Finite element modelling of reinforced concrete beams ...

International Review of Civil Engineering (I.RE.C.E.), Vol. xx, n. x

July 2019

Manuscript received and revised xx 2019, accepted xx 2019 Copyright © 2019 Praise Worthy Prize S.r.l. - All rights reserved

Finite element modelling of reinforced concrete beams strengthened

with different configuration of carbon fiber sheets

Yasmin Murad1, Ja’afer Abu Zaid

2

Abstract – The influence of carbon fiber sheets’ orientation angle in strengthened reinforced

concrete beams is investigated in this research. Experimental and numerical programs are

conducted to study the flexural behaviour of RC beams strengthened with carbon fiber sheets that

fixed to the beam surface inducing different orientation angles of 0˚, 45˚, 60˚and 90˚. Finite

element models are developed in ABAQUS and ANSYS and then verified using the experimental

results of the test specimens. A comparison is made between the experimental and numerical

results. Both finite element models are able to predict the experimental load-deflection response

and crack pattern of the test specimens with reasonable accuracy. The results have shown that

carbon fiber orientation angle has significant influence on the flexural response of reinforced

concrete beams. The best performance is obtained with 45˚ inclined carbon fiber sheets.

Furthermore, a parametric study is performed to investigate the influence of carbon fiber sheets

orientation angle, sheet depth and sheet thickness on the behaviour of strengthened reinforced

concrete beams. Copyright © 2010 Praise Worthy Prize S.r.l. - All rights reserved.

Keywords: Finite element, CFRP, angles, ABAQUS, reinforced concrete (RC) beams,

strengthening, ANSYS.

Nomenclature: CFRP: carbon fiber reinforced polymer

FE: finite element

RC: reinforced concrete

CDP: concrete damage plasticity

IREC: International Review of Civil Engineering

I. Introduction

Previous studies have been conducted to study the

behaviour of reinforced concrete beams strengthened

with carbon fiber reinforced polymer (CFRP) sheets and

laminates. There are many factors that can influence the

behavior of strengthened reinforced concrete (RC) such

as CFRP sheets configuration, orientation and properties

[1],[2],[3],[4]. CFRP sheets have become an accepted

solution for shear and flexural strengthening and repair of

RC beams [5],[6],[7],[8],[9],[10],[11]. Khalifa [14] has

shown that the ultimate load carrying capacity of RC

member increases by increasing CFRP strip width.

Deflection of strengthened RC beams can significantly

vary while the variation of CFRP sheets orientation angle

[3],[4]. CFRP sheets play a key role in postponing the

appearance and propagation of cracks [3],[4]. Previous

experimental studies have shown that CFRP sheets and

laminates can reduce the ductility of the strengthened RC

beams [12],[13]. The direction of reinforcing fibers can

significantly influence the strength and the cracking

pattern of the strengthened RC beams [6]. RC beams

strengthened with CFRP sheets perpendicular to the beam

axis can experience high strength with brittle behaviour

[6]. However, they have found that RC beams

strengthened with 45˚ inclined CFRP sheets can

experience small increment in strength and the failure

mode is ductile [6]. Other experimental studies have

reported that the flexural strength of strengthened RC

beams with CFRP sheets can increase up to 58% [15]

compared to un-strengthened beams.

The previous studies in the literature have not clearly

explained the influence of CFRP sheets orientation angle

on the flexural behaviour of RC beams. Few studies have

experimentally studied the behaviour of RC beams

strengthened with CFRP sheets oriented at 45˚ to the axis

of the beam. The influence of CFRP sheets oriented at

60˚ or 30˚ to the axis of the beam is limited in the

literature.

This paper firstly illustrates an experimental program [3]

that was carried out by the author to investigate the

flexural behaviour of RC beams strengthened with CFRP

sheets that epoxy bonded to the beam surface inducing

different orientation angles. Numerical finite element

(FE) models are then constructed in ABAQUS and

ANSYS, FE programs, and validated using the

experimental results of the RC beams strengthened with

CFRP sheets under different orientation angles. The FE

section in this paper includes the material and element

models that used for each finite element model. The FE

section also includes the validation of the FE models.

A comparison is then made in this paper between the

numerical results obtained from both FE programs

ABAQUS and ANSYS. Numerical analysis is an efficient

tool to better explaining the behaviour of strengthened

Y.Z.Murad, J.AbuZaid

Copyright © 2019 Praise Worthy Prize S.r.l. - All rights reserved International Review of Civil Engineering, Vol. x, N. x

RC beams at lower costs. Therefore, a parametric study is

finally carried out in the last section of this paper to

evaluate the numerical effect of CFRP sheets orientation

angle, sheet thickness and sheet depth on RC beams’

strength, deflection and damage pattern.

II. Experimental Program

II.1. Test Setup

Test specimens are simply supported beams that are

tested under incremental static loading where a hydraulic

jack is used to apply the loads as shown in Figure 1.

Figure 2 illustrates the distance between the two

concentrated loads (720 mm) and that between the point

load and the support (640 mm). Linear variable

displacement transducers (LVDT) are instrumented at the

middle span of the beam to measure the mid-span vertical

deflection as shown in Figure 1.

Figure 1 Test setup

Figure 2 Illustration of the Test Specimens Dimensions, Supports, and

Loads

II.2. Material Properties

The mean concrete compressive strength, longitudinal

bars’ yield strength, stirrups’ yield strength of all test

specimens are 30 MPa, 500 MPa and 280 MPa

respectively. The width, thickness, elastic modulus and

ultimate tensile strength of CFRP sheets are 500 mm,

0.166 mm, 230 GPa and 4900 MPa respectively. An

epoxy resin is used to connect CFRP sheets with the

concrete surface. The density of the epoxy is 1.06 kg/ Lt.

II.3. Specimens’ Details

Five full-scale specimens are tested. The specimens are

RC beams with rectangular cross-section of 150 mm by

200 mm. The span between the supports is 2 m. All

beams have typical details that shown in Figure 3 with

two top longitudinal bars of No.10. and two bottom

longitudinal bars of No.14. CFRP sheets are fixed to the

beam surface inducing different configuration and

orientation angles as shown in Figure 4. CFRP sheets are

fixed obliquely to the half depth of the beam inducing

angles of 45˚ and 60˚ in specimens F-45 and F-60

respectively as shown in Figure 4. Specimens F-90 and F-

0 are strengthened with longitudinal and transverse CFRP

sheets inducing angles of 90˚ and 0˚ to the beam

longitudinal axis as shown in Figure 4.

columns cross-sections

Figure 3 Detailing of the Test Specimens.

90 degree

0 degree

60 degree

45 degree

Figure 4 Strengthening Configuration Scheme



III. Finite Element Modelling

Numerical analysis is a useful tool to predict the

behaviour of RC beams strengthened with CFRP sheets at

lower costs. Two finite element programs ABAQUS and

ANASYS are used in this research to predict the

behaviour of the strengthened beams. A comparison is

made between the numerical results obtained from the

two FE programs.

III.1. ABAQUS Software

Three dimensional full scale models are built in

ABAQUS to simulate the response of all test specimens.

After performing a sensitivity analysis, the selected mesh

shown in Figure 5 is used. Steel bars are embedded in

concrete with the same degree of freedom inducing

perfect bond between concrete and reinforcement.

Figure 5 Typical finite element mesh

Element Model

A general purpose linear brick element C3D8R, with

reduced integration (1 integration point), is used to model

concrete in ABAQUS. C3D8R is a three dimensional

element model with eight nodes. Steel reinforcement

elements are modelled using 2 noded -3D truss element

T3D2. Shell element (S4R), which is a 4-noded general

purpose element, is used to simulate the behaviour of

carbon fibre sheets CFRP. Cohesive, friction or tie

elements are usually used to model the bond between

concrete and CFRP sheets. In this study, concrete and

CFRP sheets are connected using ties. Tied contact in

ABAQUS ties two surfaces forming a contact pair

together for the duration of a simulation [16].

Concrete Material Model

Concrete damage plasticity model (CDP) is used in this

research to simulate the constitutive behaviour of

concrete. CDP model is based on the models proposed by

Lubliner et al. [17] and Lee and Fenves [18]. The model

is able to simulate the softening behaviour in concrete

where softening is accounted for using scalar damage

parameters and that control stress-strain relations.

The damage parameters take values from zero to one

where zero refers to the undamaged material and one

represents total loss of strength [19]. Many researchers

[17] [20] [21] suggested input parameters that required

for the CDP model in ABAQUS. In this study, the

damage parameters are selected to best fit the

experimental results. Based on a parametric study, the

plastic input parameters are taken as follows: dilation

angle 35˚, eccentricity 0.1, K 0.667 and fb0/fc0 1.16

Reinforcement Material Model

The elasto-plastic model is used to simulate the

constitutive behaviour of the main reinforcement and

stirrups in ABAQUS. The model assumes that the stress-

strain response is elastic perfectly plastic where

reinforcement does not harden after yielding.

CFRP Material Model

The constitutive behaviour of CFRP sheets is simulated

in this research using an elastic-perfectly plastic isotropic

model. The input parameters are: elastic modulus

(230,000 MPa), Poisson’s ratio (0.3), and ultimate tensile

strength (4900 MPa). CFRP sheet orientation angle is

simulated using ABAQUS material orientation option

which is used to define the material directions in

membrane, shell, and surface elements.

III.2. ANSYS Software

Three dimensional full scale models are built in ANSYS

to simulate the response of all test specimens. A

rectangular structural mesh is used for the RC beams with

an approximate mesh size of 3.7 cm as shown in Figure

6.

Figure 6 Typical finite element mesh

Concrete Element Model

Concrete behaviour is modelled using 3 dimensional 8-

noded solid element (SOLID65) [22]. The model is

capable to simulate cracking in three orthogonal

directions in tension, crushing in compression and plastic

and creep behaviour. Furthermore, the model

experiences plasticity before cracking and crushing

checks.



Reinforcement Element Model

Reinforcement is usually modelled in ANSYS using

LINK180. LINK180 is a three dimensional spar elemnet

with two nodes [22]. It is a truss element that cannot bend

and can support only uniaxial tension and compression

forces. Each node has three translational degrees of

freedom and the element is usually used to simulate the

behaviour of trusses, sagging cables, links, springs etc.

LINK180 can simulate large deflection.

CFRP Element model

Shell elements are usually used in ANSYS to simulate the

behaviour of carbon fiber sheets. A three dimenional 4-

noded shell element called (SHELL181) [22] is used to

simulate the beahviour of CFRP sheets in this research.

Each node has three translational and three rotational

degrees of freedom in the x, y, and z directions. The

orientaion angle of CFRP sheets are determined using

composites layer orientation angle option.

Material Model

The constitutive behaviour of concrete is defined using

multi-linear isotropic model that utilizes the von Mises

failure criterion with Willam and Warnke model [23] to

define the damage in concrete. The constitutive

behaviour of the reinforcement steel and stirrups is

simulated using bilinear isotropic material model which is

based on the von Mises failure criteria. The bilinear

model is elastic perfectly plastic model that does not

allow for hardening and it assumes that the material

response remains constant after yielding. The constitutive

behaviour of CFRP sheets is simulated using an elastic-

perfectly plastic isotropic model.

IV. Model Verification

The numerical finite element models generated by

ABAQUS and ANSYS are verified using the

experimental results of the test specimens. A comparison

is made between the load-displacement curves and cracks

pattern obtained from the numerical and experimental

responses in order to validate the FE model. The FE

model can satisfactorily predict the experimental

response of the test specimens. The load-displacement

curves obtained from the test results, ABAQUS FE

model and ANSYS FE model are shown in Figure 7 for

all test specimens where the numerical response is close

enough to the experimental response obtained from both

programs. The results obtained from ANSYS do not

include the softening branch in the simulation because

ANSYS doesn't support softening due to the negative

slope arising during convergence. Test results of the five

specimens are used to verify the proposed FE model.

V. Results and Discussion

The results are presented in this section with respect to

the load-deflection curve and cracks pattern. A

comparison is made between the experimental response

and numerical responses obtained from ABAQUS and

ANSYS finite element models.

V.1. Load-deflection curve

A comparison between the experimental and numerical

load-deflection curves of all test specimens is shown in

Figure 7. It is shown that the FE model can satisfactorily

predict the experimental load-deflection curves of all test

specimens. The FE model constructed in ABAQUS is

able to capture the softening branch in the RC beams

because concrete response is simulated using concrete

damage model that accounts for concrete softening using

damage parameters. The results obtained from ANSYS

do not include the softening branch in the simulation

because ANSYS doesn't support softening due to the

negative slope arising during convergence as mentioned

earlier.

It is shown in Figure 7 that the ultimate load of the

strengthened beams is slightly greater than that measured

in the control beam. The elastic stiffness obtained from

ABAQUS and ANSYS numerical response is slightly

greater than that obtained from the experimental response

as shown in Figure 7. The FE models constructed in

ABAQUS can satisfactorily predict the full experimental

response while that constructed in ANSYS can only

predict the response without the softening branch. Thus,

ANSYS model can satisfactorily predict the ultimate load

but it is unable to predict the ultimate deflection.

Experimental and numerical results have confirmed that

the orientation angle of CFRP sheets is significantly

important when strengthening RC beams. The results

have shown that the best performance is obtained when

using 45˚ inclined CFRP sheets followed by that

measured with 30˚ and 60˚ inclined CFRP sheets. An

additional flexural strength of 12% is measured in the

strengthened specimen F-45 compared to the control

beam. Test specimens strengthened with longitudinal and

transverse CFRP sheets have experienced less ductility,

flexural strength, and ultimate deflection compared to the

beams strengthened with inclined CFRP sheets. CFRP

sheets have increased the ultimate deflection of specimen

F-45 and F-60 that strengthened with inclined 45˚ and

60˚ CFRP sheets by 14% and 9 % respectively. By

contrast, CFRP sheets have reduced the deflection of RC

beams strengthened with transverse and longitudinal

CFRP sheets by 50 % and 34% respectively compared to

the control beam. CFRP sheets have reduced the ductility

of all strengthened beams where the reduction is most

remarkable in beams strengthened with longitudinal and

transverse CFRP sheets.



(a)

(b)

(c)

(d)

(e)

Figure 7 The experimental and numerical load-displacement curves of

test specimens

V.2. Crack pattern

A comparison is made in this section between the

numerical and experimental crack patterns for all test

specimens. Figure 8 compares between the experimental

crack pattern and the numerical one that is obtained from

ABAQUS while (j)

Figure 9 illustrates the experimental and the numerical

crack pattern obtained from ANSYS. The crack pattern

of the control beam is shown in Figure 8 and (j)

Figure 9 (a) and (b) for ABAQUS and ANSYS numerical

models respectively. The crack pattern of beam F0 is

shown in Figure 8 and (j)

Figure 9 (c) and (d) and that for beam F45 is shown in

Figure 8 and (j)

Figure 9 (e) and (f). The crack patterns in beam F60 is

shown in Figure 8 and (j)

Figure 9 (g) and (h) while that for beam F90 is illustrated

in Figure 8 and (j)

Figure 9 (i) and (j).

The FE model can reasonably predict the cracks pattern

and failure points of the test specimens. The red colour in

Figure 8 indicates to the points with severe tensile strains

(major cracks) and the light blue illustrates beams’ minor

cracks. (j)

Figure 9 illustrates the experimental and numerical crack

pattern obtained from ANSYS where the red colour

indicates to the first minor cracks, the green colour

represents the second crack and the blue colour refers to

the major third cracks.

(a)

(b)

(c)

(d)

(e)



(f)

(g)

(h)

(i)

(j)

Figure 8 The experimental and numerical (ABAQUS) crack patterns of

test specimens

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

Figure 9 The experimental and numerical (ANSYS) crack patterns of

test specimens

VI. Parametric Study

The FE models constructed in ABAQUS and ANSYS

can reasonably predict the experimental response as

investigated in the previous section. Experimental

programs simulate the actual behaviour of RC elements

and hence can accurately predict their actual response.

However, numerical analysis is beneficial in

understanding their behaviour at lower costs. Therefore, a

parametric study is extended in this section to investigate

the influence of other parameters on the response of RC

beams externally strengthened with CFRP sheets. The

selected parameters are CFRP orientation angle, CFRP

sheet thickness and CFRP sheet depth.

VI.1. Fiber orientation angles

Five FE models are constructed in ABAQUS and

ANSYS in order to investigate the effect of CFRP

orientation angle on the strengthened RC beams. The

models simulate the behaviour of RC beams strengthened

with CFRP sheets under different orientation angles

including 0˚, 30˚, 45˚, 60˚and 90˚. Figure 10 (a) and (b)

compare between the numerical load-deflection response

of RC beams strengthened using CFRP sheets under

different orientation angles using ABAQUS and ANSYS

respectively. CFRP sheets’ orientation angle has

significant influence on the RC beams’ ductility, energy,

stiffness, strength and deflection. The numerical

responses obtained from ABAQUS and ANSYS are close

to each other up to the maximum load. Softening is not

accounted for in ANSYS numerical model while

ABAQUS model is able to simulate the full response of

the strengthened RC beams.



The beams strengthened with inclined CFRP sheets (30˚,

45˚, 60˚) are more ductile and have higher accumulated

energy, deflection and strength compared to the other

beams strengthened with transverse and longitudinal

CFRP sheets. The best performance is obtained in beam

F45 with 45˚ inclined CFRP sheets followed by beam F-

30. By contrast, beam F-0 that strengthened with 0˚

CFRP sheet has the lowest deflection and energy

compared to the other beams. The deflection in beam F-

90 is slightly greater than that found in beam F-0.

However, the ultimate strength of beam F-0 is slightly

greater than that measured in beam F-90.

(a)

(a)

Figure 10 CFRP orientation angle effect (a) ABAQUS results (b)

ANSYS results

VI.2. Fiber sheet thickness

The influence of CFRP sheets thickness on the behaviour

of strengthened RC beams is investigated in this section.

Therefore, four FE models that simulate the behaviour of

RC beams strengthened with CFRP using different sheet

thicknesses are implemented in ABAQUS and ANSYS.

The selected sheets’ thicknesses are 0.111 mm, 0.167

mm, 0.255 mm and 0.337 mm. The FE model simulating

the response of RC beam strengthened with 45˚ inclined

CFRP sheet F-45 is selected for the numerical

comparison. (b)

Figure 11 a and b compare between ABAQUS and

ANSYS numerical response respectively simulated with

different CFRP sheet thicknesses. The numerical

responses obtained from ABAQUS and ANSYS are close

to each other up to the maximum load.

Sheet thickness has significant influence on the flexural

strength of strengthened RC beam. The greater the sheet

thickness, the higher the ultimate strength is. By contrast,

there is slight decrease in the deflection with the increase

of CFRP sheet thickness.

(a)

(b)

Figure 11 CFRP sheet thickness effect (a) ABAQUS results (b)

ANSYS results

VI.3. Fiber sheet depth

The influence of CFRP sheet depth covering the RC

beam is discussed in this section. Three FE models are

constructed in ABAQUS and ANSYS to simulate the

behaviour of RC beams strengthened with CFRP sheets

attached to the half, three-quarter and full depth of the

beam. The numerical responses obtained from ABAQUS

and ANSYS are close to each other up to the maximum

load.

Beam F-45 is selected for the parametric study. The

numerical results obtained from ABAQUS and ANSYS

are shown in (b)

Figure 12 a and b respectively. (b)

Figure 12 compares between the load-deflection curves of

strengthened beams with different CFRP sheet depths.

There is slight increase in the deflection and strength of

the strengthened RC beams with the increase of CFRP

depth covering the beam. The depth of CFRP sheet

covering the RC beam has slight influence on the strength

and deflection of the strengthened beams. It is beneficial

to increase the sheet thickness instead of increasing the

covering sheet depth in order to enhance the response of

strengthened RC beams.



(a)

(b)

Figure 12 CFRP sheet depth effect (a) ABAQUS results (b) ANSYS

results

VII. Conclusion

The flexural behaviour of RC beams strengthened with

CFRP sheets is investigated in this research. CFRP sheets

have fixed up to the half depth of beam inducing different

orientation including 0˚, 45˚, 60˚and 90˚. Numerical

finite (FE) element models are proposed in this research

using ABAQUS and ANSYS and verified using the

experimental results. The proposed FE models are able

predict the experimental load-deflection response and

crack pattern of the test specimens with reasonable

accuracy. A comparison is made between the

experimental results and the numerical results obtained

from ABAQUS and ANSYS. Furthermore, a parametric

study is performed in this research to investigate the

influence of CFRP sheets’ orientation angle, sheet depth

and sheet thickness on the behaviour of strengthened RC

beams. The following key points summarize the research

out comings:

The experimental and numerical results have

shown that the flexural strength of RC beams is

significantly influenced by CFRP orientation

angle.

CFRP sheets have slightly increased the ultimate

load of the test specimens. An additional

flexural strength and deflection of 12% and 14%

respectively are measured in Beam F-45

compared to the control specimen. The use of

45˚ inclined CFRP sheets has shown promising

results in strengthening RC beams.

The flexural strength measured in beams

strengthened with inclined CFRP sheets (30˚,

45˚, 60˚) is greater than that obtained in other

beams strengthened with longitudinal and

transverse CFRP sheets.

CFRP sheets have decreased the ultimate

deflection of the RC beams that strengthened

with transverse and longitudinal CFRP sheets by

50 % and 34% respectively compared to the

control beam.

CFRP sheets have reduced the ductility of beams.

The beams strengthened with inclined CFRP

sheets (30˚, 45˚, 60˚) are more ductile and have

higher accumulated energy, deflection and

strength compared to the other beams

strengthened with transverse and longitudinal

CFRP sheets.

Specimens strengthened with 45˚ inclined CFRP

sheets have the best performance while those

strengthened with 0˚ CFRP sheet has the lowest

deflection and energy compared to the other

beams.

The proposed FE models constructed in

ABAQUS can satisfactorily predict the full

experimental response while that constructed in

ANSYS can only predict the response without

the softening branch. Thus, ANSYS model can

satisfactorily predict the ultimate load but it is

unable to predict the ultimate deflection.

The elastic stiffness obtained from ABAQUS and

ANSYS numerical response is slightly greater

than that obtained from the experimental

response.

The numerical responses obtained from

ABAQUS and ANSYS are close to each other

up to the maximum load. Softening is not

accounted for in ANSYS numerical model while

ABAQUS model is able to simulate the full

response of the strengthened RC beams.

Sheet thickness has significant influence on the

flexural strength of strengthened RC beam. The

greater the sheet thickness, the higher the

ultimate strength is. By contrast, there is slight

decrease in the deflection with the increase of

CFRP sheet thickness.

The depth of CFRP sheet covering the RC beam

has slight influence on the strength and

deflection of the strengthened beams.

The FE model can satisfactorily predict the crack

pattern of RC beams. Strengthened specimens

remain coherent at failure. CFRP sheets have

postponed the appearance and propagation of

the cracks.

VIII. Acknowledgements

Technical comments of Dr.Wassel Al-Bodour and Eng.

Khaled Sadeq are acknowledged.



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X. Authors’ information 1,2 University of Jordan

Yasmin Murad, Ph.D., DIC.

Civil Engineering Department

Faculty of Engineering

The University of Jordan

Amman 11942, Jordan

Email: [email protected]

The educational background of Dr.Murad is

listed below:

PhD Structural Engineering, Imperial College London, London,

UK,2016

DIC, Diploma Imperial College London, UK

MSc Structural Engineering, University of Jordan, Amman,

Jordan,2010 (Excellent grade).

BSc Civil Engineering, University of Jordan, Amman, Jordan

(Excellent grade).

Dr. Murad is currently an assistant professor in civil Engineering

department at the University of Jordan. She is a judging team member

at the Ministry of Public Works and Housing for accreditation new

products. She is a team member in ABET accreditation program at the

University of Jordan. She is a member in the Jordan Engineers

Association (JEA).

.

mailto:[email protected]



Ja’afer Abu Zaid, MSc

The University of Jordan

Amman, Jordan 11942

Phone Number: + 962-79- 5703592

E-mail: [email protected]

The educational background of Mr. Ja’afer

is listed below:

Master’s Degree in Structural Engineering "Excellent"

Bachelor’s Degree in Civil Engineering "Very Good"

Mr.Ja’afer is a member in the Jordan Engineers Association (JEA).

mailto:[email protected]

Finite element modelling of reinforced concrete beams ...

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