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TRL Limited PUBLISHED PROJECT REPORT PPR053 Strengthening of concrete structures using near surface mounted FRP reinforcement by A F Daly (TRL Limited), J Shave and S Denton (Parsons Brinckerhoff) Prepared for: Project Reference: TF 3/359-Y104197 Client: Mr Ben Sadka Highways Agency Copyright TRL Limited June 2006. This report was prepared for the Safety Standards and Research Directorate, Highways Agency. The views expressed are those of the authors and not necessarily those of the Highways Agency. Published Project Reports are prepared primarily for the Customer rather than for a general audience and are published with the Customer’s approval. Approvals Project Manager Albert F Daly Quality Reviewed Richard J Woodward
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PUBLISHED PROJECT REPORT PPR053 Strengthening of concrete ... · polymer) laminate or bar. As the additional reinforcement is fully embedded below the surface of the concrete, there

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Page 1: PUBLISHED PROJECT REPORT PPR053 Strengthening of concrete ... · polymer) laminate or bar. As the additional reinforcement is fully embedded below the surface of the concrete, there

TRL Limited

PUBLISHED PROJECT REPORT PPR053

Strengthening of concrete structures using near surface mounted FRP reinforcement

by A F Daly (TRL Limited), J Shave and S Denton (Parsons Brinckerhoff)

Prepared for: Project Reference: TF 3/359-Y104197 Client: Mr Ben Sadka

Highways Agency

Copyright TRL Limited June 2006. This report was prepared for the Safety Standards and Research Directorate, Highways Agency. The views expressed are those of the authors and not necessarily those of the Highways Agency. Published Project Reports are prepared primarily for the Customer rather than for a general audience and are published with the Customer’s approval.

Approvals

Project Manager Albert F Daly

Quality Reviewed Richard J Woodward

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This report has been produced by TRL Limited, under/as part of a Contract placed by the Highways Agency. Any views expressed are not necessarily those of the Highways Agency.

TRL is committed to optimising energy efficiency, reducing waste and promoting recycling and re-use. In support of these environmental goals, this report has been printed on recycled paper, comprising 100% post-consumer waste, manufactured using a TCF (totally chlorine free) process.

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Strengthening of concrete structures using near surface mounted FRP reinforcement

Table of contents

page EXECUTIVE SUMMARY .................................................................................................................. (i)

1 Introduction and scope ............................................................................................................. 1 1.1 Background...................................................................................................................... 1 1.2 Objectives ........................................................................................................................ 2 1.3 Contents of report ............................................................................................................ 2

2 Literature review...................................................................................................................... 2 2.1 Introduction ..................................................................................................................... 2 2.2 Mechanisms of failure ..................................................................................................... 3 2.3 Research approaches........................................................................................................ 4 2.4 Bond-slip characterisation ............................................................................................... 4 2.5 Elastic analysis of bond strength ..................................................................................... 5 2.6 Semi-empirical bond models ........................................................................................... 7 2.7 Analogy with externally bonded FRP strengthening design ............................................ 8 2.8 Environmental effects .................................................................................................... 11 2.9 Future research needs .................................................................................................... 12

3 Experimental programme....................................................................................................... 12 3.1 Introduction ................................................................................................................... 12 3.2 Description of test beams............................................................................................... 13 3.3 Strengthening system..................................................................................................... 15 3.4 Loading configuration and instrumentation ................................................................... 16 3.5 Schedule of tests ............................................................................................................ 18 3.6 Test results..................................................................................................................... 18

3.6.1 Beam NSM1 ............................................................................................................ 19 3.6.2 Beam NSM2 ............................................................................................................ 20 3.6.3 Beam NSM3 ............................................................................................................ 20 3.6.4 Beam NSM4 ............................................................................................................ 20 3.6.5 Beam SM5 ............................................................................................................... 21 3.6.6 Beam NSM6 ............................................................................................................ 21 3.6.7 Test NSM7............................................................................................................... 21

3.7 Comparison of all test results......................................................................................... 21

4 Comparison with theoretical analysis..................................................................................... 32

5 Development of design guidelines ......................................................................................... 36

6 Conclusion ............................................................................................................................. 39

7 Acknowledgement.................................................................................................................. 39

8 References.............................................................................................................................. 39

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EXECUTIVE SUMMARY Strengthening of concrete structures using near surface mounted FRP reinforcement TRL Project Report PPR053

by Albert F Daly (TRL Limited), Jonathan Shave and Steve Denton (Parsons Brinckerhoff)

SCOPE

This report was produced as the main output of a research project carried out by TRL Limited and Parsons Brinckerhoff on behalf of the Highways Agency. The project focused on the performance of near surface mounted (NSM) reinforcement as a technique for increasing the flexural capacity of concrete bridges. The principle of NSM reinforcement is to introduce additional reinforcement into the concrete section in such a way that it acts compositely with the rest of the section in the same way as if it were cast into the concrete. Application consists of cutting a long rectangular chase or groove in the cover concrete. The reinforcement is then put in the groove and fixed in place using a high strength epoxy or cement grout. The reinforcement can be in the form of an FRP (fibre reinforce polymer) laminate or bar. As the additional reinforcement is fully embedded below the surface of the concrete, there is little risk of it being damaged by vandalism, impact or maintenance operations. Furthermore the FRP is less susceptible to premature failure due to local bond or delamination than externally bonded FRP strengthening systems. The main objective of the project was to investigate the performance of concrete beams and slabs strengthened with NSM FRP reinforcement. The specific objectives were to review available information on the use of NSM reinforcement, to provide guidance on its use for concrete bridge deck strengthening and to incorporate the use of NSM strengthening into the Highways Agency standard for FRP strengthening (BD 85).

SUMMARY The project consisted primarily of a desk study, aimed at making use of existing information and practice to provide guidance to enable the technique to be used in a safe, consistent and cost-effective manner. A small series of tests was also undertaken and used to verify any proposed design approach and to provide information on the practical issues that could be incorporated into the design guidelines. The focus of the study was on flexural strengthening. While it is recognised that the technique may provide significant benefits for shear strengthening, detailed study of this application was beyond the scope of this project. The bond characteristics of NSM reinforcement share similarities with both externally bonded FRP and with conventional embedded reinforcing bars. Therefore, in addition to research undertaken into NSM reinforcement, the more substantial body of research literature on the bond behaviour of conventional reinforcement was also reviewed and relevant findings reported. This information was used to develop a design approach for strengthening concrete bridge decks using NSM FRP reinforcement. Details of the test programme were formulated based on the results of the literature review. The results of the load tests were used to supplement the information already available and to validate the proposed design approach. This report contains a description of the design, fabrication and strengthening of the beams. It also presents details of the load tests including behaviour under load,

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strength, mode of failure, and comparisons of the load test capacity with that derived from theoretical calculations. Finally, the report includes a practical design procedure which can be used for NSM FRP strengthening systems. The procedure is based on the literature review and test programme described in the earlier sections of the report. It is consistent with the design approach previously developed for externally bonded FRP strengthening which forms the basis of BD 85, the Highways Agency standard relating to the strengthening of bridges using FRP.

IMPLEMENTATION The results of this research have been incorporated into the draft standard for the strengthening of bridge using fibre reinforced polymer (BD 85) in the Highways Agency’s Design Manual for Roads and Bridges.

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Strengthening of concrete structures using near surface mounted FRP reinforcement

1 Introduction and scope

1.1 Background

Over the last couple of decades fibre reinforced polymer (FRP) materials have gradually found significant applications in Civil Engineering and their use is continuously increasing as more experience is gained. Their properties and behaviour have been studied extensively and are now well understood in principle at least. In conjunction with this, design standards have been developed and designers now regard FRP as a viable alternative to the more traditional steel and concrete. The use of externally bonded FRP systems for the flexural strengthening of existing bridges has now become commonplace and has already superseded steel plate bonding as the method of choice from the point of view of cost and access requirements. Major strengthening works to bridge soffits and supports have been carried out on a number of structures with considerable savings in traffic management costs and disruption to road users. However there are some critical issues that have not been fully solved, particularly in relation to the effective transfer of force between the existing concrete and the bonded FRP material. One serious issue is the degradation of the bond due to the influence of adverse environmental conditions and the possibility of damage to the FRP through vandalism or through accidental impact. In addition, there are concerns about applying bonded FRP systems in locations where inspection and monitoring is difficult, for example on the top surface of decks where the FRP is hidden under surfacing and waterproofing systems. In these locations, there is also the considerable risk of damage to the FRP during re-surfacing. One possible way around these problems is to embed the FRP completely in the concrete. This would enhance the bond between the two materials as the FRP/adhesive system would be bonded to three sides of a rectangular groove. It would also provide a greater degree of protection to the FRP from damage due to vehicle impact, fire, ultraviolet rays and moisture absorption. It would be particularly useful in the strengthening of the top surface of bridge decks as the FRP would be protected from damage during re-surfacing operations. The principle of near surface mounted (NSM) reinforcement is to introduce additional reinforcement into the concrete section in such a way that it acts compositely with the rest of the section in the same way as if it were cast into the concrete. Application consists of cutting a long rectangular chase or groove in the cover concrete. The reinforcement is then put in the groove and fixed in place using a high strength epoxy or cement grout. The reinforcement can be in the form of an FRP laminate or bar. As the additional reinforcement is fully embedded below the surface of the concrete, there is little risk of damage by vandalism, impact or maintenance operations. Furthermore the FRP is less susceptible to premature failure due to local bond or delamination than externally bonded FRP laminates:. Alternatively, stainless steel or even conventional reinforcing bars could be used. This approach has already been adopted for the strengthening of masonry arch bridges and testing at TRL on large-scale model bridges has shown that strength and behaviour can be considerably enhanced (Sumon 2005).

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1.2 Objectives

The main objective of the project was to investigate the technique of strengthening concrete bridge decks using NSM FRP reinforcement. The specific objectives were:

♦ To review available information on the use of NSM FRP reinforcement;

♦ Provide guidance on its use for concrete bridge deck strengthening and develop design and specification requirements;

♦ Devise clauses for incorporation into BD 85 (Highways Agency 2004);

♦ Formulate proposals for monitoring NSM FRP applications;

♦ Identify future research needs. The project consisted primarily of a desk study, aimed at making use of existing information and practice to provide guidance to enable the technique to be used in a safe, consistent and cost-effective manner. The aim was to develop a design approach for strengthening using NSM FRP reinforcement which could be incorporated into the Design Manual for Roads and Bridges (DMRB). A small series of tests was also planned and used to verify the proposed design approach and to provide information on the practical issues that could be incorporated into the design guidelines. The focus of the study was on flexural strengthening. While it is recognised that the technique may provide significant benefits for shear strengthening, detailed study of this application was beyond the scope of this project. 1.3 Contents of report

This document comprises the final report of the research project and presents the conclusions of the literature review and details of the experimental programme. The bond characteristics of NSM reinforcement share similarities with both externally bonded FRP and with conventional embedded reinforcing bars. Therefore, in addition to research undertaken into NSM reinforcement, the more substantial body of research literature on the bond behaviour of conventional reinforcement was also reviewed and relevant findings reported. This information was used to develop a design approach for strengthening using NSM FRP reinforcement to be incorporated into the Highways Agency standard BD 85 relating to the strengthening of bridges using FRP. Details of the test programme were formulated based on the results of the literature review. It was intended that the results would be used to supplement the information already available and to validate the proposed design approach. This report contains a description of the design, fabrication and strengthening of the beams. It also presents details of the load tests including behaviour under load, strength, mode of failure, and comparisons of the load test capacity with that derived from theoretical calculations. Finally, the report includes a practical design procedure which can be used for NSM FRP strengthening systems. The procedure is based on the literature review and test programme described in the earlier sections of the report.

2 Literature review

2.1 Introduction

Fibre-reinforced polymer (FRP) has been shown to be highly effective for strengthening concrete structures in a variety of configurations (Nanni 2000). Design guidelines exist for

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externally bonded FRP strengthening (Concrete Society, 2004; Highways Agency, 2004; ACI 2002), and it has become a particularly useful technique for extending the life of concrete structures. Another technique that is the subject of ongoing research is the strengthening of concrete structures using NSM FRP reinforcement. The principle of strengthening with NSM FRP is to cut a long chase or groove into the cover concrete and fix the FRP in place using an adhesive resin. The FRP is then able to act compositely with the concrete section, providing additional structural reinforcement. Since the FRP is embedded into the concrete, there are particular advantages over externally bonded FRP strengthening systems including:

♦ The bond between the FRP and the concrete is enhanced;

♦ The FRP is protected from mechanical and chemical damage;

♦ NSM FRP provides a good solution for strengthening the top surface of bridge decks, avoiding potential damage during re-surfacing operations.

This literature review considers all the available research on NSM FRP for flexural strengthening and summarises the current state of knowledge and future research needs. 2.2 Mechanisms of failure

The principles to be used for the design of NSM FRP flexural strengthening systems are similar to those for externally bonded FRP, since both are based on the following limit states:

♦ Concrete crushing;

♦ FRP fracture;

♦ Debonding or “separation” of the FRP.

In the cases of concrete crushing and FRP fracture, composite action is maintained between the FRP and the concrete. These criteria are well-understood and may be treated in a similar way to the design of externally bonded FRP systems. However, where the bond between the FRP and the concrete is critical, leading to a separation failure, the design requires more care. In the vast majority of experimental cases, bond failure has been more critical than FRP fracture (see for example the various reports by De Lorenzis et al in the references list). Furthermore, the bond behaviour of NSM FRP is different to that of externally bonded FRP (Smith and Teng, 2002). The debonding force could be influenced by many factors, including:

♦ the geometry, stiffness, and surface type of the FRP;

♦ the groove geometry;

♦ the adhesive properties;

♦ the tensile strength and surface preparation of the concrete. The debonding mechanism of externally bonded FRP is typically dominated by the tensile splitting of the surface concrete, but NSM FRP can debond in a variety of mechanisms:

♦ Failure at the interface between the bar and the adhesive;

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♦ Splitting of the adhesive;

♦ Failure at the interface between the adhesive and the concrete;

♦ Splitting of the concrete. Mixed mode mechanisms have also been reported. Due to the different behaviour of NSM FRP and externally bonded FRP, it is necessary to develop a new design method that deals specifically with the bond and anchorage of NSM FRP. 2.3 Research approaches

Research on NSM FRP generally falls into the following categories:

♦ Experimental test results (Taljsten et al, 2003; De Lorenzis and Nanni, 2003; De Lorenzis et al 2000a, 2000b, 2002a, 2002b, 2004; El-Hacha and Rizkalla, 2004);

♦ Bond-slip characterisation (De Lorenzis and Nanni, 2002; De Lorenzis et al 2002b, 2004);

♦ Elastic analysis of bond strength (Rizkalla and Hassan, 2003a, 2003b; De Lorenzis and La Tegola. 2003);

♦ Semi-empirical bond models (De Lorenzis and Nanni, 2003; Blaschko 2003). 2.4 Bond-slip characterisation

Bond-slip models for NSM FRP have been developed by De Lorenzis and Nanni (2002), and De Lorenzis et al (2002b, 2004), leading to a proposed design approach for anchorage of NSM FRP bars (De Lorenzis et al, 2002b).

Figure 1 (taken from De Lorenzis et al 2002b) shows typical average bond stress versus slip curves for specimens with epoxy-filled grooves that failed at the concrete-epoxy interface (Figure 1a) or by splitting and concrete cracking (Figure 1b). The form of the stress-slip relationship is given by:

ατ sCs =)(

where τ(s) is the bond stress at slip s, and C and α are constants. In theory, this approach appears to provide a good, rational solution to the anchorage problem, but its application as a design method has its drawbacks. The parameters for the model are calibrated from experimental bond-slip measurements. These parameters are critical to the design method. However, there is very little test information available on which to base the design values, and the existing bond-slip data shows significant variability. In addition, the design methodology is not as simple as the existing anchorage models for externally bonded FRP (Concrete Society, 2004; Highways Agency, 2004; ACI, 2002).

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Figure 1 Bond stress versus slip curves. (from De Lorenzis et al 2002b)

2.5 Elastic analysis of bond strength

Rizkalla and Hassan (2003a, 2003b) carried out elastic modelling of the anchorage region of NSM bars. They have developed different methods for the design of NSM bars and strips, respectively. The design criteria for NSM bars are based on the following assumptions:

♦ The shear stress in the anchorage region is constant;

♦ The tensile stresses are based on linear elastic finite element analysis;

♦ Failure occurs when the principal tensile stress exceeds the tensile strength of the concrete or the adhesive.

This method can be used to design NSM bars. Hand calculations can be used, along with coefficients obtained from linear elastic finite element analysis to take account of groove geometry.

(a) Failure at concrete-epoxy interface

(b) Failure by splitting

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Figure 2 (taken from Rizkalla and Hassan, 2003a) illustrates the elastic tensile stress distribution around NSM FRP bars expressed as a function of the stress in the FRP (ffrp).While this method attempts to deal with both mechanisms involving splitting of the adhesive or splitting of the concrete, it has the following disadvantages:

♦ It assumes that the shear stress is constant; in reality it will vary considerably at the ends of the bars;

♦ It assumes that the anchorage region behaves elastically; experimental results exhibit non-linear behaviour;

♦ The method requires the value of the coefficient of friction between the bar and the adhesive to be known. The authors do not suggest values to be used for the coefficient of friction in design.

De Lorenzis and La Tegola (2003) derived explicit analytical solutions for the limiting bond force, based on a similar analysis of the transverse plane, but considering various ultimate crack patterns. The analysis was able to confirm the optimum ratio of groove size to bar diameter to be between 1.5 and 2.0, as observed in experimental tests. Three-dimensional finite element analyses of the anchorage region have also been carried out (De Lorenzis and Lundgren, 2002; De Lorenzis et al, 2004). The latter of these papers provides an analytical method for deriving the bond-slip characteristics of the anchorage system. A second elastic method developed by Rizkalla and Hassan (2003b) deals with NSM FRP strips, and models the distribution of shear stress in the anchorage region. The method assumes that failure is initiated when the peak shear stress at the end of the strip exceeds a limit that is derived from the concrete tensile and compressive strengths. The closed-form solution for the peak shear stress is a function of the geometry of the FRP strip and the groove, the elastic modulus of the FRP and the shear modulus of the adhesive, and the concrete tensile stress. While this elastic method would be appropriate for modelling FRP-strengthened metallic structures (Denton, 2001; Highways Agency, 2004), it appears too simplistic to be representative of concrete structures where the bond behaviour is significantly non-linear.

d

frp

Ldf

Gµ42

d

frp

Ldf

Gµ41

d

frp

Ldf

'2

Concrete

Epoxy

NSM bar

Figure 2 Typical tensile stress distribution around NSM FRP bars. (from Rizkalla and Hassan 2003a)

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2.6 Semi-empirical bond models

De Lorenzis and Nanni (2003) developed a “concrete tooth model” that considers the FRP force that would cause a “tooth” of concrete to break off at the level of the steel reinforcement. The analysis depends on the crack spacing, which is assumed to be the minimum value derived from the section geometry and the bond strengths assumed to be associated with the steel and the FRP. Furthermore, the relationship between the FRP stress and the average shear stress in the anchorage region is characterised by an equivalent anchorage length Lp, which is assumed to be a function of the crack spacing, l. The suggested function is a quadratic of the form CBlAl ++2 with a maximum limit of another constant, D.The values of the 4 constants A, B, C and D have been calibrated from their own test data, but only 3 data points have been used for this calibration. The design method therefore lacks verification and justification. Blaschko (2003) investigated the bond behaviour of CFRP strips glued into slits in concrete structures, observing that the bond-slip behaviour appears to be influenced by the distance from the strip to the edge of the beam. Where strips are placed within 150mm of the edge, transverse deformation of the concrete becomes a significant parameter in the bond behaviour. On the basis of his test data and an elastic analysis that considered the transverse deflections of the concrete, Blaschko developed a simplified approach for design that has been calibrated using test data. The anchorage force is a parabolic function of bond length up to a bond length of 115mm, after which it increases linearly with bond length - see Figure 3.

Figure 3 Model for bond force versus bond length (Blaschko, 2003).(ar = distance from the strip to the edge of the beam)

This method is simple to apply and the curve describing anchorage force against bond length has a similar form to the design models for externally bonded FRP (Highways Agency, 2004; Smith and Teng 2002; Denton et al 2004). However, the method is only suitable for FRP strips, not bars, and it refers only to splitting of the adhesive, with no criteria relating to concrete splitting. Further research would be necessary to extend the methodology to include design criteria relating to concrete splitting. Concrete splitting is not such a problem for NSM strips as it is for NSM bars, because of the differences in geometry between the two cases. The bond stresses in the concrete arising from circular bars tend to form in a pattern of radial compression and circumferential tension, so that there will be some vertical tensile stresses near the concrete surface, which can easily lead to spalling of the concrete. However, when FRP strips are used, the compressive bond stresses are perpendicular to the strip, and there is much less likelihood of a vertical tension failure in the concrete. The region that is most likely to fail in concrete splitting is the corner,

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particularly if the edge strip is close to the edge of the beam. However, it appears from Blaschko’s research that as long as the edge strip is at least 150mm from the edge of the beam then there is no deterioration in bond strength. For strips that are more than 150mm away from the edge of the beam or slab, Blaschko’s proposed model can be simplified and summarised as follows:

♦ Initial parabola up to a bond length of 115mm, when kKLkV bF ,, 56.91 τ=o FV,k is the characteristic bond force in N, o bL is the width of the FRP strip in mm, o τK,k is the characteristic shear strength of the adhesive in N/mm2

♦ At bond lengths greater than 115mm the bond force increases at a constant rate, equivalent to a longitudinal shear stress of kK ,0988.0 ττ =

This method is therefore broadly analogous to the approach for externally bonded FRP presented in draft Standard BD 85 (Highways Agency, 2004), where the anchorage region (up to a certain bond length) is designed using a similar curve describing the bond force as a function of bond length; outside this region a limiting longitudinal shear stress applies. It appears that the use of NSM strips could be an efficient strengthening technique. However, there is little experimental data with which to verify any design methodologies. The vast majority of experimental data for NSM FRP relates to FRP bars, not strips. 2.7 Analogy with externally bonded FRP strengthening design

The design philosophy for NSM FRP strengthening will have aspects in common with that of externally bonded FRP. The limit states to be considered in design of both types of strengthening are:

♦ Concrete crushing;

♦ FRP fracture;

♦ Debonding or separation of the FRP Design for FRP fracture and concrete crushing may be carried out in the same way for NSM FRP as for externally bonded FRP. The key difference between the performance of NSM FRP and externally bonded FRP is the bond behaviour. Debonding of externally bonded FRP has been reviewed by Smith and Teng (2002) and Denton et al (2004). The anchorage model that has generally been adopted in UK design guidelines (Highways Agency, 2004; Concrete Society, 2004) is based on the research of Neubauer and Rostasy (1997), who have modelled the anchorage force that may be developed in CFRP plates bonded to concrete. Test results have shown that the bond force is not proportional to the bond length, and that at a certain anchorage length the bond force reaches a plateau. Neubauer and Rostasy have hypothesised that the peak bond stress is proportional to the concrete tensile strength, and that the bond-slip characteristic is independent of the bond length (as long as the bond length exceeds a certain anchorage length). The fracture energy, which is the area under the bond-slip curve, can therefore be written as

ctmff fCG = [3]

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where Gf is the fracture energy, fctm is the concrete tensile strength, and Cf is a constant with units of length, related to the characteristic slip. Neubauer and Rostasy calibrated Cf using their own experimental test results, giving a mean value of 0.204mm with reasonably good consistency between specimens. Based on this fracture energy, the maximum anchorage force has then been derived as

ctmfffbctmffffb ftEbkKfCtEbkF 1max 2 == [4] where kb is a factor that depends on the ratio of the FRP strip width to the width of concrete, bf is the FRP strip width, Ef is the FRP stiffness and tf is the FRP plate thickness. K1 is a constant with a mean value of 0.64 in units of mm0.5 and a characteristic design value of 0.5mm0.5.

The anchorage length required to activate Fmax is proportional to Fmax/kbbffctm, and can therefore be written as

ctm

ff

ftEK

L 2max = [5]

where K2 has been calibrated as 0.5mm. At bond lengths L that are less than Lmax, the anchorage force has been modelled as a parabola, as suggested by Holzenkampfer (1994), so that

−=

maxmaxmax 2

LL

LLFF for maxLL < [6]

NSM FRP has better bond properties than externally bonded FRP, because it is embedded in the concrete rather than bonded to the surface concrete (Nanni, 2000). The guidelines for externally bonded FRP could be conservatively applied for the design of NSM FRP. However, there are problems with this approach:

♦ The differences in geometry between NSM bars and strips and external FRP would make it impossible to apply the design formulae in their current form;

♦ It would not model the mechanics of the various NSM failure modes;

♦ It would be very conservative;

♦ It would suggest that NSM FRP was no more efficient and generally less cost-effective than externally bonded FRP.

However, a methodology that was analogous to the design process for externally bonded FRP would be desirable, if it modelled the mechanics appropriately, since this would provide commonality of approach in the design standards. Debonding of NSM FRP can often occur due to concrete splitting. This mechanism may be modelled in a similar way to external FRP, making appropriate adjustments to account for the different geometry of NSM FRP. Assuming that Equation [3] is valid, and by analogy with Equations [4],[5], and [6], it is proposed that the anchorage capacity of an FRP bar could be modelled using equations [8], [9] and [10]:

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ctmgbarf fpAEKF 3max = [8]

ctmg

barf

fpAE

KL 4max = [9]

−=

maxmaxmax 2

LL

LLFF for maxLL < [10]

where Abar is the area of an FRP bar, pg is the total length of the groove perimeter between the adhesive and the concrete, and K3 and K4 are constants. Analysis of the previously published experimental data for NSM bars in epoxy adhesive confirms that a model of this type appears to represent the data fairly well with K3=1.9 and K4=4.5, as illustrated in Figure 4. Only debonding failures have been plotted; failures in the adhesive have been omitted. For comparison, the equivalent Neubauer and Rostasy model for external FRP is also plotted; it is clear that the use of this model for NSM would be inappropriately conservative.

0

0.5

1

1.5

2

2.5

3

0 5 10

L/(EA/p g f ctm )0.5

F/(E

Apgf

ctm

)0.5

De Lorenzis et al (2004) (epoxy, CFRP spirally woundbars)

De Lorenzis & Nanni (2002) (epoxy, CFRP sandblastedbars)

De Lorenzis et al (2002a) (epoxy, CFRP, spirallywound, sandcoated)

De Lorenzis et al (2002b) (epoxy, CFRP spirallywound)

De Lorenzis et al (2002b) (epoxy, CFRP deformedbars)

De Lorenzis & Nanni (2002) (epoxy, CFRP deformedbars)

De Lorenzis et al (2004) (epoxy, CFRP deformed bars)

De Lorenzis et al (2004) (epoxy, GFRP deformed bars)

De Lorenzis et al (2000) (epoxy, GFRP deformed bars)

De Lorenzis & Nanni (2002) (epoxy, GFRP deformedbars)

De Lorenzis et al (2002b) (epoxy, GFRP deformedbars)

Taljsten et al (2003) (epoxy, CFRP square rods)

Preliminary NSM FRP model

Neubauer and Rostasy external FRP model

(4.5,1.9)

Figure 4: Model for NSM debonding (adhesive failures not shown). The model shown in Figure 4 has been incorporated into the Concrete Society’s second edition of TR55 (2004), along with a separate model that was developed to account for adhesive splitting. The adhesive splitting model comprises a limiting average bond strength in the anchorage region of 0.1 times the adhesive tensile strength for plain sand-coated and spirally wound bars, and 0.3 times the adhesive tensile strength for deformed bars. After the guidelines in TR55 were drafted, the methodology was reviewed using the latest published research. Subsequent analysis of the adhesive splitting model using an up-to-date data set showed that, although it was representative for the majority of the published data, it could be prohibitively conservative when adhesives with lower tensile strengths were used. In the UK market, epoxy adhesives with tensile strengths of around 6.5N/mm2 are commonly used, and the adhesive bond strength predicted by TR55 could be particularly conservative for

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these products. It therefore appears that the adhesive splitting model in TR55 could be updated to be more representative of the adhesives that are likely to be used. For this reason, combined with the observation that it was sometimes difficult to identify the debonding failure mechanism in experimental tests, the debonding model was re-calibrated to include all debonding failures, and the issue of adhesive splitting was re-examined in the development of design guidelines. By including all debonding failures, the data can be better represented by using the values of K3 = 1.5 and K4 = 4.5 in the debonding model, as illustrated in Figure 5.

0

0.5

1

1.5

2

2.5

3

0 5 10 15

L/(EA/p g f ctm ) 0.5

F/(E

Apgf

ctm

)0.5

De Lorenzis & Nanni (2002) (epoxy, GFRP deformedbars)De Lorenzis & Nanni (2002) (epoxy, CFRP sandblastedbars)De Lorenzis & Nanni (2002) (epoxy, CFRP deformedbars)De Lorenzis et al (2002a) (epoxy, CFRP, spirally wound,sandcoated)De Lorenzis et al (2000) (epoxy, CFRP sandblasted)

De Lorenzis et al (2000) (epoxy, GFRP defo rmed bars)

De Lorenzis et al (2002b) (epoxy, CFRP spirally wound)

De Lorenzis et al (2002b) (epoxy, CFRP deformed bars)

De Lorenzis et al (2002b) (epoxy, GFRP deformed bars)

Taljsten et al (2003) (epoxy, CFRP square rods)

El-Hacha and Rizkalla (2004) epoxy, CFRP plain bars

De Lorenzis et al (2004) (epoxy, CFRP defo rmed bars)

De Lorenzis et al (2004) (epoxy, GFRP defo rmed bars)

De Lorenzis et al (2004) (epoxy, CFRP spirally woundbars)Proposed NSM FRP model

Neubauer and Rostasy external FRP model

(4.5,1.5)

Figure 5 Debonding model for NSM FRP (all debonding failures shown). The UK guidelines for externally bonded FRP (Concrete Society, 2004; Highways Agency, 2004) also specify a limiting FRP strain of 0.008 and a limit to the longitudinal shear stress outside the anchorage region. The limiting shear stress is 0.8N/mm2 in TR55 (Concrete Society, 2004); in draft BD 85 (Highways Agency, 2004) the limiting shear stress is taken from BS 5400: Part 4. Due to the improved bond performance of NSM FRP, it is likely that these limits could err on the conservative side for NSM FRP. However, given that the application of NSM FRP is still relatively new, it appears sensible that some strain limit should be retained for the design of NSM FRP. 2.8 Environmental effects

Micelli et al (2003) investigated the effects of adverse environmental conditions on concrete beams strengthened with NSM FRP. Four beams were exposed to environmental agents including freeze-thaw, high temperature and high relative humidity cycles, with indirect UV exposure, while two beams were kept at normal laboratory conditions to serve as control specimens. FRP coupons were also treated to the same conditions. Their conclusions were as follows:

♦ The longitudinal and transverse properties of the FRP coupons were unaffected by the conditioning;

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♦ Environmental exposure did not adversely affect the SLS and ULS capacity of the strengthened beams;

♦ NSM FRP appears to have minimal long-term degradation due to environmental conditions.

2.9 Future research needs

The material behaviour of FRP, epoxy and concrete is well understood. However, challenges remain in modelling the interaction of the three materials in a strengthening system. The behaviour of the interfaces is a particular area that would benefit from further research. More test data for concrete specimens strengthened with NSM FRP is required, particularly using FRP strips, or square or rectangular bars, rather than round bars. There is little data regarding the relative merits of different types of FRP. Most research has been carried out for plain sand-coated CFRP bars, and the potential benefits of using different fibre materials, bar types and surface finishes remain unclear. NSM FRP strengthening can also be used to increase the shear capacity of concrete beams. The benefits presented above for flexural strengthening are equally applicable. The provision of sufficient anchorage is the main limitation associated with externally bonded FRP systems: this might be less critical if the FRP is provided in NSM form. Some information was identified in the literature review but this application was beyond the scope of the present project. More test data in particular are required.

3 Experimental programme

3.1 Introduction

The objective of the test programme was to supplement the test information previously published so that any proposed design approach could be validated. Within the scope of the project, only a limited experimental programme was possible so it was decided to use small scale beam specimens and target the testing at particular parameters. Details were determined following the literature review. If full composite action between the existing concrete section and the applied FRP can be ensured, then design is straight-forward. The FRP material acts as additional external reinforcement and flexural capacity can be determined using strain compatibility along with appropriate properties for concrete, steel and FRP. The failure modes of concrete crushing and FRP rupture must be considered. With near surface mounted reinforcement, as with externally bonded FRP, the main concern is the effectiveness of the bond between the FRP/adhesive system and the concrete, particularly near the end of the bar where anchorage bond might be critical. Any design approach must include consideration of these additional modes of failure. Previous testing has demonstrated that bond failure tends to be the critical factor, either at the FRP/adhesive interface or the adhesive/concrete interface, leading ultimately to separation of the FRP/adhesive system from the concrete. As a result the testing focused on the following parameters:

♦ size of FRP bar

♦ size of groove

♦ length of beam over which the bar is applied.

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Details of the beam and loading configuration were devised following the literature review on the basis of a preliminary design approach as outlined in Section 2 above. The following sections contain the details of the test beams, a description the strengthening system, and the behaviour of each beam as it was loaded to failure.

Table 1: Results of tests on 100mm cubes.

Dimensions Failure Load Compressive Strength Averagemm3 kN N/mm2 N/mm3

100 556 55.6100 595 59.5100 583 58.3100 570 57.0100 535 53.5100 570 57.0100 561 56.1100 571 57.1100 580 58.0100 567 56.7100 640 64.0100 639 63.9100 615 61.5100 662 66.2100 632 63.2

Cubes tested at 28 days

Cubes tested at time of beam tests

63.8

57.4

55.3

57.6

57.7

56.6

3.2 Description of test beams

The general dimensions and layout of the test beams are shown in Figure 6. In all, 6 beams were fabricated and strengthened. An additional load test was carried on an unstrengthened part of one of the beams to determine its flexural capacity. All the beams were 3.05m in length and 120mm x 240mm in cross-section. They were reinforced longitudinally with three 6mm diameter high strength deformed reinforcing bars (T6), giving a reinforcement ratio (Ac/bdeff) of 0.35%. The anchorage consisted of a straight bar, extending at least 20 times the diameter past the centre of the support. A similar amount of top steel was provided, primarily to hold the shear links in place: these consisted of T10 links spaced at 150mm centres. This vertical steel was sufficient to prevent shear failure occurring prior to failure of the strengthened beam in flexure. A consistent cover of 25mm was provided to the links and ends of the bars.

The beams were cast in batches of three, with care taken to ensure that all beams had concrete of consistent quality and strength. Cubes were be taken at the time of casting and tested at 7 days, 28 days and within a few days of the test. The target mean strength was 55N/mm2. The cube test results are shown in Table 1. The test day cube strengths varied between 61 N/mm2

and 66 N/mm2. with a mean of 63.8 N/mm2.

Tensile tests were carried out on the reinforcement to determine appropriate values of strength and modulus to use in the analysis. The results are shown in Table 2: the mean yield strength of the bars was 539 N/mm2.

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a) Elevation

b) Cross-section

Figure 6 General layout of test beams.

240mm

120mm

cover 25mm

cover 25mm

cover 25mm

3T6

3T6

2600mm 3050mm

20T10 @ 150c/c 100mm

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Table 2: Results of tensile tests on reinforcement.

Sample Section Max load E (kN/mm2) ElongationNo (mm2) (kN) 0.20% UTS1 27.39 15.083 196.39 542 551 15.02 27.39 14.892 204.50 530 544 15.03 27.65 14.483 195.13 467 524 28.8

Average = 539.4 N/mm2

SD = 13.9 N/mm2

COV = 2.6%

Stress (N/mm2)

3.3 Strengthening system

Six reinforced concrete beams were strengthened with FRP bars provided by Degussa Construction Chemicals (UK). The bars used were pultruded MBT (Master Builders Technology) FRP bars. Two different bar types were available. The first was a plain bar with a surface roughness provided by a peel-ply system: these bars have a typical tensile strength of 2,500N/mm2, a modulus of 165,000N/mm2 and strain to failure of 1.5%. Various bar sizes were available. The second was a “spiral” bar which has an additional FRP strip wrapped around the bar to improve the bond characteristics. Spiral bars have a typical tensile strength of 2,000N/mm2, a modulus of 155,000N/mm2, a strain to failure of 1.5% and are available in the same bar sizes. These bars were manufactured specifically for near-surface mounted strengthening applications and a suitable epoxy adhesive was provided. Application of the NSM strengthening system consists of the following (taken from guidelines for NSM installation provided by MBT):

1. Cut grooves to the required width

2. Grooves should be clean, dry and free of debris

3. A minimum of 3mm clearance should be provided around the bar

4. Primer may be required on porous surfaces

5. Adhesive should be mixed as directed

6. Apply the adhesive to the prepared groove and insert bar

7. Level to adhesive to provide a smooth surface. In the strengthening of the test beams these guidelines were followed closely. The beams were inverted to provide easier access to the soffit. The grooves were cut with a circular disc cutter. The outline of the groove was marked on the concrete surface beam and two cuts were made along the edges to the required depth. The centre concrete was then removed using a hammer and chisel. Two different sizes of groove were used, nominally 16mm x 16mm and 25mm x 25mm. No other treatment was carried out on the cut concrete other than cleaning (using a wire brush and compressed air) to remove dust and debris. Primer was not required as the concrete was of good quality. Two different size of bars were used, 8mm and 14mm. Spacers were used to keep the bar in the required position and to maintain a minimum amount of adhesive between the bar and the concrete. Regarding the installation of the NSM system, the following conclusions can be made:

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♦ Cutting the grooves with a hand-held disk cutter, although dusty, was straightforward. The procedure was time consuming because of the high quality of the concrete and the cutting disks tended to wear quite quickly. Working overhead would have been more difficult and would require more care to maintain accuracy.

♦ The cut surfaces were clean and only needed light brushing and blowing out to remove dust and loose particles.

♦ Mixing and applying the adhesive was straightforward but would have been more difficult if working overhead.

♦ The 3mm cover to the bars was maintained by using spacers attached to the bars.

♦ Inserting the bars was easy, although this would have been more difficult if working overhead and would have required fixings to hold bars in position.

♦ Installation was concluded by smoothing off the adhesive surface and removing excess. No other finishing was applied, although surface could have been painted if required.

♦ No curing was required as installation was carried out in the laboratory. Details of the strengthening activities are presented in Figure 7. Details of each individual strengthening configuration are given in Section 2.5. Installation of the NSM system is generally more complicated than externally bonded FRP systems. Cutting the groove is more labour intensive than the surface preparation required for externally bonded systems, although this may not be the case where the concrete surface is dirty and more thorough cleaning is required. Priming which is always required for external systems is rarely necessary for NSM except where very porous concrete is present. It is easier to put the NSM bars in place and finishing is more straightforward as the multiple layers and final overcoating used with external systems are not required. Aside from the cutting the grooves, NSM systems can be installed in one operation, while for external systems delays occur due to the time delays between priming, installing the FRP and final finishing. 3.4 Loading configuration and instrumentation

The load tests were carried out on beams spanning 2.6m, using a single point load applied at the centre of the beam as shown in Figure 8. The beam details and test configuration were devised to produce a flexural failure in all the strengthened beams. Flexural failure of the control beam was expected to occur at a load of 14kN (for a concrete strength of 64N/mm2). The load causing shear failure was estimated to be 252kN, well above the load required to cause flexural failure in the strengthened beams. The load at which the shear capacity of the concrete is exceeded was calculated to be about 41kN. This load is indicative of when shear cracking might be expected to initiate. During the load tests on the strengthened beams, only minor shear cracking was expected. The test configuration shown in Figure 8 was devised to determine the flexural capacity of the strengthened beams. Each beam was placed on simple supports, one allowing rotation and the other allowing rotation and sliding. Load was applied using a single manual hydraulic cylinder reacting against a steel box cross-head. The cross-head was held down with high strength steel bars, threaded to allow adjustment of the position of the cross-head. The loading rig had a maximum capacity of about 150kN.

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Figure 7 Details of strengthening.

NSM1

2.5mSlot 16mmx16mm for 8Ф plain bar

NSM2

1.25mSlot 16mmx16mm for 8Ф plain bar

NSM3

1.75m

Slot 16mmx16mm for 8Ф plain bar

NSM4

1.75mSlot 25mmx25mm for 8Ф plain bar

NSM5

1.75mSlot 25mmx25mm for 8Ф spiral bar

NSM6

2.0mSlot 25mmx25mm for 14Ф plain bar

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Figure 8 Test configuration and instrumentation.

The behaviour of the beam throughout each load test was monitored using a series of Celesco displacement gauges. Any cracking, crushing, bond failure, or other signs of distress were marked on the beam and recorded, with some reference to the magnitude of the applied load. Particular care was taken to record the sequence and mode of failure. Each beam was photographed after failure to record the damage in the beam.

3.5 Schedule of tests

Table 3 shows the schedule of tests that were carried out. The beams all had identical cross section and steel reinforcement detail as described in Section 3.2. Details of the strengthening are given in the table. Test NSM7 was actually carried out on an undamaged length of Beam NSM6.

3.6 Test results

The following sections describe the behaviour of the test beams under load. For each test, a plot of applied load as a function of deflection at the load point is presented, along with a

Table 3: Schedule of tests.

Beamno Top Bottom Vetical

NSM1 120x240 3T6 3T6 T10@150 8Ф plain FRP bar in 16x16 notch over full length of beamNSM2 120x240 3T6 3T6 T10@150 8Ф plain FRP bar in 16x16 notch over 1.25m length of beamNSM3 120x240 3T6 3T6 T10@150 8Ф plain FRP bar in 16x16 notch over 1.75m length of beamNSM4 120x240 3T6 3T6 T10@150 8Ф plain FRP bar in 24x24 notch over 1.75m length of beamNSM5 120x240 3T6 3T6 T10@150 8Ф spiral FRP bar in 24x24 notch over 1.75m length of beamNSM6 120x240 3T6 3T6 T10@150 14Ф plain FRP bar in 24x24 notch over 2.0m length of beamNSM71 120x240 3T6 3T6 T10@150 Unstrengthened

1 Test carried out on Beam NSM6

Section Strengthening detailsSteel

DG5 DG4 DG3 DG2 DG1

LOAD CELL

HYDRAULIC CYLINDER

Rocker bearing

Roller bearing

C

2.6m

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photograph of the beam after failure. Table 4 summarises the test results, giving the applied load to failure and the mode of failure.

Table 5 presents predicted capacity, as determined using the methodology outlined in Section 4 with all partial factors set to 1.0 and using mean rather than characteristic values of concrete and steel strengths. Discussion of the test results in terms of the analysis is presented later in Section 4.

Table 5: Predicted failure loads.Values given in terms of applied load (kN)

FlexureBeam (at 10D from FRP Concrete FRP

no Flexure Vc Vc+Vst end of bar) rupture crushing debondNSM1 13.9 40.7 252.4 169.1 56.0 56.0 43.0NSM2 13.9 40.7 252.4 25.3 56.0 56.0 23.0NSM3 13.9 40.7 252.4 38.4 56.0 56.0 33.0NSM4 13.9 40.7 252.4 38.4 56.0 56.0 39.0NSM5 13.9 40.7 252.4 38.4 56.0 56.0 39.0NSM6 13.9 40.7 252.4 71.5 125.0 87.0 45.0NSM71 13.9 40.7 252.4 - - - -

1 Test carried out on Beam NSM6

Unstrengthened Strengthened

3.6.1 Beam NSM1 Beam NSM1 was strengthened using a single plain 8mm carbon FRP bar bonded into a 16mm x 16mm groove. The bar extended between the supports for almost the full length of the beam using the application procedure described in Section 3.3. The length of the FRP bar was 2.5m, so that each end was 50mm away from the centre of the support. The test was carried out using the loading configuration and methodology described in Section 3.4.

Figure 9 shows Beam NSM1 after the test, along with a plot of load against deflection recorded during the load test.

The first flexural crack occurred close to the load point at a load of 6.0kN. The size and extent of flexural cracking increased as more load was applied. These cracks were present on the soffit of the beam but did not extend into the epoxy mortar until a load of 14.0kN was achieved. The first signs of local debonding occurred at a load of 24.0kN when cracks were seen to extend along the interface between the epoxy and the concrete (see photograph of soffit in Figure 10). These were close to the load point and extended for only about 20mm.

Table 4: Summary of test results.Values given in terms of applied load (kN)

Beam Max Deflectionno Flexure Shear Debond load at max load

NSM1 4.0 26.5 11.3 45.2 40.9 Crushing of concrete followed by rupture of steel reinforcementNSM2 9.0 23.0 24.2 25.1 19.6 Failure of section outside strengthened region: Rupture of steelNSM3 7.7 32.0 21.2 33.7 23.2 Debonding of FRP bar and epoxy at end of barNSM4 7.7 33.0 33.8 39.4 29.2 Debonding of FRP bar and epoxy at end of barNSM5 7.0 34.0 31.8 39.3 23.6 Debonding of FRP bar and epoxy at end of barNSM6 9.5 - - 45.3 15.8 Debonding of FRP bar and epoxy at end of bar

NSM71 7.0 - - 15.92 28.22 Rupture of steel reinforcement1 Test carried out on Beam NSM6 2Corrected for different span

First crackingMode of failure

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When the applied load reached 42.3kN, these interfacial cracks had grown in length to about 75mm. The first signs of crushing of the concrete in the compression zone were observed at a load of 45.2kN and a deflection of 40.9mm. Subsequent increments resulted in loss of load capacity. The crushing continued to progress until a deflection of about 42mm when the three steel reinforcing bars fractured and sudden failure occurred. The maximum load achieved by beam NSM1 was 45.2kN. Figure 10 shows the condition of the soffit of the beam under the loading point after failure. This was the only location of damage in the adhesive. The progress of the debonding cracks is clear. No damage occurred near the ends of the FRP bar.

3.6.2 Beam NSM2 Beam NSM2 was strengthened using a single plain 8mm carbon FRP rod in a 16mm x 16mm groove. However, the beam was only strengthened over a length of 1.25m centred on the midpoint of the beam. The objective was to examine the effect of curtailing the FRP bar in an area of high bending moment. The test was carried out using the loading configuration and methodology as for beam NSM1. Figure 11 shows the beam after the test, along with a plot of load against deflection.

The first flexural crack occurred close to the load point at a load of 8.0kN. The first crack through the epoxy occurred at a load of 17.5kN. At a load of 19.6kN, a crack occurred through the epoxy and concrete at one end of the FRP bar. At a load of 24.3kN this crack extended horizontally and the FRP bar and cover concrete began to peel away from the rest of the beam - see Figure 12. Further increments resulted in a slightly higher load. The maximum load achieved was 25.1kN at a deflection of 19.6mm. The load then started to decrease and concrete crushing started to develop at the top of the beam at the section where the FRP bar was curtained. Figure 12 shows a close-up of the failure zone. At a deflection of about 25mm sudden failure occurred when one of the three steel reinforcing bars ruptured at this point.

3.6.3 Beam NSM3 Beam NSM3 was strengthened in the same way as beam NSM2 except that the FRP curtailment point was moved by increasing the length of the FRP bar to 1.75mm. The test was carried out using the loading configuration and methodology as for the previous tests. Figure 13 shows the beam after the test, along with a plot of load against deflection.

The first flexural crack occurred close to the load point at a load of 7.7kN. At a load of 21.2kN a crack occurred in the concrete at one end of the FRP bar. With the next increment, load 24.1kN, a crack occurred along the concrete/epoxy interface close to mid span. These did not develop with further application of load. At a load of 32.1kN a horizontal crack developed at one end of the FRP bar and the FRP bar and cover concrete began to peel away in the same way as in Beam NSM2. Further increments resulted in a slightly higher load with a maximum load of 33.8kN at a deflection of 23.3mm. The load then started to decrease. The test was terminated at a deflection of 32mm when the capacity had reduced to 27.7kN.

3.6.4 Beam NSM4 Beam NSM4 was strengthened in the same way as beam NSM3 but for this beam the groove size was increased to 25mm x 25mm. Figure 14 shows the beam after the test, along with a plot of load against deflection. Initially the beam behaved in a very similar way to beam NSM3, with first flexural crack at 7.7kN at mid-span. At a load of 26.4kN a flexural crack occurred at one end of the bar. This flexural crack began to widen at a load of 36.7kN and horizontal cracks occurred at the FRP curtailment point at a load of 38.6kN. These horizontal cracks continued to extend until a load of 39.4kN and a deflection of 29.2mm, when the load suddenly fell to 26.9kN as the FRP bar/epoxy/cover concrete began to detach. The maximum load (39.4kN) was 17% higher than that carried by NSM3. The test was terminated at a deflection of 30.5mm.

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3.6.5 Beam SM5 With beam NSM5, a spiral bar was used to strengthen the beam. This was inserted in a 25mm x 25mm groove over a length of 1.75mm. It was expected that this would have better bond with the epoxy adhesive but the effect on overall load capacity was unclear. Figure 15 shows the beam after the test, along with a plot of load against deflection. This beam behaved in a very similar way to beam NSM4, with first flexural crack at 6.9kN at mid-span and a flexural crack at one end of the bar at 29.8kN. Horizontal cracking occurred at a load of 31.8kN. These horizontal cracks continued to extend until a load of 39.3kN when the FRP bar/epoxy/cover began to detach. The test was terminated at a deflection of 31mm.

3.6.6 Beam NSM6 For this test, a 14mm FRP bar was used. This was inserted into a 25mm x 25mm groove over a length of 2.0m. Figure 16 shows the beam after the test, along with a plot of load against deflection. First flexural cracking occurred at a load of 9.4kN and the first signs of flexural cracking at the end of the FRP bar occurred at 30.9kN. At 40.2kN, flexural cracking developed at the other end, and horizontal cracks were observed at both ends. When the load reached 45.3kN (deflection 15.8mm), the FRP bar/ epoxy/cover concrete began to detach from one end (see Figure 16) and the load reduced. The test was terminated at a deflection of 21mm.

3.6.7 Test NSM7 This test was carried out on an undamaged portion of beam NSM 6 and was used to determine the flexural capacity of the unstrengthened section. The specimen was turned upside down and the span was reduced to 2.0m so as to avoid damage in the specimen from the previous test. First flexural cracking occurred at a load of 7.0kN. At 18.0 kN the first signs of concrete crushing were evident. The maximum load achieved was 20.6kN: this is equivalent to a load of 15.9kN over a span of 2.6m. Failure occurred at a deflection of 23mm when one of the three reinforcing bars ruptured. On the next loading increment the two remaining bars fractured. Figure 17 shows the beam after the test, along with a plot of load against deflection (corrected for span of 2.6m). 3.7 Comparison of all test results

Figure 18 shows the behaviour of all the beams on the same plot for comparison. For NSM7, the load and deflection were corrected to allow for the shorter span. The increase in strength obtained from the NSM FRP bars is evident. For all the strengthened beams the initial behaviour was similar to the unstrengthened case except for a small increase in stiffness due to the addition of the FRP bars. At loads above the unstrengthened beam capacity, all the beams had similar stiffness except NSM 6 which had a much bigger FRP bar (14mm). While crack widths were not measured during the loads tests, visual examination during the loading suggested that they were not excessive (<0.25mm). Full comparisons with theoretical behaviour is given in the following section.

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a) Photograph of beam after test.

0

10

20

30

40

50

0 10 20 30 40 50 60Deflection (mm)

Load

(kN

)

first cracking

first crack in epoxy

local debond in epoxy/concrete

unload to straighten jack

further cracking in epoxy

first shear crack

further debonding

first crushing

unload

rupture of steel

b) Plot of load against deflection.

Figure 9 Behaviour of Beam NSM1.

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Figure 10 Cracking on soffit of Beam NSM1 after failure.

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a) Photograph of beam after test.

0

5

10

15

20

25

30

0 5 10 15 20 25 30Deflection (mm)

Load

(kN

)

first cracking

first crack in epoxy

crack through epoxy at end of bar

horizontal crack

"peeling" rupture of one steel bar

b) Plot of load against deflection.

Figure 11 Behaviour of Beam NSM2.

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Figure 12 Close up of failure zone in Beam NSM2.

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a) Photograph of beam after test.

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35Deflection (mm)

Load

(kN

)

first cracking

crack in epoxy at mid-span

crack through epoxy at end of bar

maximum load

"peeling"

unload

cracks at epoxy-concrete interface

b) Plot of load against deflection.

Figure 13 Behaviour of Beam NSM3.

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a) Photograph of beam after test.

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35Deflection (mm)

Load

(kN

)

first cracking

crack in epoxy at mid-span

crack through concrete at end of bar

maximum load

"peeling"

crack through epoxy at end of bar

b) Plot of load against deflection.

Figure 14 Behaviour of Beam NSM4.

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a) Photograph of beam after test.

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35Deflection (mm)

Load

(kN

)

first cracking

crack in epoxy at mid-span

crack through concrete at end of bar

maximum load

"peeling"

crack through epoxy at end of bar

horizontal crack

b) Plot of load against deflection.

Figure 15 Behaviour of Beam NSM5.

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a) Photograph of beam after test.

0

5

10

15

20

25

30

35

40

45

50

0 5 10 15 20 25 30 35Deflection (mm)

Load

(kN

)

first cracking

crack through concrete at end of bar

maximum load

"peeling"

flexural crack at end of bar

horizontal crack

b) Plot of load against deflection.

Figure 16 Behaviour of Beam NSM6.

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a) Photograph of beam after test.

0

5

10

15

20

25

0 5 10 15 20 25 30 35Deflection (mm)

Load

(kN

)

first cracking

maximum load

crushing

b) Plot of load against deflection.

Figure 17 Behaviour of Beam NSM7.

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0

5

10

15

20

25

30

35

40

45

50

0 10 20 30 40 50 60Deflection (mm)

Load

(kN

)

NSM1NSM2NSM3NSM4NSM5NSM6Control

Figure 18 Comparison of all tests.

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4 Comparison with theoretical analysis

The test results have been analysed using software developed by PB specifically for the design of FRP strengthening. By considering the response of the strengthened section to gradually increasing loads, it has been possible to model the strains at every point in the span at various loads. Limit states where composite action is maintained have been investigated by assuming that plane sections remain plane. The relationship between the applied load and the strain in the FRP is plotted in Figure 19. The theoretical loads required to cause shear failure and concrete crushing are shown. FRP fracture is predicted at an ultimate FRP strain of 0.015, which is at the end of the curve in the figure. Since failure could also potentially be influenced by large longitudinal shear stresses at the point where the steel yields, or shear cracking in the concrete, the loads causing the steel to yield and the shear capacity neglecting the stirrups are also shown in Figure 19. The load causing an FRP strain of 0.008 can also be inferred: this is the maximum strain limit in TR55 (Concrete Society, 2004) and BD 85 (Highways Agency, 2004). Limit states involving loss of composite action have been investigated using the proposed debonding model. The FRP strain profile has been calculated for various values of the applied load, and by comparison with the limiting anchorage force determined using the proposed debonding model, the theoretical load to cause debonding of the FRP has been calculated. In Figure 20 three curves are shown to illustrate the FRP strain profile at three different values of the applied load for Beam NSM1. The limiting strain in the FRP predicted by the debonding model is also shown. The curve corresponding to an applied load of 43kN just intersects with the debonding curve at the end of the anchorage region, hence the proposed model predicts that a load of 43kN will cause FRP debonding.

Section Behaviour

0.000

20.000

40.000

60.000

80.000

100.000

120.000

140.000

160.000

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018Strain in NSM Bars

Equi

vale

ntM

idsp

anLo

ad(k

N)

Reinforced SectionConcrete Crushing LimitSteel YieldUnstrengthened Flex Capacity.Shear Cap. w ithout stirrupsShear Cap. w ith stirrups

Figure 19 Strain in FRP as a function of applied load.

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0

0.002

0.004

0.006

0.008

0.01

0.012

0 0.5 1 1.5 2 2.5 3

Distance along span

NSM

stra

in

Load 43.0 kN (3 pt bending)

Load 36.0 kN (3 pt bending)

Load 24.5 kN (3 pt bending)

Anchorage debonding model

Figure 20 NSM strain profiles for various loads for Beam NSM1.

NSM1: 8mm bar, 2.5m long

0

5

10

15

20

25

30

0 0.5 1 1.5 2 2.5 3

Distance along span

Mom

entk

Nm

Load 43.0 kN (3 pt bending)

Load 36.0 kN (3 pt bending)

Load 24.5 kN (3 pt bending)

Moment capacity

Figure 21 Bending moment diagram for various loads for Beam NSM1.

It is also possible to calculate the bending moment that would cause the tension in the FRP to reach its anchorage limit, assuming that plane sections remain plane. Since the FRP was only applied within part of the span for these specimens, the bending moments in the unstrengthened regions were limited by the unstrengthened moment capacity. Towards the ends of the bars, the anchorage capacity decreases to zero, and so the associated moment to cause debonding will also decrease to zero if plane sections are assumed to remain plane. Hence, towards the ends of the bars the assumed debonding moment will be less than the unstrengthened capacity, and so the overall moment capacity is limited by the unstrengthened capacity. For these specimens the strengthened moment capacity only begins to exceed the unstrengthened capacity at a distance of about 150mm from the ends of the bars. The variation in moment capacity over the whole span can therefore be plotted and compared with the bending moments due to various magnitudes of applied loads. This plot is illustrated in Figure 21 for Beam NSM1. As the loads increase, eventually the bending moment exceeds that expected to cause anchorage failure. For these beams, the anchorage strength is generally exceeded at one of two positions in the span:

♦ At a distance equal to the anchorage length Lcmax from the end of the FRP (for these beams, near mid-span)

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♦ Near the ends of the FRP where the anchorage capacity of the FRP is very low, leading to a flexural failure at a bending moment equal to the unstrengthened flexural capacity.

The limiting bending moments for theoretical anchorage failure and the corresponding loads for the test beams are plotted in Figures 22-25. Beam NSM5 is identical to NSM4, with the exception that the FRP bar is spirally wound instead of a plain bar. The debonding theory currently makes no distinction between these cases, and so the plot for NSM4 also applies to NSM5. The results of this analysis are summarised in Table 6 and compared with the actual failure loads in Figure 26.

Table 6: Summary of predicted failures according to debonding model.

Specimen no

Theoretical mechanism Actual mechanism

Theoretical debonding load

(kN)

Actual failure

load (kN) NSM1 Debonding over most of the span Concrete crushing 43 45NSM2 Debonding of end 156mm,

followed by flexural failure Flexural failure at approx 150mm from end of bar

23 25

NSM3 Debonding of end 156mm, followed by flexural failure. A slightly higher load of 36kN would cause debonding over entire span.

Anchorage debonding of FRP

33 34

NSM4 Debonding over entire span Anchorage debonding of FRP

39 39

NSM5 Debonding over entire span Anchorage debonding of FRP

39 39

NSM6 Debonding of end 240mm, followed by flexural failure

Anchorage debonding of FRP

37 45

NSM2: 8mm bar, 1.25m long

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3

Distance along span, m

Mom

ent,

kNm

Load 33.0 kN (3 pt bending)

Load 23.0 kN (3 pt bending)

Load 24.1 kN (3 pt bending)

Moment capacity

Figure 22 Bending moment diagrams for Beam NSM2 for various loads.

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NSM3: 8mm bar, 1.75m long

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3

Distance along span

Mom

entk

Nm

Load 36.0 kN (3 pt bending)

Load 33.0 kN (3 pt bending)

Load 24.0 kN (3 pt bending)

Moment capacity

Figure 23 Bending moment diagrams for Beam NSM3 for various loads.

NSM4: 8mm bar, 1.75m long

0

5

10

15

20

25

30

0 0.5 1 1.5 2 2.5 3

Distance along span

Mom

entk

Nm

Load 39.0 kN (3 pt bending)

Load 39.0 kN (3 pt bending)

Load 24.7 kN (3 pt bending)

Moment capacity

Figure 24 Bending moment diagrams for Beam NSM4 (and NSM5) for various loads.

NSM6: 14mm bar, 2.0m long

05

101520253035

0 0.5 1 1.5 2 2.5 3

Distance along span

Mom

entk

Nm

Load 45.0 kN (3 pt bending)

Load 37.0 kN (3 pt bending)

Load 24.7 kN (3 pt bending)

Moment capacity

Figure 25 Bending moment diagrams for Beam NSM6 for various loads.

The test results as shown in Figure 26 appear to correlate very well with the debonding model, providing further verification for the model.

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05

101520253035404550

NSM1 NSM2 NSM3 NSM4 NSM5 NSM6

Theoretical failure loadActual failure load

Figure 26 Comparison of predicted and test failure loads. In design, it is also usual to limit the maximum strain to 0.008 and the maximum longitudinal shear stress to around 0.8N/mm2. In the case of these beams, these limits would correspond to the loads in Table 7. In every case except NSM2, the longitudinal shear stress criterion of 0.8N/mm2 would appear to be critical. It therefore appears that for NSM FRP, the longitudinal shear stress limit is rather conservative as it stands. A theoretical analysis of the beams indicates that the longitudinal shear stresses at the failure loads have values ranging from 0.92N/mm2 (for NSM2) to 2.15N/mm2 (NSM6). However, the case under consideration of 3 point bending with a short shear span is particularly onerous for longitudinal shear, and whilst it may appear to govern in the present test cases, it is unlikely to do so in real design situations.

Table 7: Loads based on strain and stress limits.

Beam No

Load for 0.008 strain limit

Load for 0.8N/mm2 longitudinal shear stress limit

Load for debonding model

NSM1 36 24 43 NSM2 36 24 23 NSM3 36 24 33 NSM4 36 24 39 NSM5 36 24 39 NSM6 77 25 37

5 Development of design guidelines

The design of NSM FRP systems should consider the following limit states:

♦ FRP Fracture

♦ Concrete Crushing

♦ Debonding or separation of the FRP. Design for FRP fracture and concrete crushing can be carried out in the same way as for externally bonded FRP.

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As for externally bonded FRP, debonding failures can be avoided in design by limiting:

(i) the strain in the FRP;

(ii) the longitudinal shear stress between the FRP and the concrete section;

(iii) irregularities in the profile of the surface to which the FRP is bonded;

(iv) the stress in the FRP near its end (ie, in the anchorage region).

The same maximum strain and longitudinal shear stress limits can be used for NSM as for externally bonded FRP, although it appears that the longitudinal shear stress limit can be rather conservative. This limit is also known to be somewhat conservative for externally bonded FRP, but prudently so. There does not appear to be sufficient justification based on the current knowledge to allow designs with unlimited longitudinal shear stress, and it is recommended that a limit on longitudinal shear be retained for NSM. This is currently set at a value of 0.008%, ie, the same as that for externally bonded applications. While it is clear that the level of conservatism is greater for NSM applications, there is currently insufficient test information to justify a relaxation of this limit. The shear stress is calculated based on the total length of the perimeter of the interface between the concrete and the adhesive. The Concrete Society guidelines (2004) suggest that this perimeter should be reduced because the sides of the groove will have a smooth surface, which may be less effective in resisting the longitudinal shear stress than the top of the groove. However, it is considered that the longitudinal shear stress limit is already rather conservative for NSM FRP, and reducing the perimeter in this way would make it even more conservative. The risk of failure of the interface itself appears to be low based on the published research, and epoxy adhesives appear to be able to bond adequately to a smooth concrete surface. Hence it is recommended that the longitudinal shear stress be calculated based on the total perimeter of the interface. However, the possibility of limited bond effectiveness is acknowledged in the proposed design guidelines. Geometric irregularities and concavity of the FRP can be avoided with NSM strengthening by ensuring that the groove allows the FRP bars to be installed straight. Debonding of the FRP due to concrete splitting can be considered using the following model, based on many of the same assumptions behind the existing guidelines for externally bonded FRP. Sufficient anchorage should be provided beyond where the strengthening is required, and the force F in an FRP bar within the anchorage length should be limited using the following equations:

ctmgbarf fpAEF 5.1max =

ctmg

barf

fpAE

L 5.4max =

−=

maxmaxmax 2

LL

LLFF for maxLL <

where Abar is the area of an FRP bar in mm2, pg is the total length of the groove perimeter between the adhesive and the concrete in mm, fctm is the characteristic concrete tensile strength in N/mm2 and Ef is the Young’s Modulus in N/mm2.

Splitting failure can occur in the adhesive when the principal tensile stress exceeds the tensile strength of the adhesive. According to Rizkalla and Hassan (2003), the ratio of the tensile

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stress in the adhesive to the tensile stress in the concrete can be expressed as a function of the groove geometry, as illustrated in Figure 2. For groove widths between 1.5 and 2.5 bar diameters and depths of cover between 0.5 and 2.0 bar diameters, the ratio of the tensile stresses based on this method does not exceed 3.5, as illustrated in Figure 27. It appears that for groove geometries within these parameters, adhesive splitting could be avoided by ensuring that the ratio of the adhesive tensile strength to the concrete tensile strength has a minimum value that is well above 3.5. It is suggested that for design, this ratio should be set at 5. Analysis of the published data shows that there is a much greater risk of failure in the adhesive for those tests where the adhesive tensile strength is less than 5 times the concrete tensile strength. Design guidelines need to consider all aspects of the installation and performance of the NSM strengthening system. Application of the system is straight-forward, although it involves more preparation than externally bonded systems. The grooves can be cut into the cover concrete using a circular saw along the edges of the groove and a hammer and chisel to form the rectangular slot. This results in a groove with smooth walls and a relatively rough base. Care must be taken to ensure that existing reinforcement is not damaged during the cutting

operations: a cover-meter survey is required to determine the presence of the existing reinforcement. No other surface treatment is required other than cleaning out loose dirt and debris which can be achieved by brushing and blowing out the debris. However, if the concrete is very porous then the use of a primer may be required: advice should be sought. The groove should be kept clean and dry particularly if there is a time lapse between forming the groove and inserting the bars. The FRP material will be supplied in the form of pultruded rods or strips. Careful transport and handling is required to avoid surface damaging. If the FRP is supplied with a peel-ply protective layer, this should be removed after all the concrete preparation has been carried out and just before the FRP is inserted into the groove. If not, then the surface of the FRP should be thoroughly cleaned with an appropriate solvent. The adhesive supplied with the system should be used. Manufacturer’s instructions regarding mixing, shelf life and curing time should be carefully followed. Installation should consist of firstly filling the groove with adhesive and then inserting the FRP rod: this ensures that the FRP is completely surrounded by adhesive. There should be at least 3mm of adhesive between the FRP and the concrete. Air voids in the adhesive should be avoided by careful compaction of the adhesive. After installation the adhesive can be levelled off to provide a

00.5

11.5

22.5

33.5

4

0.5 1 1.5 2

Cover / bar diameter

Ratio

ofte

nsile

stre

ssin

adhe

sive

tote

nsile

stre

ssin

conc

rete

notch width = 2.5bar diametersnotch width = 2 bardiametersnotch width = 1.5bar diameters

Figure 27 Ratio of tensile stresses in adhesive and concrete, as a function of groove geometry.

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smooth surface. Additional surface treatment can be carried out after the adhesive has fully cured. The design guidelines outlined in this section have been incorporated into Section 4 of BD 85.

6 Conclusion

This report summarises a research project carried out at TRL on behalf of the Highways Agency to investigate the performance of near surface mounted FRP reinforcement as a strengthening technique for concrete bridges. It presents the conclusions of a literature review, details of a small series of load tests on strengthened beams, the background to the development of design guidelines, and draft clauses to incorporate the technique into BD 85. It is accepted that the proposed design approach is conservative, particularly in relation to a proposed strain limit of 0.8% imposed on the FRP which will probably control most design situations. Further experimental work is required before relaxation of this limit can be considered. The project was confined in scope to the flexural strengthening of concrete members using NSM FRP reinforcement. Conventional steel or stainless steel reinforcement could also be used. However, the design approach presented here would not be applicable due to the different bond characteristics. In addition, the technique also has the potential for increasing shear capacity. Further research is required before the technique can be extended to cover these areas.

7 Acknowledgement

The work described in this report was carried out by the Structures Team of TRL Limited. The author is grateful to the various members of the Structures staff who were involved in the fabrication, strengthening and testing of the beams. Particular thanks are due to Bob Owen and Frank McGinley whose help in the fabrication and testing of the beams was invaluable.

8 References

ACI (2002). Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures. ACI Committee 440.2R-02. Blaschko, M (2003). Bond behaviour of CFRP strips glued into slits. Proceedings of the 6th International Symposium of FRP Reinforcement for Concrete Structures (FRPRCS-6), Singapore, 2003, pp 205-214. Concrete Society (2004), Design guidance for strengthening concrete structures using fibre composite materials. Technical Report 55, Second Edition, The Concrete Society, Crowthorne.

De Lorenzis, L, K Lundgren and A Rizzo (2004). Anchorage length of NSM FRP bars for concrete strengthening - Experimental investigation and numerical modelling. ACI Structural Journal Vol 101 No2 Mar-April 2004, pp269-278

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De Lorenzis, L and A La Tegola (2003). Analytical modelling of splitting bond failure for NSM reinforcement in concrete. Proceedings of the 6th International Symposium of FRP Reinforcement for Concrete Structures (FRPRCS-6), Singapore, 2003, pp 975-984. De Lorenzis, L and K Lundgren (2002). Finite element modelling of bond of near-surface mounted FRP reinforcement in concrete. Proc. International FIB Symposium “Bond in Concrete”, Budapest, 2002. De Lorenzis, L, F Micelli and A La Tegola (2002a). Passive and active near surface mounted FRP rods for flexural strengthening of RC beams. Proceedings of ICCI '02, San Francisco. De Lorenzis, L and A Nanni (2001a). Characterization of FRP rods as near-surface mounted reinforcement. Journal of Composites for Construction, Volume. 5, No. 2, May 2001, pp 114-121. De Lorenzis, L and A Nanni (2001b). Shear strengthening of reinforced concrete beams with near-surface mounted fiber-reinforced polymer rods. ACI Structural Journal, Volume 98, No.1, Jan-Feb 2001, pp 60-68.

De Lorenzis, L and A Nanni (2002). Bond between near surface mounted FRP rods and concrete in structural strengthening. ACI Structures Journal, Vol. 99, No. 2, March-April 2002, pp.123-133. De Lorenzis, L and A Nanni (2003). Design procedure of NSM FRP reinforcement for strengthening of RC beams. Proceedings of the 6th International Symposium of FRP Reinforcement for Concrete Structures (FRPRCS-6), Singapore, 2003, pp 1455-1464. De Lorenzis, L, A Nanni and A La Tegola (2000a). Strengthening of reinforced concrete structures with near surface mounted FRP rods. International Meeting on Composite Materials, PLAST 2000, Milan. De Lorenzis, L, A Nanni and A La Tegola (2000b). Flexural and shear strengthening of reinforced concrete structures with near surface mounted FRP rods. Proceedings of the 3rd International Conference on Advanced Composite Materials in Bridges and Structures (ACMBS-III), Ottawa, 2000, pp521-528. De Lorenzis, L, A Rizzo and A La Tegola (2002b). A modified pull-out test for bond of near-surface mounted FRP rods in concrete. Composites: Part B , Volume 33, 2002, pp 589–603. Denton, S R (2001). Analysis of stresses developed in FRP plated beams due to thermal effects. International Conference on FRP Composites in Civil Engineering, Hong Kong, 2001. Denton, S R, J D Shave and A D Porter (2004). Shear strengthening of reinforced concrete structures using FRP composites. Proc. ACIC 2004.

El-Hacha, R and S Rizkalla (2004). Near-surface-mounted fiber-reinforced polymer reinforcements for flexural strengthening of concrete structures. ACI Structural Journal, Volume 101, No 5, Sept-Oct 2004, pp 717-726. Holzenkampfer, P (1994). Ingenieurmodell des Verbunds geklebter Bewehrung fur Betonbauteile. Dissertation TU Braunschweig, 1994, Highways Agency (2004). BD 85: Strengthening of highway structures using externally bonded fibre reinforced polymer. Draft Standard, Highways Agency, London.

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Micelli, F A, A La Tegola and J J Myers (2003). Environmental effects on RC beams with near surface mounted FRP rods. Proceedings of the 6th International Symposium of FRP Reinforcement for Concrete Structures (FRPRCS-6), Singapore, 2003, pp 749-758. Nanni, A (2000). Carbon fibers in civil structures: Rehabilitation and new construction.Proceedings, The Global Outlook for Carbon Fiber 2000, Intertech, San Antonio, Texas. Neubauer, U and F S Rostasy (1997) Design aspects of concrete structures strengthened with externally bonded CFRP-plates. Structural Faults and Repair 1997, Edinburgh, Vol 2 pp109-118 Rizkalla, S H and T Hassan (2003a). Bond characteristics of various FRP strengthening techniques. Proceedings of the 6th International Symposium of FRP Reinforcement for Concrete Structures (FRPRCS-6), Singapore, 2003, pp 123-132. Rizkalla, S.H and T Hassan (2003b). Investigation of bond in concrete structures strengthened with near surface mounted carbon fiber reinforced polymer strips. Journal of Composites for Construction, Volume 7, No. 3, August 2003, pp 248-257. Smith, S T and J G Teng (2002). FRP-strengthened RC beams. I: Review of debonding strength models. Engineering Structures, Volume 24, 2002, pp 385-395. Sumon, S K (2005). Innovative retrofitted reinforcing techniques for masonry arch bridges. Proceedings of the Institution of Civil Engineers, Bridge engineering Journal, Volume 158, September 2005, Issue BE3, London, UK. Taljsten, B, A Carolin and H Nordin, H (2003). Concrete structures strengthened with near surface mounted reinforcement of CFRP. Advances in Structural Engineering, Volume 6, No 3, 2003, pp 201-213.