/
ISSN 2071-0305
DOI: 10.18720/MCE.92.4
Bending and torsion behaviour of CFRP strengthened RC beams
R. Al-Rousan*, I. Abo-Msamh
Jordan University of Science and Technology, Irbid, Jordan, * E-mail: [email protected]
Keywords: engineering, materials science, technology, civil engineering, structural concrete
Abstract. In the construction industry, there is growing attention of using effective external strengthening techniques such as bonding of Carbon Fiber Reinforced Polymers (CFRP) composites onto the external deficient faces of the structural members due to their ease of installation, low invasiveness, high corrosion resistance, and high strength to weight ratio. As a result, the center of consideration of the majority of previously published studies was either only on the impact of fibers on the structural behavior of reinforced concrete elements or using CFRP composite as external strengthening for flexural or shear. The intent was to arrive at the vital CFRP strengthening technique that provides an effective increase in the flexural and shear strength while maintaining ductile failure mode. Therefore, this paper investigated the behavior of simply supported RC beams strengthened using CFRP and subjected to combined bending and torsion using Nonlinear Finite Element Analysis (NLFEA). Twenty-six models have been constructed and divided into six groups to scrutinize the effect of clear span to depth ratio; CFRP length; CFRP strip spacing; and CFRP depth. The results showed that the increase in the clear span to depth ratio as well as length of CFRP leads to a notable increase in the ductility and decreases the ultimate load. The models with zero spacing CFRP strips (Fully) showed a higher considerable effect than the models with strips wrapping. Furthermore, this enhancement was the highest for group six which contains the models with the highest CFRP depth.
Effect of combined bending and torsion occurs if the beam is loaded with out of plane eccentricity. Where the load is located away from the shear center axis which results in twisting the structural member with an undesirable brittle mode of failure. Although torsion is considered as a secondary effect compared to the flexural effect. Also, the torsion is negligible in most cases during the designing process. It is not the case for reinforced concrete (RC) structural members which are exposed to torsional loading in addition to the shear and flexure. The edge beams located on each floor of multi-story buildings, ring beams, spiral stairs, spandrel beams and flanged beams with T cross-section are exposed to torsion, shear, and flexure [1, 2].
Some experimental studies had been performed with different load setups to study the effect of pure shear. Pure bending combined bending and torsion or combined shear and torsion [3-5]. The effect of span length of cantilever RC beams under pure torsion had been studied using a non-linear finite element analysis. The results showed that when the span/depth ratio is equal to 4 or more, the beams have the same torsional strength but less than the beams that have smaller ratios [6]. The Modified Compression Field Theory (MCFT) was evaluated for reinforced and prestressed concrete beams subjected to combined bending and torsion. It was concluded that the MCFT could accurately determine the full behavior of such beams compared to the experimental results [7].
Existing structures may need torsional strengthening or rehabilitation due to several reasons. Some of these reasons are the increase in service load, inadequate design, change on the structure utilization, an improvement in the code regulations and seismic problems in some cases. Using Fiber Reinforced Polymers (FRP) as a strengthening material is the most recent and promising technology. It is a flexible material that can be made in any desired shape and can be introduced through a structural member either externally or internally. It is preferable in civil engineering applications because it is high corrosion resistance, high strength,
Al-Rousan, R., Abo-Msamh, I. Bending and torsion behaviour of CFRP strengthened RC beams. Magazine of Civil Engineering. 2019. 92(8). Pp. 48-62. DOI: 10.18720/MCE.92.4
Аль-Рушан Р., Або-Мсамх И. Поведение при изгибе и кручении железобетонных балок, усиленных композитным углеволокном // Инженерно-строительный журнал. 2019. № 8(92). С. 48-62. DOI: 10.18720/MCE.92.4
[©—This work is licensed under a CC BY-NC 4.0
1. Introduction
high stiffness, excellent fatigue performance, low weight, easy installation and good resistance to chemical attacks [8-11].
The efficiency of using CFRP for the torsional strengthening of RC beams had been studied either for rectangular or T-cross sections when subjected to pure torsion in most studies. Studying the combined effect of bending and torsion can be hardly found in the literature. Using the CFRP material can significantly increase the torsional strength and ductility. However, this enhancement can be affected by several factors such as concrete class, reinforcement ratio, number of layers, strip spacing, and wrapping scheme. Although the fully wrapping scheme is the best wrapping scheme, the difficulties of its application tend to use the U strip wrapping instead of fully wrapping. It is also recommended to increase the number of layers and decreasing the distance spaced between CFRP strips [12-18].
A new model was developed to predict the full behavior till failure of the strengthened RC beams subjected to torsion. Good agreements with the experimental results were achieved by that model comparing the torsional strength, FRP strain, and failure modes for different wrapping configurations [19]. To reduce the complexity of load setup, effort, time and cost during the experimental testing, ANSYS software had been used by many researchers. It was recommended about this software to be used since their results achieved good agreement with experimental results [20-24]. Therefore, essential issues to produce effective, economical, and successful CFRP strengthening were discussed. Also, the impact of CFRP external strengthening on the behavior of reinforced concrete beams subjected to bending and torsion received miniature consideration. The scientific problem considered in the study is indeed one of the problems in the modern theory of reinforced concrete. Despite a significant number of studies on the problem of bending with torsion, to date. There are no sufficiently reliable solutions to this problem that most fully reflect the physical nature of the problem. As a result, the torsional behavior of simply supported RC beams subjected to combined bending and torsion is studied using the nonlinear finite element analysis (NLFEA). For this purpose, validation against the previous experimental study reported by Gesund et al. [25] is firstly simulated. After that, a parametric study is extended for strengthened RC beams using different configurations of CFRP in terms of clear span to depth ratio, CFRP length, CFRP depth, and CFRP strips c-c spacing.
The NLFEA is a numerical method used to simplify the analysis of a variety of engineering problems. Also, to obtain their approximate solutions at a lesser cost, time, and effort compared to experimental testing. ANSYS is a general-purpose software used in this study. Twenty-six full-scale models strengthened using CFRP are developed to carry out different investigated parameters.
The experimental work performed by Gesund et al. [25] was used to validate the finite element model in this study. A total of twelve simply supported RC beams tested until failure under combined bending and torsion (Figure 1). The cross-section of the beam is 200 x 200 mm with a 1600 mm clear span length. All beams were reinforced using three bars of tension reinforcement and two bars of compression reinforcement with a 13 mm nominal diameter. Besides, a 10 mm nominal diameter for closed stirrups was applied at 50 mm spacing c-c (Figure 1). The beams were loaded by two-point loads at the end of two-moment arms providing out of plane eccentricity. Hence the beams were subjected to the combined effect of bending and torsion (Figure 1).
2. Methods
Figure 1. View of the model under load [25].
2.1. Experimental Work Review
o
a)
c) E'
Figure 2. Stress-Strain Curve for (a) Concrete, (b) Steel, and (c) CFRP composite.
2.2. Description of Non-linear Finite Element Analysis (NLFEA)
SOLID 65 is used to model the concrete which is suitable for tension cracking, crushing in compression and plastic deformations. It is a three-dimensional element defined by eight nodes. Each node has three degrees of freedom with a presence of translations in the three nodal directions; x, y, and z for each node. Steel reinforcement is modeled using link 180, which is a uniaxial tension-compression element. It includes two nodes, and each node has three degrees of freedom. This element can predict large deflection, large strain, rotation, creep, and plasticity. SOLID 45 is used to model the loading and supporting steel plates. This element is suitable to model the dimensional solid structures defined by eight nodes. There is a presence of translations in the three nodal directions; x, y, and z for each node. This element can predict large deflection, large strain, stress stiffening, creep, and plasticity. For CFRP, the SHELL 181 element type, having four nodes is used in modeling. It is chosen because it is appropriate to analyze thin layered applications. Three translations and three rotations are considered to include the six degrees of freedom at each node.
Concrete is a brittle material having high compressive strength compared to tensile strength. The cylindrical compressive strength of concrete is 36.54 MPa. The elastic modulus of elasticity (Ec) and modulus of rupture (fr) of concrete are 28410 MPa and 3.75 MPa, respectively, as shown in Figure 2(a). Concrete poison's ratio is assumed 0.17 for all models. Shear transfer coefficient for open and closed cracks, pt and pc respectively, are important inputs needed for concrete, which indicate the condition of crack surface. In this study, a value of 0.2 and 0.9 is set for the pt and pc, respectively. Steel reinforcement is modeled as a bilinear isotropic material with 200 GPa for the elastic modulus of elasticity and 0.3 of poison's ratio. Its behavior is assumed to be elastic-perfectly plastic, and the same assumption is set for tension and compression reinforcement with yielding stress of 350 MPa, as shown in Figure 2(b). Steel plates are added to the finite element model to avoid stress concentrations at the support and loading locations. These plates are steel type and defined as linear elastic isotropic material with 200 GPa for the elastic modulus of elasticity and 0.3 of poison's ratio. Sika Wrap Hex 300C 0/90 is the CFRP type used in this study. It is a bi-directional material property with 0.166 mm thickness and having fibers in longitudinal and transverse directions. The linear elastic tensile stress-strain curve for CFRP composites is shown in Figure 2(c) and the detailed mechanical properties and poison's ratio in all directions, are shown in Table 1.
Table 1. CFRP composites properties.
.. , , , . .... . „ . , .. Shear modulus of elasticity Ultimate tensile strength ..... . . .
Modulus of elasticity (GPa) Poisons ratio (GPa) (MPa) Ultimate strain
Ex 260 Vxy 0.22 Gxy 106.6
Ey 260 Vyz 0.22 Gyz 106.6 3900 0.015
Ez 4.5 Vzx 0.30 Gzx 1.73
The concrete beam and steel plates were modeled as solid elements while steel reinforcement was modeled as link elements. In the case of strengthened RC beams, the CFRP sheets were modeled as shell element with a mesh size of 25 mm. To ensure the perfect bond between concrete and reinforcement, the link element of steel is connected between each adjacent Solid 65 elements, hence the same nodes are shared between the two materials. The same approach is used for the CFRP sheets to provide the perfect bonding as well as for the Steel plates. The geometry of the control and strengthened model, along with the reinforcement specimens are shown in Figure 3(a), Figure 3(b) and Figure 3(c), respectively. The meshing of the CFRP sheet for both fully U wraps and strips wrapping is also shown in Figure 3(d) and Figure 3(e), respectively.
ANSYS ANSVS
HI 6.0 R1S.0
e)
Figure 3. Geometry and meshing.
The loads are applied on the two steel plates at the end of the moment arms as line loads distributed over nine nodes. The purpose of these moment arms is to provide the twisting of the main beam. To constrain the model, displacement boundary conditions are required. At the left end of the beam the Ux, Uy, and Uz displacements are set to zero to ensure hinge support. While roller support is added at the right end of the beam by setting zero value to the Uy displacement. Figure 4 shows the loads and boundary conditions of the model. The total applied load is divided into multiple load steps or load increments. Newton-Raphson equilibrium iterations give convergence at the end of each load increment within tolerance limit equal to (0.001) and a load increment of 0.22 kN. When large numbers of cracks appear throughout the concrete, the loads are applied gradually with smaller load increments.
a)
ANSYS
R1S.0
b)
ANSYS
S 16,0
ii;;[:Hnnii:;i:i[aaat
ANSYS
R1S.0
iw i M1P
Figure 4. Loads and boundary conditions: (a) 3-D view, (b) Front view, and (c) Zoomed view.
2.3. Investigated Parameters Twenty-six full-scale models strengthened using CFRP are developed to carry out different investigated parameters. A parametric study conducted in this research consists of six groups. The first group contains three models to study the effect of a clear span to depth ratio. 8, 6, and 4 are the clear span to depth ratios used. These models are strengthened using fully CFRP U wrap along the clear span length, and BC3 with ratios 8, 6, and 4 respectively. The other groups are modeled with the ratio equal to 8. Group 2 includes three models with different lengths of 1600 mm, 1100 mm and 800 mm. The rest four groups study the effect of two parameters; CFRP depth, and CFRP strip spacing. Four different CFRP depths of 50 mm, 100 mm, 150 mm, and 200 mm are studied for groups 3, 4, 5, and 6, respectively. Each depth group includes five models with different c-c spacing between 50 mm U strips, which are 225 mm, 175 mm, 125 mm, 75 mm and zero spacing. Figure 5 and Figure 6 show the schematic representation of CFRP strengthening configurations for the two cases of fully U-wrap and 50 mm U strip wrapping, respectively. A full description of the finite element modeling groups is shown in Table 2.
Figure 5. Schematic representation of fully CFRP U-WRAP.
Clear span length = 1600 mm
m D im I I |in m I
?
13 mm bar
Figure 6. Schematic representation of 50 mm U strip wrapping where S is the c-c spacing between CFRP strips, and D is the CFRP depth.
S
Table 2. Investigated parameters.
Group number Test section to depth ratio CFRP CFRP
Parameter number Clear span length (mm) Depth (mm) Ratio CFRP strengthening configuration length (mm) Depth (mm)
1 Clear span B1 1600 200 8 Fully FRP U wrap 1600 200
length to depth ratio CO l\J 1200 800 200 200 6 4 Fully FRP U wrap Fully FRP U wrap 1200 800
2 CFRP length B4 1600 200 8 Fully FRP U wrap 1600 200
B5 1600 200 8 Fully FRP U wrap 1100
B6 1600 200 8 Fully FRP U wrap 800
3 CFRP B7 1600 200 8 50 mm U strip wrapping at 225 mm c/c 1600 50
depth B8 1600 200 8 50 mm U strip wrapping at 175 mm c/c
B9 1600 200 8 50 mm U strip wrapping at 125 mm c/c
B10 1600 200 8 50 mm U strip wrapping at 75 mm c/c
B11 1600 200 8 Fully FRP U wrap
4 CFRP B12 1600 200 8 50 mm U strip wrapping at 225 mm c/c 1600 100
depth B13 1600 200 8 50 mm U strip wrapping at 175 mm c/c
B14 1600 200 8 50 mm U strip wrapping at 125 mm c/c
B15 1600 200 8 50 mm U strip wrapping at 75 mm c/c
B16 1600 200 8 Fully FRP U wrap
5 B17 1600 200 8 50 mm U strip wrapping at 225 mm c/c 1600 150
B18 1600 200 8 50 mm U strip wrapping at 175 mm c/c
B19 1600 200 8 50 mm U strip wrapping at 125 mm c/c
B20 1600 200 8 50 mm U strip wrapping at 75 mm c/c
B21 1600 200 8 Fully FRP U wrap
6 B22 1600 200 8 50 mm U strip wrapping at 225 mm c/c 1600 200
B23 1600 200 8 50 mm U strip wrapping at 175 mm c/c
B24 1600 200 8 50 mm U strip wrapping at 125 mm c/c
B25 1600 200 8 50 mm U strip wrapping at 75 mm c/c
B26 1600 200 8 Fully FRP U wrap
2.4. Validation Process
The model validation is conducted in this study for the experimental study performed by Gesund et al. [25]. Bending and twisting moments at failure as well as the strain in the center bar of longitudinal reinforcement are compared with the NLFEA results. Figure 7 and Table 3 show good agreements between the finite element method and experimental results.
Strain in center bar of longitudinal tension reinforcement
(a) Beam 2 (b) Beam 4
Figure 7. Validation of the NLFEA results.
Table 3. Validation summary.
Beam number Torsion to Bending moment at failure (kN.m) The torsional moment at failure (kN.m) ■ Absolute Error %
Bending moment ratio Experiment FEM Experiment FEM
2 1 11.52 10.9 11.52 10.9 5.3
4 0.5 15.14 16.2 7.6 8.1 -6.9
3. Results and Discussion
3.1. Load-Deflection and Torsion-Twist Behavior
Both the torsion-twist and load-deflection curves consist of three regions; the first region represents the stiffness for the un-cracked beam. The second region for the cracked beam. Whiles, the third region relates to the damaged cross-section with large cracks, yielding of steel and CFRP failure. Table 4 illustrates the obtained results for all simulated models. The slope of each region of the load-deflection curves gives the flexural stiffness of the corresponding beam. All strengthened beams represent higher stiffness compared to the control beam in the three regions. Table 4 also shows the calculated stiffness in each region for all simulated models.
Table 4. Results for all simulated models.
Group number Model number Ultimate load (kN) Ultimate deflection(mm) Ultimate Ultimate angle of twist (rad) Stiffness (kN/mm)
torsion (kN.m) Region 1 Region 2 Region 3
Control BC1 22.28 3.05 06.68 0.0120 21.50 1.46 5.02
beams BC2 24.26 2.36 7.27 0.0117 31.60 1.81 8.68
BC3 26.77 1.73 8.03 0.0110 34.70 3.63 13.3
1 B1 44.10 4.88 13.22 0.0320 23.50 2.82 8.54
B2 45.30 3.58 13.80 0.0237 34.60 3.18 11.8
B3 49.20 2.69 14.75 0.0220 54.00 5.54 16.7
2 B4orB1 44.10 4.88 13.22 0.0320 23.50 2.82 8.54
B5 36.20 4.14 10.87 0.0260 23.30 2.54 8.00
B6 32.80 4.00 9.86 0.0230 23.10 2.40 7.82
3 B7 24.82 3.39 07.44 0.0142 21.60 1.48 5.58
B8 25.63 3.44 07.68 0.0143 21.70 1.54 5.73
B9 26.24 3.52 07.87 0.0152 22.30 1.69 5.78
B10 27.36 3.60 08.21 0.0155 22.50 1.79 6.00
B11 36.21 3.94 10.86 0.0248 23.10 2.38 7.91
4 B12 25.86 3.57 07.75 0.0152 21.70 1.52 5.74
B13 26.45 3.61 07.93 0.0155 22.20 1.57 5.78
B14 27.38 3.68 08.21 0.0160 22.60 1.73 5.83
B15 29.03 3.84 08.71 0.0174 22.70 1.91 6.04
B16 38.84 4.25 11.65 0.0252 23.20 2.49 8.00
5 B17 28.25 3.97 08.47 0.0183 22.20 1.57 5.87
B18 29.51 4.08 08.85 0.0192 22.40 1.60 5.91
B19 30.10 4.13 09.02 0.0193 22.70 1.78 6.00
B20 31.52 4.21 09.45 0.0196 22.90 1.96 6.07
B21 42.60 4.61 12.81 0.0266 23.30 2.76 8.46
6 B22 31.57 4.43 09.34 0.0225 22.40 1.59 5.91
B23 32.43 4.45 09.65 0.0231 22.60 1.62 6.12
B24 34.60 4.56 10.01 0.0237 22.90 1.76 6.15
B25 36.20 4.81 10.86 0.0242 23.10 1.97 6.18
B26orB1 44.1 4.88 13.22 0.0320 23.50 2.82 8.54
3.2. Ductility and Strength ratios
The ductility indicates how much the strengthened RC beams can sustain deformations without failure. The ductility ratio is defined as the ratio of the ultimate deflection of the strengthened beam to the ultimate deflection of the control beam. Similarly, strength ratio also predicts the increase of load that the model can sustain. Table 5 shows the ductility and strength ratios for all simulated models.
3.3. CFRP strain
Figure 8 shows the typical distribution of CFRP strain through its depth for the first group. It is noticed that all simulated beams had CFRP strain below the maximum value of 0.015 as mentioned in Table 2.
-B1 (Ratio=8) -B2 (Ratio=6) -B3 (Ratio=4)
Strai n/ulti m ate strai n, %
Figure 8. Typical CFRP strain for Group 1 versus ultimate strain. Table 5. Enhancement percentage to control beam for all investigated parameters.
Group number Model Torsional Flexural Torsional Percent enhancement in Stiffness The percentage
number strength ratio ductility ratio ductility ratio Region 1 Region 2 Region 3 of CFRP strain to the ultimate strain
Control beams BC1 --- — — — --- --- —
1 B1 83 55 100 109 193 170 13.4
B2 98 60 167 115 175 135 14.8
B3 62 36 117 155 152 125 15.0
2 B4 or B1 47 31 92 109 193 170 15.0
B5 11 11 18 108 174 159 8.0
B6 15 13 19 107 164 155 6.2
3 B7 18 15 27 100 101 111 1.5
B8 23 18 29 101 105 114 2.0
B9 71 29 107 104 115 115 2.0
B10 16 17 27 105 122 119 2.7
B11 19 18 29 107 163 158 8.0
4 B12 23 21 33 101 104 114 3.4
B13 30 26 45 103 107 115 3.5
B14 74 39 110 105 118 116 3.7
B15 27 30 53 106 130 120 5.0
B16 32 34 60 108 170 159 10.4
5 B17 35 35 61 103 108 117 4.9
B18 41 38 63 104 110 118 5.1
B19 91 51 122 106 122 119 6.0
B20 42 45 88 107 134 121 6.0
B21 46 46 93 108 189 169 13.7
6 B22 55 50 98 104 109 118 5.0
B23 62 58 102 105 111 122 6.2
B24 98 60 167 107 123 123 7.0
B25 98 75 160 107 135 123 7.0
B26 or B1 87 56 103 109 193 170 15.0
-B1 (Ratio=8) -B2 (Ratio=6) -B3 (Ratio=4)
Strai n/ulti m ate strai n, %
Figure 8. Typical CFRP strain for Group 1 versus ultimate strain.
3.4. Failure Mode
Figure 9 shows the crack pattern for the typically simulated beams. The first crack at an integration point is shown with a red circle outline, the second crack with a green outline, and the third crack with a blue outline. The first crack initiated from the support and then propagated towered the top of the beam in a diagonal shape. Due to the lack of CFRP wrapping along the control beam, this propagation spreads at a faster rate with individual cracks along the beam compared to the strengthened beams.
The FRP helps in distribution the stresses on the whole body of the beam. Also, the cracks were smaller and closer to each other, giving higher strength and capacity for those beams. All strengthened beams show almost similar diagonal cracks initiation. This due to the reality of similar loading and boundary conditions and the reinforcement details. However, the fully FRP U- wrap inhibits the propagation of crakes more than FRP strips. The beam strengthened with Fully FRP U wrap could sustain higher loads and deflections. The failure occurred due to the substantial wide diagonal cracks and concrete crushing followed by FRP failure.
a)
Figure 9. Crack pattern at failure: (a) control beam, (b) strengthened beams using FRP strips, and (c) strengthened beam using fully FRP U-wrap.
3.5. Effect of the clear span to depth ratio
To study the influence of the clear span to depth ratio factor, group 1 consists of three beams. B1, B2, and B3 are modeled with 8, 6 and 4 ratios, respectively. All of them are strengthened using fully CFRP U wrap. The torsional strength of the strengthened beams in this group is improved by 198 %, 187 % and 183 % for B1, B2, and B3, respectively. The flexural ductility is improved by 175 %, 156 % and 155 % over the control beam for B1, B2, and B3, respectively. While the torsional ductility is enhanced by 260 %, 203 % and 200 % for B1, B2, and B3, respectively, as shown in Table 5. Figure 10(a) and Figure 10(b) show the load-deflection and torsion-twist curves for group 1. It is noticed that the increase in the ratio leads to more increase in the flexural and torsional ductility. While the ultimate load that the beam can sustain decreases. Figure 10(c) shows the comparison between the three ratios to the ultimate load, ultimate deflection, and the ultimate angle of twist.
Furthermore, the results show the enhancement in the FRP strain and the stiffness at the three regions of the load-deflection curve. The percentage of CFRP strain value to the ultimate strain is 13.4 %, 14.8 %, and 15 % for B1, B2, and B3, respectively (Table 5). The stiffness at the initial part of the load-deflection curve is enhanced by 109 %, 115 %, and 155 % for B1, B2, and B3, respectively. In the second part the stiffness increases by 193 %, 175 % and 152 % for B1, B2, and B3, respectively. In the third part the stiffness increases by 170 %, 135 % and 125 % for B1, B2, and B3, respectively, as shown in Table 5.
3.6. Effect of CFRP length
To investigate the effect of CFRP length, a parametric study in group 2 is conducted for three different lengths; 1600 mm, 1100 mm and 800 mm. The torsional strength of the beams is enhanced by 198 %, 162 %, and 147 % for B4, B5, and B6, respectively. The flexural ductility is enhanced by 160 %, 136 % and 131 % for B4, B5, and B6, respectively, while the torsional ductility is enhanced by 267 %, 217 % and 192 % for B4, B5, and B6, respectively (Table 5). The ultimate load, ultimate torsion, and the ductility of the RC beam increase as the length of the CFRP increases. Figure 11 also verifies this conclusion.
The load-deflection and torsion-twist curves are shown in Figure 11(a) and Figure 11(b), respectively. The percentage of CFRP strain value to the ultimate strain is 15 %, 8 %, and 6.2 % for B4, B5, and B6, respectively. The stiffness at the initial part is enhanced by 109 %, 108 %, and 107 % for B4, B5, and B6, respectively. In the second part the stiffness increases by 193 %, 174 % and 164 % for B4, B5, and B6, respectively. In the third part the stiffness increases by 170 %, 159 % and 155 %for B4, B5, and B6, respectively (Table 5). These results indicate that increasing the length of CFRP lead to more enhancements in the FRP strain. Also, the stiffness at the three regions of the load-deflection curve.
B1 (Ratio=8) -BC1 (Ratio=8)
B2 (Ratio=6) -BC2 (Ratio=6)
B3 (Ratio=4) BC3 (Ratio=4)
B1 (Ratio=8) BC1 (Ratio=8)
B2 (Ratio=6) BC2 (Ratio=6)
B3 (Ratio=4) BC3 (Ratio=4)
12 3 4 5
Deflection (mm) (a) Load-deflection curve
Ultimate load
0.005 0.01 0.015 0.02 Angle of twist (rad)
0.025
0.03
Ultimate deflection
(b) Torsion-angle of twist curve
Ultimate angle of twist
2 4
z Clear span to depth ratio
(c) Comparison with respect to the ultimate load, ultimate deflection and ultimate angle of twist Figure 10. Group 1 results
B4 (Length=1600 mm)-B5 (Length = 1100 mm) -B4 (Length=1600 mm)-B5 (Length = 1100 mm)
B6 (Length=800 mm) -BC1 (control beam) -B6 (Length=800 mm) -BC1 (Control beam)
14
12 E 10
I 8
C
.2 6
tn
£ 4
2 0
12 3 4
Deflection (mm) (a) Load-deflection curve
Ultimate load „ 1.98
0 1.58
6 0 0.005 0.01 0.015 0.02 0.025
Angle of twist (rad) (b) Torsion-angle of twist curve
Ultimate deflection Ultimate angle of twist
0.03
1.38
0.98
CFRP length (mm)
(c) Comparison with respect to the ultimate load, ultimate deflection and ultimate angle of twist Figure 11. Group 2 results.
0
6
0
0
5
1.18
0
500
2000
3.7. Effect of the CFRP Depth and CFRP Strip Spacing
To study the effect of the CFRP depth parameter, this study conducts four different depth of the beam; 50 mm, 100 mm, 150 mm, and 200 mm for groups 3, 4, 5, and 6, respectively. Each depth group includes five beams with different CFRP configuration of U strip wrapping with the spacing of 75 mm,125 mm,175 mm and 225 mm. The fifth beam is considered with fully U-wrap. Group 3 exhibits strength enhancement by 111 %, 115 %, 118 %, 123 % and 171 % for B7, B8, B9, B10, and B11, respectively (Figure 12 and Table 5). The flexural ductility is enhancement by 111 %, 113 %, 115 %, 118 % and 129 % for B7, B8, B9, B10, and B11, respectively. While the torsional ductility is enhanced by 118 %, 119 %, 127 %, 129 % and 207 % for B7, B8, B9, B10, and B11, respectively (Figure 12 and Table 5). The percentage of CFRP strain value to the ultimate strain is 1.5 %, 2 %, 2 %, 2.7 and 8 % for B7, B8, B9, B10, and B11, respectively (Figure 12 and Table 5). The stiffness at the initial region of the load-deflection curve is enhanced by 100.4 %, 101 %, 103.7 %, 104.7 %, and 107.4 % for B7, B8, B9, B10, and B11, respectively (Table 5). In the second region the stiffness increases by 101 %, 105 %, 115 %, 122 % and 163 % for B7, B8, B9, B10, and B11, respectively (Table 5). In the third region the stiffness increases by 111 %, 114 %, 115 %, 119 % and 158 % for B7, B8, B9, B10, and B11, respectively (Figure 12 and Table 5).
-B7 (Spacing=225mm) B9 (Spacing=125mm) B11 (Fully)
-B8 (Spacing=l75mm) -B10 (Spacing=75mm) BC1 (control)
B7 (Spacing=225 mm) B9 (Spacing=125 mm) B11 (Fully)
-B8 (Spacing=175 mm) -B10 (Spacing=75 mm) BC1 (Control beam)
1 2 3
Deflection (mm) (a) Load-deflection curve
Ultimate load 1.14
Ultimate deflection
0.005 0.01 0.015 0.02
Angle of twist (rad) (b) Torsion-angle of twist curve
Ultimate angle of twist
0.025
0.03
m
1.12
S. 11 f 108
£ 106 a 1.04 g 1.02 « 1
™ 0.98
50 100 150
Strip spacing (mm)
200
250
(c) Comparison with respect to the ultimate load, ultimate deflection and ultimate angle of twist
Figure 12. Group 3 results
Group 4 shows strength enhancement by 116 %, 119 %, 123 %, 130 % and 174 % for B12, B13, B14, B15, and B16, respectively (Table 5). The flexural ductility is enhanced by 117 %, 118 %, 121 %, 126 % and 139 % for B12, B13, B14, B15, and B16, respectively. While the torsional ductility is enhanced by 127 %, 129 %, 133 %, 145 % and 210 % for B12, B13, B14, B15, and B16, respectively (Figure 13 and Table 5). The percentage of CFRP strain value with respect to the ultimate strain is 3.4 %, 3.5 %, 3.7 %, 5 % and 10.4 % for B12, B13, B14, B15 and B16, respectively (Figure 13 and Table 5). The stiffness at the initial region of load-deflection curve is enhanced by 101 %, 103 %, 105 %, 106 %, and 108 % for B12, B13, B14, B15, and B16 respectively (Table 5). In the second region the stiffness increases by 104 %, 107 %, 118 %, 130 % and 170 % for B12, B13, B14, B15, and B16, respectively. In the third region the stiffness increases by 114 %, 115 %, 116 %, 120 % and 159 % for B12, B13, B14, B15, and B16, respectively (Figure 13 and Table 5).
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Figure 13. Group 4 results.
Group 5 exhibits torsional strength enhancement by 127 %, 132 %, 135 %, 141 % and 191 % for B17, B18, B19, B20, and B21, respectively (Table 5). The flexural ductility is enhanced by 127 %, 132 %, 135 %, 141 % and 191 % for B17, B18, B19, B20, and B21, respectively. While the torsional ductility is enhanced by 188 %, 193 %, 198 %, 202 % and 267 % for B17, B18, B19, B20, and B21, respectively (Figure 14 and Table 5). The percentage of CFRP strain value to the ultimate strain is 4.9 %, 5.1 %, 6 %, 6 % and 13.7 % for B17, B18, B19, B20, and B21, respectively (Figure 14 and Table 5). The stiffness at the initial region of the load-deflection curve is enhanced by 103 %, 104 %, 106 %, 107 %, and 108.4 % for B17, B18, B19, B20, and B21, respectively. In the second region the stiffness increases by 108 %, 110 %, 122 %, 134 % and 189 % for B17, B18, B19, B20 and B21, respectively. In the third region, the stiffness increases by 117 %, 118 %, 119 %, 121 % and 169 % for B17, B18, B19, B20, and B21, respectively (Figure 14).
Group 6 exhibits torsional strength enhancement by 142 %, 146 %, 155 %, 162 % and 218 % for B22, B23, B24, B25 and B26, respectively (Figure 15 and Table 5). The flexural ductility is enhanced by 145 %, 146 %, 150 %, 158 % and 160 % for B22, B23, B24, B25 and B26, respectively (Figure 15). The percentage of CFRP strain value to the ultimate strain is 5 %, 6.2 %, 7 %, 7 % and 15 % for B22, B23, B24, B25, and B26, respectively (Figure 15 and Table 5). The stiffness at the initial region of the load-deflection curve is enhanced by 104 %, 105 %, 107 %, 107.4 %, and 109 % for B22, B23, B24, B25, and B26, respectively (Figure 15 and Table 5). At the second region the stiffness increases by 109 %, 111 %, 123 %, 135 % and 193 % for B22, B23, B24, B25 and B26, respectively (Figure 15 and Table 5). At the third region the stiffness increases by 118 %, 122 %, 122.5 %, 123 % and 170 % for B22, B23, B24, B25 and B26, respectively (Figure 15 and Table 5). Figure 10 to Figure 15 shows the load-deflection curves, torsion-twist curves, and the comparison between the models of each group that are 3, 4, 5, and 6. It is clear that decreasing strip spacing. The beam can sustain higher load, deflection, torsion and hence higher angle of twist.
For the same CFRP strip spacing with different depth, the enhancement increases as the CFRP depth increases, as shown in Figure 16 and Table 5. The model wrapped using fully FRP U-wrap records the highest values with the enhancement range of (171-198 %) for ultimate torsional strength and (207-267) % for ultimate torsional ductility. Furthermore, the results show better enhancement in the FRP strain and the stiffness at the three regions of the load-deflection curve as increasing the depth of CFRP and decreasing the strip spacing.
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Figure 14. Group 5 results.
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Figure 15. Group 6 results.
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3.8. Comparison of NLFEA with other results
Comparison of NLFEA with Vishnu et al. [1], the bending moment and torque for all specimens at first crack are closed to NLFEA. Due to FRP torsional resistance of beam is increased in all types of wrapping configuration. Maximum bending moment and torsional moment are resisted by Full Transverse FRP wrapping. Also, all specimens wrapped with GFRP show better torsional resistance compared to the control specimen. Results show an increase in structural behavior of the strengthened beam is almost the same performance as the NLFEA. Besides, Vishnu et al. [1] reached the same conclusion as NLFEA that the fully U wrap strengthening technique of RC beam with FRP is more efficient in resisting torsional moment compared to the vertical strip.
4. Conclusions
1. The three-dimensional finite element model provided by this study was suitable to predict the behavior of strengthened RC beams subjected to combined bending and torsion. The mode of failure, ultimate strength, ductility, stiffness, and FRP strain can be accurately predicted.
2. As increasing the length of CFRP, the beam can sustain higher load, deflection, moment and hence higher orientation.
3. The efficiency of using CFRP strips increases as decreasing the center to center spacing between them. For the same spacing, this efficiency increases as increasing the depth of CFRP.
4. Using fully FRP U wrap is more effective than CFRP strips with higher torsional strength and ductility.
5. All strengthened beams represent higher stiffness compared to the control beam in the three regions of the load-deflection curves.
6. The control beam shows a faster rate of diagonal crack propagation than the strengthened beams. This is due to the lack of CFRP wrapping along the beam. The failure occurred after substantial wide diagonal cracks and concrete crushing followed by CFRP rupture.
References
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Contacts:
Rajai Al-Rousan, +962799887574; [email protected] Isra'a Abo-Msamh, +96227201000; [email protected]
Al-Rousan, R., Abo-Msamh, I., 2019
