chapter 5 experimental investigation on moment …

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CHAPTER

5 EXPERIMENTAL INVESTIGATION ON MOMENT REDISTRIBUTION

CONTENTS

5 EXPERIMENTAL INVESTIGATION ON MOMENT REDISTRIBUTION 277

5.1 Introduction 279

5.2 Literature Review 280

5.2.1 Definition of Ductility 280

5.2.2 Definition of Moment redistribution 281

5.2.3 Tests on Continuous Plated RC Beams 283

5.3 Experimental Studies on RC Beams with Externally Bonded Steel/FRP Plates 286

5.3.1 Geometry of Test Specimens 286

5.3.2 Test Setup and Instrumentation 288

5.3.3 Material Properties 290

5.3.4 Test Results 293

5.3.4.1 Beam SS1 (Steel 75x3) 294

5.3.4.2 Beam SS2 (Steel 112x2) 300

5.3.4.3 Beam SS3 (Steel 224x1) 306

5.3.4.4 Beam SF1 (CFRP 25x2.4) 312

5.3.4.5 Beam SF2 (CFRP 50x1.2) 317

5.3.4.6 Beam SF3 (CFRP 80x1.2) 322

5.3.4.7 Beam SF4 (CFRP 100x0.6) 327

5.3.5 Summary and Discussions 333

5.3.5.1 Journal Paper: Moment Redistribution in Continuous Plated RC Flexural Members Part 1 - Neutral Axis

Depth Approach and Tests 333

5.4 Experimental Studies on RC Beams with Near Surface Mounted Steel/FRP Strips 351

5.4.1 Geometry of Test Specimens 351

5.4.2 Test Setup and Instrumentation 355

5.4.3 Material Properties 359

5.4.4 Test Results 361

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5.4.4.1 Beam NS_F1 (5 x CFRP1.2mm) 362

5.4.4.2 Beam NS_F2 (2 x CFRP1.2mm) 369

5.4.4.3 Beam NS_F3 (1 x CFRP1.2mm) 376

5.4.4.4 Beam NS_F4 (1 x 2CFRP1.2mm) 383

5.4.4.5 Beam NS_S1 (4 x Steel 0.9mm) 389

5.4.4.6 Beam NS_S2 (2 x 2 Steel 0.9mm) 394

5.4.4.7 Beam NB_F1 (2 x CFRP1.2mm) 400

5.4.4.8 Beam NB_F2 (2 x CFRP1.2mm) 407

5.4.4.9 Beam NB_F3 (2 x 2CFRP1.2mm) 414

5.4.5 Summary and Discussions 421

5.4.5.1 Journal Paper: Tests on the Ductility of Reinforced Concrete Beams Retrofitted with FRP and Steel

Near Surface Mounted Plates 421

5.5 Summary 441

5.6 References 442

5.7 Notations 444

Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution

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5.1 INTRODUCTION

Reinforced concrete beams retrofitted with externally bonded (EB) or near surface mounted (NSM)

plates can effectively increase the strength of members (Oehlers & Seracino 2004; Swamy & Gaul

1996; Spadea et al. 2001), however, due to premature debonding of the plates as previously

discussed in Chapter 1, the ductility of plated beams can be severely reduced to such an extent that

plating guidelines often exclude moment redistribution (fib 2001; Concrete Society 2000). This

exclusion may reduce the application of plating, particularly when retrofitting buildings where ductility

is often a requirement.

It has been shown in Chapter 1 that plate end (PE) debonding can be prevented by the position of the

termination of the plates. Critical diagonal crack (CDC) debonding can also be prevented through

proper design using the passive prestressed model proposed in Chapter 4. The problem is

intermediate crack (IC) debonding, which is difficult to prevent even though an analytical model has

been proposed in Chapter 2 to model its behaviour. Studies conducted by various researchers have

showed that even though the use of end anchorage can prevent premature PE debonding, local

debonding, that is IC debonding, can still occur along the span of the beam and lead to premature

failure prior to achieving the desired strength or ductility (Ashour et al. 2004; Swamy &

Mukhopadhyaya 1999; Garden & Hollaway 1998; Spadea et al. 1998; Lamanna et al. 2001).

Therefore, the ductility, and consequently the moment redistribution capacity of plated continuous

members is dependent on the IC debonding resistance.

Very little research has been carried out on moment redistribution of EB or NSM beams, even though

many in-situ RC beams are continuous members (El-Rafaie et al. 2002, 2003; Khalifa et al. 1999). It is

suggested by both fib (2001) and Concrete Society (2000) that moment redistribution should not be

allowed for plated RC beams, however Mukhopadhyaya et al. (1998) showed that the ductility of a

plated beam could be higher than that of an unplated beam if designed properly, and from a few tests

carried out by various researchers (El-Rafaie et al. 2002, 2003; Ashour et al. 2004), moment

redistribution is observed. Tests on simply supported RC beams with NSM strips (Hassan & Rizkalla

2003; Taljsten & Carolin 2003; Blaschko 2003) have shown that NSM plates debond or fail at much

higher strains than EB plates, and, hence, it would be expected that NSM plated beams show

substantially greater ductility than EB plated beams. It is therefore necessary to perform further

research on the moment redistribution of EB and NSM members.


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In this Chapter, a literature review is carried out on the existing tests performed by different

researchers on continuous plated RC beams. Through these limited test results, it is shown that

moment redistribution can be obtained in plated members, however further experimental studies are

needed to investigate the moment redistribution behaviour of plated members so that design

approaches can be developed to analyse the moment redistribution of continuous plated members. In

this research, an experimental program was carried out to investigate the behaviour of continuous RC

beams with EB and NSM plates. A series of seven full-scale tests on two span continuous beams with

EB steel or CFRP plates was performed and analysed, and is described in detail in Section 5.3 with a

summary and discussion of the test results presented in the journal paper Oehlers et al. (2004)

included in Section 5.3.5.1. In Section 5.4, nine two-span continuous beams retrofitted with NSM steel

or CFRP strips were tested to examine the ductility capacity as measured directly by the moment

redistributed. A summary and discussion of the test results are presented in the journal paper Liu et al.

(2005) included in Section 5.4.5.1. The test results presented in this Chapter will be used later in

Chapter 6 to verify the flexural rigidity approach developed in this research for analysing the moment

redistribution of plated members.

5.2 LITERATURE REVIEW

In this Section, the importance of ductility and how the member ductility can be affected by externally

bonded plates is first discussed. The definition and ways of measuring moment redistribution is

described in Section 5.2.2. Finally, a review of the existing literature of tests performed by various

researchers on continuous plated RC beams is presented in Section 5.2.3.

5.2.1 DEFINITION OF DUCTILITY

Ductility is an important property of structural members that allows large deformations and deflections

to occur under overload (plastic) conditions. It provides warning of the imminence of failure for

statically determinate beams, and it allows moment redistribution to occur in statically indeterminate

beam at overload (Warner et al. 1998). The ductility of a member can be determined from moment

curvature relation, where larger deformations indicate better ductility. Factors such as material ductility

and sectional properties influence the ductility of the member. For moment redistribution to occur,


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sufficient ductility is required in the structure, hence it is a fundamental behaviour when designing for

continuous plated beams.

Ductility has always been a concern when retrofitting a beam using external plates, as it is widely

acknowledged that this retrofitting technique will reduce the ductility of the member due to the external

plate (Bencardino et al. 1996, 2002; Swamy et al. 1996; Spadea et al. 2001; El-Refaie et al. 2002,

2003). The ductility of a member is largely dependent on the material and the geometry of the plates

used. For beams externally bonded with FRP plates, because of the linear elastic stress-strain

behaviour of FRP and its high tensile strength and high strain at fracture, tests have shown that these

beams are prone to brittle premature debonding failure, well before the design capacity is reached

(Spadea et al. 2001; Ritchie et al. 1991; Saadatmanesh & Ehsani 1991). Beams plated with steel

plates can provide good ductility, but depending on the plating geometry, it is possible that brittle

debonding failure occurs prior to concrete crushing as have been shown by numerous tests performed

by different researchers (Mohamed Ali 2000; Ashrafuddin et al. 1999; Oehlers & Moran 1990; Nguyen

& Oehlers 1997).

Due to the additional plate and the bond in the plate/concrete interface, the strain at which failure of

the beam occurs is reduced, therefore the ductility of plated members and their ability to redistribute

moment is less than that of unplated RC beams. At present, there are only rules of thumb (i.e. fib

2001), such as ensuring that internal reinforcing bars yield before plates debond or fracture, to

guarantee that there is adequate amount of ductility. The ductility index used in many international RC

codes that places limits on the neutral axis depth dn cannot be used in plated beams. This is because

the curvature of an RC member is based on the strain in the concrete, whereas for plated members

the curvature is usually dependent on the strain in the plate. A few researchers have looked into

defining the ductility of plated RC beams based on deflection and energy. Although ductility indices

were found to give good representation of the physical aspects of the ductility of the beams (Spadea

et al. 2001; El-Refaie et al. 2002, 2003), how the concept of ductility indices can be applied in practice

is unclear.

5.2.2 DEFINITION OF MOMENT REDISTRIBUTION

Moment redistribution in a statically indeterminate beam is the transfer of moment between high

moment regions in the member, while maintaining the overall strength. At the initial stage of loading,

the continuous beam will behave linear elastically such that both span moments and support moments


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will increase proportional to the increase in applied load. Eventually, the ultimate strength will be

reached at the maximum moment sections upon further increase in the applied moment. Now as the

load is increased further, the moments will redistribute from the maximum moment sections to other

parts of the beam, such that the total static moment in the beam remains unchanged.

There are various ways of measuring the degree of moment redistribution β as shown in Table 5.1

(Rebentrost 2003), and it is found that the majority of these methods are dependent on the

comparison of the plastic and elastic moments. Rebentrost (2003), Lin & Chien (2000) and many other

researchers relate the difference between the actual and elastic moments to the elastic moment as a

percentage (Table 5.1). An approach similar to Rebentrost’s (2003) is adopted in this research, where

it is assumed that the flexural rigidity of an RC beam is constant in order to determine the elastic

distribution of moments. Therefore, the moment redistribution is defined as the change in moment

from the elastic moment based on the flexural rigidity being constant throughout the beam, with the

percentage redistribution of moment from the hogging region given by Equation 5.1.

Table 5.1 Definitions of moment redistribution (Rebentrost 2003)

Reference Definition of moment redistribution

Trichy and Rakosnik (1977)

pl

ult

w

w=β

β, βp = moment redistribution

wult = ultimate load

wpl = plastic failure load

Cohn (1986) MM el −=β M = actual moment

Mel = elastic moment due to ultimate load

Arenas (1985) fpl

fcolPAR

γγγγ

−−

= PAR=plastic adaptation ratio; γf =load

factor at failure; γcol =collapse load

factor; γfpl=plastic failure load factor

Bennett (1960); Moucassian (1988)

elpl

elnl

ww

ww

−−

=β wel,pl,nl = loads based linear elastic, plastic and non-linear analysis

Scholz (1990) max1 ββ

−+−

−=ultplel

ultfp MMM

MM

βmax = maximum % MR required for wpl

Mult = ultimate moment

Mf = factor moment

Mpl = plastic moment

Rebentrost et al. (1999)

el

el

M

MM −=β

M = actual moment

Mel, Mpl =elastic M corresponding to P, Ppl


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( ) ( )( ) 100%

.

. ×−

=constEIhog

testhogconstEIhog

M

MMMR Equation 5.1

Where in Equation 5.1 for a specific static moment, (Mhog)EI.const is the theoretical hogging moment

from a linear elastic analysis which assumes that the flexural rigidity EI is constant and (Mhog)test is the

experimental hogging moment for the same static moment, that is for the same applied load.

5.2.3 TESTS ON CONTINUOUS PLATED RC BEAMS

The majority of existing research on plated structures focuses on the debonding mechanisms of

simply supported beams and very limited research has been carried out on continuous beams with

externally bonded plates. Park (Park & Oehlers 2000) performed tests on a series of continuous

beams with externally bonded steel or FRP plates over both the sagging and hogging regions. The

plates were applied on either the tension face or the side faces of the beam. For both steel and FRP

plated beams, plate debonding was observed. This indicates that although steel is a ductile material,

the EB steel plates can still reduce the ductility of the retrofitted beam depending on the plating

dimensions and positions. Due to the geometry of the beams and the test set-up, almost zero moment

redistribution was obtained in all the tests.

El-Refaie et al. (2002, 2003; Ashour et al. 2004) performed tests on sixteen RC continuous beams

with different arrangements of internal and external reinforcement. All beams were plated with CFRP

sheets or plates over the hogging and/or sagging regions as shown in Figure 5.1. The specimens

were classified into three groups: H, S, and E, where the beams within each group have the same

geometrical dimensions. For the three groups of beams tested, the length, thickness, form and

position of the CFRP plates were varied to investigate its effects on the strength and ductility of the

plated members. The dimensions of the plates are shown in Table 5.2 where Np, L1, and L2 are the

number of CFRP sheets; length of the plate over the hogging and sagging regions respectively. All

specimens were plated with CFRP sheets, each layer of 0.117mm thickness, except for beams E2,

E3, E4 which were strengthened with CFRP plates of 1.2mm thickness. The percentage of moment

redistribution for the maximum sagging %MRs and hogging %MRh moments at failure are shown in

Table 5.2, where %MR was calculated based on the definition adopted by Rebentrost et al. (1999) in

Table 5.1. Note that for beams with %MRh<0, moment was redistributed from the hogging to the

sagging region i.e. group H, while the reverse occurred for beams with %MRh>0 i.e. group S.


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Figure 5.1 Tests performed by El-Refaie et al. (2002, 2003)

Table 5.2 Beam details and results of tests performed by El-Refaie et al. (2002, 2003)

hogging sagging %moment redistribution specimen

Top reinf.

Bottom reinf.

Np L1 (m) Np L2 (m) %MRh %MRs

H1 - - - - -64 38

H2 2 2.0 - - -31 19

H3 6 2.0 - - -19 11

H4 10 2.0 - - -11 6

H5 6 1.0 - - -31 19

H6

2T8 steel bars

2T20 steel bars

2 3.0 2 1.0 -35 21

S1 - - - - 87 -52

S2 - - 2 2.0 61 -37

S3 - - 6 2.0 55 -33

S4 - - 6 3.5 45 -27

S5

2T20 steel bars

2T8 steel bars

- - 10 3.5 21 -12

E1 - - - - -1 1

E2 1 2.5 - - -24 15

E3 - - 1 3.5 28 -17

E4 1 2.5 1 3.5 7 -4

E5

2T16 steel bars

2T16 steel bars

6 2.5 - - -23 14


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Through these tests, it was found that premature plate debonding was the dominant failure mode, and

significant amounts of moment redistribution were obtained in all the beams (Table 5.2). This

contradicts the existing design guidelines (fib 2001; Concrete Society 2000) which suggest that

moment redistribution should not be allowed for plated RC beams. The unplated control beams H1

and S1 showed significantly greater %MR than the plated beams, indicating reduction in ductility as a

result of plating. For the group E beams which had the same internal reinforcement at the top and

bottom of the beams, the unplated beam E1 had almost zero %MR, while moment redistribution was

observed in the plated beams in this test group, especially for the beams plated over either the

hogging or sagging region only (Table 5.2). This is because, when the hogging or sagging regions are

plated, the stiffness of this region was increased, which caused a variation of flexural stiffness along

the beam such that more moment was attracted to the strengthened region as compared to before the

region was plated. Therefore, the redistribution of the moments is largely dependent on the positions

and dimensions of the plates (Table 5.2), and consequently the variation in flexural stiffness along the

beam. The tests also showed that although CFRP was plated along the entire hogging or sagging

region, this did not prevent premature debonding of the plates. Therefore, further research into the

moment redistribution of EB beams is essential.

Tests on simply supported RC beams with NSM strips (Hassan & Rizkalla 2003; Taljsten & Carolin

2003; Blaschko 2003) have shown that NSM plates debond or fail at much higher strains than EB

plates, therefore in general NSM plated beams are expected to be more ductile than EB plated

beams. However, depending on the anchorage length of the NSM strips, premature debonding failure

prior to concrete crushing is possible (Hassan & Rizkalla 2003; Barros & Fortes 2005). This means

that the existing design approaches for ductility and moment redistribution of unplated RC beams

cannot be applied to NSM beams as the former requires that concrete crushing occurs. Most of the

tests carried out an NSM plated beams are simply support, there is no experimental nor theoretical

studies carried out on the moment redistribution of continuous NSM plated beams. As many in-situ RC

beams are of continuous construction, investigation is needed to examine the behaviour of continuous

beams with NSM plates.


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5.3 EXPERIMENTAL STUDIES ON RC BEAMS WITH EXTERNALLY BONDED STEEL/FRP PLATES

In this test program, seven continuous RC beams with externally bonded steel or CFRP plates of

various dimensions were tested. The specific aim of these tests was to both demonstrate and

measure moment redistribution in externally bonded plated flexural members and not to demonstrate

the effectiveness of the strengthening method. In this Chapter, the specimens, the test set-up and the

material properties are first described, followed by thorough descriptions of the results from each test.

Finally in Section 5.3.5, a summary of the test results are presented in the attached journal paper,

along with a comparison between the results for the different beams to illustrate the effectiveness of

the various plating systems.

5.3.1 GEOMETRY OF TEST SPECIMENS

Each of the seven specimens tested consists of the two spans of length L=2400mm as illustrated in

Figure 5.2 with the cross-section of the beams shown in Figure 5.3 and the geometry of the plates

given in Table 5.3, where tp, bp and be are the plate thickness, plate width, and the distance from the

edge of the plate to the side of the beam. The three steel plated test beams are denoted as SS1, SS2,

and SS3; and the four CFRP plated specimens are denoted as SF1, SF2, SF3, and SF4. The hogging

regions of each beam was plated over the tension face with steel or FRP plates of length Lp=2200mm,

and the sagging regions were left unplated as in Figure 5.2. The internal reinforcement is the same

throughout the beam, where two mild steel bars of diameter 12mm were placed at the top of the

beam, and four mild steel bars of diameter 16mm were placed at the bottom of the beam. Therefore,

the tensile reinforcement in the hogging region, 2Y12 bars, was much less than the tensile

reinforcement in the sagging region, 4Y16 bars, to ensure that the plated hogging region reached its

moment capacity first; this then allowed the hogging region to shed moment, or redistribute moment,

to the sagging region as the static moment was being increased, thereby, increasing the sagging

moment. The internal bars were equally spaced with a distance of 20mm from the edge of the

concrete to the centre of the bars as illustrated in Figure 5.3. All beams tested had W10 stirrups

placed at 1200mm centre to centre (c/c) to hold the longitudinal bars in position.


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All dimensions in mm

East West

Plate

2400 2400 100 100

5000

1200 1100 1100 1200 2Y12

4Y16

W10 stirrup @1200c/c

Interior support support support

P P

Figure 5.2 Two span continuous beam specimens

2Y12

4Y16

W10 @ 1200c/c

120

375

2Y12

4Y16

W10 @ 1200c/c

120

375

be bp

tp

Sagging region Hogging region

20

20

be

Figure 5.3 Cross-sectional details of EB test series

Table 5.3 Geometrical properties of externally bonded plates

Specimen material tp (mm) bp (mm) be (mm)

SS1 Steel plate 3 75 150

SS2 Steel plate 2 112 131.5

SS3 Steel plate 1 224 75.5

SF1 CFRP plate 2.4 25 175

SF2 CFRP plate 1.2 50 162.5

SF3 CFRP plate 1.2 80 147.5

SF4 3 x CFRP sheeta 2.44b 100 137.5

a 0.2mm thick carbon FRP fabric b measured thickness

The main variable of the different specimens was the plate properties with details of the plate

geometry given in Table 5.3. Specimens SS1 to SS3 used adhesively bonded mild steel plates with

plate thicknesses tp that varied from 1 mm to 3 mm. The plate widths (bp ) were varied to ensure

virtually the same cross-sectional area and, hence, the same axial rigidity (EA) so that the theoretical


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moment-curvature relationships, ignoring intermediate crack debonding, would be identical.

Specimens SF1 to SF3 used adhesively bonded pultruded carbon FRP plates of thicknesses 1.2 mm

and 2.4 mm. Whereas, Specimen SF4 used three layers of carbon FRP fabric, each with a thickness

of 0.2mm, that was applied using the wet lay-up procedure; its thickness and Young’s modulus were

measured directly from specimens that were taken from the plated beam. The plate widths were

varied from 25 mm to 100 mm and specimens SF1 and SF2 had plates of the same axial rigidity.

The specimens were designed such that CDC and PE debonding did not precede IC debonding. PE

debonding was prevented by terminating the plate beyond the point of contraflexure and onto the

compression faces of the sagging regions. CDC debonding was prevented by ensuring that a critical

diagonal crack, associated with the concrete component of the vertical shear capacity Vc, did not

occur prior to plate debonding; because of the CDC requirement the slab shaped cross-section was

used.

To explain the reason for the slab shaped cross-section shown in Figure 5.3, let us consider the

capacity of a beam or slab without stirrups so that the strength is controlled by either the flexural

capacity or the concrete component of the shear capacity Vc, as the latter controls CDC debonding.

Let us consider a rectangular beam or slab which has the same cross-sectional area of concrete and

the same cross-sectional area of longitudinal tension reinforcing bars. The beam shaped cross-

section, in which the width is less than the depth, is more prone to vertical shear failure, and CDC

debonding at Vc, than the slab shaped cross-section, in which the width is greater than the depth. This

is because the concrete component of the vertical shear capacity of these two shapes Vc is roughly

equal and, hence, their resistance to CDC debonding. However, the beam shaped cross-section will

have a higher flexural capacity than the slab shaped cross-section due to the increased depth (lever

arm) and, consequently, can resist a greater applied load at flexural failure with its associated greater

vertical shear force. Therefore, beam shapes without stirrups are more prone to shear failure at Vc and

consequently CDC debonding than slab shapes. Hence a relatively large but realistic span-to-depth

ratio of 20 was required and the use of a slab shaped cross-section in which the width was greater

than the depth as shown in Figure 5.3.

5.3.2 TEST SETUP AND INSTRUMENTATION

Identical test setup and instrumentation was used in all seven specimens. The concentrated loads P

were applied at mid-span as in Figure 5.4 so that, for an elastic distribution of moment with an


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assumed constant flexural rigidity, the maximum hogging moment would be 20% greater than the

maximum sagging moment. As the system is symmetrical, the specimen can be analysed as a single

span with the moment distribution illustrated in Figure 5.5, where Mstatic, Mhog, and Msag are the static,

hogging and sagging moments respectively. From similar triangles, Mstatic is also given by Equation

5.2. The loads were applied on the top of the beam by hand operated hydraulic jack through load cells

and knife edge bearings of 100mm in width. The test rig over one span is shown in Figure 5.6.

Deflections were measured under the applied loads P using LVDTs, load cells were placed at the

applied loads and at the west support in Figure 5.4 so that the distribution of forces could be

determined directly. Two LVDTs were placed over the externally bonded plate at 100mm from the

interior support as illustrated in Figure 5.7 to measure the slip between the concrete and the plates.

LC3 LVDT 1 LVDT 1

East West

LC1 LC2

Plate

2400 2400 100 100

5000

1200 1100 1100 1200 P P

100 100

Figure 5.4 Test set-up

Mhog

P

Msag Mstatic=PL/4

L/2 L

R

Figure 5.5 Moment distribution

24hog

sagstatic

MM

PLM +== Equation 5.2


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Figure 5.6 Test rig

100

LVDT 3 LVDT 4

Plate

1100 1100

900 900 100 100 100

Figure 5.7 LVDT positions for slip between concrete and EB plates

Seven strain gauges (SG) were bonded along the centre of the external plate of each specimen over

the interior support at 200mm centre to centre spacing, and two strain gauges were placed at 100mm

from each end of the plate as illustrated in Figure 5.8. These strain gauges were used to measure the

strains in the plates, as well as to detect the propagation of the debonding cracks.

200

Plate

1100 1100

100 200 200 400 200

100 200 200 400

SG5

SG6

SG7

SG8

SG9

SG4

SG3

SG2

SG1

Figure 5.8 Strain gauges positions for externally bonded plated

5.3.3 MATERIAL PROPERTIES

The test beams were cast from a single concrete pour, but because the specimens where tested at

different times, the concrete properties for the specimens were substantially different. The concrete

Interior support

Hydraulic jack


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properties of specimens SS1, SF1, SF2 and SF3 are given in Table 5.4, where Ec and fc are the

Young’s modulus and the cylinder compressive strength respectively. The remaining specimens had

concrete properties given in Table 5.5, where indirect tensile tests were also carried out to measure

the tensile strength ft of the concrete.

Table 5.4 Concrete properties for beams SS1, SF1, SF2, SF3

Age Sample No. Ec (MPa) fc (MPa) Density (x10-3 g/mm3)

1 36,327 39.1 2.33

2 35,251 38.8 2.32

3 35,705 39.8 2.36

50a

(Days) Average 35,761 39.2 2.34

1 33,797 35.9 2.32

2 35,661 38.2 2.32

3 35,626 40.8 2.33

59b

(Days) Average 35,028 38.3 2.32

Average 35,394 38.8 2.33

a Concrete age of the first test b Concrete age of last test

Table 5.5 Concrete properties for beams SS2, SS3, SF4

Age Sample No. Ec (MPa) ft (MPa) fc (MPa) Density (x10-3 g/mm3)

1 39814 4.39 48.03 2.31

2 44597 4.98 49.29 2.36

3 39578 4.96 47.49 2.32

4 39023 - 48.27 2.33

330

(Days)

Average 40753 4.78 48.27 2.33

Tensile tests were performed on the internal reinforcing bars used in the test specimens to obtain the

yield fy and fracture frac strengths of the bars as given in Table 5.6. Being mild steel, the bar’s Young’s

modulus Eb can be assumed to be 200GPa.

The material properties of the externally bonded plates were obtained from tensile tests and are given

in Table 5.7. For the mild steel plates, a Young’s modulus Ep of 200GPa is assumed. Being FRP

plates, the plates do not yield and the longitudinal Young’s modulus (i.e. parallel to the directions of

the fibres) was measured directly. For the CFRP wet lay-up used in specimen SF4, its thickness and

material properties were measured directly from specimens that were taken from the plated beam.


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Table 5.6 Material properties of reinforcing bars for EB test series

Bars Sample no. fy (MPa) fu (MPa)

1 592 711

2 592 720

3 619 714 Y12

Average 601 715

1 532 686

2 549 679

3 537 674 Y16

Average 540 680

Table 5.7 Properties of EB plates

Material Sample no. tp (mm) fy (MPa) fu (MPa) Ep (GPa)

1 3 331 462 -

2 3 340 468 -

3 3 340 466 -

average 3 337 466 200

1 2 245 317 -

2 2 244 317 -

3 2 243 319 -

average 2 244 (223a) 318 200

1 1 247 302 -

2 1 248 304 -

3 1 248 303 -

Steel

average 1 248 (211a) 303 200

1 2.4 - 2800 144 Pultruded CFRP 1 1.2 - 2800 144

1 2.35 - 398 43843

2 2.38 - 336 45202

3 2.60 - 317 40618

CFRP wet lay-up

average 2.44b - 350 43221

a Proof stress

b tp is the measured thickness of 3 layers of 0.2mm thick CFRP fibres plus the adhesive

Proper preparation of the plates and the concrete surface before application is necessary to allow a

good bond to form between the plate and the concrete. Before adhesively bonding the plates to the


- 293 -

concrete surface, the surface was prepared by grit blasting to remove laitance and expose the

aggregates. The surface was then brushed mechanically to remove all loose particles. The remaining

dust and debris was then removed by blowing air. The steel plates were sand blasted to remove rust

or loose particles, and any grease or oil was removed by applying non-inflammable solvents. The

CFRP pultruded plates were cleaned with any grease or oil removed using a solvent prior to

application.

Araldite K340 and MBrace Laminate adhesive were the epoxy resins used for the steel and CFRP

plates respectively. The manufacturer’s specifications of the material properties of the epoxy resins

are given in Table 5.8. The tensile strength, longitudinal (i.e. parallel to the directions of the fibres)

Young’s modulus (Ea)l, and the perpendicular (i.e. perpendicular to the directions of the fibres)

Young’s modulus (Ea)p of the adhesives tested in this research are also shown in Table 5.8. The

adhesives used were mixed according to the specifications recommended by the resin manufacturer,

which ensured that no air bubbles or voids were entrapped in the adhesive when cured. For steel

plates, the adhesive was applied to the beam surface and the plate was pressed onto concrete all

over, and surplus adhesive was squeezed out at the edges. For CFRP plates, a coat of MBrace

Primer was applied on the bonding surface using a roller or brush and when it was tack-free the plate

was adhesively bonded as follows: the laminate surface was cleaned with MBT Thinner and a 1.5mm

thick layer of MBrace Laminate Adhesive was applied on both the concrete and laminate surfaces;

then a layer of laminate was applied to the concrete substrate by hand and pressed onto the adhesive

with a rubber roller. Additional CFRP layers were applied the same way on the uncured wet adhesive,

and finally, the plates were left for curing for at least seven days.

Table 5.8 Properties of adhesives from manufacturer’s specifications

Manufacturer’s specifications From tests

Epoxy resin

Compressive strength

(MPa)

Tensile strength

(MPa)

Flexural strength

(MPa)

Tensile bond

strength (MPa)

Max. operating

temp.

Tensile strength

(MPa)

(Ea)l (MPa)

(Ea)p (MPa)

Araldite K340

100-120 30-40 20-30 15-17 85oC 24.7 4538 12109

MBrace >60 N/A >30 >3.5 N/A 16.1 5352 17030

5.3.4 TEST RESULTS

In the following section, descriptions of the behaviour of the beams as loads were gradually applied,

and analyses of the test results are presented for each test specimen.


- 294 -

5.3.4.1 BEAM SS1 (STEEL 75X3)

The beam was plated with a 3mm thick steel plate on the tension face over the interior support. As the

hogging region of the beam is much weaker than the sagging region, failure was expected in the

hogging region. The test specimen was designed against CDC and PE debonding failure, therefore IC

debonding failure was expected to occur. The beams were initially tested under load control where a

load P was applied at small increments at each span as shown in Figure 5.4 until the maximum

applied load was obtained, and thereafter the beam was loaded under deflection control up to failure.

As the beam was gradually loaded, the first flexural crack was found at the interior support at an

applied load P of 9kN, with an average reaction force R of 2.9kN at the external supports. This caused

a maximum moment at the hogging Mhog and sagging Msag regions of 3.72kNm and 3.45kNm

respectively. As the beam was further loaded, more flexural cracks formed over the hogging region as

shown in Figure 5.9, where the cracks were marked by the black lines and the numbers denote the

load P at which the crack formed. At P=30kN (R=9.9kN, Mhog=12.2kNm, Msag=11.9kNm), the plate

yielding strain was recorded at SG5 and still no sign of debonding was observed.

Figure 5.9 Beam SS1: Prior to debonding (P=32kN)

Initial debonding occurred at a load P of 37kN (R=12.6kN, Mhog=14.2kNm, Msag=15.1kNm), as shown

by the formation of the IC interface cracks propagating from the root of the flexural crack over the

interior support in Figure 5.10. Upon further loading, more IC interface cracks formed at the roots of

the flexural cracks near the interior support as shown in Figure 5.11 for an applied load of 47kN

(R=16.6kN, Mhog=16.7kNm, Msag=19.9kNm). Initially, the IC interface cracks propagated gradually

towards the plate end, joining other IC interface cracks as they moved along. When a load P=48kN

(R=17kN, Mhog=16.9kNm, Msag=20.3kNm) was applied, the IC interface cracks propagated very rapidly


- 295 -

to the east plate end, causing sudden complete debonding of the plate at a displacement of 10.3mm

in the east span as shown in Figure 5.12. A maximum plate strain of 0.004446 at SG5 was measured

just prior to IC debonding failure.

After the plate completely debonded, the beam continued to be loaded until vertical shear failure

occurred at a load P=76.45kN, at a maximum displacement of 45.84mm. Based on the measured

plate strain and from full interaction analysis, it is estimated that the tensile bars yielded at a load of

44.9kN, before complete debonding of the plate. The distribution of flexural cracks in the hogging

region over the east span is shown in Figure 5.12, where it is evident that the cracks spacings varied,

with the last flexural crack in the region, crack D, at approximately 400mm from the interior support.

Figure 5.10 Beam SS1: Initial debonding (P=37kN)

Figure 5.11 Beam SS1: Debonding propagation (P=47kN)

IC Interface cracks

Interior support

Debonding propagation


- 296 -

Figure 5.12 Beam SS1: Debonding failure (P=48kN)

The variation of moment, at the position of maximum hogging Mhog and sagging Msag moments as

shown in Figure 5.5, with the mean deflection under the applied loads at mid-spans, are plotted in

Figure 5.13. It can be seen that near the start, in region A, the hogging moment was slightly greater

than the sagging moment as would be expected from an elastic analysis. After the plate yielded at

point B, the hogging moment then reduced relative to the sagging moment. Initial debonding occurred

at point C, and it was estimated that the tensile bars yielded at point D. The maximum hogging

moment and the maximum plate strain were obtained just prior to IC debonding failure, after which a

sudden reduction in Mhog occurred and the behaviour of the hogging region reverts back to that of the

unplated section at E.

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40 50displacement (mm)

Mom

ent

(kN

m)

Msag

A

B

shear failure

CD

IC debonding failure

EMhog

Figure 5.13 Beam SS1: Moment vs displacement

After the plate completely debonded at point E, the sagging moment continually increased relative to

the hogging moment which signifies moment redistribution; it was for this reason that the sagging

region was made much stronger than the hogging region in order to achieve as much moment

East

support

P

Debonding propagation ABD C


- 297 -

redistribution as possible. It is worth noting that the continuous beam eventually failed by vertical

shear failure in Figure 5.13. However, this occurred well after the plate had IC debonded so that the

vertical shear failure had no effect on the redistribution of moment.

Figure 5.14 shows the plate strains measured along the plate as the moment over the interior support

increased up to IC debonding failure, where the positions of the strain gauges SG are given in Figure

5.8. The steel plate first yielded at strain gauge SG5 over the interior support at a moment

Mhog=12.2kNm. After the plate yielded, the plate strain at SG5 increased rapidly due to the ductile

behaviour of steel. When the moment at interior support Mhog was 15.6kNm, the plate yielding strain

εp.y was also reached at SG4. The strain along the plate continued to increase as Mhog increased up to

IC debonding failure. This shows that the bond at the plate/concrete interface remained strong along

the beam until rapid debonding occurred, which resulted in zero bond at the interface. Therefore, the

maximum plate strain was achieved just prior to debonding failure.

0

2

4

6

8

10

12

14

16

18

-1000 0 1000 2000 3000 4000 5000strain (x10-6)

mom

ent a

t int

erio

r su

ppor

t (kN

m)

SG1 SG2

SG3 SG4

SG5 SG6

SG7 SG8

SG9

SG7SG3SG1

EAST

SG2 SG5SG4 SG6

WEST

SG8 SG9

εεεεp.y

SG3

SG4SG5

SG6

SG7

Figure 5.14 Beam SS1: Moment vs plate strain

The variation of the maximum hogging moment in the beam Mhog as a proportion of the maximum

sagging moment in the beam Msag is shown in Figure 5.15. From an elastic analysis in which EI is

assumed to be constant, Mhog/Msag = 1.2 which is shown as line A in Figure 5.15. The abscissa in

Figure 5.15 is the applied static moment, Mstatic given by Equation 5.2, as a proportion of the ultimate

maximum static moment, (Mstatic)u = (Msag)u + (Mhog)u/2, based on nonlinear full interaction analysis of

the ultimate capacity of the hogging and sagging sections, (Mhog)u and (Msag)u, and ignoring IC

debonding in the case of the hogging region; hence the upper limit of Mstatic/(Mstatic)u = 1.0. For the

plated beam considered, (Mstatic)u=47.1kNm. The line marked B is the maximum redistribution


- 298 -

assuming the sagging region achieved its theoretical moment capacity Msag=(Msag)u, while the capacity

of the hogging region is the moment experimentally measured at failure Mhog=(Mhog)fail; and the line

marked C is the maximum redistribution after plate debonding that is when (Mhog)u is the theoretical

ultimate capacity of the unplated section.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mstatic/(Mstatic)ult

Mh

og/

Msa

g

test resultsA

B

C

D E

plate yield

1st debonding

bar yieldF

G

H


elastic (EI constant)

shear failure

I

J

Mstatic / (Mstatic)u

Figure 5.15 Beam SS1: hogging-moment/sagging-moment

When the load was first applied Mhog/Msag approaches 1.2 in region D in Figure 5.15; one can still

notice a slight divergence from this value because the beam was bedding or settling down under very

small loads. Soon after, Mhog/Msag reduced gradually and the divergence from Mhog/Msag equal to 1.2

signifies moment redistribution. The first flexural crack was observed at point E, and at point F yielding

of the plate occurred over the interior support. This was shortly followed by the appearance of the first

IC interface crack at G and eventually IC debonding failure at point H which coincided with the

maximum plate strain. After the plate completely debonded in region I, the behaviour of the hogging

region reverts back to that of the unplated section. The unplated beam eventually failed in shear at

point J. It can be seen from Figure 5.15 that due to premature debonding, the maximum allowable

moment redistribution of the plated beam, line B, could not be achieved.

Figure 5.16 shows the variation of the maximum hogging Mhog and sagging Msag moments as the

applied loads P increased. (Mhog)el and (Msag)el are the hogging and sagging moments obtained based

on elastic analysis of constant EI. The greater the divergence from the elastic moments means that

more moment is being redistributed. It can be seen from Figure 5.16 that the beam behaved elastically

until the first flexural crack occurred at point A, after which small amounts of hogging moment were

redistributed to the sagging regions. It was after the yielding of the plate at point B when significant

amounts of moment redistribution were observed. When the plate debonded at point E, a sudden


- 299 -

reduction in applied load, and hence the moments, was observed. However, as the unplated RC beam

had not yet failed, the load increased again with the behaviour of the hogging region now that of the

unplated section, such that Mhog is now significantly less than prior to debonding. Mhog remained

roughly constant up to shear failure at point F, while much moment was taken up by the sagging

region, indicating that the flexural capacity of the unplated hogging section was reached.

0

5

10

15

20

25

30

0 20 40 60 80

applied load P (kN)

Mho

g (k

Nm

)

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80applied load P (kN)

Msa

g (k

Nm

)

1st flexuralcrack

plateyield

1st debonding

baryield IC debonding

failure

shearfailure

shearfailure

A B C

DE F

A

BC

D

E

F

(Mhog)el

(Msag)el

Figure 5.16 Beam SS1: Maximum hogging and sagging moments

The variation of percentage of moment redistribution %MR, calculated using Equation 5.1, is shown in

Figure 5.17 for different Mstatic applied. As the applied load, and hence Mstatic increased, the %MR

increased up to a maximum of 20% at IC debonding failure. After the plate debonded, the flexural

strength of the hogging region reduced, therefore the hogging moment had to redistribute to the

sagging region to allow for this reduction in strength as shown in Figure 5.16. This resulted in a

sudden increase in %MR as shown by region A in Figure 5.17. As the ductility of the unplated hogging

region is much greater than before, large %MR occurred and a maximum of 62% moment

redistribution was obtained at shear failure of the unplated beam.

0

10

20

30

40

50

60

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Mstatic/(Mstatic)ult

% M

omen

t red

istr

ibut

ion

u

1st flexuralcrack

plate yield

1st debonding

baryield

IC debondingfailure

shearfailureA

Figure 5.17 Beam SS1: percentage of moment redistribution


- 300 -


No sign of cracking was observed until, at an applied load P of 14.8kN, three flexural cracks appeared

near the interior support. A resultant reaction force R of 4.6kN was measured at the external supports,

which caused a maximum moment at the hogging Mhog and sagging Msag regions of 5.5kNm and

6.7kNm respectively. As the beam was further loaded, more flexural cracks formed over the hogging

region. At P=19.8kN (R=6.38kN, Mhog=8.4kNm, Msag=7.65kNm), the plate reached the yielding strain

at SG5.

IC debonding first occurred at a load P of 29.8kN (R=10 kN, Mhog=11.8kNm, Msag=12kNm) near the

interior, as shown by the formation of the IC interface cracks propagating from the root of the flexural

cracks in Figure 5.18, where the cracks were marked by the black lines and the numbers denote the

load P at which the crack formed. The IC interface cracks that formed between cracks B and C in

Figure 5.18 were propagating in opposite directions, as shown by the arrows, which indicate that there

was a reverse in slip in between the two cracks. Upon further loading, more IC interface cracks formed

at the roots of the flexural cracks near the interior support as shown in Figure 5.19 for an applied load

of 38kN. These debonding cracks propagated mainly towards the plate end, joining other IC interface

cracks as they moved along, such as between cracks A, B and C in Figure 5.20. It is worth noting that

eventually no more flexural cracks formed as more load was applied, and cracks D and E in Figure

5.20 are the last flexural cracks in the hogging region, i.e. no further flexural cracking occurred in the

hogging region beyond cracks D and E.


A B C D

IC interface cracks

Interior support

East

West


- 301 -



The IC interface cracks propagated rather gradually until they reached the last flexural crack, crack D

in Figure 5.21, after which the cracks propagated rapidly towards the plate end causing complete

debonding of the plate at P=64.5kN (R=24.2kN, Mhog=19.3kNm, Msag=29kNm) as shown in Figure

5.22. A maximum displacement of 17.3mm was recorded in the east span beneath the applied load at

failure. Just prior to IC debonding failure, the plate reached a maximum strain of 0.005926 at SG5.

Based on the measured plate strain and from full interaction analysis, it is estimated that the tensile

bars yielded at a load of 46.8kN, before complete debonding of the plate. Irregular flexural crack

spacings were observed in the test. The distribution of flexural cracks was similar to Specimen SS1,

A B C D

Interior support

East


E

A B C D

Interior support

East

West



- 302 -

where four cracks formed in the hogging region of the east span as shown in Figure 5.22, with the last

crack, crack D, at approximately 300mm from the interior support.



Figure 5.23 shows the variation of moment, at the position of maximum hogging Mhog and sagging

Msag moments, with the mean deflection under the applied loads at mid-spans. It can be seen that

near the start, in region A, the hogging moment was greater than the sagging moment as would be

expected from an elastic analysis. After flexural cracking (point B) occurred and the plate yielded

(point C), the hogging moment then reduced relative to the sagging moment. Once IC debonding

began at point D, the divergence between Mhog and Msag becomes greater, indicating that more

moment is being redistributed from the hogging to the sagging region. The maximum hogging moment

and the maximum plate strain were obtained just prior to IC debonding failure.

A B C D

Interior support

East


E

A B C D

Interior support

East



- 303 -

0

5

10

15

20

25

30

35

0 5 10 15 20displacement (mm)

Mom

ent (

kNm

)

Msag

AB

C

1st ICdebonding


barsyield

Mhogplateyield

D



increased up to IC debonding failure, with the positions of the strain gauges SG given by Figure 5.8.

The steel plate first yielded at strain gauge SG5 over the interior support at a moment Mhog=8.4kNm.

Soon after, the plate yielding strain εp.y was reached at SG6 and SG4 at moments Mhog of 10kNm and

10.3kNm respectively. After the plate yielded, the plate strains at SG4, SG5 and SG6 increased more

rapidly due to the ductile behaviour of steel. The strain along the plate continued to increase as Mhog

increased up to IC debonding failure, and a maximum plate strain of 0.0059 was achieved just prior to

debonding failure at Mhog=19.3kNm.

0

5

10

15

20

25

-1500 0 1500 3000 4500 6000plate strain (x10-6)

Mho

g (k

Nm

)

SG1 (east)SG2SG3SG4SG5 (centre)SG6SG7SG8SG9 (west)

εεεεp.y

SG3

SG4SG5

SG6SG7

SG9

SG1



- 304 -


sagging moment in the beam Msag is shown in Figure 5.25, where the ultimate maximum static

moment (Mstatic)u=47.8kNm for the plated beam considered. Line A in Figure 5.25 is the elastic

distribution assuming EI is constant i.e. Mhog/Msag = 1.2, line marked B is the maximum redistribution

for the plated section and the line marked C is the maximum redistribution for the unplated section.

When the load is first applied Mhog/Msag approaches 1.2 in region D in Figure 5.25. The slight

divergence from this value is because the beam was bedding or settling down under very small loads.

Soon after, Mhog/Msag reduces gradually and the divergence from Mhog/Msag equal to 1.2 signifies

moment redistribution. The first flexural crack is observed at point E, this is shortly followed by the

appearance of the first IC interface crack at F and eventually IC debonding failure at point G which

coincided with the maximum plate strain. From Figure 5.25, it can be seen that the beam was

relatively close to reaching the maximum allowable moment redistribution, Line B.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1

Mstatic/(Mstatic)u

Mh

og/M

sag

IC debonding max plate strain reached

A

B

C

test resultsD

F

1st IC interface crack1st flexutral crack

occurred

E

G

maximum moment redistribution for unplated structures

max. moment redistribution for plated structures





on elastic analysis of constant EI. It can be seen from Figure 5.26 that the beam behaved elastically

until the plate yielded at point B, after which the moments obtained diverged from the elastic

moments, indicating that moment is being redistributed. After the yielding of the tensile reinforcing

bars in the hogging region at point D, much of the load was taken by the sagging region, as indicated

by the rapid increase in Msag. This shows that more moment is being redistributed from the hogging to

the sagging region.


- 305 -

0

5

10

15

20

25

30

0 20 40 60

applied load (kN)

Mho

g (k

Nm

)

0

5

10

15

20

25

30

35

0 20 40 60 80applied load (kN)

Msa

g (k

Nm

)

1st flexuralcrack

plateyield

1st debondingbar

yield

IC debondingfailure

A

BC D

E

(Mhog)el

(Msag)el

1st flexuralcrack

plateyield

1st debondingbar

yield

IC debondingfailure

AB

CD E


The variation of percentage of moment redistribution %MR calculate ed using Equation 5.1 is shown

in Figure 5.27 for different Mstatic applied. Initially, before flexural cracking, the beam behaved

elastically such that there is zero moment redistribution. The discrepancy of results before flexural

cracking is because the beam was bedding or settling down under very small loads. As the applied

load, and hence Mstatic increased, the %MR increased up to a maximum of 33% at IC debonding

failure. This shows that although premature debonding occurred in the beam, large moment

redistribution still occurred, and the beam achieved 80% of the ultimate static moment.

-10

0

10

20

30

40

50

0 0.2 0.4 0.6 0.8 1

Mstatic/(Mstatic)ult

% M

omen

t red

istr

ibut

ion

1st flexuralcrack

plate yield

1st debonding

baryield

IC debondingfailure

u



- 306 -


The externally bonded steel plate used in this specimen had a low yielding strain εp.y of 0.00124.

Therefore, the yielding strain was recorded at the centre of the interior support even before any

flexural cracks were visible. The plate first yielded at SG5 at an applied load P of 13.6kN, with a

reaction force R of 4.25kN measured at the external supports, resulting in maximum moments at the

hogging Mhog and sagging Msag regions of 6.12kNm and 5.1kNm respectively. Flexural cracks formed

soon after the yielding of the plate at an applied load P of 17.7kN (R=5.65kN, Mhog=7.68kNm,

Msag=6.78kNm), where two cracks, cracks A and B in Figure 5.28 appeared near the interior support.


The formation of herringbone cracks close to the plate/concrete interface in Figure 5.28 indicates that

IC debonding occurred at a load P of 24.5kN (R=8.28kN, Mhog=9.48kNm, Msag=9.93kNm) near the

interior.

A secondary crack, crack C in Figure 5.29, formed in between cracks A and B, which caused IC

debonding to occur propagating from the roots of the crack. The IC interface cracks that formed

between cracks B and C in Figure 5.29 were propagating in opposite directions, as shown by the

arrows, which indicate that there was a reverse in slip in between the two cracks. However, the

dominant direction of propagation was towards the plate end as evident from the extent of propagation

of the IC interface cracks east of crack B in Figure 5.29. Figure 5.30 shows a close up of IC debonding

A B

IC interface cracks

Interior support

East West A B


- 307 -

of the plate. It is interesting to note how ripples appeared in the plate where the flexural cracks

intercepted, which indicates that the plate had been stretched.


Figure 5.30 Beam SS3: IC debonding

Upon further loading, the IC interface cracks continued to propagate towards the plate end, however

at P=78.4kN (R=31.1kN, Mhog=19.4kNm, Msag=37.7kNm) a critical diagonal crack formed near the

applied load in the east span resulting in shear failure of the beam as shown in Figure 5.31. A

maximum displacement of 28.2mm was recorded in the east span beneath the applied load at failure.

IC debonding Intermediate crack

A B

Interior support


East West

C


- 308 -

A maximum plate strain of 0.015 was reached at SG5 upon failure. Figure 5.32 shows the extent of IC

debonding over the hogging region at failure. It can be seen from the test that, although the low

stiffness and high ductile nature of the steel plate prevented premature IC debonding failure from

occurring, severe debonding was still evident in the beam. The extent of the permanent elongation of

the steel plate due to yielding can be seen from Figure 5.33 when the beam was unloaded after

failure.


bars yielded at a load of 34.5kN. From the test, it can be seen that as secondary cracks form in

between cracks, it affects the debonding behaviour of the beam. The flexural cracks of this Specimen

were more closely spaced than Specimen SS1 and SS2, where three cracks formed in the hogging

region of the east span as shown in Figure 5.22, with the last crack, crack B, at less than 200mm from

the interior support as shown in Figure 5.32.

Figure 5.31 Beam SS3: shear failure in sagging region (P=81kN)

Figure 5.32 Beam SS3: hogging region at failure (P=81kN)

A B

IC interface cracks

Interior support

East West

C

Critical diagonal crack

East

P EB plate


- 309 -

Figure 5.33 Beam SS3: deformation of EB plate (P=81kN)


Msag moments, with the mean deflection under the applied loads at mid-spans. At initial stages of

loading, the beam behaved elastically, i.e. region A in Figure 5.34, so the hogging moment was

greater than the sagging moment. Yielding of the plate was found to occur while the beam was still

linear elastic as shown by point B in Figure 5.34. Soon after, flexural cracking (point C) occurred and

the hogging moment then reduced relative to the sagging moment. After IC debonding began at point

D, the moment in the hogging region became less than that in the sagging region, indicating that

moment is being redistributed from the hogging to the sagging region. Upon further loading, the tensile

bars yielded at point E, and soon after, Mhog began to level off, which suggests that the flexural

capacity has been reached in the hogging region and additional moments were redistributed to the

sagging region until shear failure occurred.

0

5

10

15

20

25

30

35

40

0 10 20 30 40displacement (mm)

mom

ent (

kNm

)

Msag

A

BC

1st ICdebonding

shear failure at midspan (east)

barsyield

Mhog

1st flexuralcrack

DE


Interior support

EB steel plate

east west


- 310 -


increased up to shear failure, with the positions of the strain gauges SG given by Figure 5.8. The steel

plate first yielded at strain gauge SG5 over the interior support at a moment Mhog=6.12kNm. At

Mhog=8kNm the plate yielding strain εp.y was reached at SG6, and SG4 at moments Mhog=11kNm. After

the plate yielded, the plate strains at SG4, SG5 and SG6 increased very rapidly due to the ductile

behaviour of steel. The strain along the plate continued to increase as Mhog increased up to shear

failure. The strains at SG4, SG5 and SG6 intercepted at point A in Figure 5.35 , after which the strains

at SG4 and SG5 began to converge. This suggests that major debonding occurred between SG4 and

SG5 at A, which caused a loss of bond, and hence, resulted in rapid increases in plate strains and the

convergence of strains at SG4 and SG5. It is worth noting that although the plate strains obtained at

SG4, SG5, and SG6 were much higher than those achieved in specimens SS1 (Figure 5.14) and SS2

(Figure 5.24), the plate strains at 400mm from the interior support (SG3 and SG7) were significantly

less than SS1 and SS2.

0

5

10

15

20

25

-2000 0 2000 4000 6000 8000 10000 12000 14000 16000

strain (x10-6)

Mho

g (k

Nm

)

SG1 (east)SG2SG3SG4SG5SG6SG7SG8SG9 (west)

εεεεp.y

SG1 & SG9

SG4

SG5

SG6SG3 & SG7

A



sagging moment in the beam Msag is shown in Figure 5.36, where for the plated beam considered

(Mstatic)u=47.6kNm. Line A in Figure 5.36 is the elastic distribution assuming EI is constant i.e.

Mhog/Msag = 1.2, the line marked B is the maximum redistribution for the plated section and the line

marked C is the maximum redistribution for the unplated section. When the load is first applied

Mhog/Msag approaches 1.2 in region D in Figure 5.36. The slight divergence from this value is because


- 311 -

the beam was bedding or settling down under very small loads. After the plate yields at point E, and

the flexural cracks forms at point F, Mhog/Msag reduces gradually and the divergence from Mhog/Msag

equal to 1.2 signifies moment redistribution. From Figure 5.36, it can be seen that the beam achieved

the maximum allowable moment redistribution, Line B, at failure at Mstatic/(Mstatic)u=1.0, i.e. the ultimate

static moment was achieved.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1Mstatic/(Mstatic)u

Mh

og/M

sag

test results

A

B

C

D

E

plate yield

1st debonding

bar yieldFG

H


shear failure

I




on elastic analysis of constant EI. It can be seen from Figure 5.37 that the beam behaved elastically

until the flexural cracks occurred at point B, after which the moments obtained diverged from the

elastic moments, indicating that moment is being redistributed.

0

5

10

15

20

25

30

35

40


Mho

g (k

Nm

)

0

5

10

15

20

25

30

35

40


Msa

g (

kNm

)

1st flexuralcrack

plateyield

1st debondingbar

yield

A

B C D

(Mhog)el

E

A

B

C D

(Msag)el

E



- 312 -

The variation of percentage of moment redistribution %MR calculated using Equation 5.1 is shown in

Figure 5.38 for different Mstatic applied. Initially, before flexural cracking, the beam behaved elastically

such that there is zero moment redistribution. The discrepancy of results at initial loading is because

the beam was bedding or settling down under very small loads. As the applied load, and hence Mstatic

increased, the %MR increased up to a maximum of 45% at shear failure. It is interesting to note how

the %MR obtained in SS3 was much greater than SS1 and SS2, however the length of the cracked

region, which is also defined as the partial interaction or hinge region as previously discussed in

Chapter 2, is significantly less than in SS1 and SS2, which suggests that the hinge length, i.e. the

region where large rotation occurs, reduces as more moment is redistributed.

-10

0

10

20

30

40

50

60

70

80

90

100

0 0.2 0.4 0.6 0.8 1

Mstatic/(Mstatic)u

% M

omen

t red

istr

ibut

ion

1st flexuralcrack

plate yield

1st debonding

baryield

shearfailure


5.3.4.4 BEAM SF1 (CFRP 25X2.4)

This beam was externally bonded with a 2.4mm thick CFRP pultruded plate. As the beam was

gradually loaded, the first flexural crack, crack A in Figure 5.39, formed at an applied load P of 8kN

(R=2.53kN, Mhog=3.12kNm, Msag=3.0kNm) at the interior support. At P=14.6kN (R=4.8kN, Mhog=6kNm,

Msag=5.76kNm), IC debonding was initiated at the plate/concrete interface as indicated by the

formation of IC interface crack, D in Figure 5.39, which propagated from the root of crack A towards

the west plate end as indicated by the arrows. This IC interface crack propagated gradually along the

beam upon further loading, until at P=23kN (R=8.2kN, Mhog=8.6kNm, Msag=9.9kNm) when the second

flexural crack, crack B, formed east of crack A, followed almost immediately by the formation of

another flexural crack, crack C, west of crack A as shown in Figure 5.39. Formation of IC interface

cracks E and F were then observed, propagating from the roots of crack B and C respectively as more

load was applied, while IC interface crack D did not propagate any further. A maximum plate strain of


- 313 -

0.00203 was recorded at strain gauge SG6, 200mm from interior support, at P=32.5kN (R=11.9kN,

Mhog=10.4kNm, Msag=14.3kNm).

Figure 5.39 Beam SF1: Debonding propagation (P=31kN)

The debonding propagation was gradual at first, with the debonding at the east span being more

severe. However, as the IC interface crack E propagated to approximately 400mm from the interior

support (near SG3) at P=32.5kN, the debonding propagation became very rapid as shown in Figure

5.40, where crack E travelled a long distance along the beam as the load was increased from 33kN to

34kN. Eventually complete debonding of the east plate end occurred at P=39.5kN (R=14.8kN,

Mhog=12kNm, Msag=17.7kNm) in Figure 5.41.


A B


Interior support

East West

C

D E F Debonding

propagation

A B Debonding propagation

Interior support

East West

E


- 314 -

Figure 5.41 Beam SF1: IC debonding failure (P=40kN)

After the plate completely debonded, the beam continued to be loaded until vertical shear failure

occurred at a load P=76.5kN, at a maximum displacement of 45.8mm. Only two flexural cracks formed

in the hogging region of the east span as shown in Figure 5.40, with the last crack, crack B, at

approximately 200mm from the interior support.



loading the beam behaved elastically, i.e. region A in Figure 5.42, and so the hogging moment was

greater than the sagging moment. After crack B and IC interface crack E in Figure 5.40 formed (point

F in Figure 5.42), the moment in the hogging region became less than that in the sagging region,

indicating that moment is being redistributed from the hogging to the sagging region. Maximum plate

strain was achieved at point G in Figure 5.42, and soon after, IC debonding failure occurred which

caused a reduction in Mhog as shown by point H in Figure 5.42.

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40 50displacement (mm)

Mom

ent (

kNm

)

Msag

majordebonding

shear failure

max εp


F

MhogG

H

I

Figure 5.42 Beam SF1: Moment vs displacement

East

E



- 315 -



When the IC interface crack D in Figure 5.39 propagated towards the west plate end, it caused a rapid

increase in the plate strain at SG6 as indicated by point A in Figure 5.43a. As IC interface cracks E

and F in Figure 5.39 formed and propagated to distances 200mm and 400mm from the east and west

of the interior support respectively, this caused a rapid increase in SG4 (point B in Figure 5.43b) and

SG7 (point C in Figure 5.43a). As IC interface crack E propagated further towards the east plate end,

this caused a rapid increase in strain at SG3 (point D in Figure 5.43b). At Mhog=10.4kNm, the

maximum plate strain of 0.002027 was obtained at SG6 (point D in Figure 5.43a). Soon after, due to

severe debonding occurring in the region between SG3 and SG7 (Figure 5.39), this caused a sudden

reduction in plate strain at SG3 to SG7 while a sudden increase in SG1 and SG2 was observed, as

denoted by E and F in Figure 5.43 respectively. Eventually, IC debonding failure occurred with a

maximum plate strain of 0.00116 recorded at SG6. Note that at approximately Mhog=8kNm, the strains

at SG4, SG5 and SG6 began to converge. This indicates that there is almost zero resultant bond force

between SG4 to SG6 due to debonding. However, as the bond at the plate/concrete interface was still

strong further along the beam, this allowed the plate strains to continue to increase until at point D,

where debonding propagated further along the beam, causing the plate strains to reduce.

0

2

4

6

8

10

12

14

-1000 -500 0 500 1000 1500 2000 2500strain (x10-6)

Mho

g (k

Nm

)

SG5 (centre)SG6SG7SG8SG9 (west)

A

0

2

4

6

8

10

12

14

-500 0 500 1000 1500 2000strain (x10-6)

Mho

g (k

Nm

)

SG1 (east)SG2SG3SG4SG5 (centre)

B

C

D

EE

E

F

SG9 SG8

SG7 SG6

SG5

SG5

SG4

SG3SG2

SG1

(a)

(b)

Figure 5.43 Beam SF1: Moment vs plate strain


- 316 -


sagging moment in the beam Msag is shown in Figure 5.44. For the plated beam considered,

(Mstatic)u=49.2kNm. Line A in Figure 5.44 is the elastic distribution assuming EI is constant i.e.

Mhog/Msag = 1.2, line marked B is the maximum redistribution for the plated section and the line marked

C is the maximum redistribution for the unplated section. From Figure 5.44, it can be seen that the

plated beam only reached approximately 50% of the ultimate static moment when IC debonding failure

occurred.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1Mstatic/(Mstatic)u

Mho

g/M

sag

test results

A

B

C

1st flexural crack

1st debonding



shear failure

major debonding max εp reached

Figure 5.44 Beam SF1: hogging-moment/sagging-moment



on elastic analysis of constant EI.

02

46

810

1214

161820

0 20 40 60 80load (kN)

Mho

g (k

Nm

)

0

5

10

15

20

25

30

35

40

0 20 40 60 80load (kN)

Msa

g (k

Nm

)

1st debonding

IC debondingfailure

shear failure

major debonding

max εp reached

(Mhog)el

(Msag)el

Figure 5.45 Beam SF1: Maximum hogging and sagging moments


- 317 -



increased up to a maximum of 32.5% at IC debonding failure. After the plate debonded the flexural

strength of the hogging region is reduced, therefore the hogging moment had to be redistributed to the

sagging region to allow for this reduction in strength as shown in Figure 5.45. This resulted in a

sudden increase in %MR as shown by region A in Figure 5.46. As the ductility of the unplated hogging

region is much greater than before, large %MR was allowed and a maximum of 62% moment


0

10

20

30

40

50

60

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Mstatic/(Mstatic)u

% M

omen

t red

istr

ibut

ion

A

1st flexural crack

1st debonding


shear failure

major debonding

max εp reached

Figure 5.46 Beam SF1: percentage of moment redistribution

5.3.4.5 BEAM SF2 (CFRP 50X1.2)

The flexural crack marked A in Figure 5.47 first occurred immediately over the hogging support at an

applied load P=9kN (R=2.9kN, Mhog=3.6kNm, Msag=3.48kNm). This induced, at a higher load, the IC

interface cracks that are parallel to the plate and propagate in both directions that is B-C and B-D.

First sign of debonding was observed at P=16.8kN (R=5.57kN, Mhog=6.72kNm, Msag=6.69kNm). On

further loading in Figure 5.48, the IC interface cracks gradually propagated away from the position of

maximum moment such as from C to E and from F to G until there was rapid crack propagation at

which IC debonding occurred in Figure 5.49 from H to I which caused the plate strains to reduce which

signified IC debonding. The maximum plate strain of 0.00292 was obtained at strain gauge SG6 at

P=42kN (R=15.4kN, Mhog=13.4kNm, Msag=18.5kNm), and soon after, IC debonding failure occurred at

the east plate end at P=49kN (R=18.6kN, Mhog=14kNm, Msag=22.3kNm) with a recorded maximum

plate strain of 0.00262 at SG6 and a maximum displacement of 12.3mm in the east span. After

complete debonding of the plate, loading of the beam was continued until shear failure occurred in the


- 318 -

sagging region at P=76.5kN (R=32.7kN, Mhog=13.2kNm, Msag=39.3kNm). Like specimen SF1, in the

hogging region of the east span, where failure occurred, only two flexural cracks formed (Figure

5.49)at approximately 150mm spacing.

Figure 5.47 Beam SF2: Flexural crack and IC interface cracking (P=24kN)

Figure 5.48 Beam SF2: IC interface cracks propagation (P=35kN)


J


- 319 -


Msag moments, with the mean deflection under the applied loads at mid-spans. Mhog reduced relative

to Msag after the first appearance of the IC interface cracks at point A in Figure 5.50, which indicates

that moment is being redistributed from the hogging to the sagging region. Maximum plate strain was

achieved at point B, and soon after, IC debonding failure occurred at point C which caused a reduction

in Mhog. As loading was continued after the plate completely debonded, Msag continued to increase

while Mhog remained constant until shear failure in the sagging region at point D.

0

5

10

15

20

25

30

35

40

45

0 10 20 30 40 50

displacement (mm)

Mom

ent

(kN

m)

Msag

1stdebonding

shear failure

max εp


A Mhog

B C

D



increased up to shear failure, with the positions of the strain gauges SG given by Figure 5.8. The

behaviour was similar to that observed in specimen SF1 (Section 5.3.4.4). When a flexural crack

formed in between SG5 and SG6 at P=17kN (Figure 5.47), large increases in the plate strain occurred

at SG6 as marked by A in Figure 5.51a. As IC interface cracks formed and propagated towards SG4

at P=19.7kN, i.e. from B-C-E in Figure 5.48, this caused a rapid increase in SG4 (B in Figure 5.51b),

eventually causing strains at SG4 and SG5 to converge. As the IC interface crack propagated further

towards the SG3 (i.e. from F to G in Figure 5.48), sudden increases in strain at SG3 was observed (C

in Figure 5.51b). At Mhog=13.4kNm, the maximum plate strain of 0.00292 was obtained at SG6 (D in

Figure 5.51a). Soon after, due to severe debonding in the region between SG3 and SG5 (from interior

support to H in Figure 5.49), this caused a sudden drop in plate strains at SG3, SG4 and SG5, while

a rapid increase in SG1 and SG2 was observed, as denoted by E and F in Figure 5.51 respectively.

Eventually, IC debonding failure occurred with a maximum plate strain of 0.00262 recorded at SG6. It

is worth noting that sudden reductions in plate strains due to debonding propagation did not occur in


- 320 -

the EB steel plated specimens tested, even when severe debonding was observed i.e. specimens

SS1 (Section 5.3.4.1)and SS2 (Section 5.3.4.2). It is interesting to note that the strains at SG5 and

SG6 intercepted at point G in Figure 5.51a, after which the strains at SG6 became greater than that at

SG5. This may be because of the flexural crack that formed near SG6, i.e. crack J in Figure 5.48,

which caused large plate strains to develop as the crack widened.

0

4

8

12

16

-1000 -500 0 500 1000 1500 2000 2500 3000strain (x10-6)

Mho

g (k

Nm

)

SG1 (east)SG2SG3SG4SG5 (centre)

0

4

8

12

16

-1000 -500 0 500 1000 1500 2000 2500 3000strain (x10-6)

Mho

g (k

Nm

)

SG5 (centre)SG6SG7SG8SG9 (west)

(a)

(b)

A

B

C

D

E

E

F

SG9

SG8SG7

SG6

SG5

SG5

SG4SG3SG2

SG1

F

G



sagging moment in the beam Msag is shown in Figure 5.52. In this case, (Mhog)u is the experimentally

measured moment at plate debonding and (Msag)u is the rigid plastic strength and from which (Mstatic)u

and line B were calculated. The first IC interface crack at F occurred at a very early stage of loading.

The maximum plate strain of 0.00292 occurred at H prior to IC debonding at I. After IC debonding of

the plate, the beam behaves as an unplated beam and the test was continued until the beam failed in

shear at point J just short of its theoretical unplated flexural capacity allowing for full moment

redistribution.


- 321 -

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1

Mstatic/(Mstatic)u

Mh

og/M

sag

IC debonding

A

BC

test results

F

1st IC interface crack max plate strain

reached

HI

maximum moment redistribution for unplatedstructure

max. redistribution for plated structure

elastic (constant EI)

shear failureJ

Figure 5.52 Beam SF2: hogging- moment / sagging-moment




0

5

10

15

20

25

0 20 40 60 80load (kN)

Mh

og (k

Nm

)

0

10

20

30

40

0 20 40 60 80load (kN)

Msa

g (k

Nm

)

1st debonding

IC debondingfailure

shear failure

max εp reached

(Mhog)el

(Msag)el



Figure 5.54 for different Mstatic applied. The initial divergence from zero moment redistribution is due to

bedding of the beam. At the first sign of debonding, there was already 11% of moment redistribution,

and as more load was applied such that the maximum plate strain was obtained in the plate, 29% of

moment redistribution was recorded. Upon further loading, the strain in the plate began to reduce due

to severe debonding, but the %MR continued to increase as the stiffness in the hogging region was

less than before. At IC debonding failure, 36% moment redistribution was recorded, which is greater


- 322 -

than that obtained in Specimen SF1 as premature debonding occurred at a higher load. After the plate

debonded the flexural strength of the hogging region is reduced, therefore the hogging moment had to

be redistributed to the sagging region to allow for this reduction in strength as shown in Figure 5.53.

This resulted in a sudden increase in %MR as denoted by region A in Figure 5.54. A maximum of 62%

moment redistribution was obtained at shear failure of the unplated beam.

0

10

20

30

40

50

60

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mstatic/(Mstatic)u

% M

omen

t red

istr

ibut

ion

A

1st flexural crack

1st debonding


shear failure

max εp reached


5.3.4.6 BEAM SF3 (CFRP 80X1.2)

As the beam was gradually loaded, the first flexural crack, crack A in Figure 5.55, formed at an applied

load P of 9.8kN (R=3.35kN, Mhog=3.72kNm, Msag=4.0kNm) at the interior support. Upon further

loading, two flexural cracks, crack B and C in Figure 5.55, formed at approximately 200mm on the

east and west of the interior support. When two secondary cracks formed between crack A and C and

crack A and B, the cracking spacing was reduced to approximately 100mm. At P=28kN (R=10.1kN,

Mhog=9.36kNm, Msag=12.1kNm), the first IC interface crack, D in Figure 5.55, was found propagating

from the root of crack A towards the west plate end. At P=34kN, IC interface cracks F and G formed

from the roots of crack A and crack B respectively. As more load was applied, IC interface crack G in

Figure 5.56 started to gradually propagate towards the west plate end to point H at P=38kN, while no

further propagation was observed at other IC interface cracks. Eventually IC debonding failure

occurred from the last flexural crack, crack B in Figure 5.56, to the west plate end at P=40.9kN

(R=14.9kN, Mhog=13.3kNm, Msag=17.9kNm) in Figure 5.57 with a deflection of 9.7mm beneath the

applied load. A maximum plate strain of 0.00249 was recorded at strain gauge SG5 immediately prior

to IC debonding failure. After the plate completely debonded, the beam continued to be loaded until


- 323 -

vertical shear failure occurred at a load P=77.4kN, at a maximum displacement of 35.65mm. Three

flexural cracks formed in the hogging region of the west span, where failure occurred, (Figure 5.55) at

approximately 100mm spacing.




A BC

DF G

west east

B

G H

west

H

west


- 324 -



loading the beam behaved elastically. After the first flexural crack formed, the moment in the hogging

region became less than that in the sagging region, indicating that moment is being redistributed from

the hogging to the sagging region. Maximum plate strain was achieved just prior to IC debonding

failure, after which a reduction in Mhog occurred as shown by point A in Figure 5.58.

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40

displacement (mm)

Mom

ent (

kNm

)

Msag

1stflexural crack

shear failure

& max εp reachedIC debonding failure

A Mhog

1stdebonding



increased up to IC debonding failure, with the positions of the strain gauges SG given by Figure 5.8. It

can be seen that after the first flexural crack formed, the plate strain at SG4 and SG6 increased much

more rapidly, as shown by A in Figure 5.59. When the IC interface crack G in Figure 5.55 formed near

SG6 at Mhog=11.4kNm and propagated towards the west plate end, this caused the plate strain at SG6

to reduce (B in Figure 5.59), while a rapid increase in the plate strain at SG7 was observed (C in

Figure 5.59). IC debonding failure then followed (at Mhog=13.3kNm) with a maximum plate strain of

0.00249 recorded at SG5 as denoted by point D in Figure 5.59. It is worth noting that because IC

debonding propagated from SG6 to the west plate end and not from the interior support, therefore the

plate strain at SG4 and SG5 did not reduce prior to debonding failure.


- 325 -

0

2

4

6

8

10

12

14

16

18

-1000 -500 0 500 1000 1500 2000 2500 3000

strain (x10-6)

Mho

g(kN

m)


SG1&SG9

SG2&SG8SG3 SG7 SG6 SG4 SG5

A

C BD




(Mstatic)u=51.8kNm. Line A represents the elastic distribution assuming EI is constant i.e. Mhog/Msag =

1.2, line marked B is the maximum redistribution for the plated section and the line marked C is the

maximum redistribution for the unplated section. From Figure 5.60, it can be seen that the plated

beam only reached approximately 50% of the ultimate static moment when IC debonding failure

occurred.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mstatic/(Mstatic)u

Mh

og/M

sag

test results

A

B&C

1st flexural crack

1st debonding



shear failure

& max εp reached



- 326 -




0

5

10

15

20

25

30

35

40

0 20 40 60 80

load (kN)

Mho

g (k

Nm

)

0

5

10

15

20

25

30

35

40

0 20 40 60 80

load (kN)

Msa

g (k

Nm

)1st debonding

IC debondingfailure

shear failure(Mhog)el

(Msag)el1st flexuralcrack




increased up to a maximum of 27.6% at IC debonding failure. After the plate debonded, much of

hogging moment was redistributed to the sagging region to allow for this reduction in strength as

shown in Figure 5.61. This resulted in a sudden increase in %MR as shown by region A in Figure

5.62, and 56% moment redistribution was obtained at shear failure of the unplated beam.

0

10

20

30

40

50

60

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mstatic/(Mstatic)u

% M

omen

t red

istr

ibut

ion

A1st flexural crack

1st debonding


shear failure

& max εp reached



- 327 -

5.3.4.7 BEAM SF4 (CFRP 100X0.6)

This beam was externally bonded with three CFRP fibre sheets of 0.2mm thickness each using the

wet lay-up technique. The behaviour of the beam was similar to the other specimens with CFRP

pultruded plates, but was more ductile due to the low stiffness of the plate. As the beam was gradually

loaded, the first flexural crack, crack B in Figure 5.63, formed near strain gauge SG6 at an applied

load P of 15kN (R=5.03kN, Mhog=5.76kNm, Msag=6.03kNm). Note that crack A in Figure 5.63 is a pre-

existing crack which formed over the interior support during preparation. Upon further loading, several

primary cracks, cracks C and D, and secondary cracks, cracks E, F and G, were found. The adhesive

over the surface of the plate made it difficult to see the formation of IC interface cracks. The first

visible sign of debonding occurred near SG6, marked H in Figure 5.63, when small herringbone

cracks were found propagating from the root of crack B at P=30kN (R=10.7kN, Mhog=10.3kNm,

Msag=12.8kNm). Debonding was also observed at the roots of flexural cracks F and C, denoted by I

and J in Figure 5.63. The arrows in the Figure 5.63 represent the directions of debonding propagation.


bars yielded at P=56.9kN (R=21.2kN), before complete debonding of the plate.


Upon further loading, IC interface crack H in Figure 5.64 started to gradually propagate towards the

west plate end to point K at P=62kN, and from J to L in the east span. When the load was further

increased to P=63.4kN, a rapid debonding propagation in the west span occurred, as denoted by I-H-

K-M in Figure 5.65. Eventually the IC interface crack propagated to the plate end, from M to N in

A B C DF

G

east west

Interior support

HI

J E


- 328 -

Figure 5.66, to cause IC debonding failure to occur at P=64.8kN (R=25.6kN, Mhog=16.3kNm,

Msag=30.7kNm) with a deflection of 15.9mm beneath the applied load. A maximum plate strain of

0.0042 was recorded at strain gauge SG6 prior to IC debonding failure at P=62.7kN (R=23.7kN,

Mhog=18.2kNm, Msag=28.5kNm). After the plate completely debonded, loading continued until vertical

shear failure occurred at a load P=82kN in the east span near the applied load, at a maximum

displacement of 45.2mm. Figure 5.67 shows the hogging region over the interior support upon shear

failure occurring, where it can be seen that the plate has completely detached from the beam in the

west span.


Figure 5.65 Beam SF4: Debonding propagation before failure (P=63.4kN)

H I

KL

A BC D

J

Interior support

east west

I M

Interior support

A B D

KH


- 329 -


Figure 5.67 Beam SF4: Hogging region at shear failure (P=82kN)

The variation of the moment, at the position of the maximum hogging and sagging moments, with the

mean deflection under the applied loads at mid-spans, are plotted in Figure 5.68. It can be seen that

near the start, in region A, the hogging moment was slightly greater than the sagging moment as

would be expected from an elastic analysis. The hogging moment then reduced relative to the sagging

moment and they have an equal magnitude at point B. The maximum hogging moment and the

maximum plate strain occurred at the same applied load at C, although the plate did not debond until

after both the plate strain and hogging moment had reduced slightly at D. It is felt that this reduction in

moment and plate strain from C to D, just prior to IC debonding, may have been partly due to the slip

between the plate and the beam, that is partial interaction, which would reduce the flexural rigidity as

well as the plate strain in the hogging region. After IC plate debonding, the behaviour of the hogging

region reverts back to that of the unplated section at E.

H M NK

east west

Interior support

A B D

C


- 330 -

0

10

20

30

40

0 10 20 30 40 50

Displacement (mm)

Mom

ent (

kNm

)

Mhog

Msag

max plate strain plate IC debonding

shear failure

F

F

A B

C D

E


It is worth noting that the continuous beam eventually failed by vertical shear failure at point F in

Figure 5.68. However, this occurred well after the plate had IC debonded so that the vertical shear

failure had no effect on the redistribution of moment. It is also worth noting that the sagging moment is

continually increasing relative to the hogging moment which signifies moment redistribution; it was for

this reason that the sagging region was made much stronger than the hogging region in order to

achieve as much moment redistribution as possible.



After flexural cracks B and C in Figure 5.63 formed near SG6 and SG4 respectively, large increases in

plate strains at SG4 and SG6 were observed, as marked by A and B in Figure 5.69, and upon further

loading, the flexural cracks widened, inducing slip at the interface and causing convergence in strains

at SG5 and SG6. That is the resultant bond force between SG5 and SG6 is zero. When the IC

interface crack near SG4 propagated from J to L in Figure 5.64 at Mhog=17.6kNm, this caused the

plate strain at SG3 to increase (C in Figure 5.69). After the maximum plate strain was reached, small

reductions in SG3 and SG4 was observed. The same happened in the west span, where after the

maximum plate strain was reached at SG6 (D in Figure 5.69), the IC interface crack near SG6

propagated from H to K in Figure 5.64 which caused the plate strain at SG7 to increase rapidly (E in

Figure 5.69) and the plate strain at SG5 and SG6 reduced (F in Figure 5.69). As the debonding

propagated further from I to M in Figure 5.65, this caused sudden reductions in plate strains between

SG5 and SG8. IC debonding failure soon followed (at Mhog=16.3kNm) with a maximum plate strain of

0.00218 recorded at SG6.


- 331 -

0

4

8

12

16

20

-1000 0 1000 2000 3000 4000 5000strain (x10-6)

Mho

g (k

Nm

)


SG1SG2

SG3SG7

SG6

SG4

SG5

A

C

B

D

SG8

SG9

E F




(Mstatic)u=51.8kNm. Line A represents the elastic distribution assuming EI is constant i.e. Mhog/Msag =

1.2, line marked B is the maximum redistribution for the plated section and the line marked C is the

maximum redistribution for the unplated section. The initial discrepancy is because the beam was

bedding or settling down under very small loads. After the flexural cracks forms, Mhog/Msag reduces

gradually and the divergence from Mhog/Msag equal to 1.2 signifies moment redistribution. It can be

seen that IC debonding failure occurred close to B, and 80% of the ultimate static moment was

achieved.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1Mstatic/(Mstatic)u

Mho

g/M

sag

test results

A

B

C

1st flexural crack

1st debonding



shear failure

bar yieldmax εp reached



- 332 -




0

5

10

15

20

25

30

0 20 40 60 80 100load (kN)

Mho

g (k

Nm

)

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100load (kN)

Msa

g (k

Nm

)

1st debonding

IC debondingfailure

shear failure(Mhog)el

(Msag)el

1st flexural crack

bar yield

max εp reached



Figure 5.72 for different Mstatic applied. The initial discrepancy from zero moment redistribution is due

to the beam still settling. When flexural and debonding cracks formed the %MR increased up to 35.3%

as the maximum plate strain of 0.0042 was reached, and a maximum of 44% moment redistribution

was obtained at IC debonding failure. After the plate debonded, much of hogging moment was

redistributed to the sagging region to allow for this reduction in strength as shown in Figure 5.71. This

resulted in a sudden increase in %MR as shown by region A in Figure 5.72, and 60.3% moment


-20

-10

0

10

20

30

40

50

60

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Mstatic/(Mstatic)u

% M

om

ent

red

istr

ibu

tio

n

A

1st flexural crack

1st debonding


shear failure

max εp reached

bar yield



- 333 -

5.3.5 SUMMARY AND DISCUSSIONS

A summary of the test results is presented in the following journal paper along with a comparison of

results for the different specimens.

5.3.5.1 JOURNAL PAPER: MOMENT REDISTRIBUTION IN CONTINUOUS PLATED RC FLEXURAL MEMBERS PART 1 - NEUTRAL AXIS DEPTH APPROACH AND TESTS

This paper focuses on the moment redistribution behaviour of beams with externally bonded plates,

where the series of tests on EB beams carried out in this research are presented. The applicability of

the commonly used neutral axis depth approach for moment redistribution in RC flexural members on

plated structures was also assessed in this paper. Further discussion on the neutral axis depth

approach can be found in the literature review in Chapter 6 of this thesis.


- 334 -

Intermediate Crack Debonding of Plated RC Beams Experimental Investigation on Moment Redistribution Moment redistribution in continuous plated RC flexural members. Part 1: neutral axis depth approach and tests

- 335 -

Moment redistribution in continuous plated RC flexural members. Part

1: neutral axis depth approach and tests

*Oehlers, D.J., **Ju, G., ***Liu, I., and ****Seracino, R.

Corresponding author *Dr. D.J. Oehlers Associate Professor School of Civil and Environmental Engineering Centre for Infrastructure Diagnosis, Assessment and Rehabilitation The University of Adelaide Adelaide SA5005 AUSTRALIA Tel. 61 8 8303 5451 Fax 61 8 8303 4359 email [email protected] **Dr. G. Ju Lecturer Department of Architectural Engineering University of Yeungnam South Korea ***Ms. I. Liu Postgraduate student School of Civil and Environmental Engineering The University of Adelaide ****Dr. R. Seracino Senior Lecturer School of Civil and Environmental Engineering The University of Adelaide Published in Engineering Structures 2004, vol. 26, pg.2197-2207


- 336 -

Statement of Authorship

MOMENT REDISTRIBUTION IN CONTINUOUS PLATED RC FLEXURAL MEMBERS. PART

1: NEUTRAL AXIS DEPTH APPROACH AND TESTS

Published in Engineering Structures 2004, vol. 26, pg.2197-2207

LIU, I.S.T. (Candidate)

Performed all analyses, interpreted data and co-wrote manuscript.

Signed Date

OEHLERS, D.J.

Supervised development of work, co-wrote manuscript and acted as corresponding author.

Signed Date

SERACINO, R.

Supervised development of work, and manuscript review.

Signed Date


- 337 -

MOMENT REDISTRIBUTION IN CONTINUOUS PLATED RC FLEXURAL MEMBERS. PART 1: NEUTRAL AXIS DEPTH APPROACH AND TESTS Oehlers, D.J., Ju, G., Liu, I., and Seracino, R. ABSTRACT It is now common practice to retrofit or rehabilitate existing reinforced concrete beams and slabs by adhesively bonding fibre reinforced polymer (FRP) or metal plates to their surfaces. Advanced design rules are available for quantifying the various plate debonding mechanisms and consequently the shear and flexural capacities of the plated sections. These design rules show that even though the required increase in strength can be obtained by plating, plate debonding can severely reduce the ductility of a flexural member to such an extent that plating guidelines often exclude moment redistribution. This exclusion may reduce the application of plating, in particular to retrofitting buildings where ductility is often a requirement, or it may require the development of a radically different approach to design that does not rely implicitly on ductility. In this paper, it is shown that the commonly used neutral axis depth approach for moment redistribution in RC flexural members cannot be used for most plated structures because plate debonding often occurs before the concrete crushes. Tests on plated flexural members are also reported which show that moment redistribution can occur. In Part 2 of this paper, a moment redistribution analysis procedure is developed that can cope with plate debonding of externally bonded plates. Keywords: Retrofitting; reinforced concrete beams; externally bonded plates; ductility; moment redistribution 1. INTRODUCTION Let us consider the plated continuous beam in Fig.1; the term beam will be used in this paper in a generic sense for both beams and slabs, that is for flexural members. Plates can be adhesively bonded to any face, as shown, and it is now widely recognised1-6 that these plates are susceptible to three major modes of debonding, that will be referred to as intermediate crack (IC) debonding, critical diagonal crack (CDC) debonding and plate end (PE) debonding. PE debonding is induced by the curvature in the beam and can be easily prevented by terminating the plate near a point of contraflexure, so that this form of debonding should not affect the ductility of the continuous beam. CDC debonding is induced by the shear deformation in the beam and it is a rapid and brittle form of debonding which would prevent significant moment redistribution. Hence, it will be assumed in the following approach that the continuous beam is designed against both CDC and PE debonding and, therefore, the ductility, and consequentially the moment redistribution, depends on the IC debonding resistance4,7. The tests reported in this paper were also designed not to fail prematurely by CDC and PE debonding6 so that the effect of IC debonding on the moment redistribution was measured.


- 338 -

IC

IC

ICCDC CDC CDC

PE

PE

PE

ICIC IC

CDC

CDCCDCPE

PE PE

(c) tension face plates

(b) side plates

hogging-ve

sagging+ve

hogging-ve

Figure 1. Plate debonding mechanisms In this paper, existing design rules for moment redistribution in RC beams that are based on the well known neutral axis depth factor ku (defined as the distance of the neutral axis from the compression face as a proportion of the effective depth of the beam) is first related to the IC debonding resistance to show why existing guidelines for external or surface plating often preclude moment redistribution. A series of seven full-scale tests on two span continuous plated beams is then described in which it is shown that substantial moment redistribution can occur. In Part 2 of this paper8, a moment redistribution analysis procedure for plated beams is developed which calibrates well with the test results in Part 1. This moment redistribution procedure is then applied to plating structures and it is shown that through moment redistribution and through the judicious choice of the plating system a substantial increases in strength and ductility can be achieved. 2. MOMENT REDISTRIBUTION IN NATIONAL STANDARDS 2.1 Neutral axis depth approach ku International standards tend to base the ability of (unplated) reinforced concrete beams and slabs to redistribute moment on the neutral axis parameter ku. Typical examples from five standards9-13 are given in Fig.2 for, the commonly used, high ductility reinforcing bar steels. For these high ductility steels, it can be assumed that the strain capacity of the steels is sufficiently large to ensure that they never fracture prior to concrete crushing. Therefore, the ultimate failure of the RC beam is always

governed by concrete crushing at a strain εc that is often assumed to range between 0.003 to 0.004. As shown in Fig.2, it can be seen that there is a general agreement for an upper bound of 30% to the amount of moment redistribution that can occur. However, there is a fairly wide divergence between

predictions. For example, no moment redistribution is allowed when ku ≥ 0.4 for the Australian

Standard requirements but this is substantially increased to ku ≥ 0.6 for both the Canadian and British

Standards; the mean value for no moment redistribution from the five approaches is ku ≥ 0.48 and is shown as point A. At the other extremity, the British Standard approach allow 30% redistribution when

ku ≤ 0.3 whereas the Canadian approach uses 30% as an upper bound as ku → 0; the mean value for

30% redistribution is ku ≤ 0.15 and is shown as point B. A line joining these mean values at the extremities is shown as the mean value in Fig.2.


- 339 -

neutral axis parameter ku

10 %

0

20 %

30%

0.1 0.2 0.3 0.4 0.6

British

Canadian

European

German

Australian

momentredistribution mean value

B

A

Figure 2. Moment redistribution dependence on neutral axis parameter ku

The effect of the variation A-B in Fig.2 of the neutral axis parameter ku on the strain profile of a reinforced concrete (RC) section at failure is illustrated in Fig.3. For ease of explanation, let us consider the case of a deep RC beam in which the effective depth d approaches the depth of the beam h as shown in Fig.3(a) (which is the cross-section of a beam in the hogging or negative region).

It has been assumed that the concrete crushing strain εc is 0.0035, as shown in Fig.3(b). As the strain capacity of the reinforcing bars is assumed to be very large, as previously explained, concrete

crushing always controls failure so that the strain at the compression face of εc = 0.0035 is common to all the strain profiles shown and can be considered to be a pivotal point. It can be seen in Fig.3(b) that

the neutral axis parameter ku controls the maximum tensile strain at the tension face εtf for any depth

of beam d, as εtf = εc(1-ku)/ku and, hence, independent of d. It needs to be pointed out that the neutral

axis parameter ku does not control the curvature χ for any beam depth as this depends on the actual

depth of the beam, that is χ = εc/kud and, hence, it depends on d. However, the ku factor controls the

rotation of the plastic hinge, of length Lhinge, as this is given by χLhinge where the curvature at failure χ

= εc/kud; for example, if Lhinge ≈ d then the rotation is equal to εc/ku. It can, therefore, be seen that the

ability to redistribute moment depends on the maximum tensile strain εtf.

d = h

kud =0.48d

εc = 0.0035

(ε(ε(ε(εtf))))0.15d=0.020

0%

εεεε

30% 0% to 30%

pivotalpoint

tension face

compressionface

3 mm steel plates

1.2 mm CFRP plates

(a) (b)

(ε(ε(ε(εtf))))0.48d=0.0038

mean 30%(point B in Fig.2)

mean 0%(point A in Fig.2)

ductilereinforcingbars

kud =0.15d

Figure 3. Dependence of moment redistribution on tension face strains

The strain profile associated with the mean 0% redistribution, that is point A in Fig.2, is shown in Fig.3(b) as the line mean 0%; as the depth of the neutral axis from the compression face is 0.48d, the

strain at the tensile face is (εtf)0.48d = 0.0038. The strain profile for the mean 30% redistribution at point

B in Fig.2 is also shown in Fig.3 and this requires a tensile face strain of (εtf)0.15d = 0.020. Hence,


- 340 -

when the concrete crushes and the tensile face strain εtf < 0.0038 then no moment redistribution is

allowed, when 0.0038 < εtf < 0.020 then between 0% and 30% redistribution is allowed, and when εtf > 0.020 then 30% redistribution is allowed. Generally speaking, ductile reinforcing bars can easily accommodate these strains. However, if a plate is adhesively bonded to the tension face as shown in Fig.3(a), then these strains have also to be accommodated by the plate. The strain capacity of an FRP tension face plate depends on either its fracture strength or its IC debonding resistance4,7. For most cases, IC debonding controls the strain capacity of FRP plates which commonly debond at less than half of the fracture capacity, except for very thin plates used in the wet lay up process. Tests, reported in this paper and also those published elsewhere5, conducted on 1.2 mm pultruded carbon FRP (CFRP) plated beams found that the IC debonding strains ranged from 0.0025 to 0.0052. This range of strains is shown as the shaded region labelled 1.2 mm CFRP plates in Fig.3(b). The bounds of this range just fall either side of the mean 0% profile which suggests that in general pultruded carbon FRP plated structures have little capacity for moment redistribution. Metal plates can be designed to IC debond prior to yielding in which case the behaviour is similar to that of FRP plates. However, and in contrast to FRP plates, metal plates can be designed to yield prior to IC debonding; although it should be remembered that tests have shown that in the majority of cases the metal plated beam will still eventually debond but at a much larger strain than if it remained elastic. Beam tests, in this paper and others5,6 by the authors, have shown that the IC debonding strains for 3 mm steel plates range from 0.0045 to 0.021 which is shown as the hatched region in Fig.3(b), and which suggests that metal plates that have been designed to yield prior to IC debonding may have adequate capacity to redistribute moment. 3. MOMENT/TENSION-FACE-STRAIN RELATIONSHIP It was shown in the previous section that moment redistribution based on the neutral axis depth, ku

approach, is controlled by the strain at the tension face εtf when the concrete crushes at εc. Hence, it

is not the moment/curvature, M/χ, relationship that is important in moment redistribution but the

moment/tension-face-strain, M/εtf, relationship such as those shown in Fig.4; Fig.4 was derived from a standard non-linear full-interaction sectional analysis of the plated beams reported in this paper.

0

5

10

15

20

25

30

0 0.005 0.01 0.015 0.02 0.025

tension face strain (εεεεtf)

Mo

men

t (k

Nm

)

yield of reinforcing bars εy

A

G

D

O

C

Plate yield

HIC debonding εp.db

I plate fracture εp.fr

Jconcrete crushes at εcconcrete crushes at εc

CFRP plated

EIC debonding εp.db

Fsteel plated

unplated

concrete crushes at εc

Bconcrete crushes at εc

Figure 4. Typical moment/tension-face-strain behaviours


- 341 -

The M/εtf relationship for the unplated RC beam is shown as O-A-B in Fig.4. As the ductile reinforcing bars are assumed to have almost unlimited strain capacity in comparison with the finite concrete strain

capacity εc, the beam can only fail by concrete crushing at point B. Hence, there is typically a very

long tensile strain plateau commencing at yield of the reinforcing bars εy at point A and terminating

when the concrete crushes at a strain εc at point B. Over this plateau, A-B, the moment capacity remains almost constant. It may be worth noting that the national standards use of ku to control the amount of moment redistribution implicitly applies to sections with the behaviour represented by the curve O-A-B, that is a long tensile strain plateau that is terminated by concrete crushing.

The M/εtf relationship O-C-D-E-F in Fig.4 applies to a steel plated beam in which IC debonding has not occurred prior to concrete crushing at F. The plate yields at C and the reinforcing bars at D, after which the moment remains fairly constant until the concrete crushes at F. This steel plated beam behaviour, O-C-D-E-F has almost identical characteristics to that of the unplated beam O-A-B and, hence, the ku factor used in standards can be used to control the moment redistribution. Let us now assume that IC debonding occurs at point E in Fig.4 that is prior to concrete crushing at F but after yielding of both the tension face plate and tension reinforcing bars at D. In this case, ku cannot be used to control the moment redistribution as the ku approach implicitly requires the concrete to crush as illustrated in Fig.3(b). If the steel plate debonds prior to yielding at point C, then the behaviour is similar to that of an FRP plated section described in the following paragraph.

The M/εtf relationship for an FRP plated slab in which debonding, that is IC, PE and CDC, does not occur prior to concrete crushing is given by O-G-H-I-J in Fig.4. The moment continues to increase after the reinforcing bars yield at point G because FRP is a linear elastic material that does not yield prior to fracturing, so that the plate keeps attracting more force, thereby, increasing the moment. Hence, an FRP plated section does not have a near horizontal plateau, such as D-E-F or A-B, that is ideal for accommodating moment redistribution away from the plated section. For this reason, the FRP plated section keeps attracting more moment even though the moment is being redistributed. Because of this rising plateau (G-I-J in Fig.4), FRP plated sections are less capable of redistributing moment as compared to metal plated sections with a horizontal plateau. Furthermore, IC debonding of FRP plates such as at point H often occurs soon after the reinforcing bars yield and generally well before the plate fractures at point I in Fig.4 or the concrete crushes at point J so that the length of the rising plateau is relatively short. In conclusion, it is suggested that the use of the ku factor in standards to control moment redistribution should not be applied to FRP plated structures because invariably the concrete does not crush and there is no ductile horizontal plateau; both of which are implicitly required in national standards. Furthermore, there is usually only a short rising plateau. Hence, it is suggested that the ku factors in national standards for controlling moment redistribution should only be used for metal plated sections in which the concrete crushes prior to the plate debonding. 4. SPECIMENS, TEST RIG AND INSTRUMENTATION The specific aim of these tests was to both demonstrate and measure moment redistribution in externally bonded plated flexural members and not to demonstrate the effectiveness of the strengthening method. The specimens consisted of the two span continuous beams in Fig.5 with the cross-sections in Fig.6. The test rig over one span is shown in Fig.7. The hogging regions of the beams were plated and the sagging regions were left unplated as in Fig.5. The tensile reinforcement


- 342 -

in the hogging region, 2Y12 bars, was much less than the tensile reinforcement in the sagging region, 4Y16 bars, to ensure that the plated hogging region reached its moment capacity first; this then allowed the hogging region to shed moment, or redistribute moment, to the sagging region as the static moment was being increased, thereby, increasing the sagging moment.

LVDT LVDT

East West

Plate

L=2400 L=2400 100 100

5000

1200 1100 1100 1200 2Y12

4Y16

W10 stirrup @1200mm

P P

120

Figure 5. Two span continuous beam specimens

2Y12

4Y16

W10 at 1200mm centres

120

375

2Y12

4Y16

W10 at 1200mm centres

120

375

bp plate

(a) Sagging region (b) hogging region

20mm cover

tp

Figure 6. Specimen cross-sectional details

Figure 7. Test rig

Advanced analysis techniques6,14-16 were used to design a specimen in which CDC and PE debonding did not precede IC debonding. The specimens are shown in Figs. 5 and 6. PE debonding was prevented by terminating the plate beyond the point of contraflexure and onto the compression faces of the sagging regions. CDC debonding was prevented by ensuring that a critical diagonal crack, associated with the concrete component of the vertical shear capacity Vc, did not occur prior to plate debonding; because of the CDC requirement the slab shaped cross-section in Fig.6 was used. To explain the reason for the slab shaped cross-section in Fig.6, let us consider the capacity of a beam or slab without stirrups so that the strength is controlled by either the flexural capacity or the


- 343 -

concrete component of the shear capacity Vc, as the latter controls CDC debonding. Let us consider a rectangular beam or slab which have the same cross-sectional area of concrete and the same cross-sectional area of longitudinal tension reinforcing bars. The beam shaped cross-section, in which the width is less than the depth, is more prone to vertical shear failure, and CDC debonding at Vc, than the slab shaped cross-section, in which the width is greater than the depth. This is because the concrete component of the vertical shear capacity of these two shapes Vc is roughly equal and, hence, their resistance to CDC debonding. However, the beam shaped cross-section will have a higher flexural capacity than the slab shaped cross-section due to the increased depth (lever arm) and, consequently, can resist a greater applied load at flexural failure with its associated greater vertical shear force. Therefore, beam shapes without stirrups are more prone to shear failure at Vc and CDC debonding than slab shapes. Hence a relatively large but realistic span-to-depth ratio of 20 was required and the use of a slab shaped cross-section in which the width was greater than the depth as shown in Fig.6. The concentrated loads P were applied at mid-span as in Fig.5 so that, for an elastic distribution of moment with an assumed constant flexural rigidity, the maximum hogging moment would be 20% greater than the maximum sagging moment. Deflections were measured under the applied loads P, load cells were placed at the applied loads and at the west support in Fig.5 so that the distribution of forces could be determined directly. Nine strain gauges were placed over the central support and along the length of the adhesively bonded plate not only to measure the strains but also to detect IC debonding. Seven specimens were tested and these are listed in Table 1. The main variable was the plate properties. Specimens SS1 to SS3 used adhesively bonded mild steel plates with plate thicknesses tp that varied from 1 mm to 3 mm. The plate widths (bp ) were varied to ensure virtually the same cross-

sectional area and, hence, the same axial rigidity (EA) so that the theoretical M/χ relationships, ignoring IC debonding, would be identical. The yield capacities of the plates fp.y were measured directly and being mild steel the plate’s Young’s modulus Ep can be assumed to be 200 GPa. Specimens SF1 to SF3 in Table 1 used adhesively bonded pultruded carbon FRP plates of thicknesses 1.2 mm and 2.4 mm. Whereas, Specimen SF4 used three layers of carbon FRP fabric that was applied using the wet lay-up procedure; its thickness and Young’s modulus were measured directly from specimens that were taken from the plated beam. The plate widths were varied from 25 mm to 100 mm and specimens SF1 and SF2 had plates of the same axial rigidity. Being FRP plates, the plates do not yield and the on-axis (longitudinal) Young’s modulus was measured directly.

Table 1 Plate properties Test

Specimens Plate

material Bonding technique

tp (mm)

bp (mm) fp.y

(MPa) fp.frac

(MPa) Ep

(GPa) SS1 steel adhesive 3 75 337 466 200 SS2 steel adhesive 2 112 223* 318 200 SS3 steel adhesive 1 224 211* 303 200 SF1 CFRP adhesive 2.4 25 - 2800 144 SF2 CFRP adhesive 1.2 50 - 2800 144 SF3 CFRP adhesive 1.2 80 - 2800 144 SF4 CFRP Wet lay-up (3 layers) 2.44 100 - 350 43

* proof stress Near the time of testing, specimens SS1, SF1, SF2 and SF3 had a concrete cylinder compressive strength of 39 MPa and a concrete Young’s modulus of 35 GPa, the remaining specimens had a


- 344 -

cylinder compressive strength of 48 MPa and Young’s modulus of 41 GPa. The yield strength of the Y12 reinforcing bars was 601 MPa and that of the Y16 bars was 540 MPa. 5. TYPICAL BEHAVIOUR IN TESTS Typical examples of the beam behaviour during testing are given in the following section. 5.1 Moment/deflection The variation of the moment, at the position of the maximum hogging and sagging moments, with the mean deflection under the applied loads at mid-spans, are plotted in Fig.8 for specimen SF4 which had a wet lay-up composite laminate plate. It can be seen that near the start, in region A, the hogging moment was slightly greater than the sagging moment as would be expected from an elastic analysis. The hogging moment then reduced relative to the sagging moment and they have an equal magnitude at point B (It will be shown later from Eq.2 that for this loading configuration there is 17% moment redistribution at point B). The maximum hogging moment and the maximum plate strain occurred at the same applied load at C, although the plate did not debond until after both the plate strain and hogging moment (see Table 2) had reduced slightly at D. It is felt that this reduction in moment and plate strain from C to D, just prior to IC debonding, may have been partly due to the slip between the plate and the beam, that is partial interaction, which would reduce the flexural rigidity as well as the plate strain in the hogging region. After IC plate debonding the behaviour of the hogging region reverts back to that of the unplated section at E.

Figure 8. Moment/deflection for specimen SF4 (CFRP wet lay-up plate)

It is worth noting that the continuous beam eventually failed by vertical shear failure at point F in Fig.8. However, this occurred well after the plate had IC debonded so that the vertical shear failure had no effect on the redistribution of moment. It is also worth noting that the sagging moment is continually increasing relative to the hogging moment which signifies moment redistribution; it was for this reason that the sagging region was made much stronger than the hogging region in order to achieve as much moment redistribution as possible.

0

10

20

30

40

0 10 20 30 40 50 Displacement (mm)

Mom

ent (

kNm

)

Mhog

Msag

max plate strain plate IC debonding

shear failure

F

F

A B

C D

E


- 345 -

Table 2 Test results

First IC interface crack Maximum plate strain

reached Plate debonded at one

end Spec.

bpxtp (mm) εp

Msag (kNm)

Mhog

(kNm) εp.max

Msag (kNm)

Mhog

(kNm) εp.db

Msag (kNm)

Mhog

(kNm) SS1 75x3 0.00290 15.1 14.2 0.00445 20.4 16.9 0.00445 20.4 16.9 SS2 112x2 0.00241 12.0 11.8 0.00593 29.0 19.3 0.00593 29.0 19.3 SS3 224x1 0.00270 9.8 9.7 0.01486 37.9 18.2 0.01486 37.9 18.2 SF1 25x2.4 0.00099 5.8 6.0 0.00203 14.4 10.2 0.00116 17.9 11.6 SF2 50x1.2 0.00134 6.7 6.7 0.00292 18.5 13.4 0.00262 22.3 14.0 SF3 80x1.2 0.00199 12.1 9.4 0.00249 17.9 13.3 0.00249 17.9 13.3 SF4 100x2.44 0.00191 13.3 10.4 0.00414 28.4 18.3 0.00168 30.7 16.3

5.2 IC interface crack propagation A typical sequence of crack propagation leading to IC debonding is illustrated in Figs. 9 to 11 for specimen SF2 which had a 1.2 mm pultruded carbon FRP plate; the numbers in the figures refer to the applied loads. The flexural crack marked A in Fig.9 first occurred immediately over the hogging support and this induced, at a higher load, the IC interface cracks that are parallel to the plate and propagate in both directions that is B-C and B-D. On further loading in Fig.10, the IC interface cracks gradually propagated away from the position of maximum moment such as from C to E and from F to G until there was rapid crack propagation at which IC debonding occurred in Fig. 11 from H to I which caused the plate strains to reduce which signified IC debonding.

Figure 9. Flexural crack and IC interface cracking (SF2, 1.2 mm CFRP)

Figure 10. Propagation of IC interface cracks (SF2, 1.2 mm CFRP)


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Figure 11. IC debonding (SF2, 1.2 mm CFRP)

5.3 Hogging moment as a proportion of the sagging moment The variation of the maximum hogging moment in the beam Mhog as a proportion of the maximum sagging moment in the beam Msag is shown in Fig.12 for specimen SS2 which had a 2 mm thick steel plate. For the test set up in Fig.5 and from an elastic analysis in which EI is assumed to be constant, Mhog/Msag = 1.2 which is shown as line A in Fig.12. The abscissa in Fig.12 is the applied static moment, Mstatic = PL/4 in Fig.5, as a proportion of the ultimate maximum static moment, (Mstatic)u = (Msag)u + (Mhog)u/2, based on rigid plastic analysis principles in which both the hogging and sagging sections achieve their theoretical ultimate capacities when the tension reinforcement has yielded, (Mhog)u and (Msag)u, and ignoring IC debonding in the case of the hogging region; hence the upper limit of Mstatic/(Mstatic)u = 1.0. The line marked B is the maximum redistribution assuming both regions achieve their theoretical moment capacities (Mhog)u and (Msag)u and the line marked C is the maximum redistribution after plate debonding that is when (Mhog)u is that of the unplated section.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1

Mstatic/(Mstatic)u

Mh

og/M

sag

IC debonding max plate strain reached

A

B

C

test resultsD

F

1st IC interface crack1st flexutral crack

occurred

E

G

maximum moment redistribution for unplated structures

max. moment redistribution for plated structures


Figure 12. Hogging-moment/sagging-moment (SS2, 2mm steel plate)

When the load is first applied Mhog/Msag approaches 1.2 in region D in Fig.12; one can still notice a slight divergence from this value because the beam is bedding or settling down under very small loads. Soon after, Mhog/Msag reduces gradually and the divergence from Mhog/Msag equal to 1.2 signifies moment redistribution. The first flexural crack is observed at point E, this is shortly followed by the appearance of the first IC interface crack at F and eventually IC debonding at point G which coincided with the maximum plate strain.


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The results for specimen SF2 which had a 1.2 mm carbon FRP pultruded plate are shown in Fig.13. In this case, (Mhog)u is the experimentally measured moment at plate debonding and (Msag)u is still the rigid plastic strength and from which (Mstatic)u and line B were calculated. As with the steel plated beam in Fig.12, the first IC interface crack at F occurred at a very early stage of loading. However, unlike the steel plated specimen in Fig.12, the maximum plate strain of 0.00292 (see Table 2) occurred at H prior to IC debonding at I. After IC debonding of the plate, the beam behaves as an unplated beam and the test was continued until the beam failed in shear at point J just short of its theoretical unplated flexural capacity allowing for full moment redistribution.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1

Mstatic/(Mstatic)u

Mh

og/M

sag

IC debonding

A

BC

test results

F

1st IC interface crack max plate strain

reached

HI

maximum moment redistribution for unplatedstructure

max. redistribution for plated structure

elastic (constant EI)

shear failureJ

Figure 13. Hogging-moment/sagging-moment (SF2, 1.2mm pultruded CFRP plate)

6. TEST RESULTS

The results from all seven tests are summarised in Table 2 where the measured plate strains εp, hogging moments Mhog and sagging moments Msag are tabulated at the first appearance of an interface IC crack in columns 3 to 5, at the maximum plate strain in columns 6 to 8 and at plate debonding in columns 9 to 11. It may be worth noting that the maximum strain εp.max for the CFRP plates are considerably less than the CFRP fracture strain of 0.019 as commonly occurs in externally bonded plates4. 7. MOMENT REDISTRIBUTION IN TEST SPECIMENS It is common design practice in a frame or beam analysis to assume that the flexural rigidity of an RC beam is constant in order to determine the elastic distribution of moments. Let us, therefore, define moment redistribution as the change in moment from the elastic moment based on the flexural rigidity being constant throughout the beam. Hence the percentage redistribution of moment from the hogging region is given by

( ) ( )( ) 100%

.

. ×−

=constEIhog

testhogconstEIhog

M

MMMR (1)

where for a specific static moment, (Mhog)EI.const is the theoretical hogging moment from a linear elastic analysis which assumes that the flexural rigidity EI is constant and (Mhog)test is the experimental


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hogging moment for the same static moment, that is the same applied load. For the loading configuration in these tests, as shown in Fig.5, the percentage moment redistribution from Eq.1 becomes

( ) ( )

( ) 10075.0

75.0% ×

−=

testsstatic

testshogtestsstatic

M

MMMR (2)

where (Mstatic)test is the static moment induced by the applied load in the test. The variation of the percentage moment redistribution with the static moment is shown up to plate debonding in Fig.14 for all seven tests. The large scatter at the start is due to the beam settling down on its supports and also because the applied loads are very small. Apart from specimen SF3, the remaining six beams appear to settle down at about the load at A after which there is a gradual increase in the percentage moment redistribution. All of the beams achieved at least 20% redistribution before debonding and five beams achieved a redistribution of greater than the upper limit of 30% that international standards use as shown in Fig.2.

-10

0

10

20

30

40

50

0 0.2 0.4 0.6 0.8 1

SS1SS2SS3SF1SF2SF3SF4%

Mo

men

t re

dis

trib

tuio

n

Mstatic

/(Mstatic

)u

plate debond

A

plate debond shear

failure

Figure 14. Variation of % moment redistribution with static moment

The variation of moment redistribution with plate strains is shown in Fig.15. In general for the FRP plated beams, the strain reduces prior to debonding such as from A to B which is an additional safety mechanism, whereas for the steel plated beams debonding and the maximum strain tend to coincide such as at point C, although there is a reduction in the increase in the plate strain prior to debonding.

-10

0

10

20

30

40

50

0 0.005 0.01 0.015

SS1SS2SS3SF1SF2SF3SF4%

Mo

men

t re

dis

trib

uti

on

Plate strain (at centre)

AA

A

B

B B C

C

Figure 15. Variation of % moment redistribution with plate strain


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The percentage moment redistribution at the maximum plate strain εp.max and at debonding εp.db are listed in Table 3. It can be seen that substantial amounts of redistribution have occurred in both the steel and FRP plated specimens. For example at the maximum plate strains the percentage moment redistribution ranges from 22% to 48%. It is also worth noting that in general the FRP plated specimens have a lower percentage redistribution at the maximum plate strains which range from 28% to 35% than at debonding where the plate strains have reduced which range from 35% to 44%. As design is generally based on the maximum plate strain that can be achieved prior to debonding, it is felt that the moment redistributions at the maximum strains should be used to represent the moment redistribution and those at debonding represent an additional factor of safety.

Table 3 Percentage moment redistribution

Specimen bpxtp (mm)

plate material

εp.max %MR at

εp.max εp.db

%MR at

εp.db SS1 75x3 steel 0.00445 22 0.00445 22 SS2 112x2 steel 0.00593 33 0.00593 33 SS3 224x1 steel 0.01486 48 0.01486 48 SF1 25x2.4 CFRP 0.00203 30 0.00116 35 SF2 50x1.2 CFRP 0.00292 29 0.00262 36 SF3 80x1.2 CFRP 0.00249 28 0.00249 28 SF4 100x2.44 CFRP 0.00414 35 0.00168 44

8. SUMMARY From a consideration of the moment redistribution allowances in international standards that are based on the neutral axis parameter ku, it is suggested that the ku approach should only be used for metal plated beams in which concrete crushing precedes debonding. Tests on seven plated beams have shown that substantial amounts of moment redistribution can occur. For carbon FRP plated beams this ranged from 28% to 35% and for steel plated beams from 22% to 48%. Hence plated beams have a scope for moment redistribution. 9. REFERENCES 1) ACI 440.2R-02 (2002). “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures”. Reported by ACI Committee 440. American Concrete Institute, Farmington Hills, Michigan, USA. 2) Blaschko, M., Nierdermeier, R., and Zilch, K. (1998). “Bond failure modes of flexural members strengthened with FRP”. Proceedings of Second International Conference on Composites in Infrastructures, Saadatmanesh, H. and Ehsani, M. R., eds., Tucson, Arizona, 315-327. 3) fib bulletin 14 (2001). “Externally bonded FRP reinforcement for RC structures. Design and use of externally bonded fibre reinforced polymer reinforcement (FRP EBR) for reinforced concrete structures”. Task Group 9.3 FRP reinforcement for concrete structures. Lausanne, Switzerland. 4) Teng, J.G., Chen, J.F,. Smith, S.T., and Lam, L. (2002). “FRP Strengthened RC Structures”. John Wiley and Sons. Ltd. Chichester, England. 5) Oehlers D.J., Park S.M. and Mohamed Ali, M.S. (2003) “A Structural Engineering Approach to Adhesive Bonding Longitudinal Plates to RC Beams and Slabs.” Composites Part A, Vol. 34, pp 887-897.


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6) Oehlers, D.J. and Seracino, R. (2004) “Design of FRP and Steel Plated RC Structures: retrofitting beams and slabs for strength, stiffness and ductility.” Elsevier. September. 7) Teng, J.G., Smith, S.T., Yao, J. and Chen, J.F. (2003) “Intermediate crack-induced debonding in RC beams and slabs.” Construction and Building Materials, Vol.17, No.6-7, pp 447-462. 8) Oehlers, D.J., Liu, I., Ju,G., and Seracino, R., “Moment redistribution in continuous plated RC flexural members. Part 2: flexural rigidity approach.” Submitted to Engineering Structures (2004). 9) Deutsches Institut fur Normung - German Intstitute of Standards; (1997). DIN1045 10) International System of Unified Standard Codes of Practise for Structures; (1990) “Model code for concrete structures - Europe.” CEB-FIP 11) British Standards Institution; (1995) “Structural use of concrete – Part 1.” BS 8110 12) Canadian Standards Association; (1994) “Code for the design of concrete structures for buildings.” CAN-A23.2 13)Standards Australia; (1994) “Australian Concrete Structures Standard” AS 3600, Sydney, Australia. 14)Mohamed Ali M.S., Oehlers D.J. and Bradford M.A. (2001). “ Shear peeling of steel plates bonded to the tension faces of RC beams” ASCE Journal of Structural Engineering. Dec. Vol.127 No.12, pp1453-1460. 15)Mohamed Ali M.S., Oehlers D.J. and Bradford M.A. (2002). “Interaction between flexure and shear on the debonding of RC beams retrofitted with compression face plates” Advances in Structural Engineering. Vol.5 No.4, pp223-230 16)Smith, S.T. and Teng, J.G. (2003) “Shear-bending interaction in debonding failures of FRP-plated RC beams.” Advances in Structural Engineering, Vol.6. No. 3, August, pp183-200.

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