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Abstract

This paper presents a study on the performance of glass fiber reinforced polymer (GFRP) laminated reinforced concrete (RC) beams using non-linear Finite element analysis. The geometry of the beam used in this study was 100×150mm with an effective span of 900mm. A 5mm thick GFRP laminate is externally bonded at the soffit of the beam. The parameters of this study included first crack load, yield load, ultimate load and their corresponding deflections. From the results it is observed that the GFRP laminated RC beam exhibit better performance compared to that of RC beam.

I. Introduction

Infrastructures in and around the world are deteriorating or degrading at an unprecedented rate in recent decades, due to corrosion, inadequate design/construction deficiency and natural disasters such as: fires and earthquake. A large number of concrete structures have been damaged by severe earthquakes. Such damaged structures, have not only be repaired, but also have to be retrofitted/strengthened [1], [2].

There is a huge need for structural up-gradation so as to meet new seismic design requirements because of new design standards [3]. FRP laminates have gained popularity as external reinforcement for the strengthening or rehabilitation of RC structures and they are preferred over steel plate due to their high tensile strength, high strength–weight ratio and corrosion resistance. Externally bonded FRP laminates and fabrics can be used to increase the shear as well as flexural strength of reinforced concrete beams and columns [4].

In particular, the flexural strength of a RC beam can be extensively increased by the application of carbon (CFRP), glass (GFRP) and aramid (AFRP) FRP plates/sheets adhesively bonded to the tension face of the beam. Glass fiber reinforced polymers (GFRP) sheets are being increasingly used in rehabilitation and retrofitting of concrete structures, since low cost comparison with other types of FRP fibers [5]. Finite element analysis is an numerical/analytical method for complex structural, thermal, fluid and electromagnetic problems [6]. A numerical study has been carried out by using ANSYS software to bring into focus the versatility and powerful analytical capabilities of finite element techniques by objectively modeling the complete response of beams [7]. This model can help to confirm the theoretical calculations arrived by using ACI method [8].

II. Finite Element Modeling

A. Geometry and Material Data

In this study RC and GFRP laminated beams of 100×150×1000 mm was used. The GFRP laminate of 5mm thickness is bonded to the tension face of the beam. The properties of the material used are summarized in Table 1 and the geometry of the beam is shown in Fig. 1.

Table 1: Summary of Material Properties

 

Fig. 1: Geometry of the Beam

B. Modeling

ANSYS 15 was used for the modeling of beams [9]. Finite Element Analysis (FEA) of the model was set up to examine three different behaviors such as: initial cracking, yielding of the steel reinforcement and the ultimate strength of beam under Four-point bending.

CONCRETE: SOLID65 was used for the 3-D modeling of solids with or without reinforcing bars (rebar). The solid is capable of cracking in tension and crushing in compression. This element is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The most important aspect of this element is the treatment of nonlinear material properties. The geometry of this element is shown in Fig. 2(a).

Fig. 2: (a) Concrete: SOLID65 Element

STEEL REBAR: LINK180 is a 3-D spar element which can be used to model trusses, sagging cables, links, springs, and so on. The element is a uniaxial tension-compression element with three degrees of freedom at each node: translations in the nodal x, y, and z directions. The geometry of this element which was used to model the longitudinal and shear reinforcement is shown in Fig.

Fig. 2: (b) Steel Rebar: LINK180 Element

STEEL PLATE: SOLID185 Homogeneous Structural Solid is suitable for modeling general 3-D solid structures. This element is defined by eight nodes having three degrees of freedom at each node translations in the nodal x, y and z directions. The homogeneous structural solid with simplified enhanced strain formulation was used to model steel plates for supporting is shown in Fig. 2(c).

Fig. 2: (c) Steel Plate: Solid185

LAMINATE: SOLID185 Layered structural element used for modeling of layered thick shells or solids. This element is defined by eight nodes having three degrees of freedom at each node. The element may be stacked for modeling composites with more than 250 layers or improving solution accuracy. The geometry of this element is shown in Fig. 2(d).

Fig. 2: (d) Laminates: SOLID185

Element The typical modeling of RC beams is shown in Fig. 3.

Fig. 3: Typical Modeling of RC Beam

III. Results & Discussion

A. Load-Deflection Behavior

The load-deflection behavior of RC and GFRP laminated RC beams are shown in Fig. 4. It clearly indicates the first crack stage, yield stage and ultimate stage which shows the linear, non-linear behavior and failure region.

Fig. 4: Load-Deflection Behavior of Beams

B. Crack Pattern

The ANSYS program records a crack pattern at each applied load step. A cracking sign represented by a circle appears when a principal tensile stress exceeds the ultimate tensile strength of the concrete. The cracking sign appears perpendicular to the direction of the principal stress. 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 a blue outline. It shows the appearance of flexural cracks, diagonal tensile cracks and compression cracks. The crack pattern of beams is shown in Fig. 5 & 6 and the deformed shape of beams is shown in Figs. 7 & 8.

Fig. 5: Crack Pattern of RC Beam

 

Fig. 6: Crack Pattern of GFRP Laminated RC Beam

 

Fig. 7: Deformed Shape of RC Beam

 

Fig. 8: Deformed Shape of GFRP Laminated RC Beam

C. Load Carrying Capacity

The theoretical load carrying capacity of beams is calculated by using ACI method [10]. The strength design approach requires that the design flexural strength of a member exceed its required factored moment as indicated in (1).

The nominal flexural strength of the section with FRP external reinforcement can be computed by using the following equations.

Steel contribution to bending:

FRP contribution to bending:

A_S = Area of steel reinforcement, Ψ_f = Additional reduction factor, A_f = Area of FRP external reinforcement, f_c^’ = specified compressive strength of concrete, c = distance from extreme compression fiber to the neutral axis, d_f = depth of FRP flexural reinforcement, d = distance from extreme compression fiber to centroid of tension reinforcement, f_fe = effective stress in the FRP, E_f = modulus of elasticity for the FRP in MPa, ε_fo = initial strain in the beam evaluated at the centroid of FRP due to preexisting dead loads, ε_c = strain level in concrete, ε_c^’ = maximum strain of unconfined concrete corresponding to f_c^’.

The ultimate loads arrived from the numerical study are compared with the theoretical loads. The comparisons of results are presented in Table 2. The comparison of beam results at various stages is given in Table 3. From the table it is observed that the GFRP laminated RC beam exhibit higher load carrying capacity at all load stages compared to that of RC beam. The maximum increase in yield and ultimate load was found to be 48% and 32% respectively compared to that of RC beam.

Table II: Comparison of Theoretical and Numerical Results

 

Table III: Comparison of Results of Beams

IV. Conclusion

Based on the results, the following conclusions are drawn.

• On overall evaluation, GFRP laminated RC beam exhibit higher load carrying capacity when compared to that of RC beam. The maximum increase in yield and ultimate load was upto 48% and 32% respectively when compared with RC beam.
• The maximum reduction in yield and ultimate GFRP deflection was upto 35% and 67% respectively.
• The result obtained from the numerical study agrees reasonably well with the theoretical values.

Acknowledgment

The authors wish to acknowledge the Department of Civil Engineering, Pondicherry Engineering College, Puducherry, for providing CAD lab facility to carry out the dissertation project work.

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