International Journal of Advanced Engineering Technology E-ISSN 0976-3945

/ Research Article
DESIGN GUIDELINES FOR FLEXURAL STRENGTH OF SINGLY REINFORCED CONCRETE BEAM STRENGTHENED WITH FIBRE REINFORCED POLYMER LAMINATE AT BOTTOM
K. B. Parikh1 and Dr. C. D. Modhera2

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282

Address for Correspondence

1Department of Applied Mechanics, Government Engineering College, Surat, Gujarat, India

Research scholar, Department of Applied Mechanics, SVNIT, Surat

2Department of Applied Mechanics, Sardar Vallabhbhai National Institute of Technology, Surat, India

E-mail: ,

Abstract

The design guidelines for the determination of limiting moment capacity of reinforced concrete beam strengthened with fiber reinforced polymer laminate at bottom is presented. The results derived from this design oriented model compared with analytical finite element model and others available researchers’ experimental data. This study also presents the design of laminate thickness to attain a specified limiting moment capacity in a given beam. The results show that the design guidelines presented in this study, performed well in the prediction of experimental results.

KEYWORDS Fiber reinforced polymer laminate; reinforced concrete beam; design guidelines; thickness of frp.

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

Introduction

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International Journal of Advanced Engineering Technology E-ISSN 0976-3945

Fiber reinforced polymer laminates are increasingly being applied for the rehabilitation and strengthening of infrastructure in lieu of traditional repair techniques such as steel plates bonding. FRP plates have many advantages over steel plates in this application, and their use can be extended to situations where it would be impossible or impractical to use steel. For example, FRP plates are lighter than steel plates of equivalent strength, which eliminates the need for temporary support for the plates while the adhesive gains strength. Also, since FRP plates used for external bonding are relatively thin, neither the weight of the structure nor its dimensions are signiﬁcantly increased. In addition, FRP plates can easily be cut to length on site. These various factors in combination make installation much simpler and quicker than when using steel plates.

There were few analytical studies available for the prediction of flexural capacity of reinforced concrete beam strengthened with external laminates. Concrete society technical report 55, was used the rectangular stress block for concrete. Jones et al. used the conventional procedure to determine the ultimate moment capacity of RC beams externally strengthened with bonded steel plates. They employed rectangular stress blocks for concrete and the actual stress-strain curves of the internal steel reinforcement and external steel plates to evaluate the internal forces and moment. Several researchers have come up with techniques for attempting to predict flexural capacities and failure modes for FRP reinforced structural elements. Results of research performed by Saadatmanesh and Ehsani suggested that reasonably accurate strength predictions of FRP reinforced beams could be made using simple force equilibrium equations. Work by Triantafillou and Pleveris indicated that the failure mode of FRP-reinforced beams was highly influenced by the reinforcement ratios of the FRP and steel. Their research also offers equations for strength based on the various modes of FRP-reinforced beam failure. Perhaps the most accurate method of predicting strength of FRP-reinforced beams, for flexural, is through the use of finite element modeling programs, as suggested by some researchers. A critical factor for flexure capacity design is the adhesion between the concrete and the composite.

This paper presents a very simple, easy and efficient computational design oriented model for the determination of flexural strength of reinforced concrete beam strengthened at bottom with fiber reinforced polymer laminate. It also provides for the determination of limit of laminate thickness in order to avoid the tensile failure of beam due to fiber reinforced polymer and assure the tensile failure due to steel i.e. reinforcement yielding. This design oriented model also allows for the estimation of laminate thickness to attain a specified limiting moment capacity. The results from design oriented model compares with the results of author’s analytical finite element model as well as available researches experimental data.

DESIGN ORIENTED MODEL

IS 456:2000 is Indian standard code of practice for plain and reinforced concrete. With the help of this code, a systematic procedure/model had been introduced by K.B.Parikh et al. for the determination of flexural strength of singly RC beam strengthened with fiber reinforced polymer at bottom. For the determination of this model following assumptions should be made.

· The tensile strength of the concrete is ignored.

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

· For design purpose the compressive strength of concrete in the structure shall be assumed to be 0.67 times the characteristics strength.

· The maximum strain in concrete at the outermost compression fiber is taken as 0.0035.

· The maximum strain in the tension reinforcement in the section at failure shall not be less than

· Partial safety factor for steel is 1.15 and concrete is 1.50.

· The fiber reinforced polymer sheet or laminate has a linear elastic stress-strain relationship to failure.

· There is no relative slip between external fiber reinforced polymer sheet and concrete.

From the above assumptions, a stress-strain diagram has been drawn.

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

Fig. 1 Stress & strain diagram for RC beam with FRP

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

From the above stress and strain diagram of RC beam moment capacity of beam can easily determined from the following equation.

The depth of neutral axis is to be determined from the following equation.

t thickness of frp laminate/plate/sheet

DESIGN THICKNESS OF FRP LAMINA

Balanced Condition

The thickness of fiber reinforced polymer sheet can be determined for balanced condition. As per above assumption, there is a linear relationship of strain diagram. So, the ratio of can be found as follows.

Using equation (2), it is very easy to obtain an equation of thickness of fiber reinforced polymer lamina in balanced condition.

For, hence the equation for the thickness of FRP laminate becomes as,

Maximum Thickness of FRP Sheet

The maximum thickness of fiber reinforced polymer sheet can be evaluated by using the criteria of minimum value of percentage of reinforcement as per IS 456:2000. The basic equation of minimum percentage of reinforcement for beam as per code is as follows.

Using the equation (8), modified the equation (5), (6) and (7) are as follows.

Using, various grade of concrete and grade of reinforcement, the equation of thickness of sheet under balanced condition with minimum reinforcement can be generated as,

Where the k is the multiplication factor, as shown in table 1.

Table 1: multiplication Factor ‘k’

Grade of Concrete/Grade of Reinforcement / /
M15 / 2.1225 / 1.8526
M 20 / 3.0765 / 2.7166
M 25 / 4.0305 / 3.5806
M 30 / 4.9845 / 4.4446

General Equation

The general equation for the determination, of thickness of fiber reinforced polymer sheet can be expresses as follows.

If moment capacity is known, then it is very easy to determine the depth of neutral axis from following equation,

Table 2: Physical and Mechanical properties of materials

Author(s) / Index / L (mm) / b (mm) / D (mm) / Ast (mm2) /
(Mpa) /
(Mpa) /
(Mpa)
H. Saadatmanesh and R. Ehsani / A / 4875 / 205 / 455 / 1472.6 / 35 / 456 / 400
B / 4875 / 205 / 455 / 981.8 / 35 / 456 / 400
C / 4875 / 205 / 455 / 265.5 / 35 / 456 / 400
D / 4875 / 205 / 455 / 981.8 / 35 / 456 / 400
Yousef A. Al-Salloum / Control / 1350 / 150 / 200 / 157 / 40.1 / 412 / --
G-SBL / 1350 / 150 / 200 / 157 / 40.1 / 412 / 540
C-SBL / 1350 / 150 / 200 / 157 / 40.1 / 412 / 930

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International Journal of Advanced Engineering Technology E-ISSN 0976-3945

VERIFICATION EXAMPLES

In order to evaluate the effectiveness of the above equation, various available experimental research data is used. Also, the verification of these equations has been carried by analytical model suggested by K.B.Parikh et. al. Following table 1, shows the physical and mechanical properties of materials and table 2 shows the comparison of moment capacity of beams found from equation 1, using author finite element model and experimental results of researches. The following table 3 shows the maximum thickness and required thickness of fiber reinforced polymer sheet under balanced condition

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International Journal of Advanced Engineering Technology E-ISSN 0976-3945

The following are the comparative charts for the ultimate moments of beam.

Fig. 2 Comparative charts of ultimate moment

Table 3: Comparison of ultimate moment of beams

Author(s) / Index / Moment capacity or Ultimate Moment
Design oriented model Results / Finite element Model Results (K.B.Parikh et. al) / Experimental Results
H. Saadatmanesh and R. Ehsani / A / 326.2 / 330 / 337
B / 263.6 / 268 / 257.7
C / 173.3 / 181 / 188.3
D / 263.6 / 270 / 257.7
Yousef A. Al-Salloum / Control / 8.96 / 12.2 / 15.27
G-SBL / 22.15 / 23 / 23.67
C-SBL / 35.25 / 29.8 / 26.60

Table 4: FRP thickness

Author(s) / Index /
Under balanced Condition / Maximum Value / Provided
Sing-Ping Chiew et. al / A - group / 2.38 / 3.66 / 1.7
Yousef A. Al-Salloum / G-SBL / 1.48 / 1.94 / 1.0
C-SBL / 0.86 / 1.13 / 1.19
ZHANG
Aihui / A - group / 0.140 / 0.233 / 0.111

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

CONCLUSION

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

Here simple and efficient design guidelines for the determination of ultimate moment of a beam with fiber reinforced polymer sheet at bottom provided with the help of IS 456: 2000. These guidelines provide effective and convince procedure for the determination of thickness of fiber reinforced polymer sheet under balanced condition. This design model validated through analytical and researchers experimental results of beam strengthened with fiber reinforced polymer sheet at bottom. From the results following conclusions can be drawn:

· The design oriented computational analysis to determine the ultimate moment capacity of singly reinforced RC beams strengthened with FRP at bottom proved to be efficient and good.

· The results obtained from this design oriented model were well compared with finite element model results and experimental results.

· One can easily determine the moment capacity of a beam strengthened with FRP at bottom by using simple approach.

· It also very easy to determine the thickness of FRP sheet under balanced condition.

· The design of FRP sheet thickness to attain a desired moment capacity in a given beam can be found out easily.

· The results showed that all computational models presented here performed well for the determination of experimental results.

REFERENCES

[1] Sing-Ping Chiew, Qin Sun and Yi Yu, “flexural Strength of RC Beams with GFRP laminates”, Journal of composites for Construction, Vol. 11, No. 5, October 2007, pp. 497-506.

[2] K.B. Parikh and C.D. Modhera, “Application of glass fibre reinforced polymer to structural components – A state of art review”, International Conference on Advances in Concrete, Structural and Geotechnical Engineering, BITS, Pilani (India), October 25-27, 2009, pp. 1-10.

[3] Zhang Ai-hui, Jin Wei-liang and Li gui-bing, “Behavior of preloaded RC beams strengthened with CFRP laminates”, Journal of Zhejiang University SCIENCE A, Vol. 7, No. 3, November 2005, pp. 436-444.

[4] Hamid Saadatmanesh and MR Ehsani, “RC beams strengthened with GFRP plate I: Experimental study”, Journal of Structural engineering, ASCE, Vol. 117, No. 11, November 1991, pp. 3417-3433.

[5] Almusallam, R.H. and Y.A.Al-Salloum, “Ultimate strength prediction for RC beams externally strengthened by composite materials”, Journals of composites: Part B Engineering, Vol. 32, February 2001, pp. 609-619.

[6] IS 456:2000, “Plain and Reinforced Concrete-Code of Practice, Fourth Revision”, Bureau of Indian Standard, New Delhi.

[7] Hutchinson A, Rahimi H., “Flexural Strengthening of Concrete Beams with Externally Bonded FRP reinforcement’, Proceedings of the Second International Conference on Advanced Composite materials in Bridges and Structures, CSCE, Montreal, Canada, 1996.

[8] K.B.Parikh and C.D.Modhera, “Analytical model of reinforced concrete beam using glass fiber reinforced polymer”, International journal of Advanced Engineering Technology, Vol. I, No. I, April-June, 2010, pp. 46-58.

[9] K.B. Parikh, M.M. Shirgar, K.M. Shiraj and C.D. Modhera, “Experimental Work on Beam by using GFRP Laminates”, A national conference on current trends on research and development in civil and environment engineering – An Indian perspective, SVIT, Vasad (India), January 21-22, 2010, pp. 1-8.

[10] C.Arya, J.L. Clarke, E.A. Kay and P.D. O’Regan, “TR 55: Design Guidance for Strengthening Concrete Structures Using Fibre Composite Materials: A Review”, Engineering Structures, Vol. 24, 2002, pp. 889-900.

[11] K. Chansawat, T. Potosuk, T. H. Miller, S. C. Yim and D. I. Kachlakev, “FE models of GFRP and CFRP strengthening reinforced concrete beams”, Advances in civil Engineering, Hindawi publishing corporation, 2009, pp. 1-13.

IJAET/Vol.I/ Issue II/July-Sept.,2010/274-282