Parametric study of anti-explosion performance of reinforced concrete T-shaped beam strengthened with steel plates

Construction and Building Materials 156 (2017) 692–707

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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Parametric study of anti-explosion performance of reinforced concrete T-shaped beam strengthened with steel plates Yandong Qu ⇑, Wanli Liu, Musa Gwarzo, Wenjiao Zhang, Cheng Zhai, Xiangqing Kong School of Civil and Architecture Engineering, Liaoning University of Technology, Jinzhou 121001, China

h i g h l i g h t s
Parametric studies of anti-explosion performance of the RC T-shaped beam strengthened with steel plates are carried out.
The main reinforcement ways of the RC T-shaped beam strengthened with steel plates are discussed by using a nonlinear finite element method.
The influence of the weight and position of explosive charges, reinforcement methods, and reinforcement lengths of steel plates is investigated.
The main failure modes of the RC T-shaped beam and RC T-shaped beam strengthened with steel plates under blasting load are investigated.

a r t i c l e

i n f o

Article history: Received 19 April 2017 Received in revised form 3 July 2017 Accepted 28 August 2017 Available online 26 September 2017 Keywords: Reinforced concrete beam Blast loading Dynamic behavior Failure mode Steel plate

a b s t r a c t Parametric studies are performed to investigate the influence of the weight and position of explosive charges, reinforcement lengths of steel plates, and reinforcement methods, such as pasting steel plate on the bottom of reinforced concrete T-shaped (RCTS) beam, pasting steel plate on both sides of web plate, pasting U-shaped steel plate on the web of RCTS beam, fully packaged the beam with steel plate and pasting steel plate on the top and bottom of RCTS beam, on the dynamic behavior of the RCTS beam under blasting load by numerical simulation method. Numerical results show that the failure modes of the RCTS beam are closely related to the weight and position of explosive charges. With the increase of explosive charges, the deformation modes of the beam are changed from elastic deformation to tension bending deformation, and finally the flexural shear failure is occurred. With the height increase of vertical direction of explosion, the failure patterns of the beam are changed from bending shear to tensile bending. Changing the explosion positions from the mid-span to the end of the beam, the damage positions are also changed with the moving of explosive. The damage modes of the beam and the positions, where the cracks are formed, have a strong dependence on the position and the weight of explosive charges due to the local effect of blasting load. Compared with the ordinary RCTS beam, the initiation time of cracks of the RCTS beam strengthened with steel plates is delayed and the growth speed of the cracks is also significantly reduced. The crack distributions of the beam strengthened with steel plates are mainly concentrated on the reinforced area. Moreover, the number of the formed cracks is also reduced and the compressive stresses of concrete in the compression zone of the beam strengthened with steel plates are lowered down. Among the reinforcement methods in the present study, the best reinforcement method to improve anti-explosion performances of the beams is the beam strengthened with steel plates on the top and bottom of it. The optimal size of reinforcement length of steel plate is about 80 cm by comparing the different reinforcement lengths of steel plates in the same explosion case. To some extend, this study could provide some basis for evaluating antiexplosion performances and scheme design of structural strengthening of the beam. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Over the last several decades, many attacks all over the world have shown that terrorism related activity is dramatically increas-

⇑ Corresponding author. E-mail address: [email protected] (Y. Qu). http://dx.doi.org/10.1016/j.conbuildmat.2017.08.150 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.

ing [1]. Reinforced concrete (RC) structures might be subjected to blast and explosive loading during their service life because of accidental gas explosion or terrorist bombing [2]. In the explosion accident, the damage of beam, plate, column and other main components of building structures subjected to blast shock wave usually leads to the overall collapse of the structures. Though a tremendous amount of research on the behavior of RC structures

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has been carried out, it remains one of the largest sources of uncertainty in civil engineering [2–5]. As one of the main bearing components of RC structure commonly used in protective design against potential blast loading conditions, dynamic analysis of RC beam has important significance in anti-explosion design and reinforcement for building structures. At present, there are two common methods to study the dynamic response of RC structures, especially RC beams under blast loading: experiment and numerical simulation [6]. A few experimental studies on the RC beams under blast loading have been reported, such as the close-in blast loading trials on RC beam conducted by Zhang et al. [7], and Yao et al. [8] analyzed the influence of stirrup ratio on anti-explosion behavior and damage characteristics of RC beams by experimental and numerical study. Chen and his coworkers [9] carried out a series of model tests on the RC beams to study the performances of RC structures under blast loadings after fire exposure. Along with the development of computer technology, numerical study has been another commonly used method to study the dynamic behaviors of concrete, besides experimental study and theoretical analysis. It is more compressive, safe and efficient analysis of dynamic loading problems. The numerical method to study the anti-explosion performance of RC structures cannot be affected by the environments and it can get a more comprehensive data. The dynamic response and damage of structures under blast loading can be evaluated comprehensively and profoundly. Qu et al. [5,6] numerically modeled the dynamic behavior of RC beam with initial cracks under air blast loading and made a study about the effects of CFRP sheets and sizes on the properties of the antiexplosion properties of the RC beams with rectangular section. They found that the appropriate number and width of CFRP sheets can effectively improve anti-explosion performances of RC beam. Xia et al. [10] carried out a blast test program to study the mitigation effect of density-graded aluminum foams on RC slabs. Chen et al. [11] numerically studied the dynamic behavior of a simplysupported prestressed RC beam with rectangular section under blasting load by using finite element codes LS-DYNA. LS-DYNA software is also to investigate the dynamic behavior and damage mechanism of RC slabs under blast loading [12]. Xu and Lu [13] proposed a 3D finite element model using LS-DYNA for modelling of RC plates subjected to blast loading. They investigated different degrees of damage in the concrete under blast loading. Johnson and his coworkers [14] conducted a series of quasi-static and blast tests to study the resistance capacity of concrete slabs, in which conventional crushed granite aggregates were wholly replaced with oil palm shell as a coarse aggregate. Wang et al. [15] presented the research on behavior of one-way square RC slabs under blast loading. Qu et al. [16] also make a survey about the differences of anti-explosion performance between the perfect RC beam and the RC beam with initial cracks. Limited studies have been conducted to investigate the mechanical properties of RCTS beam under quasi-static loading. For instance, Cladera et al. [17] predicted the shear–flexural strength of slender RC T- and I- shaped beams. Panigrahi et al. [18] proposed a simple design model to calculate the contribution of anchored TRM jackets to the shear capacity of RC T-beam. Zoi et al. [19] discussed the shear strengthening of full-scale RCTS beams using textile-reinforced mortar and textile-based anchors. Yan and his coworkers [20] numerically investigated the damage mechanism of prestressed RCTS beam under close-in blast loading. It is noticed from the above literature review, the structural behaviors of RC beams under extreme loadings, such as blast and explosive loads, have been extensively studied from a theoretical as well as experimental point of view. Limited studies have been conducted to investigate the mechanical properties of RCTS beam under quasi-static loading. Few studies have been conducted on

the dynamic response of RCTS beam under blasting load, however. In the present study, a series of numerical studies are conducted aiming to the response of the ordinary RCTS beams under blasting loads by using a nonlinear finite element method based on LS-DYNA software. The influences of the weight and position of explosive charges, reinforcement lengths of steel plates, and reinforcement methods on the dynamic behaviors of the RCTS beam under blasting load are discussed on the basis of the numerical results. Failure patterns of the RCTS beams under blasting load are also studied.

2. Numerical model 2.1. Material models In the study, four used material models and three used cell types are as follows: concrete and steel gasket use 3D solid element, steel reinforcements uses 3D beam type, and steel plate uses thin shell element, respectively. Concrete is a complex material and a lot of factors can affect the compressive strength and tensile strength of concrete. The mechanical properties of concrete under high strain rate are different from the quasi-static strength. Here the material model named MAT-JOHNSON-HOLMQUISTCONCRETE (HJC) is used to model the behavior of concrete material under blasting load. HJC model can be used to simulate concrete subjected to large strains, high pressure, and high strain rates [21–23]. The damage is accumulated as a function of the plastic volumetric strain, equivalent plastic strain and pressure. A large number of experiments show that the dynamic strength of concrete is dependent on the law of variation. The dynamic enhancement factor is a function of law of strain-rate effect [24]. The material parameters of ordinary concrete are shown in Table 1 [7,25]. MAT_PLASTIC_KINEMATIC model is suited to model the behavior of steel reinforcements. The material parameters of steel reinforcements are shown in Table 2 [7,26]. MAT_RIGID model was used to model the support spacers. The material parameters of support plates are shown in Table 3. Shell element is usually adopted to simulate steel plates. MATJOHNSON-COOK model is used to model steel plate. The material parameters and equation of state of steel plate are shown in Tables 4 and 5, respectively [26,27]. Based on the existing simulation methods of RC beam antiexplosion and its progress [6], the material models and the corresponding material parameters obtained can well realize the

Table 1 Material parameters of ordinary concrete [25]. Mass density, RO

2440 kgm3

Normalized cohesive strength, A Normalized pressure hardening, B Pressure hardening exponent, N Strain rate coefficient, C Quasi-static uniaxial compressive strength, FC Normalized maximum strength, SFMAX Damage constant, D1

0.79

Damage constant, D2

1.0

Amount of plastic strain before fracture, EFMIN Crushing pressure, PC

0.01

0.001

0.6

Crushing volumetric strain, UC Pressure constant, K1

0.007 0.040 GPa

Pressure constant, K2 Pressure constant, K3

171 GPa 208 GPa

7.0

Locking pressure, PL

0.80 GPa

0.004

Locking volumetric strain, UL Maximum tensile hydrostatic pressure, T

0.10

1.6

0.016 GPa

85 GPa

0.004 GPa

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Table 2 Material parameters of steel [26].

Table 5 The material parameters of rigid spacer [27]. 7800 kgm3 2.0  105 MPa 0.3 395 MPa 2.0  103 MPa 0 40 5 0.12

Mass density, RO Young’s modulus, E Poisson’s ratio, PR Yield stress, SIGY Tangent modulus, ETAN Hardening parameter, BETA Strain rate parameter, SRC Strain rate parameter, SRP Failure strain for eroding elements, FS

Mass density, RO Young’s modulus, E Poisson’s ratio, PR N COUPLE M Center of mass constraint option, CMO First constraint, CON1 Second constraint parameter, CON2

Table 3 Material parameters of rigid spacer [6]. Mass density, RO Young’s modulus, E Poisson’s ratio, PR N COUPLE M Center of mass constraint option, CMO First constraint, CON1 Second constraint parameter, CON2

7.80 2.10 0.30 0.0 0.0 0.0 1.00 0.00 0.00

numerical simulation of ordinary RCTS beam and the RCTS beam strengthened with steel plates. Therefore, the numerical simulation results can be well descriptive and referential. 2.2. Strain rate effect A lot of research results show that most of the mechanical properties of civil engineering materials have shown strain rate sensitivity [28–34]. Both steel reinforcement and concrete are strain-rate-sensitive materials, the mechanical parameters provided by the conventional static and quasi-static experiments under high strain rate have great limitations, to withstand the rapid loading of milliseconds or even microsecond under blast loading, the strain rate of the two kinds of materials can be as high as 100 s1–10,000 s1. With the increase of strain rate, the ductility and strength of the material will be improved in different degrees. For instance, the compressive strength and tensile strength of concrete can be increased to 2 times and 6 times of the original strength and the strength of reinforcement can be increased by 50%. The material properties of steel and concrete under blast loading are different from those of the two materials under quasi-static loading, the strain law effect of steel bar and concrete should be considered. In the numerical simulation, the increasing coefficient DIF (Dynamic Increase Factor) is usually introduced to analyze the law of strain-rate effect. DIF is the function about strain rate and is the ratio of dynamic load and static load. (1) Dynamic load increase coefficient of steel bar. The mechanical properties of reinforcement are very sensitive to the increase of strain rate, which leads to the obvious change of the mechanical properties of steel bar. The ultimate strength

and yield strength of steel bar increase with the increase of strain rate. The effect of high strain rate on the yield strength of reinforcing steel is more than that on the ultimate strength of steel bar. The ductility of steel bar decreases with strain rate increasing. The elastic modulus of steel bar is not affected by the law of strain-rate effect. The strength of steel bar is increased significantly in the process of rapid deformation of the low strength steel bar under quasistatic loading; while the DIF of the low yield strength steel bar under high strain rate can be approximately to 2 and the DIF values of high strength steel is higher. Dynamic increase factor (DIF) for the tensile strength of steel is defined according to Ref. [35]. The expression of the dynamic load increase coefficient DIF is as follows:


DIF ¼

e_

a ð1Þ

104

When calculating the yield strength of steel, a = afy = 0.074– 0.04 fy/60; and when calculating the ultimate yield strength of steel bars, a = afu = 0.019–0.009 fy/60. (2) Dynamic load increase coefficient of concrete. The mechanical parameters of concrete are very sensitive to the increase of strain rate under blast loading and impact loading, which leads to the obvious change of the mechanical properties of concrete. According to the experimental and numerical methods, the relevant researchers put forward a variety of calculation models about the dynamic tension compression strength enhancement factor (DIF) of concrete. A large number of experiments have shown that the damage evolution of concrete is dependent on the rate of strain. The dependence effect of dynamic enhancement factor on the corresponding variable rate of concrete strength is described in the practical engineering. Dynamic increase factor (DIF) is the function of dynamic compressive strength and quasistatic strength in unconfined uniaxial compression. According to the experiment and numerical simulation, the relationship between DIF and strain rate of concrete is determined by many researchers, and that for of concrete is defined according to a series of SHPB experiments with different strength grades and moisture content of concrete are given to show the DIF expression under uniaxial compression. The SHPB experimental device can provide a single axis high strain rate law, and has the advantages of stress, strain reliability, simple and easy to control, and wide strain law range (1/s–104/s), The compressive strength and tensile strength

Table 4 Material parameters of steel plate [26]. Mass density, RO Shear modulus, G Constant, A Constant, B Constant, N Constant, C Constant, M

7.83 0.32 7.920E03 5.100E03 0.260 1.40E02 1.03

7.80 2.10 0.30 0.0 0.0 0.0 1.00 0.00 0.00

Melt temperature, TM Room temperature, TR Strain rate normalization factor, EPSO Specific heat, CP Failure stress or pressure cutoff, PC Spall type, SPALL Failure parameters, D1

1.793E+03 294 0.100E05 0.477E05 0.900E+00 3.00 0.80

Y. Qu et al. / Construction and Building Materials 156 (2017) 692–707

of concrete increase with the increase of strain rate at high strain rate; the maximum volumetric strain, and the energy dissipation capacity increase with the increase of strain rate; the initial shear modulus increase with the increase of strain rate; the initial shear modulus is almost not affected by the tension. The strain peak value of concrete decreases with the increase of strain rate under pressure and when the tensile strain of concrete is subjected to the strain, the strain is almost not changed with the change of strain rate. Zhou and Hao [36] conducted the simulation of failure process of concrete specimens under dynamic load by LS-DYNA software. The expression of tensile strength of concrete under dynamic load in the numerical simulation is as follows:

( DIF ¼

1:12 þ 0:0225lge_

e_  0:1s1 0:07325ðlge_ Þ þ 1:235ðloge_ Þ þ 1:6 e_ > 0:1s1 2

ð2Þ

where fts is the static tensile strength at e_ ; ft is the dynamic tensile strength at e_ . ft/fts represents the ratio of uniaxial tensile stress at the dynamic load rates to the quasi-static value. According to the results of mortar for three different slenderness ratios (i.e. length-to-diameter ratios), the expression of compressive strength of concrete under dynamic load was suggested by Li and Meng [37], is as follows:

( DIF ¼

1 þ A1 ðloge_ þ A2 Þ A3 ðloge_ Þ þ A4 loge_ þ A5 2

e_  102 s1 e_ > 102 s1

ð3Þ

where A1 = 0.0344, A2 = 3.0, A3 = 1.729, A4 = 7.137, and A5 = 8.530 are determined by Li and Meng [37]. They defined 104 s1 as the quasi-static strain-rate, but the value of the DIF becomes unity when the strain-rate is 103 s1 according to Eq. (3), which could cause a local drop at the transition strain-rate. This abnormality can be eliminated though changing the values of A1 and A2 to 0.0258 and 4.0 [37]. 2.3. Element erosion algorithm In this study, the size of finite element model is 5 mm  5 mm  5 mm to realize joint force between steel bar and concrete. Many constitutive models do not allow failure and erosion in LS-DYNA. The ADD_EROSION option could provide a way of failure in these models. The erosion algorithm is usually used to simulate physical fracture, shear fracture, spalling, and crushing of concrete materials under shock or explosion loading. In many previous studies, the erosion algorithm has been extensively used to simulate the dynamic response of concrete materials under blast loading [38–41]. Gong and his coworkers [42] used an erosion criterion according to the principle tensile strain of 0.001 to simulate the failure of concrete under blast loading. Considering the convergence of numerical simulation and the literatures mentioned above, an erosion criterion according to the principle tensile strain of 0.0015 in the present study is adopted to model the failure of concrete and leads to reliable predictions of dynamic behaviors of the ordinary RCTS beam and the RCTS beam strengthened with steel plates. 2.4. Boundary conditions, contact algorithm and applied explosion load Boundary conditions of RCTS beam (see Fig. 1) are defined as simply supported beam, which is supported by two rigid spacers. The rigid spacers are simulated by three dimensional solid elements, which constrained on the surroundings and the bottom of the rigid spacer to fix the end positions of RC beam. The force of the vertical and horizontal directions can only be delivered at the

695

supports and bending moment cannot be transferred. In order to simulate the actual situation, the web of the simply supported RCTS beam is respectively provided rigid support cushion block, which is composed of solid 164 elements. All the degrees of freedom of the bottom surface of the support pad are constrained to ensure the simulation of the RC beam fixed on the supporting pad without rotation and translation. The contact between the beam and the rigid support pad is defined by the keyword named ⁄CONTACT_AUTOMATIC_SINGLE_SURFACE. The algorithm automatically generates master and slave surface and a plenty method is used, where nominal interface springs are used to prevent the interpenetration between surface and an element. The interface stiffness is calculated according to the volume of the function, the elastic modulus of the volume and the surface area of the unit in the area of contact surface. In order to study the dynamic response of structures in long distance or even ultra distance or near field under the conditions of explosion, the CONWEP model is used to calculate the explosion load applied to the structure, which needs to add the keywords, such as ⁄LOAD_BLAST, ⁄DEFINE_SEGMENT and the ⁄LOAD_SEGMENT_SET to the keyword file, and enter the TNT explosive quality, explosion type, ignition time, ignition center coordinates, unit conversion switch and unit conversion coefficient.

3. Results and discussion 3.1. Dynamic behaviors of ordinary RCTS beams 3.1.1. Influence of different weights of explosive charges In this study, six TNT charges with different weights (500 g, 1000 g, 1500 g, 2000 g, 2500 g, and 3000 g) are detonated at the same standoff distance of 60 cm above the mid-span top of the RCTS beam to study the influence of explosive charges on the dynamic response of the beam. The standoff distance is measured from the underside of the explosive charge to the top surface of the tested beam. Here, we take the typical mid-span of the beam node to analyze the change tendency of displacements shown in Fig. 2. It is obvious that the peak displacement of the RCTS beam gradually increases with the weights of explosive charges increasing. The pressure nephograms of the RCTS beam under different explosive charges are shown in Fig. 3. When the explosive is less than 1000 g, it is obvious that the RCTS beam was at the elastic stage and that damage did not occur shown in Fig. 3(a and b). When explosive charge is 1500 g, one crack appears in the midspan of the RCTS beam under the bending moment and the beam starts to break. When the explosive charges are more than 2000 g shown in Fig. 3(d–f), the RCTS beam appear inclined cracks under the combined action of bending moment and shear force. With the further increase of explosive charges, the damage process of the RCTS beam is changed from initial elastic deformation to flexural failure, and finally changed into shear failure. It also can be seen from Fig. 3(d–f) that the lengths of the formed cracks gradually become larger with the increase of explosive charge. When the mass of explosive charge is less than 1500 g, the RCTS beam can vibrate freely with small amplitude shown in Fig. 4(a–c). But the vibration amplitude and frequency of the RCTS beam are different due to the different explosion energies of explosive charges. The similar phenomenon could also be found in the acceleration history curves of the mid-span node of the RCTS beam (see Fig. 5). Compared Figs. 3 and 4, it is concluded that the RCTS beam are destroyed due to the tension and bending deformation of it when detonating the explosive charge with 2000 g. When the explosive charge is larger than 2500 g shown in Figs. 3(e and f) and 4(e and f), the RCTS beams are destroyed due to the bending and shearing deformation, however.

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Fig. 1. Schematic diagram of the ordinary RCTS beam under blast loading (unit:mm).

0.4

500g 1500g 2500g

Displacement/cm

0.2 0.0

values of equivalent stresses of longitudinal reinforcement in the tensile zone of the RCTS beam.

1000g 2000g 3000g

-0.2 -0.4 -0.6 -0.8 -1.0

0

2000

4000

6000

8000

10000 12000

Time/μs Fig. 2. Displacement history curves of the typical mid-span node of RCTS beam when detonating different explosive charges (500 g, 1000 g, 1500 g, 2000 g, 2500 g, and 3000 g).

(a) 500 g (b) 1000 g (c) 1500 g (d) 2000 g (e) 2500 g (f) 3000 g Fig. 3. Pressure nephograms of the RCTS beam when detonating different explosive charges on the mid span of the RCTS beam.

When detonating different explosive charges, the stress history curves of concrete and longitudinal reinforcement in the RCTS beam are shown in Fig. 6. The initial peak values of equivalent stress of the concrete in compression zone of the RCTS beam increase with the increase of explosive charges shown in Fig. 6. The similar phenomenon could also be found in the initial peak

3.1.2. Influence of different blasting distances 3.1.2.1. Influence of different horizontal blasting distances from the mid-span of the RCTS beam. Fig. 7 shows that the influence of different horizontal blasting distances (0 cm, 30 cm, 60 cm, 90 cm, 120 cm, and 150 cm) from the mid-span of the RCTS beam to the explosive charge under the identical charge mass (1500 g) and the same explosion height (60 cm). As can be seen from Fig. 7 that the maximal displacement of mid-span node of the ordinary RCTS beam with the horizontal blasting distance of 0 cm (contact explosion) is nearly 4 times of the minimal displacement in the midspan of the RCTS beam with the horizontal blasting distance of 150 cm when detonating 1500 g explosive with 60 cm standoff distance. It is also concluded that the displacements of the mid-span of the RCTS beam are gradually reduced with the increase of the horizontal blasting distance in Fig. 7. Fig. 8 shows the influence of different horizontal blasting distances (0 cm, 30 cm, 60 cm, 90 cm, 120 cm, and 150 cm) from the mid-span node of the RCTS beam when detonating 1500 g explosive with the 60 cm standoff distance on the pressure of the RCTS beam. As can be seen from Fig. 8, the positions of cracks and failure modes of the RCTS beam have a strong dependence on the positions of explosive charges due to the local effect of blasting loads. For instance, the formed cracks due to blasting load are symmetrically distributed on both sides of the RC beam when detonating the explosive in the mid-span of the RCTS beam shown in Fig. 8(a). Moreover, the contact explosion could do great damage to the RCTS beam due to the direct action of explosion. When detonating explosive charge in the horizontal blasting distance of 30 cm from the mid-span of the RC beam in Fig. 8(b), the formed cracks are concentrated on the left of the RC beam where the explosive charge located. Most of the formed cracks are concentrated in the left part of the RC beam where the explosive charges located when detonating explosive charges in the horizontal blasting distance of 60– 90 cm from the span of RC beam shown in Fig. 8(c and d). With the increase of the horizontal blasting distances, the damage degree of the RC beam was firstly decreased and then increased due to the different effects of contact explosion and non-contact explosion. The stress concentration phenomenon could also be found in the sections of flange and web, which results in the initial formed cracks extending along the section of flange and web section easily.

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Fig. 4. Velocity history curves of the mid-span node in the RCTS beam when detonating different explosive charges: (a) 500 g, (b) 1000 g, (c) 1500 g, (d) 2000 g, (e) 2500 g, (f) 3000 g.

Fig. 5. Acceleration history curves of the mid-span node in the RCTS beam when detonating different explosive charges: (a) 500 g, (b) 1000 g, (c) 1500 g, (d) 2000 g, (e) 2500 g, (f) 3000 g.

Fig. 9 shows the velocity history curves of the mid-span node under different horizontal blasting distances (0 cm, 30 cm, 60 cm, 90 cm, 120 cm, and 150 cm) from the mid-span of the RCTS beam when detonating 1500 g explosive with the 60 cm standoff distance. It is obvious that the velocities of the mid-span node in the RCTS beam change more and more improved with the increase of the horizontal blasting distances from the mid-span of the RCTS beam shown in Fig. 9. From the acceleration history curves shown in Fig. 10, it is concluded easily that the peak of acceleration the mid-span node in the RCTS beam is smaller and smaller with the increase of horizontal blasting distances.

Fig. 11 shows stress history curves of concrete and longitudinal reinforcement of different horizontal blasting distances from the mid-span of the RCTS beam when detonating different explosive charges (500 g, 1000 g, 1500 g, 2000 g, 2500 g, and 3000 g). It can be seen that the initial peak value of equivalent stress of concrete in compression zone of the RCTS beam decreases with the increase of horizontal blasting distances shown in Fig. 11(a). The similar phenomenon could also be observed from the initial peak values of equivalent stress of longitudinal reinforcement in the tensile zone of the RCTS beam shown in Fig. 11(b). The amplitude also decreases gradually with the horizontal distances changing.

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Fig. 6. Stress history curves of concrete and longitudinal reinforcement in the ordinary RCTS beam when detonating different explosive charges: (a) Effective stress history curve of concrete in mid-span compressive zone; (b) Axial stress history curve of longitudinal reinforcement in mid-span tensile area.

Fig. 7. Displacement history curves of the mid-span node of the ordinary RCTS beam under different horizontal blasting distances from the mid-span node of the RCTS beam when detonating 1500 g explosive with 60 cm standoff distance.

Fig. 8. Pressure nephograms of the RCTS beam under different horizontal blasting distances from the mid-span of the ordinary RCTS beam when detonating 1500 g explosive with 60 cm standoff distance.

3.1.2.2. Influence of different vertical explosion distances. In order to study the influence of vertical explosion distances from the upper surface of the RCTS beam on the dynamic response of the RCTS beam, the six different vertical distances (15 cm, 30 cm, 45 cm, 60 cm, 75 cm, and 90 cm) are studied when detonating 1500 g explosive. The displacement history curves of the mid-span node in the RC beam are shown in Fig. 12. It is obvious that the peak displacement of the mid-span node in the RC beam gradually increases with the vertical distance increasing. The final failure of the RCTS

beam under different vertical explosion distances from the upper surface of the RCTS beam direction to the center of explosive charge when detonating 1500 g explosive are shown in Fig. 13. As can be seen from Fig. 13 that with the vertical explosion distances increasing, the damage degree of the RCTS beam under blasting load decreases gradually. When the vertical explosion distance is 15 cm, shear failure is the main failure pattern of the RCTS beam shown in Fig. 13(a). When the vertical explosion distance is 30 cm, the damage pattern of the RCTS beam is changed from shear failure to bending shear failure in Fig. 13(b). Moreover, when the vertical explosion distances are in the range of 45 cm–75 cm, flexural failure is the main damage mode of the RCTS beam under blasting load. When the vertical explosion distance is higher than 90 cm, the RCTS beam is in elastic deformation stage in Fig. 13 (c–e). The number of the formed cracks in the RCTS beam increases first, and then decreases with the increase of the vertical explosion distances in Fig. 13(f). When the vertical explosion distance is about 30 cm, the number of cracks in the RCTS beam reaches the maximum shown in Fig. 13(b). The equivalent stress nephograms of the RCTS beam under different vertical distances from the upper surface of the RCTS beam to the center of explosive charge are shown in Fig. 14. As can be seen from Fig. 14, when the vertical distances from the upper surface of the RCTS beam to the center of explosive charge are changed from 15 cm to 45 cm, the formed cracks due to blasting load appear at the junction of the flange and the web in the middlespan of the RCTS beam. When the vertical distance is more than 45 cm, the beam is not destroyed any longer and no cracks are formed in the RCTS beam. The position of the weak link in the RCTS beam is still lied on the section of flange and web. The velocity history curves of the mid-span of the RCTS beam under different vertical directions from the upper surface of the beam to the center of explosive charge are shown in Fig. 15. Combined with the pressure nephograms of the RCTS beam, it is easily concluded that the amplitude of the beam becomes larger with the increase of vertical distances, and that the peak of velocities increase firstly from 8.533 m/s to 12.105 m/s, and then it become smaller to 2.148 m/s in Fig. 15. When the vertical explosion distance is 30 cm, the velocity reaches the maximum value. By comparison of the pressure nephograms in Fig. 14 and equivalent stress nephograms of the mid-span of the RCTS beam in Fig. 15, it can be concluded that when vertical explosion distance is 30 cm, the maximum damage degree of the RCTS beam is achieved. Fig. 16 shows the stress history curves of concrete and longitudinal reinforcement of the RCTS beam under different vertical distances from the upper surface of the RCTS beam to the center of explosive charge. It is obvious that the initial peak value of equivalent stress of the concrete in compression zone of the beam and the initial peak value of equivalent stress of longitudinal reinforcement

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Fig. 9. Velocity history curves of the mid-span node in the RCTS beam under different horizontal blasting distances from the mid-span of RCTS beam when detonating 1500 g explosive with 60 cm standoff distance:(a) 0 cm, (b) 30 cm, (c) 60 cm, (d) 90 cm, (e) 120 cm, (f) 150 cm.

Fig. 10. Acceleration history curves of the mid-span node in the RCTS beam under different horizontal blasting distances from the mid-span of the RCTS beam when detonating 1500 g explosive with 60 cm standoff distance:(a) 0 cm, (b) 30 cm, (c) 60 cm, (d) 90 cm, (e) 120 cm, (f) 150 cm.

in the tensile zone of the RCTS beam decrease with the increase of the vertical distances in Fig. 16. Meanwhile, the amplitude of the beam decreases gradually with the vertical distance changing. 3.2. Dynamic behaviors of RCTS beam strengthened with steel plates 3.2.1. Influence of different reinforcement methods In order to explore the best reinforcement method to improve the anti-explosion performances of the RCTS beam strengthened

with steel plates under blasting load, the following reinforcement ways are discussed: pasting steel plate on the bottom of the beam, pasting steel plate on both sides of web plate, pasting U-shaped steel plate on the web of the beam, fully packaged the beam with steel plate and pasting steel plate on the top and bottom of the beam. The displacement history curves of the mid-span node of the RCTS beam strengthened with 160 cm steel plate in length are show in Fig. 17 when detonating 1500 g explosive above the mid-span of the RC beam at the same standoff distance of 30 cm.

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Fig. 11. Stress history curve of concrete and longitudinal reinforcement of different horizontal blasting distances from the mid-span of the RCTS beam when detonating different explosive charges: (a) Effective stress history curve of concrete in mid-span compressive zone of the RCTS beam; (b) Axial stress history curve of longitudinal reinforcement in mid-span tensile area of the RCTS beam.

0.0

Displacement/cm

-0.2 -0.4 -0.6 -0.8 500g 1500g 2500g

-1.0 -1.2 0

2000

1000g 2000g 3000g

4000

6000

8000

10000

12000

Time/ μ s Fig. 12. Displacement history curves of the mid-span node in the RCTS beam when detonating different explosive charges (500 g, 1000 g, 1500 g, 2000 g, 2500 g, and 3000 g). Fig. 14. Equivalent stress nephograms of the mid-span of the RCTS beam under different vertical distances from the upper surface of the RCTS beam to the center of explosive charge.

Fig. 13. Pressure nephograms of the mid-span node in the RCTS beam under different vertical explosion distances from the upper surface of the RCTS beam direction to the center of explosive charge.

When 1500 g explosive is detonated above the mid-span of the RC beam at the same standoff distance of 30 cm, minimal peak displacement of the mid-span node of the RCTS beam fully packaged with 160 cm steel plate in length is 0.395 cm in Fig. 17. Compared with full packaged the RC beam with steel plate, the peak displacement of pasting steel plate on the top and the bottom of the RC

beam is increased by 3.8%. The pressure nephograms and the equivalent stress nephograms of the beam strengthened with different reinforcement methods are shown in Figs. 18 and 19, respectively. By comparing the damage morphologies and damage degree of the RCTS beam strengthened with different reinforcement methods shown in Figs. 18 and 19, it is concluded that the reinforcement methods of pasting steel plate on the top and bottom of the RCTS beam is the most economical and reasonable strengthened method, which could reduce the damage of the RCTS beam and give rise to forming the least cracks in the RCTS beam. Moreover, all kinds of reinforcement methods could result in the shear failure of oblique section in the RCTS beam in Fig. 18. Compared with the ordinary RCTS beam under blasting load, the degree of damage and the number of cracks of RCTS beam strengthened with different reinforcement methods were decreased and the anti-explosion performances of the RCTS beam could be effectively improved to some extent. Stress history curves of concrete and longitudinal reinforcement of the RCTS beam under different reinforcement methods are shown in Fig. 20. As can be seen from Fig. 20(a) that, compared with the RCTS beam strengthened with the different reinforcement methods under blasting load, the general level of the equivalent stress of concrete in the compression zone of the fully packaged RCTS beam with steel plate is lower. The similar phenomenon also occurred in the axial stress history curve of longitudinal reinforcement in the tensile area of mid-span of the beam shown in Fig. 20(b).

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Fig. 15. Velocity history curves of the mid-span of the RCTS beam under different vertical distances from the upper surface of the RCTS beam to the center of explosive charge:(a) 15 cm, (b) 30 cm, (c) 45 cm, (d) 60 cm, (e) 75 cm, (f) 90 cm.

Fig. 16. Stress history curve of concrete and longitudinal reinforcement of the RCTS beam under different vertical distances from the upper surface of the RCTS beam to the center of explosive charge: (a) Effective stress history curve of concrete in mid-span compressive zone of the beam; (b) Axial stress history curve of longitudinal reinforcement in mid-span tensile area of the beam.

3.2.2. Influence of different reinforcement lengths of steel plate By comparing the different reinforcement methods mentioned above, it is obvious that the most economical and reasonable reinforcement method to strengthen RCTS beam under blasting load is pasting steel plate on the top and bottom of the RCTS beam to some extent. Here, we explore the effect of reinforcement lengths of steel plates on the anti-explosion performances of the RCTS beam strengthened by pasting steel plate on the top and bottom of the RCTS beam. The reinforcement lengths of steel plates are 60 cm, 80 cm, 100 cm, 120 cm, 140 cm and 160 cm, respectively. Fig. 21 shows the displacement history curves of mid-span node of the RCTS beam strengthened by pasting steel plate with different lengths on the top and bottom of the RCTS beam under blasting load. As can be seen from Fig. 21 that the peak displacements of the mid-span in the RCTS beam strengthened by pasting steel plate on the top and bottom of the RCTS beam are 0.51 m, 0.39 m, 0.44 m, 0.43 m, 0.41 m, and 0.41 m, respectively. That is, when the reinforcement length of steel plate is 80 cm, the RCTS beam strengthened by pasting steel plate on the top and bottom of the RCTS beam under blasting load can effectively improve the antiexplosion effect of the RCTS beam.

Pressure nephograms of concrete in the RCTS beam strengthened by pasting steel plates with different lengths (60 cm, 100 cm, 120 cm, 140 cm, and 160 cm) on the top and bottom of the RCTS beam under blasting load are shown in Fig. 22. As can be seen from Fig. 22, there are some cracks in the shear span of the top and the bottom of the RCTS beam. With the increase of the reinforcement lengths of steel plates, the lengths of the formed cracks on the flange and the web of the mid-span of the RC beam are significantly developed and the cracks also appear at shear span of the RC beam. When the reinforcement length of steel plate is 80 cm, the formed cracks in the RCTS beam due to blast loading are mainly concentrated on the mid-span of the RCTS beam and no discernible cracks appear in the shear span of RCTS beam. When the reinforcement length of steel plate is 80 cm, the number of formed cracks in the RCTS beam is least shown in Fig. 22(b). It further shows that the optimal reinforcement length of steel plate is 80 cm on the conditions of pasting steel plates on the top and bottom of the RCTS beam under blasting load. Stress history curves of concrete and longitudinal reinforcement of different positions of the RCTS beam are shown in Fig. 23. As can be seen from Fig. 23(a), the peak values of equivalent stress of the

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0.2

(a) (b) (c) (d) (e)

Displacement/cm

0.1 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 0

2000

4000

6000

Time/μs

8000

10000

12000

Fig. 17. Displacement history curves of the mid-span node of RCTS beam strengthened with 160 cm steel plate in length when detonating 1500 g explosive above the mid-span of the RC beam at the same standoff distance of 30 cm; (a) Pasting steel plate on the bottom of the beam; (b) pasting steel plate on both sides of web plate; (c) Pasting U-shaped steel plate on the web of the beam; (d) Full packaged the RC beam with steel plate; (e) Pasting steel plate on the top and bottom of the beam.

concrete in mid-span compressive zone of the RCTS beam increase with the increase of reinforcement length of steel plate in the initial stage of explosion. While the peak value of equivalent stress of the concrete in mid-span compressive zone of the RCTS beam decreases rapidly with the increase of reinforcement length of steel plate in the later stage of explosion. When the reinforcement length of steel plate is 80 cm in Fig. 23(b), the axial stress of longitudinal reinforcement in mid-span tensile area of RCTS beam is maximal. This may be associated with the fact that the tensile strength of reinforcement is higher than the tensile strength of concrete. It will weaken the damage degree of concrete to some extend. In conclusion, the optimal reinforcement length of steel plate is 80 cm on the conditions of pasting steel plate on the top and bottom of the RCTS beam under blasting load. 3.3. Comparative analysis of mechanical properties of the RCTS beam before and after reinforcement Fig. 24 shows the displacement, vertical velocity and acceleration history curves of the mid-span node of the ordinary RCTS beam and the RCTS beam strengthened with steel plate with 80 cm in length on the top and bottom of it when detonating 1500 g explosive in the mid span of the beam with at the same standoff distance of 30 cm. As can be seen from Fig. 24(a), the peak

displacements of the mid-span node of the RCTS beam and the RCTS beam strengthened with steel plates with 80 cm in length are 0.39 cm and 0.84 cm, respectively. The maximal deflection of the RCTS beam is reduced by 53.5% after the RC beam strengthened with steel plate with 80 cm in length when detonating 1500 g explosive in the mid span of the RC beam with the same standoff distance of 30 cm. Vertical velocity and acceleration history curves of the midspan node of the RCTS beam and the RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the RCTS beam when detonating 1500 g explosive in the mid span of the RC beam with at the same standoff distance of 30 cm are shown in Fig. 24(b and c). As can be seen from Fig. 24(b), the velocity peaks of the RCTS beam and the RCTS beam strengthened with steel plates on the top and bottom of the RCTS beam under blasting load are 1.21 m.s1 and 1.08 m.s1, respectively. The acceleration peaks of the RCTS beam and the RCTS beam strengthened with steel plate on the top and bottom of the RCTS beam under blasting load are 6.61 m.s2 and 7.97 m.s2, respectively. Compared with the RCTS beam, the maximal vertical velocity and the maximum vertical acceleration of the RCTS beam strengthened with steel plates on the top and bottom of the RCTS beam under the same blasting load are reduced by 10.8% and 17.1%, respectively. It means that the best reinforcement method to improve anti-explosion performances of the RCTS beam is that the beam is strengthened with steel plates on the top and bottom of the RCTS beam. Fig. 25 shows the effective stress history curves of concrete in the mid-span compressive zone of the RCTS beam and RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the RCTS beam when detonating 1500 g explosive in the mid span of the beam with the same standoff distance of 30 cm. The peak value of equivalent stresses of the concrete in the midspan compressive zone of the RCTS beam are lower than that of the RCTS beam strengthened with steel plate with 80 cm in length on the top and bottom of the beam shown in Fig. 25. Compared with the ordinary RCTS beam, the peak value of equivalent stress of the concrete in the mid-span compressive zone of the RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the beam is reduced by 8.3%. Axial stress history curves of longitudinal reinforcement in mid-span tensile zone of the RCTS beam and RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the RCTS beam when detonating 1500 g explosive in the mid span of the beam with the same standoff distance of 30 cm are shown in Fig. 26. The axial stress peaks of longitudinal reinforcement in mid-span tensile zone of the RCTS beam is no different from that of the RCTS beam strengthened with steel plates with 80 cm in length on the top

Fig. 18. Pressure nephograms of the RCTS beam strengthened with 160 cm steel plate in length when detonating 1500 g explosive charge above the mid-span of the beam at the same standoff distance of 30 cm.

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Fig. 19. Equivalent stress nephograms of the RCTS beam strengthened with 160 cm steel plate in length when detonating 1500 g explosive charge above the mid-span of the beam at the same standoff distance of 30 cm.

Fig. 20. Stress history curve of concrete and longitudinal reinforcement of the RCTS beam under different reinforcement methods: (1) Effective stress history curve of concrete in the compressive area of mid-span of the beam; (2) Axial stress history curve of longitudinal reinforcement in the tensile area of mid-span of the beam; (a) Pasting steel plate on the bottom of the beam; (b) pasting steel plate on both sides of web plate; (c) Full packaged the beam with steel plate; (d) Pasting steel plate on the top and bottom of the beam; (e) Pasting U-shaped steel plate on the web of the beam.

Fig. 21. Displacement history curves of mid-span node of the RCTS beam strengthened by pasting steel plates with different lengths on the top and bottom of the beam under blasting load.

and bottom of the RCTS beam when detonating 1500 g explosive in the mid span of the beam with the same standoff distance of 30 cm shown in Fig. 26. To a certain extent, the degree of stress concentration is reduced due to the RCTS beam strengthened with steel plate on the top and bottom of the beam. In summary, the overall stiffness of the RCTS beam strengthened with steel plate with 80 cm in length on the top and bottom of the beam is improved, and the stress concentration degree of the beam in the compression zone and the tension zone of the beam is reduced. Moreover, the deformation of the RCTS beam under blast loading is reduced. The anti-explosion performances of the RC beam could be improved to some extent.

Fig. 22. Pressure nephograms of concrete in the RCTS beam strengthened by pasting steel plates with different lengths on the top and bottom of the RCTS beam under blasting load.

3.4. Comparative analysis of damage morphologies of concrete in the compression zone of RCTS beam before and after reinforcement The failure pressure nephograms of concrete in the RCTS beam and the RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the RCTS beam when detonating

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Fig. 23. Stress history curves of concrete and longitudinal reinforcement of the RCTS beam strengthened with different lengths of reinforcement: (a) Effective stress history curves of concrete in mid-span compressive zone of the beam; (b) Axial stress history curves of longitudinal reinforcement in mid-span tensile area of the beam.

Fig. 24. Displacement, vertical velocity and acceleration history curves of the mid-span node of the RCTS beam and RCTS beam strengthened with steel plate with 80 cm in length on the top and bottom of the RCTS beam when detonating 1500 g explosive in the mid span of the beam with the same standoff distance of 30 cm: (a) displacement history curves, (b) vertical velocity history curves, (c) acceleration history curves.

Fig. 25. Effective stress history curves of concrete in the mid-span compressive zone of the RCTS beam and RCTS beam strengthened with steel plate with 80 cm in length on the top and bottom of the RCTS beam when detonating 1500 g explosive in the mid span of the beam with at the same standoff distance of 30 cm.

1500 g explosive in the mid span of the beam with the same standoff distance of 30 cm at different times are shown in Fig. 27. Explosion shock wave is propagated in the spherical form at 179 ls shown in Fig. 27(a). There are three visible cracks in the web of the RCTS beam. The biggest crack is formed in the mid span of the beam due to the local effect of blasting load at 1859 ls shown in Fig. 27(b). While, there are few cracks at the same propagation time in the RCTS beam strengthened with steel plate with 80 cm in length on the top and bottom of the beam. Therefore, it is con-

Fig. 26. Axial stress history curves of longitudinal reinforcement in mid-span tensile zone of the RCTS beam and RCTS beam strengthened with steel plate with 80 cm in length on the top and bottom of the RCTS beam when detonating 1500 g explosive in the mid span of the beam with the same standoff distance of 30 cm.

cluded that the occurrence and propagation of formed cracks in the RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the beam due to blasting load are delayed greatly. The anti-explosion performances of the RCTS beam strengthened with steel plate are improved effectively. At 5519 ls, five and four visible cracks are formed in the RCTS beam and the RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the beam in Fig. 27(c), respectively. Moreover, the five formed cracks are distributed uniformly on the RCTS beam. While, the four formed cracks are mainly concentrated in the middle of the beam strengthened with steel plates. The depths of the formed cracks are developed to the maximum

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Fig. 27. The failure pressure nephograms of concrete in the RCTS beam and RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the RCTS beam when detonating 1500 g explosive in the mid span of the beam with the same standoff distance of 30 cm at different times.

Fig. 28. Comparatives analysis of mechanical properties of reinforcing steel bar in the RCTS beam and the RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the RCTS beam when detonating 1500 g explosive in the mid span of the beam with the same standoff distance of 30 cm: (a) The beam without reinforcement; (b) The beam strengthened with steel plate.

extent. The stress level of concrete in the middle of the beam is also decreased after the RC beam strengthened with steel plates at 10580 ls shown in Fig. 27(d). It is concluded that the antiexplosion performances of the RCTS beam strengthened with steel plates could be significantly improved from the number of the formed cracks and damage degree of the beam.

4. Comparative analysis of mechanical properties of steel bar in the RCTS beam before and after reinforcement Fig. 28 shows the mechanical properties of reinforcing steel bar in the RCTS beam and the RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the beam

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when detonating 1500 g explosive in the mid span of the beam with the same standoff distance of 30 cm. As can be seen from Fig. 28, the vibration amplitudes of velocity and acceleration in the direction of x increase firstly and then decrease. However, the vibration amplitudes of velocity and acceleration in the y and z directions gradually decrease in a short time. By comparing the displacement, velocity, and acceleration history curves of the reinforcing steel bar in the RCTS beam and the RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the RCTS beam under blasting load, it is concluded that all of physical magnitudes have been decreased in different degrees and the ant-explosion performances of RCTS beam strengthened with steel plates with 80 cm in length on the top and bottom of the RCTS beam under blasting load have been improved to some extend.

5. Conclusions The structural behaviors of RC beams under extreme loadings, such as blast and explosive loads, have been extensively studied from a theoretical as well as experimental point of view. Few studies have been conducted on the dynamic response of RCTS beam under blasting load, however. In the present study, parametric study is carried out to investigate the anti-explosion performances of the ordinary RCTS beam and the RCTS beam strengthened with steel plates. Moreover, the following reinforcement ways of the beam are discussed to explore the best reinforcement method to improve the anti-explosion performances of the beam: pasting steel plate on the bottom of the beam, pasting steel plate on both sides of web plate, pasting U-shaped steel plate on the web of the beam, fully packaged the beam with steel plate, and pasting steel plates on the top and bottom of the beam. The simulated results show that, the failure modes of RCTS beam are closely related to the weight and position of explosive charges. With the increase of explosive charges, the deformation modes of the RCTS beam are changed from elastic deformation to tension bending deformation, and finally the flexural shear failure is occurred. With the height increase of vertical direction of explosion, the failure modes of the RCTS beam are changed from bending shear failure to tensile bending failure. The elastic deformation of the RCTS beam only occurs at a limited height. The damage positions of the RCTS beam are also changed with the moving of explosive charges. The positions of forming cracks and the damage modes of the RCTS beam have a strong dependence on the positions and the weights of explosive charges due to the local effect of blasting loads. Compared with the ordinary RCTS beam, the initiation time of the cracks of the RCTS beam strengthened with steel plates is delayed and the growth speed of cracks is also significantly reduced. The crack distributions of the RCTS beam strengthened with steel plates are mainly concentrated on the reinforced area. Moreover, the number of formed cracks is also reduced and the compressive stress of concrete in the compression zone of the RCTS beam strengthened with steel plates is improved. The optimal size of reinforcement length of steel plate is about 80 cm by comparing the different reinforcement lengths of steel plates in the same explosion case. The anti-explosion performance of the RCTS beam strengthened with steel plates could be improved significantly.

Acknowledgements This research was financially supported by the National Science Foundation of China (grand no. 11302094), the National Science Foundation of Liaoning province in China (grand no. 201603), the Program for Liaoning Excellent Talents in University (grand no.

LJQ2014063) and the Scientific Research Foundation of Teachers in Liaoning University of Technology in China (grand no. X201403).

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