Numerical Investigation on Dynamic Response of RC T-Beams Strengthened with CFRP under Impact Loading

: To precisely evaluate the retroﬁtting e ﬀ ectiveness of Carbon Fiber Reinforced Plastic (CFRP) sheets on the impact response of reinforced concrete (RC) T-beams, a non-linear ﬁnite element model was developed to simulate the structural response of T-beams with CFRP under impact loads. The numerical model was ﬁrstly veriﬁed by comparing the numerical simulation results with the experimental data, i.e., impact force, reaction force, and mid-span displacement. The strengthening e ﬀ ect of CFRP was analyzed from the section damage evaluation. Then the impact force, mid-span displacement, and failure mode of CFRP-strengthened RC T-beams were studied in comparison with those of un-strengthened T-beams. In addition, the inﬂuence of the impact resistance of T-beams strengthened with FRP was investigated in terms of CFRP strengthening mode, CFRP strengthening sizes, CFRP layers and FRP material types. The numerical simulation results indicate that the overall sti ﬀ ness of the T-beams was improved signiﬁcantly due to external CFRP strips. Compared with the un-strengthened beam, the maximum mid-span displacement of the CFRP-strengthened beam was reduced by 7.9%. Additionally, the sectional damage factors of the whole span of the CFRP-strengthened beam were reduced to less than 0.3, indicating that the impact resistance of the T-beams was e ﬀ ectively enhanced.


Introduction
Reinforced concrete (RC) beams are important load-bearing components in building structures that might be subjected to unexpected impact loads. Compared with the high cost of rebuilding, reinforcing and transforming old structures can bring more beneficial social benefits, the safety and durability of the structure, reduced costs and impact on the surrounding environment, etc. Fiber-reinforced polymer (FRP) materials are an essential and vibrant structural composite material, owing to their high strength, light weight, corrosion resistance, and magnetic resistance properties [1]. Compared with traditional structural reinforcement methods, e.g., stick steel strengthening, increasing the sectional law, concrete replacement, additional fulcrum, and the external prestressing strengthening method, the external FRP reinforcement method is an ideal choice due to its advantages of easy construction and barely increased structural dead weight [2].
Many researchers have carried out studies on the flexural and shearing properties of FRP-strengthened concrete beams under static load [3][4][5][6][7]. In recent years, numerous experimental and numerical studies have been conducted in order to evaluate the effectiveness of FRP reinforcement on the impact resistance performance of RC beams. Tang and Saadatmanesh [8,9] conducted a set of drop

Finite Element Model
A three-dimensional (3D) elastic plastic finite element (FE) analysis was performed in ANSYS/LS-DYNA. The 3D FE model for the T-beam with CFRP is shown in Figure 3. In the finite element model, the concrete, drop hammer and supports were modeled using 3D solid element (Solid164). The 3D truss element (Link160) was used for longitudinal steel bars and auxiliary steel bars. The spring damping element (Combi165) was used to simulate the rod between the upper and lower supports. CFRP sheet was modeled using thin shell element (Shell163). After convergence verification, there was a total number of 81,958 elements, with 54,360 concrete elements and 1113 steel elements. The structural model mesh sizes were 15 mm. Automatic face-to-face contact was adopted in this paper, in order to model the contact behavior between the beam and the drop hammer, and the beam and supports; a description of the parameters can be found using the Keyword *CONTACT_AUTOMATIC_SURFACE _TO_SURFACE of LS-DYNA. To simplify the calculation, the bond was assumed between concrete and steel bars or CFRP strips by sharing the common nodes, which have been widely used for simulation of the impact resistance of RC structures. Roller support  in Figure 2. The hammer head diameter was 200 mm, and the impact position was in the T-beam's mid-span. The mass of the drop-weight was 296 kg, and the velocity when it impacted was 3780 mm·s −1 .

Finite Element Model
A three-dimensional (3D) elastic plastic finite element (FE) analysis was performed in ANSYS/LS-DYNA. The 3D FE model for the T-beam with CFRP is shown in Figure 3. In the finite element model, the concrete, drop hammer and supports were modeled using 3D solid element (Solid164). The 3D truss element (Link160) was used for longitudinal steel bars and auxiliary steel bars. The spring damping element (Combi165) was used to simulate the rod between the upper and lower supports. CFRP sheet was modeled using thin shell element (Shell163). After convergence verification, there was a total number of 81,958 elements, with 54,360 concrete elements and 1113 steel elements. The structural model mesh sizes were 15 mm. Automatic face-to-face contact was adopted in this paper, in order to model the contact behavior between the beam and the drop hammer, and the beam and supports; a description of the parameters can be found using the Keyword *CONTACT_AUTOMATIC_SURFACE _TO_SURFACE of LS-DYNA. To simplify the calculation, the bond was assumed between concrete and steel bars or CFRP strips by sharing the common nodes, which have been widely used for simulation of the impact resistance of RC structures. Roller support

Finite Element Model
A three-dimensional (3D) elastic plastic finite element (FE) analysis was performed in ANSYS/LS-DYNA. The 3D FE model for the T-beam with CFRP is shown in Figure 3. In the finite element model, the concrete, drop hammer and supports were modeled using 3D solid element (Solid164). The 3D truss element (Link160) was used for longitudinal steel bars and auxiliary steel bars. The spring damping element (Combi165) was used to simulate the rod between the upper and lower supports. CFRP sheet was modeled using thin shell element (Shell163). After convergence verification, there was a total number of 81,958 elements, with 54,360 concrete elements and 1113 steel elements. The structural model mesh sizes were 15 mm. Automatic face-to-face contact was adopted in this paper, in order to model the contact behavior between the beam and the drop hammer, and the beam and supports; a description of the parameters can be found using the Keyword *CONTACT_AUTOMATIC_SURFACE _TO_SURFACE of LS-DYNA. To simplify the calculation, Crystals 2020, 10, 890 4 of 16 the bond was assumed between concrete and steel bars or CFRP strips by sharing the common nodes, which have been widely used for simulation of the impact resistance of RC structures. Roller support was modeled by constraining the vertical and axial translational freedom of the center axis of lower support, other nodes only constrain in the axial direction, and constrain the axial translational freedom of all upper support nodes in the pressure beam. The impact force can be modeled using the keyword *INITIAL _VELOCITY, where the initial velocity was applied to the hammer.
Crystals 2020, 10, x FOR PEER REVIEW 4 of 15 was modeled by constraining the vertical and axial translational freedom of the center axis of lower support, other nodes only constrain in the axial direction, and constrain the axial translational freedom of all upper support nodes in the pressure beam. The impact force can be modeled using the keyword *INITIAL _VELOCITY, where the initial velocity was applied to the hammer.

Constitutive Model and Material Parameters
The Continuous Surface Cap Model (CSCM) is compared with the other concrete damage model to verify better to simulate the low-speed impact behavior under low confining pressure and low hydrostatic pressure. Therefore, CSCM (MAT_CSCM_CONCRETE) is used to model the dynamic properties of concrete; the theoretical formula of this model is presented in [23]. The specific material parameters of concrete are provided in Table 1. The Nonlinear Plasticity Kinematic Model (MAT_PLASTIC_KINEMATIC) is used to model the steel material. The steel strain rate effect is expressed by the Cowper-Symonds constitutive equation (Equation (1)): where 0 σ represents the static flow stress, 0 σ ′ represents the dynamic flow stress when the plastic strain rate is ε , C and p represent the strain rate parameters, which are 40.4 and 5, respectively, for mild steel [24]. The specific material parameters of steel are provided in Table 2. To save run-time costs during the transit analysis, the hammer is defined as *MAT_RIGID. Linear elastic material (MAT_ELASTIC) is used to model the support, with the elastic modulus and Poisson's ratio are 2 × 10 5 MPa and 0.3. The spring-damper element is given by the elastic spring material (MAT_SPRING_ELASTIC), the elastic stiffness is 5 × 10 4 N/mm. The *MAT_ENHANCED_COMPOSITE_DAMAGE material constitutive model is used to model CFRP sheets. This model can describe arbitrary orthotropic materials and based on Chang-Chang laminate failure criteria [25]. The specific material model parameters of FRP are shown in Table 3 [26-28].

Constitutive Model and Material Parameters
The Continuous Surface Cap Model (CSCM) is compared with the other concrete damage model to verify better to simulate the low-speed impact behavior under low confining pressure and low hydrostatic pressure. Therefore, CSCM (MAT_CSCM_CONCRETE) is used to model the dynamic properties of concrete; the theoretical formula of this model is presented in [23]. The specific material parameters of concrete are provided in Table 1. The Nonlinear Plasticity Kinematic Model (MAT_PLASTIC_KINEMATIC) is used to model the steel material. The steel strain rate effect is expressed by the Cowper-Symonds constitutive equation (Equation (1)): where σ 0 represents the static flow stress, σ 0 represents the dynamic flow stress when the plastic strain rate is . ε, C and p represent the strain rate parameters, which are 40.4 and 5, respectively, for mild steel [24]. The specific material parameters of steel are provided in Table 2. To save run-time costs during the transit analysis, the hammer is defined as *MAT_RIGID. Linear elastic material (MAT_ELASTIC) is used to model the support, with the elastic modulus and Poisson's ratio are 2 × 10 5 MPa and 0.3. The spring-damper element is given by the elastic spring material (MAT_SPRING_ELASTIC), the elastic stiffness is 5 × 10 4 N/mm. The *MAT_ENHANCED_COMPOSITE_DAMAGE material constitutive model is used to model CFRP sheets. This model can describe arbitrary orthotropic materials and based on Chang-Chang laminate failure criteria [25]. The specific material model parameters of FRP are shown in Table 3 [26-28].

Impact Force and Reaction Force
The impact force time history curve of the specimen beams is shown in Figure 4. The impact force peak and the impact duration are consistent between the finite element simulation and the experimental test results. The impact force curve can be divided into three stages: pulse stage, storming stage and recovery stage. In the pulse stage, the impact force rises to a peak steeply and falls rapidly, forming the main peak of impact force, lasting about 1.2 ms. The simulation and experimental results of the maximum impact force are 664 KN and 623 KN, respectively, with a calculation error of 6.6%. Subsequently, several secondary impact force peaks can be obviously found in the shock stage. The maximum mid-span displacement of the specimen can be obtained, and the shock duration is about 14 ms. The impact force drops to zero during the recovery phase. The comparison of numerical simulation and test results of the reaction force for RC T-beams under impact load is shown in Figure 5. The maximum reaction force simulation result of the CFRP-strengthened beam is 316 kN, the test value is 345 kN, and the discrepancy is 8.4%. The numerical results are highly consistent with the experimental results.
in the shock stage. The maximum mid-span displacement of the specimen can be obtained, and the shock duration is about 14 ms. The impact force drops to zero during the recovery phase. The comparison of numerical simulation and test results of the reaction force for RC T-beams under impact load is shown in Figure 5. The maximum reaction force simulation result of the CFRPstrengthened beam is 316 kN, the test value is 345 kN, and the discrepancy is 8.4%. The numerical results are highly consistent with the experimental results.

Displacement
The comparison of mid-span displacement obtained from the FE simulation and the experimental test are shown in Figure 6. It can be noted that mid-span displacement time history presents a half-sine wave. This indicates the partial elastic recovery when the displacement achieves maximum, with the dissipated energy that the structural plastic deformation and damage caused residual displacement. The maximum mid-span displacement of the numerical model is 10.54 mm and the maximum mid-span displacement of the test is 10.88 mm. The difference between them is only 3.1%. In summary, the numerical simulation results are in good agreement with the experimental results.

Displacement
The comparison of mid-span displacement obtained from the FE simulation and the experimental test are shown in Figure 6. It can be noted that mid-span displacement time history presents a half-sine wave. This indicates the partial elastic recovery when the displacement achieves maximum, with the dissipated energy that the structural plastic deformation and damage caused residual displacement. The maximum mid-span displacement of the numerical model is 10.54 mm and the maximum mid-span displacement of the test is 10.88 mm. The difference between them is only 3.1%. In summary, the numerical simulation results are in good agreement with the experimental results.
presents a half-sine wave. This indicates the partial elastic recovery when the displacement achieves maximum, with the dissipated energy that the structural plastic deformation and damage caused residual displacement. The maximum mid-span displacement of the numerical model is 10.54 mm and the maximum mid-span displacement of the test is 10.88 mm. The difference between them is only 3.1%. In summary, the numerical simulation results are in good agreement with the experimental results.

Fracture Development Process and Failure Mode
The comparison of numerical simulation and test results of failure modes for RC T-beam with CFRP under impact load is shown in Figure 7. The failure mode of the CFRP-strengthened beam is mainly subject to oblique cracks caused by shear force, which shows a typical shear failure mode. When the impact force reaches its peak (0.5 ms), two 45° diagonal cracks appear symmetrically on the beam web. At the end of the pulse phase (1.2 ms), the main oblique crack develops downward to the horizontal height of longitudinal reinforcement. When the impact force reaches its second peak

Fracture Development Process and Failure Mode
The comparison of numerical simulation and test results of failure modes for RC T-beam with CFRP under impact load is shown in Figure 7. The failure mode of the CFRP-strengthened beam is mainly subject to oblique cracks caused by shear force, which shows a typical shear failure mode. When the impact force reaches its peak (0.5 ms), two 45 • diagonal cracks appear symmetrically on the beam web. At the end of the pulse phase (1.2 ms), the main oblique crack develops downward to the horizontal height of longitudinal reinforcement. When the impact force reaches its second peak (3 ms), short shear cracks appear at the CFRP strips' spacing. When the displacement reaches the maximum (7.5 ms), the main change is that the number of small shear cracks between the CFRP strips in the mid-span area increases. At the end of impact (40 ms), some small cracks in the mid-span are closed due to the beam's rebound. Overall, the simulation model shows a favorable agreement with the test results for the failure mode. (3 ms), short shear cracks appear at the CFRP strips' spacing. When the displacement reaches the maximum (7.5 ms), the main change is that the number of small shear cracks between the CFRP strips in the mid-span area increases. At the end of impact (40 ms), some small cracks in the mid-span are closed due to the beam's rebound.
Overall, the simulation model shows a favorable agreement with the test results for the failure mode. The strain-time history of CFRP is shown in Figure 8. The initial rapid increase of strain of CFRP strips divided by the corresponding time interval was taken as the CFRP average strain rate. In this study, the average strain rate of CFRP is 9 s −1 . When the strain rate is less than 10 s −1 , the increase of dynamic tensile strength and elastic modulus of CFRP materials is only about 3% [29,30]. Therefore, the influence of strain rate on CFRP is in dynamic debonding or fracture strain [13].   The strain-time history of CFRP is shown in Figure 8. The initial rapid increase of strain of CFRP strips divided by the corresponding time interval was taken as the CFRP average strain rate. In this study, the average strain rate of CFRP is 9 s −1 . When the strain rate is less than 10 s −1 , the increase of dynamic tensile strength and elastic modulus of CFRP materials is only about 3% [29,30]. Therefore, the influence of strain rate on CFRP is in dynamic debonding or fracture strain [13].

Section Damage Assessment
The concrete CSCM constitutive model reflects the damage of concrete under impact loads. The damage stress σ d ij is defined as follows: where d is damage factor; d = 0 is no damage; d =1 is complete damage; and σ vp ij is the no damage stress tensor. Equation (2) expresses the isotropic and proportional reduction of the volume modulus and shear modulus of the material. The failure mode generally shows a limitation of the RC beam structure under impact loads, which has a short acting time and limited area of action. In this study, the damage assessment method [21] is used to determine the most serious damage section in the T-beam, while damage factor d s is the damage factors average value in T-beam cross-section: where d is the unit damage factor; n is the sum of section elements. To conveniently and intuitively measure the degree of damage in each section, the section damage factor d s is specified as follows [21], where d s = 0~0.3 is slight damage; d s = 0.3~0.6 is moderate damage; d s = 0.6~0.9 is severe damage; d s = 0.9~1 is component failure. Figure 9 shows the distribution of section damage factor (d s ) along the beam axis of the beam with CFRP, it can reflect that each section impact damage degree and CFRP impact resistance effect. d s is calculated by Equation (3). Overall, the T-beam with CFRP has exhibited a lightly damaged stage and the d s of all sections are below 0.3. In general, the T-beam with CFRP U-wraps can obviously reduce the section damage degree, this confirms an effective mode for improving the structure impact resistance. Figure 9 shows the distribution of section damage factor (ds) along the beam axis of the beam with CFRP, it can reflect that each section impact damage degree and CFRP impact resistance effect. ds is calculated by Equation (3). Overall, the T-beam with CFRP has exhibited a lightly damaged stage and the ds of all sections are below 0.3. In general, the T-beam with CFRP U-wraps can obviously reduce the section damage degree, this confirms an effective mode for improving the structure impact resistance.

Parametric Study
From the current literature, it is clear that when external FRP is used to strengthen the structure, e.g., thickness, strength and strengthening mode of FRP play central roles [8,13]. In this paper, the dynamic responses of CFRP-strengthened beams and un-strengthened beams under impact load are analyzed based on impact force, reaction force and crack patterns. To have a deeper understanding of the impact resistance of T-beams strengthened with FRP, different CFRP strengthening modes, CFRP strengthening dimensions, CFRP strengthening layers and FRP material types are used to study the dynamic response of T-beam without stirrup.

Parametric Study
From the current literature, it is clear that when external FRP is used to strengthen the structure, e.g., thickness, strength and strengthening mode of FRP play central roles [8,13]. In this paper, the dynamic responses of CFRP-strengthened beams and un-strengthened beams under impact load are analyzed based on impact force, reaction force and crack patterns. To have a deeper understanding of the impact resistance of T-beams strengthened with FRP, different CFRP strengthening modes, CFRP strengthening dimensions, CFRP strengthening layers and FRP material types are used to study the dynamic response of T-beam without stirrup.

Strengthening Effect of FRP
The displacement of the T-beam with and without CFRP at the mid-span is given in Figure 10a. According to the numerical simulation result, the maximum mid-span displacement and residual displacement of the un-strengthened beam are 11.44 mm and 6.23 mm. Simultaneously, the maximum mid-span displacement and residual displacement of beams with CFRP are reduced by 7.9% and 23.3%, respectively. The reason for this is that the CFRP U-wraps can improve the shear capacity and restrain the shear cracks generated by the T-beam under impact load, thus improving the structural stiffness and reducing the overall deformation [8,22]. Figure 10b shows the reaction force time history for the T-beams with and without CFRP. It can be seen that the maximum reaction force of the CFRP-strengthened beam increases by 3.6% with respect to that of the un-strengthened beam. In addition, the semi-sinusoidal fluctuations of un-strengthened beams are violent and massive compared with the CFRP-strengthened beams. This is consistent with the fluctuation of the reaction force observed in the impact test of CFRP-strengthened and un-strengthened beams [22]. Figure 11 illustrates the crack patterns of the RC T-beam without CFRP. The RC T-beam cracks very quickly on account of there being no stirrup. It can be seen that, similar to the RC T-beam strengthened with CFRP, the damage of the un-strengthened beam was also mainly caused by two 45-degree inclined cracks on the web. However, compared with the beam strengthened with CFRP, the un-strengthened beam's damage under impact load is more severe. In addition, only one shear crack appears in the span of the un-strengthened beam, but several thin and dense cracks appear in the web of the strengthened beam. This indicates that the CFRP can not only restrain oblique fracture development, but also dissipates the impact of kinetic energy by developing many small cracks, thus improving the impact resistance [22]. the structural stiffness and reducing the overall deformation [8,22]. Figure 10b shows the reaction force time history for the T-beams with and without CFRP. It can be seen that the maximum reaction force of the CFRP-strengthened beam increases by 3.6% with respect to that of the un-strengthened beam. In addition, the semi-sinusoidal fluctuations of un-strengthened beams are violent and massive compared with the CFRP-strengthened beams. This is consistent with the fluctuation of the reaction force observed in the impact test of CFRP-strengthened and un-strengthened beams [22].  Figure 11 illustrates the crack patterns of the RC T-beam without CFRP. The RC T-beam cracks very quickly on account of there being no stirrup. It can be seen that, similar to the RC T-beam strengthened with CFRP, the damage of the un-strengthened beam was also mainly caused by two 45-degree inclined cracks on the web. However, compared with the beam strengthened with CFRP, the un-strengthened beam's damage under impact load is more severe. In addition, only one shear crack appears in the span of the un-strengthened beam, but several thin and dense cracks appear in the web of the strengthened beam. This indicates that the CFRP can not only restrain oblique fracture development, but also dissipates the impact of kinetic energy by developing many small cracks, thus improving the impact resistance [22].

Effect of Strengthening Modes
In this section, the effect of different U-shaped strengthening modes on the impact response of the T-beam is analyzed. The details of four different FRP strengthening modes (i.e., vertical U-wraps, 45° U-wraps, U-wraps in the mid-span and U-wraps in the shear-span, which are named A, B, C and D, respectively), which are common strengthening techniques, are illustrated in Figure 12. For the four models, the other conditions are all the same. The mid-span displacement time histories under four CFRP strengthening modes are given in Figure 13. The maximum displacement and residual displacement under different strengthening modes are shown in Table 4. It can be seen that the maximum mid-span displacement for the RC T-

Effect of Strengthening Modes
In this section, the effect of different U-shaped strengthening modes on the impact response of the T-beam is analyzed. The details of four different FRP strengthening modes (i.e., vertical U-wraps, 45 • U-wraps, U-wraps in the mid-span and U-wraps in the shear-span, which are named A, B, C and D, respectively), which are common strengthening techniques, are illustrated in Figure 12. For the four models, the other conditions are all the same.

Effect of Strengthening Modes
In this section, the effect of different U-shaped strengthening modes on the impact response of the T-beam is analyzed. The details of four different FRP strengthening modes (i.e., vertical U-wraps, 45° U-wraps, U-wraps in the mid-span and U-wraps in the shear-span, which are named A, B, C and D, respectively), which are common strengthening techniques, are illustrated in Figure 12. For the four models, the other conditions are all the same. The mid-span displacement time histories under four CFRP strengthening modes are given in Figure 13. The maximum displacement and residual displacement under different strengthening modes are shown in Table 4. It can be seen that the maximum mid-span displacement for the RC Tbeams in the four modes A, B, C and D are 10.54 mm, 8.31 mm, 9.07 mm and 9.49 mm, respectively. The mid-span displacement time histories under four CFRP strengthening modes are given in Figure 13. The maximum displacement and residual displacement under different strengthening modes are shown in Table 4. It can be seen that the maximum mid-span displacement for the RC T-beams in the four modes A, B, C and D are 10.54 mm, 8.31 mm, 9.07 mm and 9.49 mm, respectively. Compared with the un-strengthened beam, the maximum mid-span displacement decreased by 7.9%, 27.4%, 20.7% and 17.0%, respectively. Among the four different strengthening types, mode A has the lowest reinforcement effect, while mode B is the highest. The longitudinal tensile strength is about 40 times the transverse tensile strength due to CFRP is an anisotropic material. Therefore, the 45 • U-wraps of the fiber strip can reflect the advantages of the high longitudinal tensile strength of CFRP, and this can constrain the development of oblique cracks. The CFRP is perpendicular to the beam axis in the longitudinal direction for reinforcement modes A, C and D, equivalent to adding external stirrups in the reinforcement area [31]; the difference is the additional stirrup position. Therefore, it is observed that the CFRP should be placed in the severe damage section, which can restrain fracture development and reduce impact deformation.

Effect of Strengthening Sizes
An investigation is performed on the CFRP sizes, which can affect reinforced beams subjected to impact loads. As can be seen in Figure 14, four beams are reinforced with U-shaped CFRP strips, the dimensions of CFRP are 372,600 mm 2 , 621,000 mm 2 , 869,400 mm 2 and 1,242,000 mm 2 .

Effect of Strengthening Sizes
An investigation is performed on the CFRP sizes, which can affect reinforced beams subjected to impact loads. As can be seen in Figure 14, four beams are reinforced with U-shaped CFRP strips, the dimensions of CFRP are 372,600 mm 2 , 621,000 mm 2 , 869,400 mm 2 and 1,242,000 mm 2 .
Crystals 2020, 10, x FOR PEER REVIEW 12 of 15 Figure 14. Four kinds of CFRP strengthening sizes. Figure 15 and Table 4 present the dynamic response of different CFRP strengthening sizes of Tbeams under impact loads. The mid-span displacement of the strengthened beam decreases with the CFRP size and amount increase. This indicates the CFRP reinforcement has significant advantages in impact resistance. The maximum mid-span displacement and residual displacement of the unstrengthened beam are 11.44 mm and 6.23 mm, respectively. The strengthening sizes of the T-beams are 372,600 mm 2 , 621,000 mm 2 , 869,400 mm 2 and 1,242,000 mm 2 ; the maximum mid-span displacement decreases by 6.2%, 7.9%, 18.0% and 21.7%, respectively; and the residual displacement decreases by 5.5%, 23.3%, 26.8% and 42.7%, respectively. With the increase of CFRP strengthening size, the stiffness, flexural and shear capacities of the beams increase, the structural deformation reduces.

Effect of Strengthening Layers
The effect of the different CFRP strengthening layers on the impact response of the T-beams is studied in this part. CFRP-strengthened beams with different numbers of layers (1-5-layer), all of which have the same strengthening mode A (size of CFRP is 621,000 mm 2 ), are analyzed. Figure 16a and Table 4 show the results of the mid-span displacement for beams with different layers. It is found that the maximum mid-span displacement and residual displacement decrease with the increase in CFRP layers. This is attributed to the fact that impact resistance improves with the increase in CFRP layers. However, the increase in CFRP layers is limited in improving the impact resistance. Figure 16b presents the mid-span maximum displacement of T-beams with different CFRP-strengthened layers. It is clear that the mid-span displacement decreases by 4.7% as the number   Table 4 present the dynamic response of different CFRP strengthening sizes of T-beams under impact loads. The mid-span displacement of the strengthened beam decreases with the CFRP size and amount increase. This indicates the CFRP reinforcement has significant advantages in impact resistance. The maximum mid-span displacement and residual displacement of the un-strengthened beam are 11.44 mm and 6.23 mm, respectively. The strengthening sizes of the T-beams are 372,600 mm 2 , 621,000 mm 2 , 869,400 mm 2 and 1,242,000 mm 2 ; the maximum mid-span displacement decreases by 6.2%, 7.9%, 18.0% and 21.7%, respectively; and the residual displacement decreases by 5.5%, 23.3%, 26.8% and 42.7%, respectively. With the increase of CFRP strengthening size, the stiffness, flexural and shear capacities of the beams increase, the structural deformation reduces.  Figure 15 and Table 4 present the dynamic response of different CFRP strengthening sizes of Tbeams under impact loads. The mid-span displacement of the strengthened beam decreases with the CFRP size and amount increase. This indicates the CFRP reinforcement has significant advantages in impact resistance. The maximum mid-span displacement and residual displacement of the unstrengthened beam are 11.44 mm and 6.23 mm, respectively. The strengthening sizes of the T-beams are 372,600 mm 2 , 621,000 mm 2 , 869,400 mm 2 and 1,242,000 mm 2 ; the maximum mid-span displacement decreases by 6.2%, 7.9%, 18.0% and 21.7%, respectively; and the residual displacement decreases by 5.5%, 23.3%, 26.8% and 42.7%, respectively. With the increase of CFRP strengthening size, the stiffness, flexural and shear capacities of the beams increase, the structural deformation reduces.

Effect of Strengthening Layers
The effect of the different CFRP strengthening layers on the impact response of the T-beams is studied in this part. CFRP-strengthened beams with different numbers of layers (1-5-layer), all of which have the same strengthening mode A (size of CFRP is 621,000 mm 2 ), are analyzed. Figure 16a and Table 4 show the results of the mid-span displacement for beams with different layers. It is found that the maximum mid-span displacement and residual displacement decrease with the increase in CFRP layers. This is attributed to the fact that impact resistance improves with the increase in CFRP layers. However, the increase in CFRP layers is limited in improving the impact resistance. Figure 16b presents the mid-span maximum displacement of T-beams with different CFRP-strengthened layers. It is clear that the mid-span displacement decreases by 4.7% as the number of CFRP layers increases from 1 to 3. Nevertheless, the mid-span displacement only decreases by

Effect of Strengthening Layers
The effect of the different CFRP strengthening layers on the impact response of the T-beams is studied in this part. CFRP-strengthened beams with different numbers of layers (1-5-layer), all of which have the same strengthening mode A (size of CFRP is 621,000 mm 2 ), are analyzed. Figure 16a and Table 4 show the results of the mid-span displacement for beams with different layers. It is found that the maximum mid-span displacement and residual displacement decrease with the increase in CFRP layers. This is attributed to the fact that impact resistance improves with the increase in CFRP layers. However, the increase in CFRP layers is limited in improving the impact resistance. Figure 16b presents the mid-span maximum displacement of T-beams with different CFRP-strengthened layers. It is clear that the mid-span displacement decreases by 4.7% as the number of CFRP layers increases from 1 to 3. Nevertheless, the mid-span displacement only decreases by 0.7% and 0.5% with the increase in layers from 3 to 4 and 5. The main reason for this is that it is difficult for the many layers to work collaboratively. Therefore, by considering the strengthening effectiveness as well as economic considerations, for the strengthened RC beams in this case, the T-beams with 2-3-layer CFRP are adequate for improving the impact resistance.

Effect of Strengthening Material Types
Considering the high cost of CFRP, other FRP materials can be adopted to strengthen the structure. This study compared the influence of CFRP, Aramid Fiber Reinforced Polymer (AFRP), GFRP on the impact resistance of T-beam. The FRP main mechanical properties parameters are shown in Table 3.
The mid-span displacement of three numerical models with different FRP materials is summarized in Figure 17 and Table 4. As can be seen, the tendencies of the displacement-time histories of the three T-beams strengthened by different FRP are similar. The maximum mid-span displacement and residual displacement of AFRP strengthened beams are 10.88 mm and 4.98 mm, which are 3.2% and 4.2% more than CFRP-strengthened beams. The maximum mid-span displacement and residual displacement of GFRP strengthened beams are 11.01 mm and 5.13 mm, which are increased by 4.5% and 7.3% compare with CFRP-strengthened beams. This indicates that the CFRP is superior to AFRP and GFRP at improving the impact resistance of the RC beam. However, it should be emphasized that the displacement change is within 8%; there is little difference in the reinforcement effect of different FRP materials. In consequence, it is more economical to choose AFRP and GFRP.

Effect of Strengthening Material Types
Considering the high cost of CFRP, other FRP materials can be adopted to strengthen the structure. This study compared the influence of CFRP, Aramid Fiber Reinforced Polymer (AFRP), GFRP on the impact resistance of T-beam. The FRP main mechanical properties parameters are shown in Table 3.
The mid-span displacement of three numerical models with different FRP materials is summarized in Figure 17 and Table 4. As can be seen, the tendencies of the displacement-time histories of the three T-beams strengthened by different FRP are similar. The maximum mid-span displacement and residual displacement of AFRP strengthened beams are 10.88 mm and 4.98 mm, which are 3.2% and 4.2% more than CFRP-strengthened beams. The maximum mid-span displacement and residual displacement of GFRP strengthened beams are 11.01 mm and 5.13 mm, which are increased by 4.5% and 7.3% compare with CFRP-strengthened beams. This indicates that the CFRP is superior to AFRP and GFRP at improving the impact resistance of the RC beam. However, it should be emphasized that the displacement change is within 8%; there is little difference in the reinforcement effect of different FRP materials. In consequence, it is more economical to choose AFRP and GFRP. displacement and residual displacement of GFRP strengthened beams are 11.01 mm and 5.13 mm, which are increased by 4.5% and 7.3% compare with CFRP-strengthened beams. This indicates that the CFRP is superior to AFRP and GFRP at improving the impact resistance of the RC beam. However, it should be emphasized that the displacement change is within 8%; there is little difference in the reinforcement effect of different FRP materials. In consequence, it is more economical to choose AFRP and GFRP.

Conclusions
In this study, ANSYS/LS-DYNA is used to study numerical simulation on the dynamic response of CFRP-strengthened T-beam under impact loads. This paper compared the beams with and without CFRP in terms of mid-span displacement, reaction force and failure mode. Moreover, the effects of CFRP strengthening modes, CFRP strengthening sizes, CFRP strengthening layers and different FRP material types on the impact behavior of RC T-beams were explored. The following can be concluded.
Within the range of 700 mm at the mid-span, it can be observed that all sections d s within the CFRP-strengthened beams are below 0.3 and are slight damage. Therefore, CFRP reinforcement can significantly reduce the beam damage degree under impact loads.
Compared with the un-strengthened beams, the maximum displacement and residual displacement of the CFRP-strengthened beams are reduced by 7.9% and 23.3%, respectively. In addition, the beams with CFRP can dissipate the impact energy by developing small cracks. Thus, CFRP reinforcement enhances the beam impact resistance.
Furthermore, comprehensive parametric studies on FRP-strengthened RC T-beams are carried out by considering various effect parameters under impact loads. It is found for the four different strengthening modes, the strengthened T-beams with 45 • U-wraps has the best reinforcement effect. Otherwise, the mid-span displacement of beams decreased with the CFRP sizes increased. Through a set of simulations, the CFRP strengthening layers can improve impact resistance of the beam. However, as the number of CFRP layer increased there was not a proportional decrease in mid-span displacement. Therefore, it is recommended the T-beams with 2-3-layer CFRP are adequate in enhancing the impact resistance. Additionally, compared the influence of CFRP, AFRP and GFRP for T-beam impact resistance, the best reinforcement material is CFRP, AFRP and GFRP are inferior.