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Finite element modeling of RC deep beams strengthened in shear with CFRP strips

Mitali R. Patel and Tejendra Tank

Carbon Fibre Reinforced Polymer (CFRP) and steel plates are adopted for strengthening of structural elements such as beams and columns. The strengthening of deep beams in particular becomes more cumbersome, as deep beam usually fails in shear. This paper aims to present an analytical model of reinforced concrete deep beam strengthened in shear with externally bonded CFRP strips using an FEM based software. Eight different cases of deep beams with same configuration have been considered with three different strengthening mechanisms. The Objective of this paper is to find out the best shear strengthening mechanism for strengthening of reinforced concrete deep beams. The results of analytical model are compared with the experimental work carried out in past and show an excellent correlation with the experimental work.

I. InTRoducTIon

Strengthening of structural elements such as beams and columns has become vital now-a-days due to many unavoidable circumstances such as revised loading conditions change in occupancy conditions and deterioration of existing structure due to environmental effects. Strengthening of structural elements by externally bonded FRP laminates is very effective technique adopted successfully worldwide [1]. Externally bonded FRP laminates can be used to increase the shear strength of reinforced concrete beams and columns [2]. Figure 1 shows the possible strengthening mechanisms. It can be seen that strengthening of column can be easily achieved by wrapping the column with continuous FRP sheets to form

a complete ring around the column. But strengthening of beams sometimes becomes more problematic as they are cast monolithically with the slabs. Although bonding of FRP on the either side of beams or at the soffit does provide some shear strengthening to the beams [3]. Many

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researchers have found that the FRP laminates applied to the reinforced concrete element provides efficiency, reliability and cost effectiveness in rehabilitation [4].

A large number of software available in market incorporate finite element based analysis [5]. In this paper, an attempt has been made using FEM based software to bring into focus, the versatility and powerful analytical capabilities of finite element technique by objectively modelling the complete response of test beams. This model can help to confirm to the laboratory investigation of the behaviour of deep beams.

In this paper, total eight Deep beams having same configuration are considered with three possible strengthening mechanisms as shown in Figure 1. In all mechanisms, CFRP strips are applied on both the sides of the Deep beam considered, to strengthen the beam against shear.

II. FInITe eleMenT ModellIng

The finite element analysis calibration study included modelling reinforced concrete deep beams in the software considering the dimensions and properties corresponding to experimental work for analysis of deep beams carried out by previous researcher [6]. Following are the steps of analysis followed in the software.

(A) Engineering data

1. Concrete Nonlinear

The concrete material requires the linear isotropic elasticity and multi-linear isotropic hardening properties to depict the exact concrete nonlinear behavior [7]. The present study assumed that the concrete is homogeneous and initially isotropic. The compressive uniaxial stress-strain relationship for concrete nonlinear is obtained by using the following equations to compute the multi-linear isotropic stress-strain curve for the concrete nonlinear and is as shown in Figure 2.

ε εε= ≤ ≤

ε ε ε εεε

=

≤ ≤+

ε ε ε= ≤ ≤

ε =

ε εε= ≤ ≤

ε ε ε εεε

=

≤ ≤+

ε ε ε= ≤ ≤

ε =

...(1)

ε εε= ≤ ≤

ε ε ε εεε

=

≤ ≤+

ε ε ε= ≤ ≤

ε =

ε εε= ≤ ≤

ε ε ε εεε

=

≤ ≤+

ε ε ε= ≤ ≤

ε =

...(2)

ε εε= ≤ ≤

ε ε ε εεε

=

≤ ≤+

ε ε ε= ≤ ≤

ε =

ε εε= ≤ ≤

ε ε ε εεε

=

≤ ≤+

ε ε ε= ≤ ≤

ε =

...(3)

ε εε= ≤ ≤

ε ε ε εεε

=

≤ ≤+

ε ε ε= ≤ ≤

ε =

...(4)

The simplified stress-strain curve for each deep beam model is as shown in Figure 2. The curve starts at zero stress and strain. Point 1, at 0.3 f ’c is calculated for the stress-strain relationship of the concrete in the linear range which is the elastic zone where stress is proportional to strain (material obeys Hook’s law which states that within elastic limit, stress is proportional to strain [8]. Thereafter the material enters plastic zone, from where material behaviour is non-linear). Points 2, 3 and 4 are obtained from Equation 2, in which ε0 is calculated from Equation 4. Point 5 and is at ε0 and f’c. The behaviour is assumed to be perfectly plastic after point 5. Table 1 shows concrete nonlinear property. Concrete non-linear material selected here adopts the smeared crack analogy for cracking of concrete in tension zone [9].

2. Structural steel

For structural steel, linear isotropic and bilinear kinematic hardening properties are required. Bilinear kinematic

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Table 1. Properties of concrete nonlinearDensity 2300 kg/m3

Reference temperature 25⁰C

Linear Isotropic

Modulus of elasticity (Ec) 3×104 MPa

Poisson’s ratio (µ) 0.2

Multi-linear Isotropic

Strain (mm/mm) Stress (MPa)

1. 0 0

2. 0.0004 12.41

3. 0.0008 22.414

4. 0.0015 35.01

5. 0.0023 40.825

6. 0.00268 41.39

7. 0.00272 41.4

Table 2. Properties of structural steelDensity 7850 kg/m3

Reference temperature 250c

Thermal expansion 1.2×10-5 /0c

Linear Isotropic

Modulus of elasticity (ES) 2×105 MPa

Poisson’s ratio(µ) 0.3

Bilinear Kinematic Hardening

Yield stress ( fy ) 413.68 MPa

Tangent modulus (E’s) 2×103 MPa

Table 3. Properties of CFRP laminatesDensity 1.6 gm/cm3

Poisson’s ratio 0.183

Modulus of elasticity 160000 MPa

Tensile yield strength 2800 MPa

Tensile ultimate strength 3050 MPa

Table 4. Properties of epoxy adhesiveDensity 1800 kg/m3

Poisson’s ratio 0.22

Modulus of elasticity 165000 MPa

Tensile yield strength 30 MPa

Compressive ultimate strength 95 MPa

Thermal expansion co-efficient 2.5×10-5/0c

hardening property for steel are required due to plastic behaviour of structural steel. The bilinear hardening property requires the yield stress of steel and hardening modulus of steel. To obtain the hardening modulus of steel or tangent modulus of steel after yielding, E’s = 0.01Es. Figure 3 shows the stress strain for reinforcing or structural steel. Table 2 shows the properties of structural steel.

3. CFRP laminates

FRP composites are material that consists 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 carbon fibres, which are typically stiffer and stronger than the matrix. The CFRP composites are orthotropic material. Hence their properties are not the same in all directions. Table 3 and Table 4 show the properties of CFRP laminates and epoxy adhesive respectively.

(B) Geometry

The geometry of all deep beams is shown in Figure 4. Considering the shear strengthening of deep beams, two stirrups of 5mm diameter are provided at the each support

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and under each point load. In the beam considered, in order to apply point load on the surface, steel plate is provided under the load, similarly for supports steel plates are provided.

In all the deep beams considered for analysis, CFRP strips are applied at 0 degree, 90 degree and 45 degree orientation to the neutral axis of the beam as shown in Figure 1. The CFRP strips are applied only in the shear span region of the beam. In all beams the width and thickness of the CFRP strips are 50mm and 1.2mm respectively. The center to center spacing of 100mm is used for both, 90 degree and 45 degree oriented CFRP strip strengthened deep beams.

Since CFRP strips are considered only in the shear span region of the deep beams in 90 degree one point loading case, eight strips are required per side of the beam while in two point loading case, six strips required per side of the beam. Similarly in 45 degree orientation mechanism

one point loading case required six CFRP strips per side of the beam while for two point loading case only four strips were needed per side of the beam. The thickness of epoxy adhesive considered is 0.5 mm.

(C) Model

In the software, multi-physics module under static structural analysis system is opened and material properties are assigned to various parts of the beam. Reinforcements were assigned structural steel property and concrete beam was assigned concrete nonlinear property.

In same module of the software, connections between various parts of the beam can easily be assigned such as connection between concrete and steel is bonded connection, steel and steel is bonded etc.

Meshing of the finite element model is also provided. Figure 5 shows the meshed beam. Fine meshing is

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preferred in cases where there are chances of problematic geometries.

(D) Setup

In the setup portion, boundary conditions such as type of support and loads are assigned. Figure 6 and Figure 7 show assigning of supports and loads.

(E) Solution

In the software, many types of solutions are obtained such as static structural, flexible dynamic, rigid dynamic, linear buckling, harmonic response etc. Since all types of structural element are considered in static structural for this particular problem, static structural analysis has been considered.

Static structural analysis gives different types of stress, strain and deformation of that particular element. Here

discussions are pertaining to deformation only, for the strengthened and non-strengthened beams.

III. ResulTs and dIscussIon

Analysis of one point loading beam and two point loading beam was carried out in the software. From the results it is clear that, 45 degree orientation of CFRP strips for strengthening is the best strengthening mechanism for enhancing the shear capacity of the beam.

Figures 8 and 9 show the comparison of experimental results and analytical results of one point load beam and two point load beam respectively. Also from Figures 8 and 9, it is clear that the analytical results show good

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agreement with the experimental results [6]. All beams of the finite element model are stiffer than the actual beam in the linear range [10]. There are many factors for higher stiffness of the software model such as the bond between the concrete and steel reinforcement is assumed to be perfect (no slip) in the software model but for the actual beams the assumption will not hold to be true and slip actually occurs, therefore the composite action between the concrete and steel reinforcing is lost in the actual deep beams. Also the micro-cracks produced by drying shrinkage and handling are present in the concrete. These would reduce the stiffness of the actual deep beam, while the software model doesn’t include micro-cracks due to factors that are not incorporated into the same.

IV. conclusIons

The results of this study indicate that the externally bonded CFRP strips can be successfully employed to enhance the shear capacity of the deep beams.

When compared with non-strengthened one-point loading beam, load carrying capacity of beam strengthened with 45 degree oriented CFRP strips is enhanced by 51.5%.

Similarly in two-point loading beam, load carrying capacity enhances up to 39.8% in 45

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2.

3.

degree orientation of CFRP strips in comparison to non-strengthened beam.

For one-point load beam, load carrying capacity of 0 degree, 90 degree and 45 degree orientation of CFRP strips show an increase up to 4%, 44% and 51.5% respectively as compared to non-strengthened beam.

Similarly in two-point load beam, load carrying capacities of 0 degree, 90 degree and 45 degree orientation of CFRP strips, are observed to increase up to 28.9%, 30.2% and 39.8% respectively compared to non-strengthened two-point load beam.

It is observed that, 45 degree orientation of CFRP strips is the best mechanism to enhance the shear capacity of deep beams, and hence improved load carrying capacity for the same beam can be achieved by adopting the mechanism.

ReferencesKhalifa Ahmed, Gold W. J., Nanni Antonio, Abdel Aziz M.I, “Contribution of Externally bonded FRP to shear capacity of RC Flexural Members” by ASCE Journal for Composite of Construction, Nov 1998.

Tavarez F. A., Bank L. C., Plesha M. E., “Analytical of Fiber-Reinforced Polymer Composite Grid Reinforced Concrete beams” by ACI Structural Journal, 2003.

Malek Amir M., Saadatmanesh Hamid, “Analytical study of reinforced concrete beams strengthened with web-bonded fiber reinforced plastics plates” by ACI structural Journal, May-June 1998.

Mehdi Alizadehnozari, Hamidreza Sharifi, “FRP Composites used in Structural” by American Journal of Scientific Research, 2011.

Godat Ahmed, W. Neale Kenneth, Labossiere P., “Numerical Modeling of FRP shear strengthened Reinforced Concrete Beams” by ASCE Journal of Composite of Construction, Nov-Dec 2007.

Jon Erik Moren, “Shear Behaviour of Reinforced concrete Deep beams strengthened in shear with CFRP laminates” by New Jersey Institute of Technology.

Ibrahim A. M., Mahmood M. Sh., “Finite Element Modeling of Reinforced Concrete beams strengthened with FRP laminates” by European Journal of Scientific Research, 2009.

Gorji M. S., “Analysis of FRP strengthened reinforced concrete beams using Energy Variation Method” by World Applied Science Journal, 2009.

Chen G. M., Chen J. F., Teng J. G., “On the Finite Element modeling of RC beams shear strengthened with FRP” by Journal of Construction and Building Material, 2010.

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9.

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Basic analysis guide ANSYS 12.1.

ANSYS structural analysis guide.

ANSYS 12 WB Engineering Data guide.

ANSYS tutorials online.

ANSYS workbench user guide version 12.1.

The software used for this study was ANSYS.

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Godat A., Labossiere P. Neale K. W., “Numerical Investigation of the parameters influencing the behavior of FRP shear strengthened beams” by Journal of Construction and Building Material, 2011.

BibliographyDeniaud C., Cheng J.J. Roger, “Reinforced Concrete T-Beams Strengthened in shear with Fiber Reinforced polymer Sheets” by Journal of Composite for Construction, Nov 2003

Lee H.K., Cheong S.H., Ha S.K., Lee C.G., “Behavior and performance of RC T-Section deep beams externally strengthened in shear with CFRP sheet” by Journal of Composite Structures, 2011.

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Mitali R Patel received her Masters in Engineering, specialising in computer aided structural analysis with a Gold Medal from Gujarat Technological University as well as Gujarat Institute of Civil Engineers and Architects. She is a Design Engineer at SNS Infrastructure Services, Ahmedabad. Her areas of interest are strengthening of existing structural elements using FRP composites and analysing behaviour of structural elements under shear and also use of various admixtures for achieving higher strength to concrete. She has published papers in various journals and conferences, and she holds an outstanding academic record.

Tejendra Tank received his Masters of Engineering in computer aided structural analysis and design from L.D. College of Engineering and is currently pursuing his doctorate degree from Applied Mechanics Department, S.V. National Institute of Technology, Surat. He is Assistant Professor at Indus Institute of Technology and Engineering, a constituent of Indus University and has over four years of experience. He is involved in student developmental activities at Indus University and has guided students at bachelors and masters level from various universities. He has published many papers in international journals and presented several at national and international conferences. His area of research include retrofitting and strengthening of existing reinforced concrete structures and curing efficiencies of various curing compounds used in current concrete industry.