Finite Element Modeling of Reinforced Concrete Beams Strengthened With FRP Laminates

European Journal of Scientific Research ISSN 1450-216X Vol.30 No.4 (2009), pp.526-541 © EuroJournals Publishing, Inc. 2009 http://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 smeared cracking 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 to   be 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 ultimate loads for all cases is 7.8%.

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

Introduction Externally 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 strengthening configurations. 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 of   beams, 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 45º or 90º to the the longitudinal axis of the member. 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

Finite Element Modeling of Reinforced Concrete Beams Strengthened with FRP Laminates

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FRP-strengthened beams failure may occur due to beam shear, flexural compression, FRP rupture, FRP [1] debonding or concrete cover ripping . Figure 1: FRP shear strengthening configurations

(b) Inclined strips

(a) Vertical 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 a  building 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 its  part 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 composite materials to the tensile face. • Increase the shear capacity of beams by adding fiber composite materials to the sides in the shear tensile zone. • Increase the axial and shear capacity of columns by wrapping fiber composite materials around 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 in [2] their use or consideration of increased loadings . Many researchers have found that FRP composites applied to the reinforced concrete members provide efficiency, reliability and cost effectiveness in [3-4-5] rehabilitation . A large number of available software like sap2000, LUSAS, and ANSYS etc incorporate finite [6] elements based analysis. In this paper an attempt has been made with ANSYS (version 10) 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 smeared cracking 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 behav ior.

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Amer M. Ibrahim and Mohammed Sh. Mahmood

Finite Element Modeling The finite elements analysis calibration study included modeling a reinforced concrete beams with the [7-8] dimensions and properties corresponding to beams tested in previous researches . 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 of   plastic deformation, cracking in three orthogonal directions, and crushing. A schematic of the element [6] is shown in  Figure2 . Smeared cracking approach has been used in modeling the concrete in the [9]  present study . Figure 2: Solid65 element geometry.

The following properties must be entered in ANSYS: • Elastic modulus ( E c). • Ultimate uniaxial compressive strength ( ).

• • •

[10]

Ultimate uniaxial tensile strength (modulus of rupture, f r ) Poisson’s ratio (ν) = 0.2. Shear transfer coefficient ( β t)  which is represents conditions of the crack face. The value of   β t  ranges from 0.0 to 1.0, with 0.0 representing a smooth crack (complete loss of shear  [6] transfer) and 1.0 representing a rough crack (no loss of shear transfer) . The shear transfer  coefficient 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 following equations to compute the multilinear isotropic stress-strain curve for the concrete is as shown in  Figure3. (1)

 f c =

 E c

ε 

⎛  ε   ⎞ 1 + ⎜⎜ ⎟⎟ ⎝ ε o  ⎠

 f c =  f c' 

2

for  for 

ε 

1

ε 

°

≤ ε  ≤ ε °

≤ ε  ≤ ε cu

(2) (3)

Finite Element Modeling of Reinforced Concrete Beams Strengthened with FRP Laminates

ε o

=

529

2 f c' 

 E c

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 the stress-strain relationship of the concrete in the linear range (must satisfy Hooke’s law). Points 2, 3, and 4 are obtained from Equation 2, in which εo is calculated from Equation 4. Point 5 is at εo and . The  behavior is assumed to be perfectly plastic after point 5. Figure 3: Simplified compressive uniaxial stress-strain curve for concrete.

+ε 

ε 

ε 

ε 

ε 

ε 

- ε 

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 two nodes with three degrees of freedom – translations in the nodal x, y, and z directions. This element is [6] also capable of plastic deformation. This element is shown in Figure4 . A perfect bond between the concrete and steel reinforcement considered. However, in the present study the steel reinforcing was connected 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 reinforcing   bars. 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 compression as shown in Figure5. A Poisson’s ratio of 0.3 is used for the steel reinforcement.

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Amer M. Ibrahim and Mohammed Sh. Mahmood 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 actual 2  beams) in order to avoid stress concentration problems. An elastic modulus equal to 200,000 N/mm and Poisson’s ratio of 0.3 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 this [6] element type are shown in Figure 6  . Figure 6: Solid 45 element geometry.

FRP Laminates

FRP composites are materials that consist of two constituents. The constituents are combined at a macroscopic 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 7 shows a schematic of FRP composites.

Finite Element Modeling of Reinforced Concrete Beams Strengthened with FRP Laminates

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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 [6] geometry and node locations for this element type are shown in Figure 8 . Figure 8: Solid 46 layered element geometry.

In the present study linear elastic properties of FRP composites are assumed as shown in Figure 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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Amer M. Ibrahim and Mohammed Sh. Mahmood 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 modulus N /mm 2

Major Poisson’s ratio

Shear modulus N /mm 2

Carbon fiber reinforced  polymer CFRP Glass fiber reinforced  polymer GFRP

Numerical Analysis In 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 [7-8] reported by previous researches . 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: Symbol B1

B1C-90 B1G-90 B2 B2C-90 B2C-90-0

Summary of beams evaluated in the present study. Description As built beam (control beam)[7]. Strengthen by one layer of unidirectional transverse carbon/epoxy laminates CFRP inclined at an angle of 90º to the longitudinal axis [7]. Strengthen by two layers of unidirectional transverse E-glass/epoxy laminates GFRP inclined at an angle of 90º to the longitudinal axis [7]. As built beam (control beam) [8]. Strengthen by warping with one layer of CFRP inclined at an angle of  90º to the longitudinal axis[8]. Strengthen by warping with one layer of CFRP inclined at an angle of  90º with an additional layer of CFRP on both sides of the web inclined at an angle of 0o to the longitudinal axis[8].

FRP Laminates thickness (mm) ----

1.6 2.1 ---0.18 0.18

Finite Element Modeling of Reinforced Concrete Beams Strengthened with FRP Laminates

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The geometry of all beams is shown in   Figure 10, and the material properties adopted in the analysis are given in Table 3. Figure 10: Loading reigns and geometrical properties of analyzed beams. 0.5P

0.5P 0.37m

0.37m

1.7m

Φ[email protected]

2 Φ10

0.25m

2 Φ13

0.15m

2.44m 3.62m (a) Dimension and reinforcement of as built beam B1.

0.5P

0.5P 0.37m

1.7m

FRP 0.05m

0.15m

0.37m

FRP 0.41m

0.41m

0.05m

2.44m 3.62m (b) Shear strengthening details for beams B1C-90, and B1G-90.

P 0.915m

0.915m

Φ[email protected]

2Φ9 2Φ25

1.83m 2.134m (c) Dimension and reinforcement of as built beam B2.

0.23m

0.38m

534 Table 3:

Amer M. Ibrahim and Mohammed Sh. Mahmood Summary of Material Properties of Selected Beams

2

Steel yield strength f  y (N/mm  ) Steel modulus of elasticity E  s (N/mm2 ) Steel Poisson's ratio v s Concrete compressive strength Concrete Poisson's ratio vc

(N/mm2 )

B1, B1C-90 & B1G-90 420 200000 0.3 27.54 0.2

B2, B2C-90 & B2C-90-0 414 200000 0.3 31 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 reduced computational time and computer disk space requirements significantly. The finite element mesh,  boundary condition and loading regions of all beams are shown in Figure11. Figure 11: Finite element mesh, boundary condition and loading regions for a quarter beam model of all beams

Loading steel plate

FRP composite Supporting steel plate

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

Finite Element Modeling of Reinforced Concrete Beams Strengthened with FRP Laminates

535

Φ10 compression

reinforcement Stirrups

Φ10@

0.6m

Φ12 tension

reinforcement

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

compression reinforcement Φ9

Stirrups

Φ9@

0.3m

Φ25 tension

reinforcement

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

Discussion of Results Load deflection curves

The experimental and numerical load-deflection curves obtained for the beams are illustrated in  Figure11. The curves show good agreement in finite element analysis with the experimental results throughout 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 actual  beams. 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 when the internal steel reinforcement began to yield.

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Amer M. Ibrahim and Mohammed Sh. Mahmood Figure11: Load deflection curves.

a. Load deflection curve for beam B1.

 b. Load deflection curve for beam B1C-90.

Finite Element Modeling of Reinforced Concrete Beams Strengthened with FRP Laminates c. Load deflection curve for beam B1G-90.

d. Load deflection curve for beam B2C-90.

537

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Amer M. Ibrahim and Mohammed Sh. Mahmood e. Load deflection curve for beam B2C-90-0.

As shown in Figure11 a ,b, and c, the strengthened beams B1C-90 and B1G-90 are stiffer than the 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 the  beam web inclined at an angle of 0º to 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 Pattern

The 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 at locations 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 [6] a blue outline .

Finite Element Modeling of Reinforced Concrete Beams Strengthened with FRP Laminates

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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 and data from the experimental full-scale beams. The addition of FRP reinforcement to the control beam

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Amer M. Ibrahim and Mohammed Sh. Mahmood

shifts the behavior of the beams from a shear failure near the ends of the beam to flexure failure at the midspan. 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 the ultimate loads of the experimental beams and the final loads from the finite element models, and the ultimate capacity of the strengthened beams with ultimate capac ity of the control beams. Table 4:

Beam

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

Comparsions between experimental and finite element ultimate loads, and ultimate capacity of the strengthened beams with ultimate capacity of the control beams. Experimental ultimate load (kN) 69 125 116 416 435 445

Numerical ultimate load (kN) 66 119 107 405 414 420

% Difference 4.3 4.8 7.8 2.6 4.8 5.6

Increased in ultimate load of  strengthened 1 1.6  1.8 1 1.02 1.03

Conclusions The 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 control  beam 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 finite element model can be used in additional studies to develop design rules for strengthening reinforced concrete members using FRP laminates.

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[3]

[4]

[5]

[6] [7]

[8]

[9]

[10]

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 M. A. Shahawy, M. Arockiasamy, T. Beitelman and R. Sowrirajan (1996) Reinforced concrete rectangular beams strengthened with CFRP laminates, composite part B: engineering , volume 27, Issues 3-4, pages 225-223, doi:10.1016/1359-8368(95)00044-5. O. Rabinovitch and Y. Frostig (2003) Experiments and analytical comparison of RC beams strengthened with CFRP composites, composite part B: engineering, volume 34, Issues 8, 1996,  pages 663-677, doi:10.1016/S1359-8368(03)00090-8. Dong-Suk Yang, Sun-Kyu Park and Kenneth W. Neale (2008) Flexural behavior of reinforced concrete 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. Hsuan-Teh Hu, Fu-Ming Lin, Yih-Yuan Jan, (2004) Nonlinear finite element analysis of  reinforced concrete beams strengthened by fiber-reinforced plastics, Composite Structures 63,  pp 271–281, doi:10.1016/S0263-8223(03)000174-0. ANSYS Manual, Version (10.0). 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. 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, KTC02-14/SPR200-99-2F. H. B. Pham, R. Al-Mahaidi and V. Saouma (2006) Modeling of CFRP- concrete bond using smeared 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. ACI 318m-05, American Concrete Institute,(2005) Building Code Requirements for Reinforced Concrete, American Concrete Institute, Farmington Hills, Michigan.

Nomenclature (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) (N/mm 2 ) (N/mm 2 )

Ultimate uniaxial compressive strength Concrete elastic modulus Steel elastic modulus stress at any strain Concrete modulus of rupture Shear transfer coefficient Strain ε

strain corresponding to ( ultimate compressive strain

)

Strain at the ultimate compressive strength Concrete Poisson’s ratio Steel Poisson’s ratio

 E c  E  s ƒc  f r   β t   Ε  ε1 εcu εo νc ν s