strengthening of rc members using near-surface...

Advances in Structural Engineering Vol. 7 No. 5 2004 1

1. INTRODUCTIONThe use of Near-Surface Mounted (NSM) FRPreinforcement is an attractive method for increasingflexural and shear strength of deficient reinforced and prestressed concrete (RC and PC) members(Alkhrdaji et al. 1999, De Lorenzis et al. 2000) as wellas strengthening unreinforced masonry walls (Tumialan et al. 2001). Advantages with respect to externallybonded FRP laminates include the possibility ofanchoring the reinforcement into adjacent members, andthe opportunity of upgrading elements in their negativemoment region with the reinforcement not exposed topotential mechanical damage typical of floor or decksystems (Nanni et al. 1999). NSM FRP technique doesnot require extensive surface preparation work and, aftergroove cutting, requires minimal installation timecompared to externally bonded FRP laminates becausethe use of primer and putty is normally not necessary.

NSM reinforcement technology becomes particularlyinteresting in seismic retrofit of RC column-beam joints

providing either additional strength or ductility whenmoving the failure zone from the column to the beam(Prota et al. 2001).

Figure 1 shows a recent application of NSMtechnology for silo strengthening (Emmons et al. 2001) where FRP bars have been used to enhance bothflexural and confinement capacity. Figure 2 illustratesthe application of this technology for upgrading a solidRC bridge deck (Alkhrdaji et al. 2000), and Figure 3represents a similar case where NSM FRP bars wereused to increase the bridge deck negative momentcapacity (Warren 1998). Figure 4 shows the grooving ofRC joists to be strengthened in shear with carbon FRPbars used as NSM reinforcement (Hogue et al., 1999).Figure 5 shows the application of rectangular-sectioncarbon FRP bars used to stitch a longitudinal crack onthe soffit of a bridge deck (Casadei et al. 2003).

Even though there are no design guidelines for the use of NSM technology in North America, ACICommittee 440 is presently considering a revision of the

Strengthening of RC Members Using Near-Surface

Mounted FRP Composites: Design Overview

Renato Parretti∗∗ and Antonio Nanni

(Received: 7 February 2004; Received revised form: 3 May 2004; Accepted: 4 May 2004)

Abstract: Strengthening of reinforced and prestressed concrete (RC and PC) membersusing externally bonded FRP laminates is today a well-accepted technology that isbecoming popular among designers and contractors. Near-surface mounted (NSM) FRPreinforcement represents an alternative way to improve flexural and shear performanceof concrete structures. In some instance, it is the only suitable technology that can beefficiently applied, for example, when upgrading beam-column joints or for flexuralstrengthening of compression members. In this paper, bond related issues, flexural andshear design recommendations, and design examples are presented. The paper is anattempt to provide designers with a comprehensive protocol for the rationalimplementation of NSM technology.

Key words: bond, design, detailing, FRP, near-surface mounted reinforcement, reinforced concrete, strengthening.

*Corresponding author. Email address: [email protected]; Fax: +39-081-768-3491 ; Tel: +39-081-768-3534.

Strengthening of RC Members Using Near-Surface Mounted FRP Composites: Design Overview

2 Advances in Structural Engineering Vol. 7 No. 5 2004

Figure 1. Strengthening of cement silos using NSM carbon

FRP bars

Figure 2. Strengthening of a bridge deck using NSM

carbon FRP

Figure 3. Negative moments regions strengthening of bridge

deck with NSM bars

Figure 4. Shear strengthening of RC joist using carbon

NSM bars

(c) Insertion of NSM bar into the groove (d) Application completed

Figure 5. Stitching of crack with rectangular NSM FRP bars

document titled: “Guide for the Design and Constructionof Externally Bonded FRP Systems for StrengtheningConcrete Structures (ACI 440.2R-02),” to include suchtechnology.

2. HISTORY OF THE TECHNOLOGYThe use of NSM reinforcement was developed in Europefor strengthening of RC structures in the early 1950s. In 1948, an RC bridge deck in Sweden needed to beupgraded in its negative moment region due to anexcessive settlement of the steel cage during construction.This was accomplished by inserting steel reinforcementbars in grooves made in the concrete surface and fillingit with cement mortar (Asplund 1949).

More recently, NSM reinforcement has been used to upgrade masonry structures to increase their tensilestrength and ductility (Atkinsosn and Schuller 1992).This technology is an effective and economical meansof repairing and strengthening low-rise masonry buildingsand arch bridges (Garrity 1995). Stainless steel hasreplaced the original black steel adopted at the onset ofthe development, while the cementitious grout used forembedding the reinforcement has been partially replacedby epoxy-based grouts.

Today, FRP bars have became attractive for their non-corrosive properties and the ability of tailoring the barstiffness to the needs of the application. Epoxy-basedpastes or latex-modified cement grouts can be used fortheir rapid setting and bond strength.

3. DESIGN PHILOSOPHYThe strength design approach with its strength reductionfactors as used in ACI 318 (1999) is recommended forRC and PC members using NSM FRP reinforcement.Reference to this version of the Building Code ratherthan the 2002 edition is necessary to remain consistentwith the design guides issued by ACI on the use of FRPfor new construction and repair. Additional strengthreduction factors applied to the contribution of the NSMreinforcement are suggested to reflect the novelty of FRPsystems compared with traditional methods.

The equations presented in this paper are based onprinciples of force equilibrium, strain compatibility,constitutive laws of the materials, and make reference tothe “Guide for the Design and Construction of ExternallyBonded FRP Systems for Strengthening ConcreteStructures” reported by ACI Committee 440 (2002), andthe “Guide for the Design and Construction of ConcreteReinforced with FRP Bars” also reported by ACICommittee 440 (2003).

Careful consideration should be given to determine a strengthening threshold. The threshold is imposed toguard against collapse of the structure should bond or

other failure of the FRP system occur due to fire,vandalism, or other causes. The existing strength of thestructure (φRn) should be sufficient to resist a level ofload described by Eqn 1:

(1)

Material properties of FRP reinforcement reported bymanufacturers, such as ultimate tensile strength, typicallydo not consider long-term exposure to environmentalconditions, and should be considered as initial properties.FRP properties to be used in all design equations aregiven as follows (ACI 440 2002 and 2003):

(2)

where ffu and εfu are the FRP design tensile strength andultimate strain considering the environmental reductionfactor (CE) as given in Table 1, and and representthe FRP guaranteed tensile strength and ultimate strainas reported by the manufacturer. FRP design modulus of elasticity is the guaranteed value reported by themanufacturer.

4. FLEXURAL DESIGNGuidance for the calculation of the flexural strengtheningeffect resulting from longitudinal FRP reinforcementmounted onto the tension face of an RC member isillustrated in Figure 6 for the case of a rectangular section.

Assumptions used in the design are: a) a plane sectionbefore loading remains plane after loading; b) themaximum usable compressive strain in the concrete is0.003, and its tensile strength is neglected; c) FRPreinforcement has a linear-elastic behavior up to failure;and d) perfect bond exists between FRP reinforcementand surrounding concrete.

The strength reduction approach follows thephilosophy of ACI 318 (1999) Appendix B, where amember with low ductility should be compensated with

ε fu*f fu

*

f C f

C

fu E fu

fu E fu

=

=

*

*ε ε

φR D Ln existing new( ) = +( )1 2 0 85. .

Renato Parretti and Antonio Nanni


Table 1. Environmental-reduction factor

CE (ACI 440 2002)

Fiber and

Exposure condition resin type CE

Interior exposure Carbon/epoxy 0.95Glass/epoxy 0.75Aramid/epoxy 0.85

Exterior exposure (bridges, Carbon/epoxy 0.85piers, and unenclosed Glass/epoxy 0.65parking garages) Aramid/epoxy 0.75

Aggressive environment Carbon/epoxy 0.85(chemical plants and waste Glass/epoxy 0.50water treatment plants) Aramid/epoxy 0.70

a higher reserve of strength. The higher reserve of strengthis achieved by applying a factor of 0.70 to brittle members,as opposed to 0.90 for ductile members. The strength-reduction factor (φ) given by Eqn 3 should be used (ACI 440 2002):

(3)

where εs and εy is the strain in the reinforcing steel atultimate and yielding, respectively.

The calculation procedure used to arrive at thenominal strength should consider the governing mode offailure. The trial and error procedure presented in thispaper involves selecting a given neutral axis depth (c) and a failure mode (i.e. selecting εc = εcu or εf = εfe);calculating the strain level in each material using straincompatibility; calculating the associated stress level ineach material from its stress-strain relationship; andchecking internal force equilibrium. If the internal forceresultants do not equilibrate, the depth to the neutral axisis revised and the procedure repeated.

When failure is controlled by concrete crushing, theWhitney stress block approach (ACI 318 1999) can beused without modifications. If FRP rupture or concretecover delamination control failure, the stress resultantfor concrete should be determined from an appropriatenon-linear stress-strain relationship or by a rectangularstress block suitable for the particular level of strain inthe concrete. Parameters for such a stress block are given in Eqns 4 and 5 (see also Figure 6) (Todeschini et al. 1982).

(4)

where:(5)

and is computed in radians.The ultimate effective strain (εfe) that should be used

for FRP reinforcement is given below:

(6)

where κm is a bond dependent coefficient meant to limitthe strain in the FRP reinforcement to prevent debondingor delamination. Debond and delamination usually takeplace whenever a crack forms in the member. End pointsof strengthening systems, representing singular points,could be more prone to debond. Limited experimentalevidences (De Lorenzis and Nanni 2002) indicate thatκm is highly affected by surface properties of the FRPbar (deformed or sandblasted), by groove size, byproperties of the epoxy paste, and concrete tensilestrength. Splitting of the epoxy cover, cracking of theconcrete surrounding the bar, and pull-out of the FRPbar were the main failure modes experimented duringthe laboratory tests reported in the literature. Experimentalvalues of κm were found to vary between 0.60 and 0.84.Further research should result in a more accurate methodfor predicting the appropriate bond dependant factor. A value of κm=0.70 has been selected in the designexample (see Appendix I). This value is consistent withboth experimental data (De Lorenzis and Nanni 2002)and the approach followed by ACI 440 (2002) whendefining an equivalent strain reduction factor forexternally bonded FRP laminates.

Nominal tension strain attained in the concretesurrounding FRP bars can be expressed as:

(7)

where df represents the depth to the FRP reinforcementas illustrated in Figure 6.

The initial strain εbi in Eqn 7 can be evaluated usingan elastic analysis of the existing member, consideringall loads present at the time of FRP installation. The firstterm in Eqn 7, , should be used whenconcrete crushing failure governs. The second term,

, should be used when FRP is the controllingfailure mode.

Assuming no compression steel reinforcement, themoment capacity of the strengthened member can beexpressed as follows:

(8)

where fs and ffe are taken from Eqn 9, and ψf is anadditional reduction factor of 0.85 recommended to take

M A f dc

A f dc

n s s f f fe f= −

+ −

βψ

β1 1

2 2

ε εfe bi+

(( )/ )d c cf cu− ε

ε ε ε εc ff

cu fe bi

d c

c, =−

≤ +

ε κ εfe m fu=

tan /− ′( )1 ε εc c

εcc

c

f

E'

'

.= 1 71

βε ε ε ε

ε ε ε ε

γε ε

β ε ε

1

1

2 2

2 2

1

24

1

0 90 1

= −′( ) − ′( )[ ]′( ) + ′( )

=+ ′( )

′

−c c c c

c c c c

c c

c c

tan

.

ln

ln

φ

εε ε

εε ε

ε ε

=

≥

+−( )−

< <

≤

0 90 0 005

0 700 20

0 0050 005

0 70

. .

..

..

.

for

for

for

s

s y

yy s

s y



b

h d df

Af

As

c

�c

s�

f�

� c1

�f ′c

f

ffe

s A

Af

s

Neutralaxis

Figure 6. Ultimate internal strain and stress distribution for

rectangular sections

into account for the novelty of FRP and it is not basedon test data (ACI 440 2002):

(9)

5. SHEAR DESIGNThe approach used to calculate the nominal shear capacityof a member strengthened using NSM bars is similar tothat used in ACI 440 (2002) for the case of externallybonded FRP laminates. However, the design approachhere presented deviates from the standard equationspractitioners are used to; it is envisioned that a morestandardized approach could be pursued in futureimplementations.

Eqn 10 is applicable for NSM systems and the samestrength reduction factor φ=0.85 suggested by ACI 318is used. An additional reduction factor ψf = 0.85 isapplied to the contribution of NSM FRP reinforcementto the shear strength of the member, as previouslysuggested for flexural design.

(10)

Several parameters influence the NSM FRP barscontribution to the shear capacity (Vf), such as quality ofbond, FRP rebar type, groove dimensions, and quality ofsubstrate material. When computing Vf , two strain limitsneed to be taken into account (De Lorenzis and Nanni2001a) namely: strain from bond-controlled failure, and maximum strain threshold of 0.004. The latter issuggested to maintain the shear integrity of the concrete(Khalifa et al. 1998), and to avoid large shear cracks thatcould compromise the aggregate interlock mechanism.

The following assumptions are made: a) the slope ofthe shear crack is assumed to be at 45 degrees; and b) bond stresses are constant along the effective lengthof the FRP bar at ultimate.

The shear strength provided by the NSM reinforcementcan be determined by calculating the force resulting fromthe tensile stress in the FRP bars across the assumedcrack, and it is expressed by Eqn 11 for circular andrectangular bars, respectively.

(11)

where db is the nominal FRP bar diameter, a and brepresent the cross-sectional dimension for rectangularFRP bar, and τb represents the average bond stress of thebars crossed by a shear crack. Experimental dataavailable on 10-mm (#3) carbon FRP deformed barsdemonstrate that when using an epoxy based resin in a

groove size at least 1.5 times the bar diameter, aconservative value of τb=6.9 MPa (1.0 ksi) can be used(De Lorenzis and Nanni 2001b).

Ltot can be expressed as Ltot = ΣiLi where Li (Figure 7)represents the length of each single NSM bar crossed bya 45-degree shear crack expressed as follows:

(12)

where α is the slope of the FRP bar with respect to thelongitudinal axis of the member (common values are 90ºfor vertical NSM bars, and 45º or 60º for inclined bars),s is the FRP bar spacing, and lnet, defined as follows:

(13)

represents the net length of a FRP bar as shown inFigure 8 to account for cracking of the concrete coverand installation tolerances. In Eqn 13, lb is the actuallength of a FRP bar, and c is the clear concrete cover of the internal longitudinal reinforcement. It is to benoted that c does not necessarily need to be consideredas clear concrete cover; Figure 9 shows a T-shaped crosssection where c represents a term to account for thedevelopment length of FRP bars.

The second limitation in Eqn 12, l0.004, takes intoaccount the shear integrity of the concrete by limiting at

l lnet b

c= −

2sinα

L

si l i

n

si l i

nn

i

net

=+

≤ =

−+

≤ = +

cos sin...

cos sin...

.

.

α α

α α

0 004

0 004

12

21l

V d L

V a b L

f b b tot

f b tot

=

= +

2

4

π τ

τ

Circular Bars

Rectangular Bars( )

φ φ ψV V V Vn c s f f= + +( )

f E f

f E E

s s s y

fe f c f f fe

= <

= ≤

ε

ε ε,



L

l

0.004l

net

3Shear

crac

k

45˚ 2L1 L4LLL 5

0.004l

sfailure

Bond-controlled

ss sss iL

NSM bars

i+1

Figure 7. Representation of bar lengths as used for shear

capacity computation

b

c

net

dbc

c

NSM FRP bars

Existing steelstirrups

b

Figure 8. Relationship between lnet and length of the NSM bar lb

Renato Parretti

Note

change the font of the letter "l" into the symbol "lnet" to match the one reported in Eqn (13)

0.004 the maximum strain in the FRP reinforcement.From the force equilibrium condition, (

), l0.004 can be determined as follows forcircular and rectangular bars, respectively:

(14)

where Ef represents Young’s modulus of FRP bars.The first limitation in Eqn 12 takes into account bond

as the controlling failure mechanism, and represents theminimum effective length of a FRP bar crossed by ashear crack. It is expressed by or

depending on the valueassumed by the term

(15)

where n is taken as the smallest integer (e.g.,), and leff represents the vertical

length of lnet written as follows:

(16)

Spacing of FRP shear reinforcement should notexceed lnet /2, or 600 mm (24 in).

To prevent crushing of concrete, the total reinforcementcontribution taken as the sum of both steel and FRPreinforcement, should be limited based on the criteriagiven for steel alone in ACI 318, as suggested in Eqn 17for US and SI customary, respectively:

(17)

6. DETAILINGThe minimum dimension of the grooves should be takenat least 1.5 times the diameter of the FRP bar. However,

when a rectangular bar with large aspect ratio is used,the limit may loose significance due to constructability.In such a case, a minimum groove size ofas depicted in Figure 10 could be suggested, where a isthe smallest bar dimension. In other instances, theminimum groove dimension could be the result ofinstallation requirements rather than engineering. Forexample a 5 mm (0.2 in) groove may be the smallestpossible because of the saw blade size.

No data is available for maximum dimensions of thegroove at this time. Tests were conducted using thesuggested above mentioned dimensions. However, De Lorenzi and Nanni, 2002, suggest that increasinggroove size will increase bond strength when failure iscontrolled by splitting of epoxy paste. This effect doesnot seem to appear when pullout failure occurs.

Bond properties between FRP reinforcement andconcrete are similar to that of steel reinforcement, and depend on FRP type, elastic modulus, surfacedeformation, and shape of the FRP bar (Al-Zahrani et al. 1996; Uppuluri et al. 1996; Gao et al. 1998). Forthe case of RC beams strengthened using NSM CFRPrectangular bars, Hassan and Rizkalla (2002) found that the development length is highly dependent on strip dimensions, groove size, concrete and adhesiveproperties, internal steel reinforcement ratio, reinforcementconfiguration, and type of loading. They suggested thatthe development length increases by increasing theinternal steel reinforcement ratio, and decreases with theincrease of either the concrete compressive strengthand/or the groove size.

Figure 11 shows the equilibrium condition of a FRPbar with an embedded length equal to its developmentlength, ld. The force in the bar is resisted by the shearstresses τb acting on the surface of the bar. Assuming atriangular stress distribution (Ibell and Valerio 2002),the average bond stress can be expressed as τb = 0.5τmax.

3 0 1 5. .a b×

V Vf bd

f bds f

c

c

+ ≤′

′

8

0 66

US Customary

SI

.

l leff b c= −sinα 2

n n= = ⇒ =32 3 10 7 10/ .

ns

eff=+l ( cot )1 α

lnet s i− ⋅ +/(cos sin )α αs i⋅ +/(cos sin )α α

ld E

la b

a b

E

b f

b

f

b

0 004

0 004

0 001

0 002

.

.

.

.

=

=⋅+

τ

τ

Circular Bars

Rectangular Bars

d lb b.0 004π τA Eb f( . )0 004 =



1.5dbab

1.5db 3.0a

1.5b

Figure 10. Minimum dimension of the grooves

ld

rbAf,bar ffe

rmax

0.5rmax

Figure 11. Transfer of force in an FRP bar

b

stirrupsExisting steel

NSM FRP bars

c

bd

net

c

b

w

d

Figure 9. Shear strengthening of T-shaped concrete

cross-sections

Renato Parretti

Note

Change the font of the letter "l" into the symbol "leff" to match the one reported in Eqn (16)

Renato Parretti

Note

Change the font of the letter "l" to match the one reported in Eqn (13)

Via equilibrium, the following equations can be derivedfor circular and rectangular bars, respectively:

(18)

Hassan and Rizkalla (2002) suggest an expression forτmax when concrete crushing is the controlling failuremode. When the controlling failure mode is not known,a conservative value of τmax=3.5 MPa (0.50 ksi) issuggested.

7. CONCLUSIONSNear-surface mounted reinforcement is an old technologyused over more than half a century to enhance flexuralcapacity of existing RC and masonry structures. Today,thanks to the availability of FRP composites, it isbecoming increasingly more attractive and sometimeseven more promising than the use of externally bondedFRP laminates.

In this paper, an overview of flexural and shear designof RC members strengthened with NSM FRP bars waspresented. The proposed procedure reflects the frameworkused in the two guides published by ACI (ACI 440.2R-02,2002, and ACI 440.1R-03, 2003) with adjustment comingfrom experimental evidences.

Unresolved issues requiring additional experimentalwork include properties and quality of bond betweenFRP bars, paste and concrete, as well as a betterunderstanding of the importance of groove size, especiallywhen using rectangular bars. Limited experience isavailable on shear strengthening with NSM bars, andmore data are needed to better validate the analysis herepresented.

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American Concrete Institute, Farmington Hills, Michigan, 391 pp.

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transportation infrastructures: solid RC decks strengthened with

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(1996). “Bond of FRP to concrete for bars with axisymmetric

deformations”, Proceedings of the Second International

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Asplund, S. O. (1949). “Strengthening of bridge slabs with grouted

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Atkinson, R. H. and Schuller, M. P. (1992). “Development of

injectible grouts for the repair of unreinforced masonry”,

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surface mounted FRP bars”, Proceedings of the Third

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concrete beams with near-surface mounted fiber-reinforced

polymer bars”, Structural Journal, ACI, V. 98, No. 1, pp. 60-68.

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structures strengthened with near surface mounted CFRP strips”

(in press).

ld

f

la b

a bf

db

fe

d fe

=

=⋅

+

4 0 5

2 0 5

( . )

( )( . )

max

max

τ

τ

Circular Bars

Rectangular Bars



Hogue, T., Cornforth, R.C. and Nanni, A. (1999). “Myriad

convention center floor system reinforcement”, Proceedings of

the FRPRCS-4, C.W. Dolan, S. Rizkalla and A. Nanni, Editors,

ACI, Baltimore, MD, pp. 1145-1161.

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concrete bridges”, Proceedings of ICE Structures and Buildings,

UK, in press.

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APPENDIX I. EXAMPLE OFFLEXURAL DESIGNIntroduction

Flexural strengthening of a one-way RC slab supportedby RC joists will be designed in this section. The eight-span floor slab was originally designed using a concretecompressive strength of 25.9 MPa (3750 psi) and steelreinforcement strength of 413.7 MPa (60 ksi). The slabthickness was selected equal to h=180 mm (7.25 in),using the dead and live loads reported in Table 2(MacGregor 1997a). The owner needs to modernizesome mechanical equipment that becomes an integralpart of the structure in the four central spans of thebuilding (Figure 12). The new loads resulting from thisequipment are shown in Table 2.

New moments due to the new loads are shown inTable 3. The moment in place (Mip) at the time of FRPinstallation is calculated using the slab self weight andthe weight due to the floor cover and ceiling. Mnew

represents the factored moment due to new loads to beresisted by the existing structure prior to thestrengthening.



Table 2. Existing and new loads

US units SI units

Existing loads New loads Existing loads New loads

[psf] [psf] [kN/m2] [kN/m2]

Slab self weight 90.6 90.6 4.34 4.34Floor cover 0.5 0.5 0.024 0.024Mechanical equipment 4.0 95.0 0.192 4.55Ceiling 2.0 2.0 0.096 0.096Dead load, ωd 97.1 188.1 4.65 9.00Live load, ωl 100.0 100.0 4.80 4.80Factored load, ωu 306 433 14.66 20.74Service load, ωs 197 288 9.44 13.80In place load, ωip — 93 — 4.46New load from Eqn 1, ωnew — 310 — 14.85

The original design called for 12-mm (#4) steel bars spaced 380 mm (15 in) on centers for positive momentregions, and 12-mm (#4) spaced at 300 mm (12 in) on centers for negative moment regions. Effective depth d andclear concrete cover were assumed equal to 160 mm (6.25 in) and 20 mm (0.75 in), respectively.

A 6-mm (#2) Carbon FRP bar is adopted for strengthening in the negative moment regions.FRP guaranteed material properties and corresponding design values are shown in Eqn 2 based on the appropriate

CE factor (Table 1):

Assuming 4 mm (0.125 in) clear cover, the effective depth is df=173 mm (6.8 in).For positive moment regions, externally bonded FRP laminates will be used. This second technique is already

well-known and outside the scope of this paper so that only the final results will be shown in this example.

Computations

As a first step, initial strain under the in-place moment needs to be evaluated. Neutral axis position before cracking(cb_cr) and gross moment of inertia (Ig) of the concrete section are shown below (calculations are carried out for a

f C f MPa MPa

C

E GPa

fu E fu

fu E fu

f

= = =

= = = ×

=

−

*

*

. ( )

. ( . ) .

0 95 1380 1311

0 95 0 01 9 5 10

138

3ε ε



SlabDesign

Beam

Beam

Beam

Jois

t

Jois

t

Jois

t

Jois

t

Jois

t

Jois

t

Jois

t

SlabsHeavy new equipmentplaced in the shaded area

New loaddl dl

NSMFRP bars

FRPLaminates

Groove 3.80 m

strip

Figure 12. Typical floor plan and cross-section

Table 3. Original and strengthening design

US units SI units

M+ [k-ft] M−− [k-ft] M+ [kN?m] M−− [kN?m]

Existing LoadService Moment, Ms 2.36 3.43 3.20 4.65Ultimate Moment, Mu 3.66 5.32 4.96 7.21Flexural Capacity, φMn 4.40 5.50 5.96 7.45

New LoadsService Moment, Ms 3.44 5.01 4.66 6.79Moment in Place, Mip 1.11 1.62 1.50 2.19Moment from Eqn 1, Mnew 3.71 5.40 5.03 7.32Ultimate Moment, Mu 5.18 7.53 7.02 10.20Flexural Capacity, φMn 7.07 8.03 9.58 12.10

Renato Parretti

Note

Replace: [kN?m] with: [kNm]

Renato Parretti

Note


Renato Parretti

Note


strip of 300 mm (1 ft)):

where:

Cracking moment is then obtained as:

Since service moment due to existing loads on the structure (4.65 kN?m, Table 3) is smaller than Mcr analysis canbe carried out referring to an uncracked cross-section. Consequently, initial strain in the bottom concrete fiber canbe expressed as:

As a first trial, assume for the neutral axis position c1=0.1h=18 mm, and that failure is controlled by FRP rupture,so that the maximum strain in the concrete surrounding FRP bars is given by the second term of Eqn 7:

where εfe is taken from Eqn 6:

Strain level in both concrete and steel can be found using strain compatibility:

Since , fs=fy=413.7 MPa, and the tensile forces in both steel and FRP reinforcement as wellas the compression force in the concrete can be expressed as follows:

T A E mm MPa N

T A f mm MPa N

C f c b MPa mm mm N

f f f fe

s s y

c c

= = ( ) ×( ) ×( ) =

= = ( )( ) =

= ′ = ( )( )( )( ) =

−ε

γ β

32 3 1 38 10 6 650 10 29 642

129 413 7 53 367

0 51 25 9 0 85 18 300 60 629

2 5 3

2

1 1

. . . ,

. ,

. . . ,

ε εs y> = × −2 07 10 3.

ε ε

ε ε

cf

c f

sf

c f

c

d c

mm

mm mm

d c

d c

mm mm

mm mm

=−

=−

×( ) = ×

=−−

=−−

×( ) = ×

− −

− −

1

1

3 4

1

1

3 3

18173 18

6 699 10 7 779 10

160 18173 18

6 699 10 6 137 10

,

,

. .

. .

ε κ εfe m fu= = × = ×− −0 7 9 50 10 6 650 103 3. ( . ) .

ε ε εc f fe bi, . . .= + = × + × = ×− − −6 650 10 4 944 10 6 699 103 5 3

εbiip

g cf b cr

M

I Ed c

N mm

mm MPamm mm= −( ) =

⋅

( )−( ) = × −

_, ,

( , , ) ,.

2 190 000150 265 008 24 174

173 91 4 944 1045

Mf I

h c

MPa mm

mm mmkN mcr

c g

b cr

=′

−=

×

( )−

= ⋅0 62 1

1 10

0 62 25 9 150 265 009

180 915 336

4. . . , ,.

_

nE

E

E

MPa

MPa

MPas

c

s= = = =4750 25 9

200 00024 174

8 27.

,,

.

Ibh

n A c d

mm mmmm mm mm mm

g s b cr= + −( ) −( )

=( )

+ −( )( ) −( ) =

32

32 2 4

121

300 180

128 27 1 129 91 160 150 265 008

_

. , ,

cbh n A d

bh n A

mm mm mm mm

mm mm mmmm

b crs

s_

.

. .

.

=+ −( )

+ −( )

=( )( ) + −( )( )( )

( ) + −( )( )=

0 5 11

0 5 300 180 8 27 1 129 160

300 180 8 27 1 12991

2

2 2

2



Renato Parretti

Note


where (Eqns 4 and 5):

Via equilibrium, one can find another position for the neutral axis:

As a second trial, a new neutral axis depth is assumed:

Repeating the calculations shown so far, using the value c2, one can find that equilibrium is satisfied and nofurther iterations are needed. Ultimate strain in concrete and steel are 1.06 × 10-3 and 7.13 × 10-3, respectively; tensileforce in FRP and steel reinforcement and compressive force in the concrete are 29,580 N, 53,379 N, and 82,959 N,respectively. To check whenever the original assumption of FRP rupture is correct the following shall be verified:

where cb represents the neutral axis position for balanced failure. Being it verified, the initial assumption was correct.The moment capacity can now be expressed as:

where:

Because εs>0.005, from Eqn 3 the strength reduction factor is φ=0.9. Finally,

NSM bars used as reinforcement in negative moment regions will be extended for a length equal to theirdevelopment length ld beyond the point of zero moment; ld can be evaluated using Eqn 18:

ldb

fe

df

mm

MPaMPa m=

( )=

( )( )=

4 0 51

10006

4 0 5 3 51237 1 0

. . ..

maxτ

φM KN m KN m M kN mn u= ⋅( ) = ⋅ > = ⋅0 9 12 10 10 89 10 2. . . .

f E f MPa

f E MPa MPa

s s s y

fe f fe

= < =

= = × × =−

ε

ε

413 7

1 38 10 6 650 10 917 75 3

.

( . )( . ) .

M A f dc

A f dc

mm MPa mm mm

mm MPa mm mm kN m

n s s f f fe f= −

+ −

=×

( ) − ( )( )[+ ( )( ) − ( )( )] = ⋅

βψ

β1 1

62

2

2 2

11 10

129 413 7 160 0 85 24 2

0 85 32 3 917 7 173 0 85 24 2 12 10

. .

. . . . .

c c d mm mmbcu

cu c ff< =

+=

+ ×( ) =−

εε ε ,

.. .

0 0030 003 6 699 10

173 543

cc c mm mm

mm21 1

218 30

224=

+ ′=

+=

T T C f c b

cT T

f b

N N

MPa mmmm

s f c c

s f

c

+ = = ′ ′

′ =+

′=

+

( )( )( )=

γ β

γ β

1 1

11

53 367 29 6420 51 25 9 0 689 300

30, ,

( . ) . .

ε

β

cc

c

f

E

MPa

MPa'

'

. ..

,.

. . tan . .

. . ( . . )

= = = ×

= −× ×( ) − × ×( )[ ]

× ×( ) + × ×( )=

−

− − − − −

− − − −

1 71 1 7125 9

24 1741 832 10

24 7 79 10 1 832 10 7 79 10 1 832 10

7 79 10 1 832 10 1 7 79 10 1 832 10

3

1

4 3 1 4 3

4 3 4 3 2ln00 689

0 90 1 7 79 10 1 832 10

0 689 7 79 10 1 832 100 51

4 3 2

4 3

.

. ( . . )

( . ) . ..γ =

+ × ×( )× ×( )

=− −

− −

ln



Renato Parretti

Note

Use lower case k for kNm. Correct form: kNm Wrong form: KNm

Renato Parretti

Note

Same as previous



Stirrups @ 300 mm

Stirrups @ 200 mm3″

Stirrups @ 150 mm

LC

300 mm

910 mm

150 mm

610 mm

No. 7, 10-mm

No. 3, 10-mm

No. 9, 10-mm

As′=260 mm2

As=4038 mm2Stirrups10-mm

Figure 13. Steel stirrups in beam

The point of zero is given at approximately 0.2l, where l=4.2 m (13.83 ft). The total length of a FRP bar is givenas: (12 ft).

For positive moment regions, design can be carried out using externally bonded CFRP laminates 100 mm (4 in)wide with strips clear spacing of 500 mm (20 in), having the following properties:

The final strengthening design is reported in Table 3 and compared with the original design. Note that Eqn 1 isverified since φMn of the existing member is larger than Mnew calculated with the new loads in both positive andnegative moment regions.

APPENDIX II. EXAMPLE OF SHEAR DESIGNAn existing simply supported 30 ft long T-beam supports a uniformly distributed service (unfactored) dead load of 19.0 N/mm (1.3 kips/ft), including its own weight and a uniformly distributed service live load of 23.4 N/mm (1.6 kips/ft), (MacGregor, 1997b). The concrete strength is 27.6 MPa (4000 psi), and the yield strength of the steelstirrups is 276 MPa (40 ksi). Overall height is h=650 mm (26 in), flange width is 910 mm (36 in), stem width is 300 mm (12 in), slab thickness is 150 mm (6 in), effective depth is d=610 mm (24 in), and clear concrete cover c = 40 mm (1.5 in). The original shear design called for 10-mm (#3) double-leg stirrups with the following spacing:a) one at 75 mm (3 in) from the support; b) seven at 150 mm (6 in); c) three at 200 mm (8 in); and d) nine at 300 mm(12 in) as shown in Figure 13.

The original flexural design called for two layers of longitudinal grade 60 steel bars used as main reinforcement;the bottom layer includes three 35-mm (#11) steel bars; the top layer includes two 25-mm (#8) steel bars. Two 12-mm (#4) steel bars were used as compression reinforcement to hold the stirrups.

Service live load needs to be increased from 23.4 to 32.0 N/mm. Flexural capacity of the beam does not need tobe improved, while an upgrading is needed in shear. The new ultimate shear value calculated at d from the supportis 324.7 kN (73.0 kips).

Strengthening design will be carried out using 6.35-mm (No. 2) NSM CFRP bars 580 mm (23 in) long, havingultimate guaranteed tensile strength , modulus of elasticity , and ultimate guaranteed elongation strain

FRP contribution to the shear capacity of the beam is expressed by Eqn 11; FRP bars will be inserted between theexisting steel stirrups leading to a center-to-center spacing of sf = 80 mm (3 in).

The number of FRP bars crossed by a 45-degree shear crack is (Eqns 15 and 16):

and the length where FRP bar strain governs (l0.004) is (Eqn 14):

ld E mm MPa

MPammb f

b0 004 0 001 0 001

6 35 124 0006 9

114. . .( . )( , )

.= = =

τ

ns

c

smm mm

mmn

eff b=+

=− +

=⋅ − +

= ⇒ =

l l( cot ) ( sin )( cot )

( sin( ) ( ))( cot( )).

1 2 1

500 90 2 40 1 9080

5 25 5

α α α

ε fu* . .= 0 017

E GPa ksif = 124 18 000( , )f MPa ksifu* , ( )= 2 068 300

f C f MPa MPa

C

E GPa

fu E fu

fu E fu

f

= = =

= = =

=

*

*

. ( )

. ( . ) .

0 95 3800 3610

0 95 0 0167 0 0159

228

ε ε

2 0 2 2 3 7( . ) .l l+ =d m

Renato Parretti

Note

Use normal font for "steel bars", not italic

Finally from Eqn 12 and Figure 14 ( ):

and

FRP contribution to the shear capacity can now be expressed as (Eqn 11):

To prevent concrete crushing, Eqn 17 shall be verified:

Design shear capacity can be obtained using Eqn 10; a sketch showing the number and spacing of NSM CFRPbars selected for the shear strengthening is reported in Figure 15.

where:

Vf

bdMPa

mm mm

kN

cc=′

=

=6

27 6

6300 610

160 2

.( )( )

.

φ φ ψV V V V

kN kN kN

kN V kN

n c s f f

u

= + +

= + +

= > =

( )

. [ . . . ( . )]

. .

0 85 160 2 159 4 0 85 117 6

356 6 324 7

VA f d

s

mm MPa mm

mmkN

V V kN kN kN

f bd MPa mm mm kN

ss y

s f

c

= = =

+ = + =

< = =

( )( )( ).

. .

. . . ( )( ) .'

142 276 610150

159 4

159 4 117 6 277

0 66 0 66 27 6 300 610 634 5

2

V d L mm MPa mm kNf b b tot= = =2 2 3 14 6 35 6 89 428 117 6π τ ( )( . )( . )( . )( ) .

L L L L L L mmtot = + + + + = + + + + =1 2 3 4 5 80 114 114 100 20 428

L l s mm mm mm

L l s mm mm mm

L l s

mm mm mm mm mm mm

L l s

net

net

1 0 004

2 0 004

3 0 004

4 0 004

1 114 80 1 80

2 114 80 2 114

3

114 420 80 3 114 180 114

4

= ⋅ = =

= ⋅ = =

= − ⋅

= − = =

= − ⋅

min( , ) min( , ( )( ))

min( , ) min( , ( )( ))

min( , )

min[ , ( )( )] min( , )

min( , )

.

.

.

.

l

l

== − = =

= − ⋅

= − = =

min[ , ( )( )] min( , )

min( , )

min[ , ( )( )] min( , ).

114 420 80 4 114 100 100

5

114 420 80 5 114 20 205 0 004

mm mm mm mm mm mm

L l s

mm mm mm mm mm mmnetl

n n/ / . /2 5 2 2 5 2 2= = ⇒ =



b=500

Shear

crac

k

FRP NSM barSteel longitudinal reinforcement

Slab thickness

L 1=80

L 2=11

4

L 3=11

4

L 4=10

0

L 5=20

net=420

l0.004

=114

l0.004

=114

Figure 14. Definition of Li for a 80 mm bar spacing (only NSM bars are shown)

NSM reinforcement is no longer needed 2.55 m (8.3 ft)apart from the support (Figure 15) since the existing steelstirrups are capable to carry the additional shear due tonew loads.

APPENDIX III. NOTATIONa = Smallest dimension of a rectangular FRP bar;Af = Area of FRP reinforcement;As = Area of steel reinforcement;b = Larger dimension of a rectangular FRP bar,

and cross-section width;c = Neutral axis depth, Clear concrete cover;cb = Neutral axis depth for balanced failure;cb_cr = Neutral axis depth before cracking of the

cross-section;CE = Environmental reduction factor;d = Effective depth of steel reinforcement;D = Dead Load;db = Diameter of FRP bar;df = Effective depth of FRP reinforcement;dnet = Reduced value of the effective length of a

FRP bar;db = Length of a FRP NSM bar;Ec = Modulus of elasticity of concrete;Ef = Modulus of elasticity of FRP reinforcement;Es = Modulus of elasticity of steel reinforcement;

= Compressive strength of concrete;ffe = Effective tensile strength of FRP

reinforcement;ffu = Ultimate design tensile strength of FRP

reinforcement;= Guaranteed tensile strength of FRP

reinforcement;fs = Tensile strength of steel reinforcement;fy = Yielding strength of steel reinforcement;h = Cross-section height;Ig = Gross moment of inertia;l = Length of the beam;lb = Length of FRP NSM bar;

ld = Development length of FRP bars;leff = Vertical length of FRP NSM bar used as shear

reinforcement;lnet = Net length of a FRP NSM bar used as shear

reinforcement;l0.004 = Length of FRP bar to maintain shear integrity

of concrete;L = Live load;Li = Length of each FRP bar crossed by a

45-degrees shear crack;Ltot = Total length of FRP bars crossed by a

45-degrees shear crack;Mn = Nominal moment strength at section;Mip = Moment in place at the time of FRP

installation;n = Modular ratio of elasticity Es/Ec, and ratio

defined by Eqn 15;Rn = Nominal strength of the structure;s = Spacing of steel and FRP shear reinforcement;Tf = Tensile force in FRP reinforcement;Ts = Tensile force in steel reinforcement;Vc = Nominal shear strength provided by concrete;Vf = Nominal shear strength provided by FRP

reinforcement;Vn = Nominal shear strength at section;Vs = Nominal shear strength provided by steel

reinforcement;α = Angle between inclined FRP stirrups and

longitudinal axis of member;γ = Coefficient of the Whitney stress block;β1 = Coefficient of the Whitney stress block;εbi = Initial strain in the concrete before FRP

installation;εc = Concrete compressive strain;εc,f = Nominal tensile strain in concrete surrounding

FRP bars;εcu = Maximum permissible compressive strain in

concrete (0.003);εfe = Effective tensile strain in FRP reinforcement;

f fu*

′fc



d=610 mm

375 kN

62 kN

(Not to scale)

2.55 m

325 kN

CFRP bars @ 80 mm

62 kN

CL

No. 17, 6-mm

200 kN

New load shear diagram (envelope)

Figure 15. Shear upgrading using NSM CFRP bars (only NSM bars are shown)

εfu = Ultimate design tensile strain of FRPreinforcement;

= Guaranteed tensile strain of FRPreinforcement;

εs = Tensile strain of steel reinforcement;εy = Yielding tensile strain of steel reinforcement;

κm = FRP Bond dependent coefficient for flexure;φ = Strength-reduction factor;ψf = Additional strength-reduction factor for FRP

reinforcement;τb = Average bond stress for FRP reinforcement;τmax = Maximum bond stress for FRP reinforcement.

ε fu*



Antonio Nanni is the V & M Jones Professor of Civil Engineering at University of Missouri-

Rolla. He is an active member in the technical committees of ACI (Fellow), ASCE (Fellow),

ASTM and TMS. He was the founding Chairman of ACI Committee 440 - FRP Reinforcement

and is the current Chairman of ACI Committee 437 – Strength Evaluation of Existing

Concrete Structures. Dr. Nanni is the Editor-in-Chief of the ASCE Journal of Materials in

Civil Engineering.

Renato Parretti is a senior structural engineer with Co-Force America, Rolla, MO

responsible for numerous FRP design projects throughout the world. He is a member of ACI

and ASCE and serves as an active member on ACI Committee 437, Strength Evaluation of

Existing Concrete Buildings, and ACI Committee 440, Fiber Reinforced Polymer

Reinforcement. Mr. Parretti holds a B.S. in Civil Engineering from the University of

Florence, Italy. He is a registered PE in Italy.

strengthening of rc members using near-surface...

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