Assessment of the behavior of reinforced concrete beams retrofitted with prestressed CFPR subjected to cyclic loading
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Abstract
Rehabilitation of weak and damaged structures has been considered widely during recent years. A relatively modern way of strengthening concrete components is to confine parts under tension and shear by means of carbon fiber reinforce polymer (CFRP). This way of strengthening due to the conditions of composite materials such as light weight, linear elastic behavior until failure point, high tensile strength, high elastic modulus, resistance against corrosion, and high fatigue resistance has become so common. During structural strengthening by means of not prestressed FRP materials, usually, it is not possible to benefit from the maximum capacity of FRP materials. In addition, sometimes, the expensive cost of such materials will not make a suitable balance between rates of strengthening and consuming spending. Thus, prestressing CFRP materials has an undeniable role in the effective use of materials. In the current research, general procedure of simulation using finiteelement method (FEM) by means of the numerical package ABAQUS has been presented. In this article, 12 reinforced concrete (RC) models in two states (strengthened with simple and prestressed CFRP) under cycling loading have been considered. A parametric study has been carried out in this research on the effects of parameters such as CFRP surface area, percentage of tensile steel rebar and prestressing stress on ultimate load carrying capacity (ULCC), stiffness, and the ability of depreciation energy for the samples. In the current article also, for design parameters, percentages of tensile steel rebars, surface area of CFPR sheets, and the effective prestressing stress in RC beams retrofitted with prestressed CFPR sheets have investigated. In this paper, it was investigated that using different amount of parameters such as steel rebar percentage, CFRP surface area percentage, and CFRP prestressing, the resulted ULCC and energy depreciation of the specimens was observed to be increasing and decreasing. Results from examined specimens with optimum steel rebar percentage, CFRP surface area percentage, and CFRP prestressing which had the most enhancement on ULCC and energy depreciation are reported in the current article.
Keywords
Reinforced concrete beams Prestressed CFRP Ultimate load carrying capacity Percentage of tensile steel rebar Ability of energy depreciation Cyclic loadingIntroduction
FRP materials to the form of outer coverage have been used for enhancing the resistance and improvement of the existing concrete structures from 1980s so far. The related FPR strengthening projects have been dramatically increased all over the world. This growth rate has started from a couple of projects to thousands during last decade. The EMPA Switzerland Institute can be mentioned as the primary researchers in the field of FPR strengthening. The researches were performed on CFRP strengthened RC beams in 1984. The most important advantages of using FRP sheets are the high ratio of resistance to weight and also high ratio of resistance to corrosion (Jankowiak 2012). The first quality would cause the ease of application in place and reduction of the wage cost. The second characteristic would cause the durability of execution. Different parts of strengthened structures with FRP systems with the forms of outer coverage are: beams, columns, walls, joints, chimneys, circular arches, tunnels, bins, pipes, and trusses. FRP coverage as an alternative for other strengthening strategies such as using steel sheets and ducts around concrete columns has been invented. The FRP coverage has been developed for the first time in 1980s in Japan and Europe for improvement of concrete structures. Nowadays, FRP systems have been used as steel sheet alternatives. FRP sheets are 2–10 times stronger than steel sheets, while they weigh 20% of steel sheets (Ahmad and van Gernert 1999). The limitations to use this sort of materials in civil engineering applications are just because of high cost. FRP composites are so resistant against the corrosion, salty, and alkali environment. Nowadays, FRP composites have been topic of wide spread studies as alternatives of steel bars and prestressed cables. The connection of steel sheets to tensile part of concrete pieces by epoxy resins to enhance bending strength of such pieces is a normal and durable method. This method has been used for strengthening of many bridges and buildings around the world. Since steel sheets would corrode and cause destruction of steel sheet connections with concrete, and also they are hard to establish and should be installed using extremely heavy machines, researchers have tried to replace FRP materials instead of steel (Darby 1999; Holloway 1999).
FRP composite materials are consisted of fibers and adhesive. In most of applied FRP composites, the behavior of fibers is unidirectional. Fibers perform capacity of FRP and adhesive distribute stress between fibers while keeping fibers unified. Among performed studies, many researchers have on the FRP strengthening of flexural members and also modes of failure specially the debonding failure mode (Zhang and Toshiyuki 2016; Pesic 2005). In addition, some researches have focused on manuals and design guide lines considering FRP applications in concrete structures (Pilakoutas et al. 2011).
In the current research, behavior of RC beams retrofitted with prestressed CFRP has been studied. It can be mentioned that the main difference between RC beams with prestressed steel cables and RC beams retrofitted with prestressed CFRP sheets is at the range of yielding. This is because FRP has linear behavior till to fracture unlike RC beams with prestressed steel cables in the failure behavior is due to yielding. Failure of RC beams with prestressed CFRP occurs with concrete crushing or FRP failure with no alert. Carbon fibers have the best behavior in prestressing application rather than other types of fibers; however, the expense is considerable (ElHacha et al. 2001; Jonsson 2011).
Strengthening beams
Depending on the level of beams destructions, several solutions can be chosen for rehabilitation and strengthening of such structures. For instance, injecting resin, attaching steel sheets or FRP, concrete replacing, and using concrete jackets, could be mentioned of such rehabilitation and strengthening methods (Ahmad and van Gernert 1999).
FEM analyses
ABAQUS software, which is a perfect mean for simulating and analyzing based on FEM, has been applied for the numerical examination of models in the current research. Materials specifications and the numerical analyses approach are discussed as the following.
Plastic failure of concrete
This method of plastic failure is a capable mean to simulate the behavior of nonlinear concrete and semi brittle materials constructing elements. This model is suitable for plain concrete and reinforced concrete. The general idea of this method is applicable for monotonic, cyclic, and dynamical loading, and is also capable to carry out stiffness recovery under cyclic loading.
With this method of simulation, it is assumed that the concrete failure with two forms of cracking in tension and crushing under pressure would be assessed. The growth of yielding would be controlled by two factors of hardening. Plastic equivalent strain in tension and pressure \(\tilde{\varepsilon }_{\text{t}}^{\text{pl}}\) and \(\tilde{\varepsilon }_{\text{c}}^{\text{pl}}\) would control the concrete failure under tension and pressure.
Details of numerical simulations (Teng 2002; Meier et al. 1992)

Connections and interactions between bars and concrete by the technique of embedded elements.

For the contact surfaces, properties of perpendicular to plane (hard contact) and tangential by method of penalty have been applied.
Type and number of elements
Model components  Type of elements  Number of elements 

Concrete  C3D8R  2128 
Steel  
Main bar  B31  53 
Stirrup  12  
FRP  S8R  112 
Geometric and mechanical characteristics of CFRP
Material  Elastic modulus  Ultimate strength  Thickness 

CFRP  150 (Gpa)  2500 (MPa)  1.4 (mm) 
Specifications of experimental steel rebars
Diameter (mm)  Elastic modulus  Yield stress  Ultimate stress  Elongation (%) 

\(E_{\text{s}}\) (GPa)  \(f_{\text{y}}\) (MPa)  \(f_{\text{u}}\) (MPa)  
6  245  500  641  23 
8  201  298  466  22 
12  145  340  518  20 
14  140  270  450  22 
16  143  300  443  23 
Mechanical characteristics of tested sample PC1 concrete
Specimen  Elastic modulus  Cubic compressive  Tensile strength 

E _{s} (GPa)  Strength (MPa)  (MPa)  
Concrete  32.5  52.3  3.6 
Specifications of beam with prestressing PC1 (Xue et al. 2010)
Specimen  Steel reinforcement in compression  Steel reinforcement in tension  CFRP plate width b_{f} (mm)  Effective prestress 

PC1  2\(\phi\)6  1\(\phi\)12+2\(\phi\)14 (1.25%)  50  1052.0 (42.1%) 
PC2  \(2\phi 6\)  \(1\phi 12 + 2\phi 14(1.25\% )\)  20  1101.9 (44.1%) 
PC3  \(2\phi 6\)  \(3\phi 12(1.25\% ))\)  20  1265.4 (50.6%) 
PC4  \(2\phi 6\)  \(1\phi 16 + 2\phi 14(1.25\% )\)  20  786.5 (31.5%) 
PC5  \(2\phi 6\)  \(1\phi 16 + 2\phi 14(1.25\% )\)  20  1087.2 (43.5%) 
Characteristics of steel rebars and CFRP
No.  Variable  Tensile rebar  CFRP  Effective prestressing  

Steel rebars  Percentage (%)  Dimensions (mm)  Percentage (%)  Stress (MPa)  
1  Effect of the percentage of tensile steel  \(1\phi 12 + 2\phi 6\)  50 × 1.4  1.90  1052  
2  \(1\phi 12 + 2\phi 14\)  1.25  50 × 1.4  1.90  1052  
3  \(1\phi 16 + 2\phi 14\)  1.36  50 × 1.4  1.90  1052  
4  \(3\phi 16\)  1.61  50 × 1.4  1.90  1052  
5  Effect of CFRP area  \(1\phi 12 + 2\phi 14\)  1.25  25 × 1.4  0.95  1052 
6  \(1\phi 12 + 2\phi 14\)  1.25  75 × 1.4  2.85  1052  
7  \(1\phi 12 + 2\phi 14\)  1.25  100 × 1.4  3.80  1052  
8  \(1\phi 12 + 2\phi 14\)  1.25  25 × 2.8  1.90  1052  
9  Effect of prestressing  \(1\phi 12 + 2\phi 14\)  1.25  50 × 1.4  1.90  250 
10  \(1\phi 12 + 2\phi 14\)  1.25  50 × 1.4  1.90  750  
11  \(1\phi 12 + 2\phi 14\)  1.25  50 × 1.4  1.90  1250  
12  \(1\phi 12 + 2\phi 14\)  1.25  50 × 1.4  1.90  1750 
Characteristics of strengthening steel rebars and prestressed CFRP
No.  Variable  Tensile steel rebar  CFRP  Effective prestressing  

Steel rebars  Percentage (%)  Dimensions (mm)  Percentage (%)  Stress (MPa)  
1  Effect of the percentage of tensile steel  \(1\phi 12 + 2\phi 6\)  0.45  50 × 1.4  1.9  1052 
2  \(1\phi 12 + 2\phi 14\)  1.25  50 × 1.4  1.9  1052  
3  \(1\phi 16 + 2\phi 14\)  1.36  50 × 1.4  1.9  1052  
4  \(3\phi 16\)  1.61  50 × 1.4  1.9  1052 
Effects of geometric characteristic of CFRP sheets
Sample  Tensile steel rebar  CFRP  Effective prestressing  

No.  Variable  Steel rebars  Percentage (%)  Dimensions (mm)  Percentage (%)  Stress (MPa) 
5  Effect of CFRP surface area  \(1\phi 12 + 2\phi 14\)  1.25  25 × 1.4  0.95  1052 
6  \(1\phi 12 + 2\phi 14\)  1.25  75 × 1.4  2.85  1052  
7  \(1\phi 12 + 2\phi 14\)  1.25  100 × 1.4  3.80  1052  
8  \(1\phi 12 + 2\phi 14\)  1.25  50 × 2.8  1.90  1052 
Specifications of tensile steel rebars, strengthening CFRP sheets, and prestressing levels of beam samples 9–12
Sample  Tensile steel rebar  CFRP  Effective prestressing  

No.  Variable  Steel rebars  Percentage (%)  Dimensions (mm)  Percentage (%)  Stress (MPa) 
9  Effect of prestressing  \(1\phi 12 + 2\phi 14\)  1.25  50 × 1.4  1.9  250 
10  \(1\phi 12 + 2\phi 14\)  1.25  50 × 1.4  1.9  750  
11  \(1\phi 12 + 2\phi 14\)  1.25  50 × 1.4  1.9  1250  
12  \(1\phi 12 + 2\phi 14\)  1.25  50 × 1.4  1.9  1750 
Effects of CFRP prestressing percentage of retrofitted reinforced concrete beams on two factors of ULCC and energy deprecation ability
Percentage of prestressing (%)  Ultimate load carrying capacity (kN)  Depreciated energy (N mm) 

0  81.13  1.84E+07 
250  83.99  1.86E+07 
750  87.91  1.92E+07 
1052  101.99  2.03E+07 
1250  91.45  1.91E+07 
1750  95.61  2.96E+07 
Validation
Monotonic examination
Geometric and mechanical characteristics of CFRP, steel rebars and concrete assigned to ABAQUS, are presented in the following tables.
Cyclic examination
As mentioned previously, after the application of the axial load, the specimen was subjected to progressively increasing lateral displacement cycles following the displacement protocol, shown in the figure below. As such, three fully reversed cycles were applied for each displacement step as required by FEMA 356 (2000).
FEM simulation process for parametric studies
In this section, procedure of FE simulation and total results originated from loading are presented. Totally, 12 RC models were strengthened with simple and prestressed CFRP and subjected to cyclic loading based on code Applied Technology Council (1992). ULCC, stiffness, and the ability of energy depreciation of these samples effected by parameters such as percentage of tensile steel, CFRP surface area, and the effect of prestressing stress. In Table 6, models specifications are represented.
In Table 6, samples 1–4 with the beam surface area of 250 × 150 mm and CFRP surface area of 50 × 1.4 mm and constant prestressing stress of 1052 MPa are presented.
For these samples with stable surface area of CFRP and prestressing stress, effects of variation in tensile steel rebar have been assessed. For samples 5–8 with stable percentage of tensile steel rebar and the rate of prestressing, the effect of CFRP surface area on ULCC and ability of depreciation were studied. Finally, for samples 9–12 effects of prestressing level was studied.
Effects of tensile steel percentage (A _{s})
In this section, four beams with tensile steel percentages of 0.45, 1.25, 1.36 and 1.61% in two states of strengthening with not prestressed and prestressed CFRP sheets were modeled and subjected to cyclic loading with displacement control of 5Δ_{y}. The rate of increasing of the resistance and the capability of energy depreciation were assessed in 4 percentages of tensile bars. In Table 7, characteristics of steel bars and strengthening CFRP are illustrated.

Maximum load of beam number 1 with tensile steel rebar percentage of 0.45% strengthened with CFRP in two states without prestressing \(\sigma_{\text{eff}} = 0\,{\text{MPa}}\) and with prestressing stress of \(\sigma_{\text{eff}} = 1052\,{\text{MPa}}\), are 77.78 and 86.36 kN, respectively. It can be observed that the CFRP prestressing state resulted in 11% increase in ULCC.

Surface areas inside both diagrams which are equal to depreciated energy during cyclic loading for the both strengthening states with CFRP, were 1.59E+07 and 1.57E+07 N mm, respectively which caused increasing of 1.3% of this factor.

The ULCC of the beam strengthened with not prestressed CFRP was 92.19 kN at the ultimate displacement of 20.86 mm.

The ULCC of the beam strengthened with prestressed CFRP was 101.99 kN at the ultimate displacement of 21.89 mm. In this sample, the prestressing of CFRP sheets enhanced capacity of about 10.46%.

Surface areas inside both diagrams, which are equal to depreciated energy during cyclic loading for the two strengthening states, were 1.84E+07 and 1.93E+07 N mm, respectively, which enhanced this factor of about 4.89%.

Beam capacity rate in two states of strengthening with prestressed and not prestressed CFRP was equal to: 104.88 and 97.13 kN, respectively. Prestressing with effective tensile stress of 1052 MPa for CFRP sheets caused 7.8% enhancement for ULCC.

On the other hand, energy depreciation ability resulted from prestressed CFRP sheets has increased from 2.06E+07 to 2.12E+07 N mm which enhanced this factor about 2.92%.

Maximum load capacity for this beam for the state of strengthened with not prestressed CFRP was calculated as 103.23 kN at the displacement of about 20.29 mm.

For the state of strengthening with prestressed CFRP, the rate of maximum load capacity of the beam reached to 110.93 kN when the displacement changed 21.79 mm. In this situation, increasing of 7.46% for ULCC has happened.

The surface area inside load–displacement diagram has changed from 2.17E+07 to 2.23E+07 N mm which showed the growth of 2.76%.
Effects of CFRP surface area
In this section, effect of geometric specifications of CFRP sheets on ULCC and ability of energy depreciation for RC beams strengthened with prestressed CFRP sheets would be presented. Samples for studying in this section are considered in Table 8. Parameters such as CFRP prestressing effect and percentage of tensile steel rebar are taken as constant parameters, and dimensions of CFRP sheets are variables.

The final load rate for the beam number 2 with tensile steel percentage of 1.25% and CFRP surface area percentage of 1.9% CFRP for two states of strengthening with not prestressed and with prestressed CFRP, were 92.33 and 101.99 kN, respectively. For this beam, the CFRP prestressing stress of 1052 MPa caused the enhancement of 10.46% in ULCC.

The surface area of both load–displacement curves which is equivalent to depreciated energy during cyclic loading was 1.84E+07 and 1.93E+07 N mm, respectively, which shows the enhancement of 4.89% for this factor.

With the prestressing of CFRP sheets with mentioned tension rate, ULCC changed from 84.94 to 93.83 kN in which this means almost 10.46% enhancement.

Surface area also has increased from 1.62E+07 to 1.67E+07 N mm which means about 3.08% enhancement.
Figure 15 illustrates diagram of load–displacement for beam number 6 with tensile steel percentage of 1.25% and CFRP surface area percentage of 2.85% (surface area 75 × 1.4 mm). The beam in this case which was strengthened with not prestressed CFRP sheets could bear maximum load of 100.12 kN. In the next step, the beam was strengthened with the same CFRP surface area with the prestressing stress of 1052 MPa, and the ULCC raised to 117.28 kN which has increased 17.14% in comparison with the previous step. In addition, enhancement of energy depreciation ability was about 5.19%.
Figure 16 depicts that using prestressed CFRP sheets with surface area percentage of about 3.80% of beam surface area, the ULCC increased from 114.67 to 126.67 kN which was about 10.46% increase. Moreover, energy depreciation in the beam increased from 1.96E+07 to 2.06E+07 N mm, which shows the enhancement of about 5.1%.
In Fig. 17, beam number 8 like number 2 had tensile steel percentage equal to 1.25% and CFRP surface area percentage of 1.90%. In the mentioned two samples, CFRP sheets were used with same surface area percentage; however, dimensions of the assembled sheets were different (1.4 × 50 mm for number 2 and 2.8 × 25 mm for number 8).

The rate of final load caused by CFRP prestressing has increased from 95.1 to 105.15 kN which represented 10.5% enhancement. This growth of the ULCC was inconsiderable in comparison with the beam number 2.

Energy depreciation growth, with the value of 4.88%, also was negligible in comparison with the beam number 2.
Effects of prestressing stress
In the final stage, effects of value of prestressing stress on ULCC and depreciation ability have been studied. To realize that such parameter how and to what extend would affect the RC ULCC, it is necessary to compare the beams strengthened with not prestresses and prestressed. In this section, beams number 2 and 9–12 were explained with an initial CFRP prestressing stress of 1052, 250, 750, 1250, and 1750 MPa, respectively.
Table 9 represents characteristics of tensile steel rebars and strengthening CFRP sheets and prestressing levels for the samples 9–12.

Considering prestressing stresses with the rates of 0, 250, 750, 1052, 1250, and 1750 MPa in concrete beam with tensile steel percentage of 1.25% and CFRP surface area percentage of 1.90%, ULCC reached to 81.13, 83.99, 87.91, 101.99, 91.45, and 95.61 kN.

Surface area which is equivalent to depreciated energy of selected 6 sample beams subjected to cyclic loading calculated as 1.84E+07, 1.86E+07, 1.92E+07, 2.03E0+7, 1.91E+07, and 2.96E+07 N mm.
Conclusion
 In the section of FEM analysis, effects of tensile steel rebar percent for strengthened RC beams with prestressed CFRP on two parameters of ULCC and energy depreciation ability have been studied. Four sample beams with steel rebar percentage of 0.45, 1.25, 1.36, and 1.61% have been simulated which are available in Fig. 16; among these beams, the one with steel rebar percentage of 1.25% had the most enhancement. These final results are presented in Figs. 19, 20.

In Sect. 5.2, effects of CFRP surface area percentage with the values of 0.95, 1.90, 2.85, 3.80, and 1.90% have been studied, which is between all of these five samples, the one with CFRP percentage of 2.85% experienced the highest percentage of ULCC and depreciated energy.
Finally, In Sect. 5.3, effects of CFRP prestressing of strengthened reinforced concrete beams on two parameters of ULCC and energy depreciation ability studied. In the current Sect. 5, beams with the initial prestressing stress values of 1052, 250, 750, 1250, and 1750 MPa have been simulated for which comparison with the results of mentioned parameters is presented in Table 10. Among all sample beams, the one with prestressing percentage of 42.1% and failure stress of 1052 MPa had the highest amount of enhancement percentage in ULCC and energy depreciation ability. Consequently, in this article, the prestressing percentage of 42.1% suggested and breaking stress is 1052 MPa.
Notes
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