Finite Element Modeling of Reinforced Concrete Beams Strengthened With FRP Laminates

8/3/2019 Finite Element Modeling of Reinforced Concrete Beams Strengthened With FRP Laminates

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European Journal of Scientific Research

ISSN 1450-216X Vol.30 No.4 (2009), pp.526-541

EuroJournals Publishing, Inc. 2009http://www.eurojournals.com/ejsr.htm

Finite Element Modeling of Reinforced Concrete Beams

Strengthened with FRP Laminates

Amer M. Ibrahim

Asst. prof, College of engineering

Diyala University, Iraq

Mohammed Sh. Mahmood

Asst. lecturer, College of engineering

Diyala University, Iraq

Abstract

In this paper an analysis model is presented for reinforced concrete beams

externally reinforced with fiber reinforced polymer (FRP) laminates using finite elements

method adopted by ANSYS. The finite element models are developed using a smearedcracking approach for concrete and three dimensional layered elements for the FRP

composites. The results obtained from the ANSYS finite element analysis are compared

with the experimental data for six beams with different conditions from researches (all beams are deficient shear reinforcement). The comparisons are made for load-deflection

curves at mid-span; and failure load. The results from finite element analysis were

calculated at the same location as the experimental test of the beams. The accuracy of the

finite element models is assessed by comparison with the experimental results, which are tobe in good agreement. The load-deflection curves from the finite element analysis agree

well with the experimental results in the linear range, but the finite elements results are

slightly stiffer than that from the experimental results. The maximum difference in ultimateloads for all cases is 7.8%.

Keywords: Finite Element Modeling; Reinforced Concrete Beams; FRP Laminates

IntroductionExternally bonded FRP laminates and fabrics can be used to increase the shear strength of reinforced

concrete beams and columns. Figure1 shows examples of possible FRP shear strengtheningconfigurations. It can be seen that the shear strength of columns can be easily improved by wrapping

with a continuous sheet of FRP to form a complete ring around the member. Shear strengthening ofbeams, however, is likely to be more problematic when they are cast monolithically with slabs. This

increases the difficulty of anchoring the FRP at the beam/slab junction and increases the risk of

debonding failure. Nevertheless, bonding FRP on either the side faces, or the side faces and soffit, will

provide some shear strengthening for such members. In both cases, it is recommended that the FRP is

placed such that the principal fiber orientation, , is either 45 or 90 to the longitudinal axis of themember. There is some evidence that the shear resistance of beams can be further improved by

bonding additional sheets with their fibers orientated at right angles to the principal fiber direction. In


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Finite Element Modeling of Reinforced Concrete Beams Strengthened with FRP Laminates 527

FRP-strengthened beams failure may occur due to beam shear, flexural compression, FRP rupture, FRPdebonding or concrete cover ripping

[1].

Figure 1: FRP shear strengthening configurations

(a) Vertical strips (b) Inclined strips

(c) Continuous

A concrete structure may need strengthening for many reasons:

To increase live-load capacity, e.g. of a bridge subject to increased vehicle loads or abuilding the use of which is to change from residential to commercial.

To add reinforcement to a member that has been under designed or wrongly constructed. To improve seismic resistance, either by providing more confinement to increase the strain

capacity of the concrete, or by improving continuity between members.

To replace or supplement reinforcement, e.g. damaged by impact or lost due to corrosion. To improve continuity, e.g. across joints between precast members.In most cases it is only practical to increase the live-load capacity of a structure. However, in

some situations it may be possible to relieve dead load, by jacking and propping, prior to the

application of the additional reinforcement. In these cases, the additional reinforcement will play itspart in carrying the structures dead load. Three basic principles underlie the strengthening of concrete

structures using fiber composite materials, which are the same irrespective of the type of structure:

Increase the bending moment capacity of beams and slabs by adding fiber compositematerials to the tensile face.

Increase the shear capacity of beams by adding fiber composite materials to the sides inthe shear tensile zone.

Increase the axial and shear capacity of columns by wrapping fiber composite materialsaround the perimeter.

In the last decade, fiber reinforced polymer FRP composites have been used for strengthening

structural members of reinforced concrete bridges, which are deficient or obsolete due to changes intheir use or consideration of increased loadings [2]. Many researchers have found that FRP composites

applied to the reinforced concrete members provide efficiency, reliability and cost effectiveness in

rehabilitation[3-4-5]

.A large number of available software like sap2000, LUSAS, and ANSYS etc incorporate finite

elements based analysis. In this paper an attempt has been made with ANSYS (version 10)[6]

software

to bring into focus the versatility and powerful analytical capabilities of finite elements technique by

objectively modeling the complete response of test beams. The finite elements model uses a smearedcracking approach to model the reinforced concrete and three dimensional layered elements to model

the fiber reinforced polymer FRP composites. This model can help to confirm the theoretical

calculations as well as to provide a valuable supplement to the laboratory investigation of behavior.


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528 Amer M. Ibrahim and Mohammed Sh. Mahmood

Finite Element ModelingThe finite elements analysis calibration study included modeling a reinforced concrete beams with thedimensions and properties corresponding to beams tested in previous researches

[7-8].

Concrete

Solid65 element was used to model the concrete. This element has eight nodes with three degrees of

freedom at each node translations in the nodal x, y, and z directions. This element is capable ofplastic deformation, cracking in three orthogonal directions, and crushing. A schematic of the elementis shown in Figure2

[6]. Smeared cracking approach has been used in modeling the concrete in the

present study[9]

.

Figure 2: Solid65 element geometry.

The following properties must be entered in ANSYS:

Elastic modulus (Ec). Ultimate uniaxial compressive strength ( ). Ultimate uniaxial tensile strength (modulus of rupture,fr) [10] Poissons ratio () = 0.2. Shear transfer coefficient (t) which is represents conditions of the crack face. The value of

t ranges from 0.0 to 1.0, with 0.0 representing a smooth crack (complete loss of shear

transfer) and 1.0 representing a rough crack (no loss of shear transfer)[6]

. The shear transfercoefficient used in present study varied between 0.3 and 0.4

Compressive uniaxial stress-strain relationship for concrete.The present study assumed that the concrete is a homogeneous and initially isotropic. The

compressive uniaxial stress-strain relationship for concrete model is obtained by using the followingequations to compute the multilinear isotropic stress-strain curve for the concrete is as shown in

Figure3.

(1)

2

1

+

=

o

cc

Ef

for 1 (2)'cc ff = for cu (3)


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c

'c

oE

f2=

4)

The simplified stress-strain curve for each beam model is constructed from six points connected

by straight lines. The curve starts at zero stress and strain. Point 1, at , is calculated for thestress-strain relationship of the concrete in the linear range (must satisfy Hookes law). Points 2, 3, and

4 are obtained from Equation 2, in which o is calculated from Equation 4. Point 5 is at o and . Thebehavior is assumed to be perfectly plastic after point 5.

Figure 3: Simplified compressive uniaxial stress-strain curve for concrete.

1 2 3 4 5 -+

Reinforcing steel

Modeling of reinforcing steel in finite elements is much simpler than the modeling of concrete. A

Link8 element was used to model steel reinforcement. This element is a 3D spar element and it has twonodes with three degrees of freedom translations in the nodal x, y, and z directions. This element is

also capable of plastic deformation. This element is shown in Figure4[6]

. A perfect bond between the

concrete and steel reinforcement considered. However, in the present study the steel reinforcing wasconnected between nodes of each adjacent concrete solid element, so the two materials shared the same

nodes. The same approach was adopted for FRP composites.

Figure 4: Link8 element geometry.

Steel reinforcement in the experimental beams was constructed with typical steel reinforcingbars. Elastic modulus and yield stress for the steel reinforcement used in this FEM study follow the

design material properties used for the experimental investigation. The steel for the finite element

models is assumed to be an elastic-perfectly plastic material and identical in tension and compressionas shown inFigure5. A Poissons ratio of 0.3 is used for the steel reinforcement.


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Figure 5: Stress-strain curve for steel reinforcement

Steel plate

Steel plates were added at support and loading locations in the finite element models (as in the actualbeams) in order to avoid stress concentration problems. An elastic modulus equal to 200,000 N/mm

2

and Poissons ratio of0.3 were used for the plates. The steel plates were assumed to be linear elastic

materials. A Solid 45 element was used to model steel plates. The geometry and node locations for thiselement type are shown inFigure 6

[6].

Figure 6: Solid 45 element geometry.

FRP Laminates

FRP composites are materials that consist of two constituents. The constituents are combined at amacroscopic level and are not soluble in each other. One constituent is the reinforcement, which is

embedded in the second constituent, a continuous polymer called the matrix. The reinforcing material

is in the form of fibers, i.e., carbon and glass, which are typically stiffer and stronger than the matrix.The FRP composites are orthotropic materials; that is, their properties are not the same in all directions.

Figure 7shows a schematic of FRP composites.


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Figure 7: Schematic of FRP composites.

A Solid 46 layered element was used to model FRP composites. The high strength of the epoxy

used to attach FRP sheets to the experimental beams supported the perfect bond assumption. The

geometry and node locations for this element type are shown in Figure 8[6]

.

Figure 8: Solid 46 layered element geometry.

In the present study linear elastic properties of FRP composites are assumed as shown inFigure

9. A summary of material properties for FRP composites used for the finite elements modeling of the

strengthened beams in the present study is shown in Table 1.


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Figure 9: Stress-strain curves for the FRP composites in the direction of the fibers.

Table 1: Summary of material properties for FRP composite.

FRP composite Elastic modulusN /mm2 Major Poissons ratio Shear modulusN /mm2

Carbon fiber reinforcedpolymer CFRP

Glass fiber reinforcedpolymer GFRP

Numerical AnalysisIn order to validate the numerical representation of the reinforced concrete beams strengthening with

fiber reinforced polymer composites, the finite elements representation using ANSYS program has

been applied to practical sections and the results will be compared with the experimental results

reported by previous researches[7-8].

Geometry and materials properties.

Six beams with different conditions (all beams are deficient shear reinforcement) will be analyzed

using the proposed ANSYS finite elements model. Table2 shows all beams evaluated in the present

study.

Table 2: Summary of beams evaluated in the present study.

Symbol Description FRP Laminates thickness (mm)

B1 As built beam (control beam)[7]. ----

B1C-90 Strengthen by one layer of unidirectional transverse carbon/epoxylaminates CFRP inclined at an angle of90to the longitudinal axis [7].

1.6

B1G-90Strengthen by two layers of unidirectional transverse E-glass/epoxy

laminates GFRP inclined at an angle of90to the longitudinal axis [7].2.1

B2 As built beam (control beam) [8]. ----

B2C-90Strengthen by warping with one layer of CFRP inclined at an angle of90to the longitudinal axis[8].

0.18

B2C-90-0

Strengthen by warping with one layer of CFRP inclined at an angle of

90with an additional layer of CFRP on both sides of the web

inclined at an angle of 0o to the longitudinal axis[8].

0.18


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The geometry of all beams is shown in Figure 10, and the material properties adopted in theanalysis are given in Table 3.

Figure 10: Loading reigns and geometrical properties of analyzed beams.

0.37m 0.37m1.7m

0.5P0.5P

2.44m

3.62m

0.15m

210

[email protected] 0.25m

(a) Dimension and reinforcement of as built beam B1.

0.37m 0.37m1.7m

0.5P0.5P

2.44m

3.62m

0.15m

0.41m 0.05m0.05m 0.41m

(b) Shear strengthening details for beams B1C-90, and B1G-90.

FRPFRP

0.915mP

1.83m

2.134m

0.23m

29

225

[email protected] 0.38m

(c) Dimension and reinforcement of as built beam B2.

0.915m


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Table 3: Summary of Material Properties of Selected Beams

B1, B1C-90 & B1G-90 B2, B2C-90 & B2C-90-0

Steel yield strengthfy(N/mm2) 420 414

Steel modulus of elasticityEs(N/mm2) 200000 200000

Steel Poisson's ratio vs 0.3 0.3

Concrete compressive strength (N/mm2) 27.54 31

Concrete Poisson's ratio vc 0.2 0.2

Due to the symmetry in cross-section of the concrete beam and loading, symmetry was utilized

in the finite elements analysis; only one quarter of the beam was modeled. This approach reducedcomputational time and computer disk space requirements significantly. The finite element mesh,

boundary condition and loading regions of all beams are shown inFigure11.

Figure 11: Finite element mesh, boundary condition and loading regions for a quarter beam model of all beams

a. Finite element modeling for B1C-90 & B1G-90

Loading steel plate

FRP composite

Supporting steel plate


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c .Stee l reinforc em ent for B1, B1C-90 & B1G-90

Stirrups 10@ 0.6m

12tension

reinforcement

10compression

reinforcement

d.Steel reinforc em ent for a B2, B2C-90 & B2C-90-0

Stirrups 9@ 0.3m

25tension

reinforcement

9 compression

reinforcement

Discussion of ResultsLoad deflection curves

The experimental and numerical load-deflection curves obtained for the beams are illustrated inFigure11. The curves show good agreement in finite element analysis with the experimental resultsthroughout the entire range of behavior and failure mode, for all beams the finite element model is

stiffer than the actual beam in the linear range. Several factors may cause the higher stiffness in the

finite element models. The bond between the concrete and steel reinforcing is assumed to be perfect(no slip) in the finite element analyses, but for the actual beams the assumption would not be true slip

occurs, therefore the composite action between the concrete and steel reinforcing is lost in the actualbeams. Also the microcracks produced by drying shrinkage and handling are present in the concrete to

some degree. These would reduce the stiffness of the actual beams, while the finite element models do

not include microcracks due to factors that are not incorporated into the models. After the initiation of

flexural cracks, the beam stiffness was reduced and the linear load deflection behavior ended whenthe internal steel reinforcement began to yield.


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Figure11: Load deflection curves.

a. Load deflection curve for beam B1.

b. Load deflection curve for beam B1C-90.


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c. Load deflection curve for beam B1G-90.

d. Load deflection curve for beam B2C-90.


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e. Load deflection curve for beam B2C-90-0.

As shown inFigure11 a ,b, and c, the strengthened beams B1C-90 and B1G-90 are stiffer thanthe control beam B1, but B1C-90 appear stiffer than B1G-90 which means that carbon fiber polymer is

better than glass fiber polymer in strengthening the reinforced concrete beams for shear. Figure11 d,and e indicate that the using of additional layer of carbon fiber polymer composite to both side of thebeam web inclined at an angle of0to the longitudinal axis increase the stiffness of the beam by 2.3% ,

so that the additional layer is not sufficient to increase the beam stiffness.

Crack PatternThe ANSYS program records a crack pattern at each applied load step.Figure12 shows evolutions of

crack patterns developing for each beam at the last loading step. ANSYS program displays circles atlocations of cracking or crushing in concrete elements. Cracking is shown with a circle outline in the

plane of the crack, and crushing is shown with an octahedron outline. The first crack at an integration

point is shown with a red circle outline, the second crack with a green outline, and the third crack with

a blue outline[6]

.


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Figure 12: Evolution of Crack Patterns.

B1

B1C-90

B1G-90

B2

B2C-90

B2C-90-0

The failure modes of the finite element models show good agreement with observations anddata from the experimental full-scale beams. The addition of FRP reinforcement to the control beam


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shifts the behavior of the beams from a shear failure near the ends of the beam to flexure failure at themidspan.

Failure load

The failure load obtained from the numerical solution for all beams is slightly smaller than

experimental load. The final loads for the finite element models are the last applied load step before the

solution diverges due to numerous cracks and large deflections. Table4 shows comparison between theultimate loads of the experimental beams and the final loads from the finite element models, and the

ultimate capacity of the strengthened beams with ultimate capacity of the control beams.

Table 4: Comparsions between experimental and finite element ultimate loads, and ultimate capacity of the

strengthened beams with ultimate capacity of the control beams.

BeamExperimental ultimate

load (kN)

Numerical ultimate

load (kN)

%

Difference

Increased in ultimate load of

strengthened

B1 69 66 4.3 1

B1C-90 125 119 4.8 1.6

B1G-90 116 107 7.8 1.8

B2 416 405 2.6 1

B2C-90 435 414 4.8 1.02

B2C-90-0 445 420 5.6 1.03

ConclusionsThe numerical solution was adopted to evaluate the ultimate shear strength of the reinforced concrete

beams reinforced with FRP laminates in simple, cheap and rapid way compared with experimental full

scale test. The general behaviors of the finite element models show good agreement with observations

and data from the experimental full-scale beam tests. The addition of FRP reinforcement to the controlbeam shifts the behavior of the control beams from shear failure near the ends of the beam to flexure

failure at the midspan. The results obtained demonstrate that carbon fiber polymer is efficient more

than glass fiber polymer in strengthening the reinforced concrete beams for shear. The present finiteelement model can be used in additional studies to develop design rules for strengthening reinforced

concrete members using FRP laminates.


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References[1] Esfahani MR, et al. Flexural behaviour of reinforced concrete beams strengthened by CFRP

sheets. Engineering Structures (2007), doi:10.1016/j.engstruct.2006.12.008

[2] M. A. Shahawy, M. Arockiasamy, T. Beitelman and R. Sowrirajan (1996) Reinforced concreterectangular beams strengthened with CFRP laminates, composite part B: engineering , volume27, Issues 3-4, pages 225-223, doi:10.1016/1359-8368(95)00044-5.

[3] O. Rabinovitch and Y. Frostig (2003) Experiments and analytical comparison of RC beamsstrengthened with CFRP composites, composite part B: engineering, volume 34, Issues 8, 1996,pages 663-677, doi:10.1016/S1359-8368(03)00090-8.

[4] Dong-Suk Yang, Sun-Kyu Park and Kenneth W. Neale (2008) Flexural behavior of reinforcedconcrete beams strengthened with prestressed carbon composites, composite part B:

engineering , volume 88, Issues 4, pages 497-508, doi:10.1016/j.compstruct.2008.05.016.

[5] Hsuan-Teh Hu, Fu-Ming Lin, Yih-Yuan Jan, (2004) Nonlinear finite element analysis ofreinforced concrete beams strengthened by fiber-reinforced plastics, Composite Structures 63,

pp 271281, doi:10.1016/S0263-8223(03)000174-0.

[6] ANSYS Manual, Version (10.0).[7] Ayman S.Mosallam, Swagata Banerjee,(2007) Shear enhancement of reinforced concrete

beams strengthened with FRP composite laminates, ScienceDirect, Composite: part B38,

pp781-793 doi:10.1016/j.compstruct b.2006.10.002.[8] P. Alagusundaramoorthy, I. E. Harik, and C.C. Choo,(2002) Shear strength of R/C beams

wrapped with CFRP fabric Kentucky transportation center, college of engineering, 2002, KTC-

02-14/SPR200-99-2F.

[9] H. B. Pham, R. Al-Mahaidi and V. Saouma (2006) Modeling of CFRP- concrete bond usingsmeared and discrete cracks, composite structures, volume 75, Issues 1-4, pages 145-150,

Thirteen International Conference on Composite Structures

ICCS/13doi:10.1016/j.compstruct.2006.04.039.[10] ACI 318m-05, American Concrete Institute,(2005) Building Code Requirements for Reinforced

Concrete, American Concrete Institute, Farmington Hills, Michigan.

Nomenclature

(N/mm2) Ultimate uniaxial compressive strength

(N/mm2) Concrete elastic modulus Ec

(N/mm2) Steel elastic modulus Es(N/mm2) stress at any strain c

(N/mm2) Concrete modulus of rupture fr

Shear transfer coefficient t

Strain

strain corresponding to ( ) 1

ultimate compressive strain cu

Strain at the ultimate compressive strength oConcrete Poissons ratio c

Steel Poissons ratio s

Finite Element Modeling of Reinforced Concrete Beams Strengthened With FRP Laminates

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