NUMERICAL ANALYSIS OF REINFORCED CONCRETE CORBEL ...corbel specimen with inclined CFRP strips scheme is 546.4kN while for HSC corbel specimen is 727.2kN with an improvement of 33.1%.

http://www.iaeme.com/IJCIET/index.asp 1554 [email protected]

International Journal of Civil Engineering and Technology (IJCIET)

Volume 9, Issue 10, October 2018, pp. 1554–1565, Article ID: IJCIET_09_10_155

Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=9&IType=10

ISSN Print: 0976-6308 and ISSN Online: 0976-6316

©IAEME Publication Scopus Indexed

NUMERICAL ANALYSIS OF REINFORCED

CONCRETE CORBEL STRENGTHENING BY

CFRP UNDER MONOTONIC LOADING

Abdulkhalik J. Abdulridha

Lecturer, College of Engineering, AL-Nahrain University, Baghdad, Iraq

Hussam K. Risan

Assistant Professor, College of Engineering, AL-Nahrain University, Baghdad, Iraq

Zahir Noori M. Taki

Assistant Lecturer, College of Engineering, AL-Nahrain University, Baghdad, Iraq

ABSTRACT

This study present a numerical analysis corbels cast with high and normal

strength reinforced concrete strengthen with Carbon Fiber Reinforced Polymers

(CFRP) strips in different pattern ways. Twenty-two corbel specimens are a

simulation in ABAQUS software program and all specimens tested under monotonic

loading. Two specimens’ normal and high strength concrete (control) without CFRP

strengthen and the rest are strengthened with two scheme of CFRP strips (horizontal

and inclined). The main parametric study is the effect of the changing in the thickness

of CFRPs on the behavior of the normal and high strength reinforced concrete

corbels. The reinforced concrete corbel specimens were strengthening in two pattern:

the first pattern was strength at both side of the specimen with three horizontal CFRP

strips and with width of 50 mm and the second pattern was strength three inclined

CFRP strips with angle of 45° and with width of 50 mm at both side of the specimen.

From the numerical consequences, it can be noted that the optimum CFRP thickness is

(0.26 mm) which equal to twice of the CFRP thickness that adopted in the

experimental test. The maximum load capacity for NSC corbel specimen with

horizontal CFRP strips scheme is 423.5 kN while for HSC corbel specimen is 713.9kN

with an improvement of 68.6%. Also, noted that the maximum load capacity for NSC

corbel specimen with inclined CFRP strips scheme is 546.4kN while for HSC corbel

specimen is 727.2kN with an improvement of 33.1%. That means the type of concrete

(NSC and HSC) has more effective on corbel specimens with horizontal CFRP strips

scheme than in inclined scheme.

Key words: Carbon Fiber, CFRP, Corbels, HSC, Normal Strength Concrete.

Abdulkhalik J. Abdulridha, Hussam K. Risan, Zahir Noori M. Taki


Cite this Article: Abdulkhalik J. Abdulridha, Hussam K. Risan, Zahir Noori M. Taki,

Numerical Analysis of Reinforced Concrete Corbel Strengthening by CFRP Under

Monotonic Loading, International Journal of Civil Engineering and Technology

(IJCIET) 9(10), 2018, pp. 1554–1565.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=9&IType=10

1. INTRODUCTION

Corbels are regularly formed monolithically with the wall or column. The a/d (shear span-to-

depth ratio) is smaller than the body. Two design methods are utilized for corbels, the first

method using the strut-and-tie and the other method matching the ACI Code, and the other

design uses the strut-and-tie models. The fail in design or the wrong positions of the steel

reinforcement in the structural members or the changing in temperatures all these reasons

causes the cracks development and leads to failure of the member. Wrapping using sheets or

strips of CFRP (Carbon Fiber Reinforced Polymer) is one of the most support ways of

supporting or enhancing the members Raghavendra et al. (2004) [1]. The corbel's failure

mode, when reinforced with the main reinforcements and stirrups, is assigned to as a beam-

shear failure, which is designated by the possibility of one or numerous inclining cracks

resulted by shear failure in the compressed region of the strut. Anis and Muhammad (2012)

[2] investigated the influence of CFRP strips on the performance of RC corbels. The results

have shown that the enhancement of the inclined strips was about 45 to 60% of the specimens

without any strengthening and the enhancement of the specimens with horizontal strips was

about 15 to 31%. El-Maaddawy and El-Sayed (2014) [3] tested 9 reinforced concrete corbel

specimens with a different pattern of externally CFRP strips. The results expression that the

slanting CFRP has an important improvement on the capability. Ivanova et al. (2015) [4]

studied the behavior of short RC corbels with CFRP wrapping fabrics. The results of the

experiment advertised that the highest effect is when the fabrics on the tensile side of the

corbel. Hussam et al. (2017) [5] obtained numerically that the change of CFRP thickness

exceedingly affects the concrete maximum plastic strain, crack models and final load limit.

Abdulkhalik et al. (2018) [6] studied numerically the effect of changing in CFRP thickness on

the behavior of square slabs with central opening strengthened with CFRP strips. The

numerical results showed that the significant thickness of CFRP strips is estimated as a

satisfactory and useful process of strengthening. The aim of this paper is to study numerically

the impact of varying in the thickness and orientation of CFRP strips on the performance of

normal and high strength reinforced concrete corbels.

2. INVESTIGATIONAL PROGRAM

In this paper, the analytical experiment results determined by Aamer and Wahig (2016) [7]

restricted to confirm results application with Finite Element Modelling (FEM) results. Aamer

and Wahig (2016) [7] experimented with six full-scale reinforced concrete corbels, all these

specimens designed to fail in shear. Three specimens were cast with HSC (high strength

concrete) of fc′= 57 MPa and the rest specimens were cast with NSC (normal strength

concrete) of fc'= 28 MPa. The columns at the top and the bottom of the corbel have

dimensions of 200 mm in width, 150 mm in depth, and 650 mm in height. The total width of

the corbel was 700 mm. The column reinforced with 4 deformed longitudinal bars with a

diameter of 10 mm. Closed stirrups used with 8mm diameter and spacing of 150mm c/c. The

main reinforcement was 3Ø12 mm steel bars. Figure .1 below shows the corbel's dimensions

and detail of reinforcement.

Numerical Analysis of Reinforced Concrete Corbel Strengthening by CFRP Under Monotonic Loading


Figure 1 Details and the dimensions of the Corbel

Aamer and Wahig (2016) [7] presented two groups of corbel specimens. The first group

cast with the normal strength concrete and included three specimens (specimen (C1) which

has not any strengthening with CFRP as shown in Fig. 2(a), specimen (C1T) which has to

strengthen with horizontal CFRP strips with a thickness of 0.13 mm and width of 50 mm @

100 mm spacing c/c as shown in Fig. 2(b), and specimen (C1S) which has to strengthen with

45o inclined CFRP strips with the thickness of 0.13 mm and width of 50 mm @ 100 mm

spacing c/c). The first group specimens’ details are as shown in Fig. 2 (c). The second group

cast with the high strength concrete and included three specimens (specimen (C2) which has

not any strengthening with CFRP as shown in Fig. 2(a), specimen (C2T) which has to

strengthen with horizontal CFRP strips with the thickness of 0.13 mm and width of 50 mm @

100 mm spacing c/c as shown in Fig. 2(b), and specimen (C2S) which has to strengthen with

45o inclined CFRP strips with the thickness of 0.13 mm and width of 50 mm @ 100 mm

spacing c/c) as shown in Fig. 2(c). The main properties of the corbel specimens are revealed

in Table 1. Materials properties of the corbel specimens are shown in Table 2.

Figure 2 Corbel specimens’ configuration.



Table 1 The assets of the selected reinforced concrete corbels.

Corbel

designation

Concrete

type

CFRP

designation

CFRP

Thickness

mm

CFRP

width @ spacing c/c

mm

CFRP Arrangement

C1

NSC

- - - ---

C1T T 0.13 50@100 Horizontal Strips (2-side)

C1S T 0.13 50@100 Inclined Strips with (45o) (2-side)

C2

HSC

- - - ---

C2T T 0.13 50@100 Horizontal Strips (2-side)

C2S T 0.13 50@100 Inclined Strips with (45o) (2-side)

Table 2 The properties of selected materials.

Element Specifications

Compressive

strength

(Mpa)

Tensile

Strength (MPa)

Modulus of

Elasticity

(Mpa)

Yield

strength

(Mpa)

Ultimate

strength

(Mpa)

Elongation

%

Steel

D = 8 mm - - 200000 412 591 10.8

D = 10 mm - - 200000 404 566 10.3

D = 12 mm - - 200000 401 548 11.1

Concrete NSC 28 1.41 - - - -

HSC 57 2.92 - - - -

CFRP T= 0.165 mm - - 230000 - 3500 1.5

3. CORBEL SPECIMENS VERIFICATION MODELING

In this paper, the software program analysis (ABAQUS) [8] is adapted to modeling the

selected corbel specimens with its parameters. Four of the selected specimens are

strengthened with CFRP strips on each side and the rest specimens are without any

strengthened with CFRP. The quadratic-order linear brick (C3D20R) is used in this study to

modeling the concrete material. In the ABAQUS software (C3D20R) defined as a 20-node

brick solid element with reduced integration in 3D system. Each node of this element has

three degrees of freedom. The (S4R) curved shell element (4-node tension membrane shell

with reduced integration) is used for modeling the CFRP strips in ABAQUS. The bonding

between CFRP sheet strips and the concrete is assumed to be a complete bond. For modeling

the CFRP, a linear elastic element is utilized. The 3-dimensional (T3D2A) element, linear

truss with 2-node is used for modeling the steel bars reinforcement in ABAQUS. The selected

(T3D2A) element is perfect to represent a discreet steel reinforcement embedded in concrete.

For modeling the steel reinforcement, an elastic-perfectly plastic element is employed. To

avoid the local failure because the concrete crushing, the 3D linear solid element (C3D8R)

with 8-node used to model the steel bearing plates. The plate placed at the top of the

specimens has dimensions 200 mm length, 150 mm width and 25 mm thickness. Also, the two

plates arranged at each post at the bottom of the specimen has dimensions of 150 mm length,

60 mm width and 25 mm thickness. Lubliner et al. (1989) [9] were the first planted the

Damage Plasticity model that used in this research. Lee and Fenves (1998) [10] were

improved this model. The ABAQUS software adopted the damage plasticity model to

simulate the behavior of concrete under tension and compression stresses. The yield surface

of damage plasticity model proposed by (Habbit et al. 2008) [10]. According to Habbit et al.

(2008) [11] the increase expansion in 2 variables of strain-hardening. The equation (e.g.

Hognestad 1951; Mostofi 2009) [12, 13] for the stress-strain curve of the concrete are adopted

in this study. The input data for chosen model that employed in ABAQUS software are: (εc =

0.00019 (strain compressive at peak), ψ =33 (dilation angle), εc for inelastic = 0.0008 to



0.0027 (inelastic strain of concrete in compression, and εt = 0.00016 (the cracking strain of

concrete in tension)). Also, the default parameters that ABAQUS included for damage

plasticity model for the concrete are applied. Hinge - roller boundary conditions system is

adapted to simulate the supports reactions for all specimens. The first support (roller) allows

the perpendicular movement and rotation. The second support (hinge) allows the rotation and

without any movement. To represent the preliminary loading condition, a perpendicular

uniform force pressure was used to simulate the load on the plate at the top of the corbel. The

applied load and the boundary conditions (reactions at supports) are presented in Figure 3.The

mesh size selection is 25 mm for all parts of the specimens that given the accurate behavior

for corbel specimens under the applied load.

Figure 3 The applied load and the boundary conditions.

3.1. Parametric Study

The main parametric study selected to investigate in this study is educations the outcome of

changes in the CFRP thickness on the shear behavior of the RC corbel under static load. The

numerical investigation divided into two main groups. The first group includes corbel

specimens cast with NSC and included two minor groups (specimens strengthened with

horizontal CFRP strips and specimens strengthened with inclined CFRP strips). The second

group includes corbel specimens cast with HSC and included two minor group (specimens

strengthened with horizontal CFRP strips and specimens strengthened with inclined CFRP

strips). The first and second groups’ parameters are shown in Table 3 and Table 4.

Table 3 The first group of corbel specimens cast with normal strength concrete (NSC).

Beam

designation CFRP type

CFRP

designation

CFRP

thickness

[mm]

CFRP

width @ spacing c/c

[mm]

Fc’

N-B-T0 Non - - -

Normal

strength

N-BH-T1 2-Side strip horizontal T 0.13 50@100

N-BH-T2 2-Side strip horizontal 0.5T 0.065 50@100


N-BH-T4 2-Side strip horizontal 2T 0.26 50@100


N-BI-T1 2-Side strip inclined (45o) T 0.13 50@100

N-BI-T2 2-Side strip inclined (45o) 0.5T 0.065 50@100


N-BI-T4 2-Side strip inclined (45o) 2T 0.26 50@100




Table 4 The second group of corbel specimens cast with high strength concrete (HSC).

Beam

designation

CFRP type

CFRP

designation

CFRP

thickness

[mm]

CFRP

width @ spacing c/c

[mm]

Fc’

H-B-T0 Non - - -

High

strength

H-BH-T1 2-Side strip horizontal T 0.13 50@100

H-BH-T2 2-Side strip horizontal 0.5T 0.065 50@100


H-BH-T4 2-Side strip horizontal 2T 0.26 50@100


H-BI-T1 2-Side strip inclined (45O) T 0.13 50@100

H-BI-T2 2-Side strip inclined (45O) 0.5T 0.065 50@100


H-BI-T4 2-Side strip inclined (45O) 2T 0.26 50@100


4. DISCUSSIONS AND RESULTS

The performance and durability of the numerical examination of the intended performance of

CFRP strips, concrete, and steel reinforcement will be confirmed with laboratory experiment

results. Also, the concrete crack patterns and the ultimate load capacity of each specimen are

listed. Fig. 4(A) shows the crack patterns of the experimental specimen (C1) and the

numerical plastic strain for the specimen (N-B-T0). Fig. 4 (B) shows the crack patterns of the

experimental specimen (C1T) and the numerical plastic strain for the specimen (N-BH-T1).

Fig. 4 (C) shows the crack patterns of the experimental specimen (C1S) and the numerical

plastic strain for the specimen (N-BI-T1). Fig. 5 (A) shows the crack patterns of the

experimental specimen (C2) and the numerical plastic strain for the specimen (H-B-T0). Fig.

5 (B) shows the crack patterns of the experimental specimen (C2T) and the numerical plastic

strain for the specimen (H-BH-T1). Fig. 5 (C) shows the crack patterns of the experimental

specimen (C2S) and the numerical plastic strain for the specimen (H-BI-T1). By analyzing the

numerical behavior of the corbel samples with the experimental results, a significant

similarity can be identified between experimental concrete crack patterns and the numerical

plastic strains of the concrete. The evaluation between the numerical recorded results data and

the experimental tested results are shown in Table 5. From the comparison, it can be

renowned that the middling of numerical loads exceeded 0.76 % of the final capacity of the

experimental load.

Table 5 The experimental and numerical of the corbel specimens’ results

Group CFRP

designation

Thickness

mm

Experimental results Numerical results

Corbel

Label

Corresponding

displacement

[mm]

Ultimate

load

[kN]

Corbel

Label

Corresponding

displacement

[mm]

Ultimate

load

[kN]

NSC

- - C1 4.70 225.1 N-B-T0 4.84 255.6

T 0.13 C1T 2.81 262.2 N-BH-T1 2.81 264.2

T 0.13 C1S 3.25 411.1 N-BI-T1 3.34 411.3

HSC

- - C2 1.70 300.2 H-B-T0 1.71 300.3

T 0.13 C2T 4.37 521 H-BH-T1 4.36 521.4

T 0.13 C2S 4.75 583.4 H-BI-T1 4.75 583.8



Figure 4 The crack patterns of the experimental and numerical plastic strain (A) for the specimens (C1) and (N-B-T0), (B) for the specimens (C1T) and (N-BH-T1), and (C) for the specimens (C1S) and (N-BI-T1).

Figure 5 The crack patterns of the experimental and numerical plastic strain (A) for the specimens (C2) and (H-

B-T0), (B) for the specimens (C2T) and (H-BH-T1), and (C) for the specimens (C2S) and (H-BI-T1).

Generally, the diagonal shear failure stylish where there are no CFRP strengthening in the

examined specimens. The numerical and experimental results showed that the crack patterns

take the path between the point load and the supports. From the preceding tables and figures,

it can be regarded that an excellent correspondence between the investigational works and the

geometric results. Consequently, it can be chosen the elected proposed numerical

interpretation method to simulation for the decided parameters of this research. The main

parametric study of this paper studies the effect of changing the CFRP thickness on the

behavior of the corbel specimens. For this reason, five different CFRP thickness has been

selected as mentioned before. The CFRP thickness is chosen change from 0.5T or (0.065 mm)

to 2.5T or (0.325 mm) as mention in Table 6. The numerical analysis results of the ultimate

load carrying capacity and the displacement at failure for the five chosen thickness of CFRP

are shown in Table 6.



Table 6 Ultimate load capacity for suggested numerical samples

Group Corbel label CFRP label

CFRP

thickness

[mm]

Numerical

Failure

Load (Pu) Num

[kN]

Mid-span

displacement at

failure [Δ

failure]

(mm)

Pu) Num / Pu) Num (control)

NSC

N-B-T0

(Control) - - 255.6 4.84 1

N-BH-T1 T 0.13 264.2 2.81 1.03

N-BH-T2 0.5T 0.065 210.0 2.98 0.82

N-BH-T3 1.5T 0.195 324.1 3.22 1.27

N-BH-T4 2T 0.26 423.5 4.09 1.66

N-BH-T5 2.5T 0.325 396.3 3.76 1.55

N-BI-T1 T 0.13 411.3 3.34 1.61

N-BI-T2 0.5T 0.065 306.3 3.36 1.19

N-BI-T3 1.5T 0.195 513.0 4.30 2.01

N-BI-T4 2T 0.26 546.4 4.05 2.14

N-BI-T5 2.5T 0.325 483.7 3.53 1.89

HSC

H-B-T0

(Control) - - 300.3 1.71 1

H-BH-T1 T 0.13 521.4 4.36 1.74

H-BH-T2 0.5T 0.065 459.2 5.57 1.53

H-BH-T3 1.5T 0.195 618.3 5.53 2.06

H-BH-T4 2T 0.26 713.9 6.31 2.38

H-BH-T5 2.5T 0.325 660.5 5.63 2.19

H-BI-T1 T 0.13 583.8 4.75 1.94

H-BI-T2 0.5T 0.065 480.1 4.29 1.60

H-BI-T3 1.5T 0.195 645.7 4.34 2.15

H-BI-T4 2T 0.26 727.2 4.45 2.42

H-BI-T5 2.5T 0.325 667.2 4.01 2.22

The results of the numerical analysis showed that the maximum ultimate load of the

samples happens when the thickness of CFRP is (2T) or 0.26 mm due to the rise in the

capacity of the shear resistance of the sample. The numerical results of corbel specimens cast

with NSC show that the maximum load capacity obtained for specimen N-BI-T4 which

strengthened with inclined CFRP strips with the thickness of (2T) or 0.26 mm reach to 546.4

kN with increases in maximum load capacity by 114 % more than the control corbel specimen

N-B-T0. The numerical results of corbel specimens cast with HSC show that the maximum

load capacity obtained for specimen N-BI-T4 which strengthened with inclined CFRP strips

with the thickness of (2T) or 0.26 mm reach to 727.2 kN with increases in maximum load

capacity by 142 % more than the control corbel specimen N-B- T0. Also, it is noted that the

increase in ultimate load capacity of HSC is 25% more than in NSC for specimen

strengthening with CFRP thickness of 0.26 mm.

4.1. Numerical Damage of the Concrete

Figures 6 to 9 show the concrete damage strain for all selected corbel specimens. It can be

mentioned in Fig. 6 and Fig. 7 that the plastic strains of concrete for the specimens’ behavior

are similar for all specimens in each type groups of strengthened with CFRP strip varying

from (0.5T) or 0.065 mm to (2.5T) or 0.325 mm and also noted that for the rest Fig. 8 and Fig.

9. The crack patterns of the concrete depending on the distribution and thickness of CFRP and

there are enhanced of the crack and upsurge in eventual capacity of the corbels when the

thickness of CFRP increased to (2T) and with the inclined pattern.



Figure 6 The concrete plastic strains and crack patterns for corbels with NSC and horizontal strengthening.

Figure 7 The concrete plastic strains and crack patterns for corbels with NSC and inclined strengthening.

Figure 8 The concrete plastic strains and crack patterns for corbels with HSC and horizontal strengthening.



Figure 9 The concrete plastic strains and crack patterns for corbels with HSC and inclined strengthening.

4.2. Load-Deflection Performance

At mid-span of each numerical beam specimen, the deflection values were recorded as in the

experimental test. The experimental load-deflection curve of the verification corbel specimens

compared with numerical load-displacement curve are shown in Figs. 10 and 11. From Figure

10 and 11, for the NSC and HSC, it can be noted that the load deflection curves are very

close between numerical result with experimental result and also noted the influence of

strengthened by CFRP strips. From Figure 12, for the NSC, it can be noted that the

numerical load-deflection curves for corbel specimens improved when rises the thickness of

CFRP strips until to the thickness of 2T (0.26 mm) and then the load deflection

descends when the thickness rises to 2.5T (0.325 mm). From Figure 13, for the HSC, it can

be noted that the numerical load-deflection curves for corbel specimens have more affected

by rises the thickness of CFRP strips especially with inclined scheme than in NSC. When

the thickness of CFRP strips until rises to the thickness of 2T (0.26 mm) and then the

load deflection descends when the thickness rises to 2.5T (0.325 mm).

Figure 10 The experimental and numerical load-displacement curves for specimens with NSC.



Figure 11 The experimental and numerical load-displacement curves for specimens with HSC.

Figure 12 The numerical load-displacement curves for NSC corbel specimens strengthened with various

thickness of horizontal and inclined CFRP strips.

Figure 13 The numerical load-displacement curves for HSC corbel specimens strengthened with various

thickness of horizontal and inclined CFRP strips.

5. CONCLUSIONS

The numerical results show that the ultimate load capacity affected by the thickness and

the scheme of CFRP strips.



Less effect of variation of CFRP thickness on the crack patterns for NSC corbel specimens

compared with HSC corbel specimens.

The load-deflection curves show that the HSC corbel specimens have a great stiffness than in

NSC corbel specimens whenever the CFRP thickness rises.

The scheme of CFRP strips (horizontal and inclined) have not affected on the type of

failure of the specimens.

From the numerical consequences, it can be noted that optimum CFRP thickness is (0.26

mm) which equal to twice of the CFRP thickness that adopted in the experimental test.

The maximum load capacity for NSC corbel specimen with horizontal CFRP strips scheme is

423.5 kN while for HSC corbel specimen with horizontal CFRP strips scheme is 713.9kN

with an improvement of 68.6%. Also, the maximum load capacity for NSC corbel specimen

with inclined CFRP strips scheme is 546.4kN while for HSC corbel specimen with

inclined CFRP strips scheme is 727.2kN with an improvement of 33.1%. That means the

type of concrete (NSC and HSC) has more effective on corbel specimens with horizontal

CFRP strips scheme than in inclined scheme.

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NUMERICAL ANALYSIS OF REINFORCED CONCRETE CORBEL ...corbel specimen with inclined CFRP strips scheme is 546.4kN while for HSC corbel specimen is 727.2kN with an improvement of 33.1%.

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