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Editor-in-Chief of the IJAST Journal:

Neal N. Xiong, School of Computer Science, Colorado Technical University, USA

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ISSN: 2005-4238 (Print) ISSN: 2207-6360 (Online)

Publisher: Science and Engineering Research Support Society

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International Journal of Advanced Science and Technology Vol. 29, No. 6, (2020), pp. 1181-1193

1181 ISSN: 2005-4238 IJAST

Numerical Analysis on Behavior of Reinforced Concrete T-Beam with Shear Strengthening using U-Strap Steel Plates and Bolts

¹I Ketut Sudarsana, ²Ida Bagus Rai Widiarsa, ³ I Gede Gegiranang Wiryadi, ⁴Putu Chandra Sajana

1,2,4Universitas Udayana ³Univ. Mahasaraswati Denpasar,

Abstract

Beams in a reinforced concrete building may suffer shear deficiency due to increasing the loads or mistaken in construction. This paper presents the analysis results of a T-beam with shear strengthening using U-strap steel plates and bolts. Modeling and analysis were done in a finite element software ABAQUS/CAE 2016. The behavior of concrete at plastic conditions were modeled using Concrete Damage Plasticity (CDP) features that require to calibrate its main parameters to match the results of an experimental T-beam. The best CDP’s validated parameters that give very close results with the behavior of tested specimens are a dilation angel ( ) of 55˚ and eccentricity (ɛ) of 0.1. The mesh size is 30mm. The friction coefficient of the steel plate and bolts to the concrete surface is 0.1 and 0.42, respectively. The results show that the CDP feature in ABAQUS is able to predict accurately the experimental behavior of the T-beam. The numerical results in terms of midspan deflection and maximum loads are about 98.84% and 100.05% of the experimental results, respectively. Concrete micro-cracks in the experimental specimen which result in stiffness’ degradation on the specimen are not considered in the numerical analysis so that a stiffer deflection response is obtained at the initial loading stage. It is also found that increasing the u-strap steel plate thickness and width can improve the beam shear capacity. However, enlarging the U-strap steel plate spacing reduces the beam shear capacity

Index Terms— ABAQUS, bolts, concrete damage plasticity, Numerical analysis, shear strengthening, steel plate, T-beams

I. INTRODUCTION

The strengthening method for an existing structure using low-cost material (economical) but efficient and effective is an interesting phenomenon to be studied. The strengthened structure must exhibit sufficient ductility so that brittle failure problems such as a brittle shear failure of the structural elements can be avoided. Steel plate is a ductile material with high deformability, wide availability, low price of low-carbon steel and ease application without required skilled laborers. Experimental studies on shear strengthening of reinforced concrete beams using epoxy-bonded steel plates on the web sides of the beams have been conducted by [1]–[5]. In general, t was found that the steel plates improve the shear strength of plated RC beams and its failure controlled by the shear strength of epoxy and concrete. The applications of anchor bolts to fix the steel plates onto the reinforced concrete beam surfaces have been studied by [6]–[10]. The steel plates fixed using anchor bolts contribute to the load-carrying capacity and the energy-absorption capacity. However, using anchor bolts to embed thin steel plates to the soffit of RC beams did not contribute significantly on the ductility and load capacity.

Most of the previous researches was using two pieces of vertical web plates with anchor bolts.

Research on using a U-strap steel plate is still worth studying. The application of U-strap steel plates fixed with anchored bolts as an external reinforcement for shear strengthening of reinforced concrete beams can be an alternative method to reduce the amount of strengthening materials.

Studies on the parameters of the U-strap steel plate applications still need to be conducted to achieve optimal strength, effectiveness, and efficiency in order to be widely used in practice. However, an

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experimental test requires a significant cost, time and high accuracy. Therefore, modeling and analysis using the finite element method (FEM) of the structural elements is currently an effective and powerful way to predict the behavior of structural elements, especially reinforced concrete. The results obtained depend on the accuracy of the modeling technique, and the parameters included in the analysis. One of the finite element method that widely used is Abaqus with its concrete damage plasticity (CDP) model Numerous numerical researches have been conducted using the Concrete Damage Plasticity (CDP) Model in Abaqus to predict the behavior of reinforced concrete structural elements [11]–[17]. It shows that the Concrete Damage Plasticity (CDP) option in Abaqus can accurately predict the failure behavior of concrete during plastic conditions by showing stress-strain variations in the concrete structural elements. However, in order to the CDP Model can be used to mimic the nonlinear behavior of concrete

materials, the suitable value of ), the

ratio of the tensile to the compressive meridian (Kc), the ratio between biaxial compressive strength and

the bo co need to be obtained through sensitivity

analysis to simulate the structural element behaviors. The definitions of those parameters are given in the following chapter for a brief presentation of the concrete damage plasticity model. A more detail presentation on the CDP Model can be found in [8] and [9].

II. METHODANDPROCEDURES A. Specimen Model

An experimental specimen (PS255) used for validating the finite element analysis is a reinforced concrete T-beam having a dimension of 100x200x2100mm with a flange size of 50x350 mm tested on four points loading setup by Sudarsana and Widiarsa (2018). The experimental specimen had two rebars D16mm and two rebars D10mm at the bottom (tension) and top (compression) sides of the beam, respectively. The shear reinforcement was provided in the form of closed stirrups using plain rebar of 6mm in diameter with a spacing of 150 mm along the beam length. The Welded Wire Fabric (WWF) grid M5 (rebars dia. 5mm with spacing 150mm) was provided for the beam flange to represents the slab reinforcement. Details on the internal reinforcement of the experimental specimen can be seen in Fig.

1(a). The tested T-beam was designed to be failed in shear both before and after the application of the strengthening materials.

The strengthening materials as external shear reinforcement in the form of U-strap steel plates and anchored bolts were begun to be installed after 14 days of concrete beam cast. The U-strap steel has width, height and thickness of 50 mm, 150 mm, and 2 mm, respectively. On each leg of the U-strap steel plates, a hole for anchored bolts diameter 8mm was provided at a distance of 50 mm from the end of both U-strap steel legs. The installation of the U-strap steels at a spacing of 50 mm as given in Fig.

1(b) were fixed using anchored bolts diameter 8mm which anchored to both sides of the beam web in previously drilled holes with a depth of 4 mm. The anchored bolts inside the holes were glued with epoxy bonding agents. The gaps between the concrete surface and steel plates were filled with prepacked grouting materials.

(a) Detail reinforcement

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(b) Detail strengthening plates and Bolts (c) Failure of the experimental specimen PS255

Fig.1. Detail specimen model

The material properties of concrete, reinforcement bars, U-strap steel plates and bolts of the tested specimen are shown in Table 1 which were also used in the numerical analysis. The concrete strength was obtained from concrete cylinders which were tested at the time of the T-beam tests (at least 28 days). For numerical analysis, in the absence of test data for the concrete stress-strain diagram, the Hognestad Model (1951) as shown in Fig. 2 was followed with a specified concrete strength of 22.5 MPa obtained from cylinder test.

The properties of reinforcement bars, U-strap steel plates and bolts were found from the tensile test and assumed to behave as elastoplastic materials. The tested specimen was simply supported and loaded with two-point loads at a distance of 575 mm from each support. The loads were applied continuously up to failure with the increments of 2.5 kN. The test results in term of load and midspan deflections is given in Fig. 3 and the failure condition of one end of the tested beam is shown in Fig. 1(c).

Fig.2. Hognestad stress-strain diagram model for normal concrete.

Fig.3. The experimental results of the specimen PS255

Table I. Properties of the materials Steel

Concrete

Rebar’s Bolt Plate

Dimesions (mm) Ø6 Ø10 Ø13 Ø8 tp 2.0 -

Density ρ (tonne/mm³) 7.85E-9 2.40E-9

Poisson Ratio υ 0.3 0.2

Young's Modulus Ε (MPa) 200000 22294.08

Yield Stress fy (MPa) 293.51 456.89 482.09 598.39 230.50 - Ultimate Strength fu (Mpa) 430.41 603.60 616.25 706.07 382.40 - Compressive Strength f’c

(MPa) - 22.50

Tensile Strength ft (MPa) - 2.025

0 10 20 30 40 50 60 70 80 90 100 110

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 27.5 30

Load (kN)

Deflection (mm) Exp. PS255

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B. Concrete Damage Plasticity (CDP)

The concrete damage plasticity (CDP) model is a continuum, plasticity-based damage model, which assumes two main failure mechanisms namely the tensile cracking and the compressive crushing. The model uses the yield function proposed by [19] with modifications by [18]. It is defined according to Eq.(1).

~ ) ( )) ( )

~ )(

( 3 1 (

1

max max

pl c c

p pl

q

F        

 ^ ^ ^ ^ ^

  (1)

The parameter α is determined using Eq. (2)

 

 /  1^;⁰ ⁰^.⁵

2

1 /

0 0

0

0  



  



 

c b

(2)

In Eq. (1), 𝑞̅ and 𝑝̅ represent the von mises-equivalent effective stress and the hydrostatic pressure stress, respectively. 𝜎̂̅_𝑚𝑎𝑥 is the maximum principal stress which is equal to zero for biaxial compression case. The 𝜎_𝑏𝑜 and 𝜎_𝑏𝑜 in Eq. (2) represent the biaxial compressive strength and the uniaxial compressive strength, respectively. The default value of the ratio (𝜎_𝑏𝑜⁄𝜎_𝑐𝑜) as given in [20]

is 1.16. The function of 𝛽(𝜀̃^𝑝𝑙) and γ in Eq (1) are calculated using Eq (3) and (4), respectively. The parameter 𝛽(𝜀̃^𝑝𝑙) presents in Eq (1) when the algebraically value of the maximum principal effective stress (𝜎̂̅_𝑚𝑎𝑥 ) is positive.

   

 

^~ ⁽¹ ⁾ ⁽¹ ⁾

~ ~  







 

    

pl t t

pl c pl c

(3)

1 2

) 1 (

3 ₁



  Kc

 K (4)

Where 𝜎̅_𝑐(𝜀̃_𝑐^𝑝𝑙) the effective compressive cohesion is stress and 𝜎̅_𝑡(𝜀̃_𝑡^𝑝𝑙) is the effective tensile cohesion stress. The parameter Kc in Eq. (4) is the ratio of von mises equivalent stress on the tensile meridian and compression meridian and defines the shape of the yield surface in the deviatory plane shown in Fig. 4. The parameter γ is active when the value of (𝜎̂̅𝑚𝑎𝑥 ) is negative.

Fig. 4. The deviatory yield surface plane (Kc = 2/3 corresponds to Rankine formulation; Kc =1 corresponds to Drucker-Prager criterion) and dilation angle [20].

The flow potential function, G(σ), in the CDP model follows the non-associated Drucker-Prager hyperbolic function as given in Eq.(5).





) ( tan ) tan

( ₀ ² q² p

G  _t   (5)

Where ∈ is the eccentricity to define the rate at which the plastic potential function approaches the asymptote and 𝜎_𝑡0 is the uniaxial tensile stress. The parameter 𝜓 in Eq. (5) is the dilation angle measured in 𝑝̅ − 𝑞̅ plane in high confining pressure as shown in Fig. 4(b).

Damage in the concrete damage plasticity model is introduced using Eq. (6). The parameter of damage, d, is defined in terms of compressive damage (dc) due to compressive crushing and tensile damage (dt) due to tensile cracking as shown in Fig. 5 and given by Eq. (7).

) ( ) 1 ( ) 1

( d d E₀  ^pl

      (6)

) 1 )(

1 ( ) 1

( d  s_td_c s_cd_t (7)

Where Eo is the initial (undamaged) elastic stiffness (deformation modulus), and st and sc are describe

(b) (a)

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the tensile and compressive stiffness recovery, respectively. The value of damage parameter, d, ranges between 0 (no damage) and 1 (total loss of strength or destruction).

(a) Uniaxial compression

(b) Uniaxial tension

Fig. 5. Stress-strain curve of concrete and identification of damage parameter dc and dt

In order to overcome severe convergence difficulties due to the softening behavior and stiffness degradation in a material model, a viscoplastic regularization according to Devaut-Lions approach can be introduced in the constitutive equation of the model. By defining the viscous parameter, µ, to represent the relaxation time of the viscoplastic system, the plastic strain tensor is upgraded as described in Eq.(8).

)

1 ( _pl

v pl pl

v  

    (8)

Similarly, a viscous stiffness degradation variable, 𝑑̇_𝑣, for the viscoplastic system is defined by Eq. (9).

) 1(

v

v d d

d  

  (9)

The parameter dv in Eq. (9) represents the viscous stiffness variable. The stress-strain relation of the viscoplastic model is given in Eq. (10).

) ( : ) 1

( d_v E₀  _v^pl

   (10)

C. Finite Element Modeling

A nonlinear analysis using a finite element-based software, Abaqus/Explicit, was conducted on an experimental T-beam specimen (PS255) tested by Sudarsana and Widiarsa (2018) to investigate the convergence parameters of the CDP for modeling and analysis a reinforced concrete T-beam strengthened with U-strap steel plates and bolts. The Abaqus/Explicit was chosen as an analysis solver to coup with the convergence problem since the strengthening T-beam model has many different material interactions, non-ordinary geometry and large deformation. All materials such as concrete, steel plates, bolts and applicators use solid eight-node linear brick elements (C3D8R) with reduced integration and hourglass control to avoid shear locking, reduce computing time and improve modeling accuracy [21]. The reinforcing steel is modeled using a three-dimensional truss element (T3D2) with 2 nodes and three degrees of freedom. The truss element was chosen because according to [14] it gives a similar output stresses to the reinforcement modeled with a solid element (C3D8R). Truss elements also

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make the computational process much faster because of the smaller amount of DOF [22]. Modeling the reinforcement with solid elements is recommended for the model with complex geometry or the focus of the analysis is on the reinforcement itself because deformation, stress and contact problems can be represented more accurate according to the expected structural behavior [7], [12]. Each type of element in a whole model can be seen in Fig. 6.

Each element in the model touches each other with a certain interaction level. The interaction of reinforcement with concrete used the embedded element option. This option assumes that there is a perfect bond between the two materials which makes the translation’s degrees of freedom at the nodal point can be eliminated to have both materials working in full composite [19], [20], [22], [23]. Surface to surface contact was used to model the contacts between steel plate surface (as master surface) and the concrete (as slave surface). This option defines a pressure-overclosure in the normal direction that is a hard contact which allows the attachment of two materials to be released when the permissible bonding stress exceeded and a penalty contact in the tangential direction that is defined using the friction coefficient range of 0.10 to 0.25 [12]. Surface to surface contact interactions of bolts and concrete was idealized by removing the gap from the chemical anchor that attaches the bolt to the concrete to speed up the computation process. Instead, the definition of bolt attachment with concrete used a range of friction coefficients for tangential direction in the contact properties of the model of 0.25 to 0.45 as shown in Fig. 6(b) according to the recommendations from [21], [24], [26], [27]. A tied constraint option for bolt interactions with steel plates was used by assuming the steel plates were restrained by the bolt nuts.

(a) 3D Model (b) Definition of contact interaction between plate and bolts

Fig.6. Detail model of T-beam in ABAQUS, (a) 3D Model. (b) Definition contact interaction III. RESULTSANDDISCUSSION

The concrete damage plasticity parameters were investigated using the experimental results of the specimen PS255 to validate the modeling technique in predicting the behavior of strengthening T-beam.

The load-deflection curve (P- test result was used as the behavior target. The sensitivity analyses were done by varying the mesh size (mesh sensitivity), dilation angle (), eccentricity (), and the coefficient of frictions on the interaction between the steel plates and bolts to the concrete material. After obtaining the best value of those parameters, the other parameters were used default values according to recommendations from many authors [11], [17], [19], [20], [28]–[30].

A. Load-Deflection Relationship

A mesh sensitivity study was performed considering that most plasticity-based models are meshed size-dependent [31]. Three mesh sizes (20mm, 30mm, 40 mm] were considered in this study. These values were chosen for the element mesh to be larger than the aggregate size (maximum 15mm) and to avoid a coarse mesh. Fig. 7 shows the analysis results for the mesh sensitivity. All the mesh sizes give similar behavior up to load 85 kN. Differences in load-deformation occur afterward and show that the

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mesh size of 30 mm gave the closest results compared to the experimental load-deflection. The mesh size of 20mm gives higher prediction on load capacity and the mesh size of 40mm results in a lower load capacity due to element mesh was too coarse. In all subsequent numerical simulations used the mesh size of 30 mm.

Fig. 7. Load-deflection response of the beam by comparing test results and numerical analysis with a variation on element mesh.

In concrete damage plasticity, the dilatancy (volume change) due to inelastic strain in brittle material such as concrete is taken into account by defining a value for the dilation angle (). Fig. 8 shows the load-deflection results for studying the effect of dilation angle of 40ô, 45ô, 50ô and 55ô on the beam behaviors. The dilation angle of 55ô gives the closest results to the experimental load-deflection behavior of T-beam and then be used in all subsequent numerical analysis.

Fig. 8. Load-deflection response of the beam by comparing test result and numerical analysis with a variation on dilation angle ().

The eccentricity () defines the rate at which the hyperbolic flow potential approaches its asymptote and that is a small positive number. Three numbers were considered in analysis namely 0.1, 0.12, and 0.15. The smallest number was recommended by [20]. Fig.9 shows that there are no significant differences in load-deflection behaviors indicated that variations on the eccentricity have no significant effects. The value of 0.1 as a default value in the CDP model of Abaqus and also recommended by [28]–[30] is chosen for the rest of the analysis.

0 10 20 30 40 50 60 70 80 90 100 110 120

0 2.5 5 7.5 10 12.5 15 17.5 20

Load (kN)

Deflection (mm)

Exp. PS255 Mesh 20mm Mesh 30mm Mesh 40mm

0 10 20 30 40 50 60 70 80 90 100 110

0 2.5 5 7.5 10 12.5 15 17.5 20

Load (kN)

Deflection (mm)

Exp. PS255 Dilation 40˚

Dilation 45˚

Dilation 50˚

Dilation 55˚

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Fig. 9. Load-deflection response of the beam by comparing test results and numerical analysis with a variation on eccentricity ().

The contact between the U-strap steel plate surface (master surface) and the concrete (slave surface) was modeled using a surface to surface contact with the steel plate and concrete as master and slave surface, respectively. A penalty contact in the tangential direction that was defined using the friction coefficient range of 0.10 to 0.2 as recommended by [12]. Fig. 10 gives the analysis results of friction coefficients study on the T-beam response. It is shown that the friction coefficient of 0.1 gives the closest result to the experimental behaviors.

Fig. 10. Load-deflection response of the beam by comparing test result and numerical analysis with variation on Friction coefficient steel plate to concrete

The surface to surface contact between the anchored bolts and the concrete, a range of friction coefficient for tangential direction in the contact properties of 0.3, 0.42, and 0.45 was considered. Those numbers were within the range of friction coefficients recommended by [21], [24], [26], [27]. The friction coefficient of 0.42 gives the closest analysis results to the experimental one. The friction coefficient seems to work near the ultimate loads both for steel plate to concrete and anchor bolts to concrete where at this time, high stress has occurred in both materials.

0 10 20 30 40 50 60 70 80 90 100 110

0 2.5 5 7.5 10 12.5 15 17.5 20

Load (kN)

Deflection (mm)

Exp. PS255 ecc_01 ecc_012 ecc_0125

0 10 20 30 40 50 60 70 80 90 100 110

0 2.5 5 7.5 10 12.5 15 17.5 20

Load (kN)

Deflection (mm) Exp. PS255 Plate_frc_coef_01 Plate_frc_coef_015 Plate_frc_coef_02

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Fig. 11. Load-deflection response of the beam by comparing test result and numerical analysis with a variation on Friction coefficient anchored bolts to the concrete.

After an extensive trial and error value of the CDP’s parameters to obtain a good correlation between experimental data and analysis results as presented in Fig. 7, 8, 9, 10, and 11, it can be summarized that the best values for the CDP’s parameters are the mesh size of 30 mm, the dilation angle of 55^o, the eccentricity of 0.1, and the contact friction coefficient of plate and bolts to the concrete of 0.1 and 0.42, respectively. The ratio of the second stress invariant on the tensile meridian to that on the compressive meridian (Kc), the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress (𝜎_𝑏𝑜/𝜎_𝑐𝑜) were kept the default value of 1.16 and 0.667, respectively. The viscosity parameter, µ, used for the visco-plastic regularization of the concrete constitutive equations was set to zero since the numerical analysis was done in Abaqus/Explicit.

All the best values of CDP’s parameters were used together in the finite element analysis to study the behavior of the strengthening T-beam. The results are shown in Fig.12. It is found that finite element analysis can predict closely the behavior of the experimental specimen by an error of 0.05% and 1.15%

for load and deflection, respectively. The onset curves between the analysis and experimental results at the loads below 90 kN may be caused by the stiffness reduction of the experimental beam due to the occurrence of micro-cracks during drilling holes for anchored bolts which was not taken into account during the finite element analysis.

Fig. 12. Comparison of experimental and finite element analysis of the load-deflection T-beam specimen

B. Stress Distributions

The stress distribution on T-beam specimen, U-strap steel plates, and bolts at ultimate loads are shown in Fig. 13. Stress direction to indicate the crack surface on the normal direction is assumed with maximum plastic strain. Initial concrete crack is indicated by the positive value of the principal plastic

0 10 20 30 40 50 60 70 80 90 100 110

0 2.5 5 7.5 10 12.5 15 17.5 20

Load (kN)

Deflection (mm) Exp. PS255 Bolt_frc_coef_03 Bolt_frc_coef_042 Bolt_frc_coef_045

0 10 20 30 40 50 60 70 80 90 100 110 120 130

0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 27.5 30

Load (kN)

Deflection (mm) Exp.

PS255

Pexp = 102.50 kN d_exp = 18.23 mm P_FEM = 102.56 kN d_FEM = 18.02 mm

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strain and the crack orientation is perpendicular to it [29], [32]. The stresses shown in Fig. 13(a) are at yield and ultimate conditions. Shear force is initially resisted by the reinforced concrete beam and then gradually transferred to the external strengthening plate to make composite actions.

There is a stress concentration around the hole area where anchor bolts are attached to the strengthening steel plates. The tension in the area of the bolt hole is caused by the bearing mechanism due to the transfer of shear forces from the concrete beam to the strengthening plate, and then the bolts.

The bearing mechanism is shown in Fig. 13(b), the steel plates work similarly to internal shear reinforcement. The dowel action that occurred on the bolt due to the large shear forces causes the bolt yields. The bolts are designed as much as possible to reach yielding in order to have the ductile behavior of the beam so that a brittle collapse can be avoided.

(a) Stress distribution of reinforced concrete T-beam (b) Stress distribution on plate and bolts

Fig.13. Stress distributions on concrete, steel plate and bolts at ultimate loads C. Results of the parametric study on strengthening properties

The parametric study was done to investigate the effect of strengthening material properties on the shear capacity of the strengthening T-beams after the modeling technique using the CDP’s parameters has been validated. The strengthening materials properties were U-strap steel plate thickness (tp), width (ws), and spacing (s).

The U-strap steel plate thickness of the experimental T-beam (PS255) was 2mm. It was increased to be 3mm, 4mm, 5mm, and 6mm with other properties kept the same. The analysis results in Fig. 14 show that the beam shear strength increases 1.2%, 3.9%, 4.8% dan 7.6% from the validated model (with 2 mm U-strap steel plate thickness) for 3mm, 4mm, 5mm and 6mm, respectively.

The effects of U-strap steel width were studied by widening the plates in the validated model PS255 from 50mm to be 65mm, 75mm, 85mm and 100mm. The U-strap steel thickness and spacing were still the same properties as the validated model which were 2 mm and 50 mm, respectively.

Fig. 14. Effect of U-strap thickness on beam shear capacity

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The width of the steel plate also improves the shear capacity of the strengthening beams as given in Fig.15. By widening the U-strap steel plate from 50mm becomes 65mm, 75mm, 85mm and 100mm can increase the beam shear capacity of 1.6%, 4.8%, 9.4% and 11.0%, respectively. Comparing the analysis results in Fig. 14 and Fig. 15, it shows that with the same U-strap spacing, widening the U-straps to obtain a certain strengthening steel plate areas gives a higher improvement on the beam shear capacity than thickening them.

Fig. 15. Effect of U-strap widths on beam shear capacity

To study the effects of the U-strap spacing on the beam shear capacity, the U-strap spacing in the validated model (PS255) was then enlarged from 50mm to be 75mm and 100mm by keeping the steel plate thickness of 2mm. The analysis results presented in Fig. 16 shows that the beam shear capacity decreases by 6% and 10% of that of the validated beam by enlarging the U-strap steel spacing of 75mm and 100mm, respectively.

The results of the parametric study given in Fig. 14, 15, and 16 show that the contribution of the external shear strengthening using the U-strap steel plate on the shear capacity is similar to the beam inside stirrups.

Fig. 16. Effect of U-strap spacing on beam shear capacity IV. CONCLUSION

The finite element (FEM) model by utilizing the Concrete Damage Plasticity (CDP) feature in ABAQUS which has been validated is able to predict very well the shear collapse behavior of strengthened concrete T-beam specimens using strip plates and bolts. The difference given by the FE model when compared with the results of laboratory tests is relatively small, especially in the ultimate conditions which is not greater than 2%. The best CDP’s parameters obtained from sensitivity analysis were dilation angle parameter () 55˚ and eccentricity (ɛ) 0.1. Other parameters are 30mm mesh size and friction coefficient of steel plates and bolts to the concrete are 0.1 and 0.42, respectively. The percentage obtained from FEM analysis when compared with laboratory specimens for load and

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deflection conditions are 100.05% and 98.84% for load and deflections, respectively. It is also found that increasing the u-strap steel plate thickness and width can improve the beam shear capacity.

However, enlarging the U-strap steel plate spacing reduces the beam shear capacity.

ACKNOWLEDGMENT

Authors thank Universitas Udayana for providing parts of the research funding through the research and community services grand No. 2494.2/UN14.2.5.11/LT/2019. Authors also thank all colleagues for the support during the research process

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