Design of FRP Reinforced and Strengthened Concrete

Transcription

1 25 Design o FRP Reinored and Strengthened Conrete Lawrene C. Bank, Ph.D., P.E., FASCE * 25.1 Introdution 25.1 Introdution Design o FRP-Reinored Conrete Memers Introdution Properties o FRP Reinoring Bars Design Basis or FRP-Reinored Conrete Design o Flexural Memers with FRP Reinoring Bars 25.3 Design o FRP-Strengthened Conrete Memers Introdution Properties o FRP Strengthening Systems Design Basis or FRP Strengthening Systems or Conrete Memers Design o FRP Flexural Strengthening Systems Design o FRP Shear Strengthening Systems Design o FRP Axial Strengthening Systems 25.4 Summary Reerenes The design o onrete memers either reinored with FRP reinoring ars or strengthened with strips or sheets o FRP laminates or aris is disussed in this hapter. The disussion in this hapter ollows the design reommendations o the most urrent versions o the design guidelines pulished y the Amerian Conrete Institute (ACI) that are used to design these onrete strutures in the United States. The material presented is an updated and expanded version o portions o the hapter Fier-Reinored Polymer Composites, whih appeared in the Handook o Strutural Engineering (Bank, 2004) and was ased on ACI design guidelines in In addition, this hapter is intended to provide a rie overview o topis overed in greater detail and aompanied y illustrative examples in Composites or Constrution: Strutural Design with FRP Materials (Bank, 2006.) Researh in the use o FRP reinorements and FRP strengthening systems or onrete strutures has een the ous o intense international researh ativity sine the late 1980s. A iannual series o symposia entitled Fier-Reinored Plastis in Reinored Conrete Strutures (FRPRCS) has een the leading venue or reporting and disseminating these researh results. The most reent symposium, the seventh in the series dating ak to 1993, was held in Patras, Greee, in 2007 (Triantitillou, 2007). * Proessor, Civil and Environmental Engineering, at the University o Wisonsin, Madison; expert in the mehanis and design o omposite material strutures with an emphasis on appliations to ivil engineering. 25-1

2 25-2 Conrete Constrution Engineering Handook FIGURE 25.1 Typial FRP reinoring ars or onrete memers Design o FRP-Reinored Conrete Memers Introdution Fier-reinored polymer (FRP) reinoring ars and grids have een ommerially produed or reinoring onrete strutures or over 30 years (ACI Committee 440, 1996; Bank, 2006; Nanni, 1993). FRP reinoring ars have een developed or prestressed and non-prestressed (onventional) onrete reinorement. This setion onsiders only non-prestressed reinorement or onrete strutures and ollows the proedures o ACI 440.1R-06, Guide or the Design and Constrution o Strutural Conrete Reinored with FRP Bars (ACI Committee 440, 2006). Note that ACI 440.1R-06 does not over reinoring with preariated FRP grids and mats. Reommendations or the design o prestressed FRP-reinored onrete an e ound in ACI 440.4R-04, Prestressing Conrete with FRP Tendons (ACI Committee 440, 2004). Current FRP reinoring ars (reerred to as FRP rears in what ollows) are ommerially produed using thermosetting polymer resins (ommonly, polyester and vinylester) and glass, aron, or aramid reinoring iers. The most ommon ars produed today are glass-ier-reinored vinylester ars. These are reommended or use in reinoring appliations or load-earing onrete strutures. The ars are primarily longitudinally reinored with volume rations o iers in the range o 50 to 60%. FRP reinoring ars are usually produed y a proess similar to pultrusion (Starr, 2000) and have a surae deormation or texture to develop the ond to onrete. More inormation on the historial development, onstituent materials, and manuaturing proesses o FRP rears an e ound in Bank (2006). A photograph o some typial FRP reinoring ars is provided in Figure In addition to the ACI design guidelines, a numer o other design guides have een pulished or FRP-reinored onrete. These inlude Japanese (BRI, 1995: JSCE, 1997) and Canadian (ISIS, 2001; CSA, 2002) guides Properties o FRP Reinoring Bars Glass-ier-reinored vinylester ars are availale rom a numer o manuaturers in the United States, Europe, and Asia. Bars are typially produed in sizes ranging rom 3/8 in. in diameter to 1-1/4 in. in diameter (i.e., #3 to #10 ars.) FRP ars have a non-smooth surae, whih is required or ond to the onrete (see Figure 25.1) and is typially produed y a sand-oated external layer, molded deormations, mahined ris, or a spiral wind. The properties o FRP rears are intended to e measured and reported y FRP rear manuaturers in aordane with ACI 440.3R-04, Guide Test Methods or Fier- Reinored Polymers (FRP) or Reinoring or Strengthening Conrete Strutures (ACI Committee 440, 2004a). A standard produt speiiation or FRP rears has reently een approved or puliation y the Canadian Standards Organization (ISIS, 2006). The ACI is urrently preparing a standard speiiation

3 Design o FRP Reinored and Strengthened Conrete 25-3 TABLE 25.1 Properties o Typial Commerially Produed FRP Reinoring Bars Glass-Reinored Vinylester Bar a,, (0.5-in. Diameter) Glass-Reinored Vinylester Bar a (1-in. Diameter) Caron-Reinored Vinylester Bar a (0.375-in. Diameter) Caron-Reinored Epoxy Bar (0.5-in. Diameter) Fier volume (estimated) Fier arhiteture Unidiretional Unidiretional Unidiretional Unidiretional Strength ( 10 3 psi) Tensile, longitudinal Compressive, longitudinal NR NR NR NR Bond strength NR Shear, out-o-plane NR NR Stiness ( 10 6 psi) Tensile, longitudinal Compressive, longitudinal NR NR NR NR CTE, longitudinal (10 6 / F) CTE, transverse (10 6 / F) NR Barol hardness NR 24-hour water asorption (% max.) NR NR NR NR Density (l/in. 3 ) NR a Data or Aslan (Hughes Brothers, Seward, Neraska). Data or V-Rod (Pultrall, Quee, Canada). Data or Leadline (Mitsuishi, Tokyo, Japan). Note: CTE, oeiient o thermal expansion; NR, not reported y the manuaturer. or FRP ars. For design, the key mehanial properties o interest are the longitudinal tensile strength and longitudinal tensile modulus o the ar. Most FRP ars are rittle and exhiit strongly linear and elasti axial stress strain or axial load-deormation harateristis up to their ailure loads. They do not yield and have no plasti deormation apaity as do steel rears. It is also important to note that, unlike steel rears, the longitudinal strength (ut not the longitudinal modulus) o FRP rears dereases with the diameter o the ar. This is attriuted to the relatively low in-plane shear modulus o FRP rears (leading to shear lag eets), the additives used to produe larger diameter ars, and a statistial size eet in rittle glass iers. Designers should always onsult the manuaturer s pulished properties or use in design. Typial properties or glass-ier FRP rears and aron-ier FRP ars are provided in Tale It should e noted that the aron-ier ars are typially used as prestressing tendons or near-surae-mounted (NSM) strengthening rods and not as onventional reinoring ars due to ost onsiderations. Fier-reinored polymer rears are onsidered to e transversely isotropi rom a mehanis perspetive (Bank, 1993). Theoretial equations are availale to predit the mehanial and physial properties o the FRP rears rom the properties o the ier and resin onstituents; however, or design purposes, measured properties o the as-produed ars must e used. At this time, theoretial methods are not yet availale to predit the ond properties and the long-term duraility harateristis o FRP rears. Test methods or determining and reporting the alkali resistane, reep, and atigue harateristis o FRP rears are provided in ACI 440.3R-04 (ACI Committee 440, 2004a). FRP rears ontaining glass iers an ail atastrophially under sustained loads at stresses lower than their tensile strengths, a phenomenon known as reep rupture or stati atigue. Design guides thereore limit the amount o sustained load on onrete strutures reinored with FRP rears. Fier-reinored polymer rears should only e used at servie temperatures elow the glass transition temperature (T g ) o the polymer resin system used in the ar. For typial vinylester polymers, this is around 200 F. The ond properties have een shown to e highly dependent on the glass transition temperature o the polymer. In addition, it is important to note that the oeiients o thermal expansion o FRP rears are not the same in the transverse (radial) diretion as in the longitudinal diretion. The oeiient o thermal expansion may e lose to an order o magnitude higher in the transverse diretion

4 25-4 Conrete Constrution Engineering Handook o the ar due to its anisotropi properties (see typial properties in Tale 25.1). This may ause longitudinal splitting in the onrete due to temperature and shrinkage eets i suiient over is not provided. Fier-reinored polymer reinoring ars made o thermosetting polymers annot e ent in the ield and must e produed y the FRP rear manuaturer with ends or anhorages or or stirrups. The strength o the FRP rear at the end is sustantially redued and must e onsidered in the design. Aording to ACI 440.1R-06, FRP rears should not e used or arrying ompressive stress in onrete memers (i.e., ompression reinorement in eams or olumns) as this time, as insuiient researh has een onduted on this topi. Where FRP ars are used in the ompression zone they should e suitaly onined to prevent loal instaility Design Basis or FRP-Reinored Conrete The load and resistane ator design (LRFD) asis is stipulated y ACI 440.1R-06, whih provides the resistane ators (φ, or phi ators) or use with FRP rears that are alirated or the load ators required or use in design with onventionally reinored onrete strutures y ACI (e.g., 1.2 or dead load and 1.6 or live load) (ACI Committee 318, 2005). For the design o lexural memers reinored with FRP rears, ACI 440.1R-06 provides the ollowing resistane ators: Flexural apaity (tensile reinorement only): φ = 0.55 or an under-reinored eam setion (ρ < ρ ). φ = 0.65 or a sustantially over-reinored eam setion (ρ > 1.4ρ ). φ = ρ /ρ or a lightly over-reinored eam setion (ρ < ρ < 1.4ρ ). Shear apaity (FRP shear reinorement in the orm o stirrups): φ = 0.75 per ACI where ρ is the FRP reinorement ratio and ρ is the alaned FRP reinorement ratio. The FRP reinorement ratio or an FRP-reinored retangular eam setion (where the susript is used to indiate FRP reinorement to distinguish it rom onventional reinorement) is given as: ρ A = d (25.1) and the alaned FRP reinorement ratio is given as: ρ E εu = 085. β 1 E ε + u u u (25.2) where A is the area o FRP reinorement, is the eam width, d is the eetive depth, β 1 is a ator that depends on onrete strength (e.g., 0.85 or 4000-psi onrete), is the ylinder ompressive strength o the onrete, E is the longitudinal modulus o the FRP rear, ε u is the nominal ultimate ompressive strain in the onrete (taken as 0.003), and u is the longitudinal design strength o the FRP rear. Figure 25.2 shows the distriution o strains, stresses, and ores at the servie ondition and at the ultimate ondition or an FRP reinored setion. The design strength ( u ) and design ailure strain (ε u ) are otained rom the manuaturer-reported guaranteed strength and guaranteed ailure strain y multiplying them y an environmental redution ator (C E ), whih depends on the ier type in the ar and the type o intended servie o the struture. For example, or glass FRP rears, C E is 0.7 or exterior onrete and 0.8 or interior onrete. The guaranteed strength and guaranteed strain to ailure o FRP rears are deined as the mean minus 3 standard deviations o a minimum o 25 test samples (ACI Committee 440, 2006). In addition to the strength riteria desried aove, the design asis or FRP-reinored onrete memers also inludes stipulations on the ehavior and appearane o the FRP-reinored memer under servie

5 Design o FRP Reinored and Strengthened Conrete 25-5 ε or ε u or 2/3 C = 0.5 ʹ 0.85 ʹ β 1 C = 0.85 β ʹ 1 d A + ε or ε u T = A u T = A u Setion Strains Stresses and ores at servie loads Stresses and ores at ultimate loads FIGURE 25.2 Strains, stresses, and ores in the FRP-reinored setion at servie and ultimate loads. loads. Maximum lexural rak widths are limited to 0.20 and 0.28 mils or exterior and interiors exposure, and the stress in the main FRP reinoring ars is limited to 0.2 u, 0.3 u, and 0.55 u or glass, aramid, and aron ars, respetively, to prevent ailure under sustained loads due to reep rupture or due to atigue. Beause FRP rears typially have a lower modulus than steel rears, the servieaility riteria (typially, deletions and rak widths) an oten ontrol the design o FRP-reinored onrete setions Design o Flexural Memers with FRP Reinoring Bars Flexural Capaity with FRP Main Tension Bars The nominal moment (or lexural) apaity o an FRP-reinored onrete memer (suh as a eam or a sla) is determined in a manner similar to that o a steel-reinored setion. However, eause FRP rears do not yield, the ultimate strength o the ar replaes the yield strength o the steel rear in the traditional onrete eam design ormula ased on strain ompatiility (assuming plane setions remain plane and ars are peretly onded to the onrete) and equilirium o ores. Both under-reinored setion design and over-reinored setion design are permitted; however, due to servieaility limits (primarily long-term deletions and rak widths), most glass FRP-reinored lexural memers will e over-reinored. When ρ > ρ, the over-reinored setion will ail due to onrete rushing, and the nominal moment apaity is given in a manner similar to that or a setion reinored with steel rears (where the rear has not reahed its yield stress). The stress in the rear thereore must e alulated to determine the apaity o the setion. The nominal moment apaity is given as: where: M A d a n = 2 A a = 085. (25.3) (25.4) 2 ( E u) = ε β1 E ε ρ 05. E ε u u (25.5) where is the stress in the FRP rear at onrete ompressive ailure, and a is the depth o the equivalent retangular (Whitney) stress lok in the onrete.

6 25-6 Conrete Constrution Engineering Handook When ρ < ρ, the under-reinored setion will ail due to rupture o the FRP rears in tension. Beause the FRP reinorement will not yield prior to its ailure, the moment apaity o the setion annot e alulated assuming the onrete rushes when the ar ruptures (as in the ase o a steel underreinored setion). For this reason, the setion apaity should e alulated using appropriate nonlinear stress strain relations o the onrete; however, this requires an iterative solution proedure, whih is not suited to design alulations. To overome this situation, ACI 440.1R-06 reommends omputing the approximate (and onservative) nominal lexural apaity as: β Mn = A u d 1 2 (25.6) where is the depth o the neutral axis at the alaned reinorement ratio, given as: = ε u εu + ε u d (25.7) A minimum amount o lexural reinorement should e provided when the FRP-reinored eam is designed to ail y FRP ar rupture to prevent ailure at onrete raking. The amount is given as: A,min = d d u u (25.8) Shear Capaity with FRP Main Tension Bars and FRP Shear Reinorement The nominal shear apaity o an FRP-reinored onrete memer loaded in lexure is inluened y the mehanial properties o the FRP main tension reinoring ars and y FRP shear reinorement, whih is typially supplied in the orm premanuatured stirrups. The lower modulus o the FRP main ars (assuming glass iers) leads to a shallower ompression zone and larger deletions at lexural ailure o FRP-reinored lexural memers than would e otained in the same setion reinored with steel ars. In addition, the strain in the FRP stirrups is limited to prevent large shear raks rom developing in the FRP-reinored onrete memer. Added to this, the strength o the FRP ar is redued when it is ent to orm a stirrup due to the linear elasti material properties and the manuaturing proess used to manuature ent FRP ars. The nominal shear apaity (V n ) o an FRP-reinored onrete eam is: Vn = V + V (25.9) where V is the nominal shear apaity o the onrete with FRP rears used as main tension reinorement and is given as: V = 5 w (25.10) where w is the width o the eam we, and is the depth o the neutral axis in the raked elasti setion as deined or the servieaility alulations and is given as: = kd 2 k = ( ρη ) + 2ρη ρη (25.11) (25.12) η E = E (25.13)

7 Design o FRP Reinored and Strengthened Conrete 25-7 where η is the modular ratio, k is the depth ratio, and V is the nominal shear apaity provided y the FRP stirrups. For vertial FRP shear stirrups, it is given as: V Av vd = s (25.14) where A v is the total area o the stirrups that ross the shear rak, and v is the strength o the FRP stirrup, whih is limited y the smaller o: v = E (25.15) and the strength o the FRP rear at its end: r = d u (25.16) where is the strength o the FRP rear at its end, r is the inside radius o the end, and d is the diameter o the FRP rear. Standard end radii are reported y manuaturers and range rom 4.25 to 6 in. or typial FRP rears. The ratio o r /d may not e less than Design or Servieaility For servieaility design o onrete memers with FRP ars three riteria, all alulated with respet to the servie loads on the memer (with no load ators applied), must e heked against ode-stipulated limits provided in ACI 440.1R-06: (1) maximum rak widths due to all loads, (2) maximum short-term and long-term deletions due to all loads aounting or long-term reep eets, and (3) maximum stresses in the FRP ars due exlusively to sustained loads and atigue. The width o a lexural rak in an FRP-reinored memer is alulated rom: 2 s w = k d + E 2 β 2 2 (25.17) where w is the rak width (in inhes), is the servie load stress in the FRP reinorement (in ksi), E is the modulus o the FRP rears (in ksi), β is the ratio o the distane etween the neutral axis and the ottom o the setion (i.e., the tension surae) and the distane etween the neutral axis and the entroid o reinorement, d is the thikness o the onrete over rom the tension ae to enter o the losest ar (in inhes), s is the enter-to-enter ar spaing o the main FRP ars (in inhes), and k is a ondrelated oeiient. k is taken as 1.4 or ommerially produed FRP rears. β is determined rom: h kd β= d 1 k ( ) (25.18) where h is the setion depth and d is the eetive setion depth. The stress in the FRP ar at servie loads an e alulated rom: where m s is the servie load moment., s= m η d 1 k s I ( ) r (25.19)

8 25-8 Conrete Constrution Engineering Handook To alulate maximum short-term and long-term deletions under servie loads, a modiied orm o the Branson equation is used: I e Mr Mr = di g M a + 1 M a I 3 3 β r I g (25.20) where I e is the eetive seond moment o area o the raked setion, I g is the seond moment o the gross setion, M r is the moment at raking, M a is the applied servie load moment, and β d is a redution oeiient or FRP reinored eams that is given as: β d 1 ρ = 5 ρ 10. (25.21) As in onventional steel-reinored onrete, the raked (transormed to onrete) seond moment o the setion is given as: I 3 d = k + η A d 1 k 3 ( ) r (25.22) The long-term deletions, inluding the eets o reep and shrinkage o the onrete under the sustained long-term servie loads (i.e., the dead load and the sustained live load), an e alulated as: ( p+ sh) = 06. ξ( i ) (25.23) where ( i ) sus is the short-term (or instantaneous) deletion due to the sustained loads only and is alulated using the modiied Branson ormula; ξ = 2.0 or sustained loads with a duration o 5 years or more as per ACI (ACI Committee 318, 2005). All FRP-reinored onrete eams must e heked or possile ailure due to reep rupture or atigue under servie loads. Creep rupture is heked with respet to all sustained servie loads, whereas atigue is heked with respet to all sustained loads plus the maximum moment indued in a atigue loading yle: sus,reep rupture = m η d 1 k sus I r ( ) (25.24) where m sus is the moment due to the sustained servie loads Detailing o FRP Reinorements The development length o an FRP rear is dierent rom the development length o a onventional steel rear. In addition, a eam reinored with FRP ars an potentially ail due to splitting ond ailure etween the FRP ar and the onrete due to the high tensile stress that an e developed in FRP ars. The required development length (l d ) or a straight FRP ar is given as: l d r α 340 = C d ( d ) (25.25) where r is the stress in the FRP ar at ailure whih is the lesser o (1) the design strength o the ar or under-reinored eams ( u ), (2) the atual stress in the ar or over-reinored setions ( ), or (3) the eetive ond ritial design stress in the ar or oth over and under-reinored setions ( e ), whih is given as:

9 Design o FRP Reinored and Strengthened Conrete 25-9 e = e C e + + α l l d d d 340 u (25.26) where C is the lesser o (1) the distane rom the enter o the ar to the nearest outer onrete surae in the tension zone, or (2) hal the on-enter spaing o the ars (side-y-side); α is the ar loation ator, whih is taken as 1.0 or ars that are in the ottom 12 in. o the ormwork when the onrete is ast and as 1.5 when the ars are more than 12 in. aove the ottom o ormwork when the eam is ast (known as top-ars). ACI 440.1R-06 urther reommends that the term C/d not e taken as larger than 3.5 and that the minimum emedment length (l e ) e at least 20 ar diameters, or 20d. For hooked ars, the development length o the portion extending eyond the end (the tail length) is given as a untion o the FRP rear design strength. For FRP rears with design strengths in the range o 75 to 150 ksi (typial o glass FRP rears), the length o the hook (l h ) is given as: l h u = d (25.27) It should not e less than 12d or 9 in. Tension lap splies or FRP rears are ased on reommendations or steel rears and limited test data. For Class A and Class B lap splies, the reommended develop lengths are 1.3l d and 1.6l d, respetively. FRP stirrups an e spaed at a maximum o d/2 (or 24 in.) and should have a minimum r /d ratio o 3. The tail length o 90 hooks in the stirrups must e at least 12d Design o FRP-Strengthened Conrete Memers Introdution Fier-reinored polymer reinoring systems or strengthening struturally deiient onrete strutural memers and or repairing damaged or deteriorated onrete strutures have een used sine the mid- 1980s (Bank, 2006). This setion provides guidane or the design o FRP strengthening systems aording to the proedures o ACI 440.2R-02, Guide to the Design and Constrution o Externally Bonded FRP Systems or Strengthening Conrete Strutures (ACI Committee 440, 2002). This guide is used or the design o most FRP strengthening systems urrently designed in the United States. This guide is still ased on ACI load ators (e.g., 1.4 or deal loads and 1.7 or live loads). It is urrently under revision and, in addition to other hanges, the next edition will e ompatile with ACI load ators (e.g., 1.2 or dead loads and 1.6 or live loads). The reader is advised to onsult the new version o this guide when it is released in The irst FRP-strengthened onrete strutures were eams strengthened to inrease their lexural apaity using high-strength, lightweight, aron-ier-reinored epoxy laminates that were onded to the undersides o the eams. The method is a modiiation o one where epoxy-onded steel plates are used to strengthen onrete eams whih has een in use sine the mid-1960s. The FRP systems were shown to provide signiiant eneits in onstrutaility and duraility over the steel plates. Thereater, signiiant work was onduted on strengthening o onrete olumns to enhane their axial apaity, shear apaity, and dutility, primarily or seismi loadings. This method is a modiiation o one using steel jakets to strengthen onrete olumns. This was ollowed losely y work on shear strengthening o eams. A review o the state o the art on the sujet an e ound Teng et al. (2001), Hollaway and Head (2001), and Bank (2006). The method has also een used to strengthen masonry and timer strutures; however, appliations o this type are not disussed in this hapter. Current FRP strengthening systems or onrete all into two popular types: preured and ormed-inplae systems. The preured systems onsist o atory manuatured laminates (known as strips or plates) o aron-or glass-reinored thermosetting polymers (typially epoxy or vinylester) that are onded to the surae o the onrete using an epoxy adhesive. The manuatured preured laminates typially have

10 25-10 Conrete Constrution Engineering Handook FIGURE 25.3 Typial FRP strengthening systems or onrete memers. a volume ration o iers in the range o 55 to 65% and are ured at high temperatures (>300 F) ut are onded in the ield at amient temperatures. The ormed-in-plae systems onsist o layers o unidiretional sheets or woven or stithed aris o dry iers (usually glass, aron, or aramid) that are saturated in the ield with a thermosetting polymer (e.g., epoxy or vinylester) whih simultaneously produes and onds the FRP material to the onrete. The proess is oten reerred to as lay-up. The ormed-in-plae FRP systems typially have a ier volume ration o etween 20 and 40% and are ured at amient temperatures in the ield. Figure 25.3 shows a numer o urrently produed FRP strengthening systems. A numer o design guides and national standards are urrently pulished that provide reommendations or the analysis, design, and onstrution o onrete strutures strengthened with FRP materials (Conrete Soiety, 2004; CSA, 2002; FIB, 2001; ICC Evaluation Servie, 1997; JSCE, 2001). In addition, manuaturers o FRP strengthening systems or onrete typially provide their own design and installation guides or their proprietary systems. Beause the perormane o the FRP strengthening system is highly dependent on the adhesive or saturating polymer used, the preparation o the onrete surae prior to appliation o the FRP strengthening system, and the ield installation and onstrution proedures, manuaturers requently ertiy approved ontrators to ensure that their systems are designed and installed orretly. Guidane to ensure that FRP strengthening systems are appropriately installed, monitored, and inspeted is provided in a numer o guides (Conrete Soiety, 2003; ICC Evaluation Servie, 2001; TRB, 2004) Properties o FRP Strengthening Systems Caron-ier-reinored epoxy laminates (or strips) are the most ommonly used o the preured FRP strengthening systems. Depending on the type o aron ier used in the strip, dierent longitudinal strengths and stiness are produed. Strips are typially thin (less than in.) and are availale in a variety o widths (typially 2 to 4 in.). Beause the strips are reinored with unidiretional iers, they are highly orthotropi with very low properties in the transverse and through the thikness diretions. Manuaturers typially only report properties in the longitudinal diretions and report very little data on physial properties. The strips are onded to the onrete with an adhesive that is supplied y the strip manuaturer. Typial properties o strips are shown in Tale It is important to note that the properties shown or the strips are properties o the FRP omposite and not the properties o the iers alone. In the ormed-in-plae FRP strengthening systems, a greater array o produts is availale depending on ier type and sheet or ari arhiteture. In this group o produts, a unidiretional, highly orthotropi aron-ier tow sheet is produed y a numer o manuaturers and is oten used in strengthening

11 Design o FRP Reinored and Strengthened Conrete TABLE 25.2 Properties o Typial Commerially Produed FRP Strengthening Strips Standard-Modulus Caron-Reinored Epoxy Strip a,, High-Modulus Caron-Reinored Epoxy Strip a Glass-Reinored Epoxy Strip Caron-Reinored Vinylester Strip d Fier volume (estimated) Fier arhiteture Unidiretional Unidiretional Unidiretional Unidiretional Nominal thikness (in.) Width (in.) Strength ( 10 3 psi) Tensile, longitudinal Rupture strain (%) Tensile, longitudinal 1.8 NR Stiness ( 10 6 psi) Tensile, longitudinal CTE, longitudinal (10 6 / F) NR NR NR CTE, transverse (10 6 / F) NR NR NR Barol hardness NR NR NR a Data or CaroDur (Sika Group; Zurih, Switzerland). Data or Tyo (Fye; San Diego, Caliornia). Data or MBrae (BASF Constrution Chemials; Seven Hills, New South Wales, Australia). d Data or Aslan (Hughes Brothers; Seward, Neraska). Note: CTE, oeiient o thermal expansion; NR, not reported y the manuaturer. All strips must e onded with manuaturer-supplied ompatile adhesives. appliations. The individual aron tows in the sheet are held together y a polymeri inder (or a light stithing). The sheet is oten supplied on a wax paper aking. Sheets are typially 10 to 40 inhes wide and an e applied in multiple layers with dierent orientations. The ommon ari materials in the ormed-in-plae group are woven or stithed ier aris having an areal density o 12 to 32 oz/yd 2. Caron-ier aris and hyrid aris (with more than one ier type) are also availale. Faris are typially muh thiker than tow sheets. They are also used in multiple layers. Beause o the wide variety o produts availale and their dierent thiknesses, it is not easy to ompare their properties diretly. In addition, the iers must e used with a ompatile resin system applied at a ontrolled volume ration to ahieve a FRP omposite with desirale properties. In the ase o sheet and ari materials, manuaturers typially report the mehanial properties o the dry iers and the thikness (or area) o the iers. It is important to note that when reported in this ashion the properties are not the properties o the FRP omposite ut o the iers alone. Properties o some ommonly availale ier sheet and ari materials are listed in Tale The perormane o the FRP strengthening system is highly inluened y the properties o the adhesive layer in the ase o the preured systems and y the properties o the saturating polymeri resin in the ase o ormed-in-plae systems. The interae etween the FRP omposite and the onrete sustrate transers the loads rom the onrete to the FRP omposite. In the ase o lexural and shear (or axial tensile) strengthening, this load transer is primarily in shear, and the strength and stiness o the interae layer etween the FRP omposite and the onrete are ritial. Suh appliations are termed ond ritial. In the ase o axial ompressive strengthening or lateral displaement dutility enhanement o olumns, the role o the strengthening system is to onine the lateral expansion o the raked onrete. In this ase, the interae ond is not as ritial as long as the FRP system is in lose ontat with the onrete and is wrapped around the onrete ontinuously so as to provide a onining pressure with appropriate hoop stiness and strength. Suh appliations are termed ontat ritial. The FRP strengthening systems desried aove all depend on uring o the polymer adhesives or the saturating resins at amient temperature in the ield; thereore, the glass transition temperature (T g ) o these systems is typially quite low (120 to 180 F). The stiness o the FRP strengthening system is dereased

12 25-12 Conrete Constrution Engineering Handook TABLE 25.3 Properties o Typial Commerially Produed FRP Sheet-Strengthening Materials Standard-Modulus Caron Fier Tow Sheet a,, High-Modulus Caron Fier Tow Sheet a, Glass Fier Roving Sheet a, Thikness (in.) Typial width (in.) Fier arhiteture Unidiretional Unidiretional Unidiretional Strength ( 10 3 psi) Fier tensile, longitudinal Rupture strain (%) Fier tensile, longitudinal Stiness ( 10 6 psi) Fier tensile, longitudinal a Data or MBrae (BASF Constrution Chemials, Seven Hills, New South Wales, Australia). Data or Tyo (Fye, San Diego, Caliornia). Replark (Mitsuishi, Tokyo, Japan). when the operating temperature approahes (and exeeds) the glass transition temperature. Designers should always e aware o the glass transition temperature o the FRP omposite or adhesive they are using in a design. In the event o a ire (at temperatures higher than the T g in the range o 750 F), the FRP material will deompose (pyrolize), and its strength and stiness may e severely ompromised in a short time Design Basis or FRP Strengthening Systems or Conrete Memers The load and resistane ator design (LRFD) asis is stipulated y ACI 440.2R-02 (ACI Committee 440, 2002). Currently, resistane ators are not proailistially ased, and the load ators stipulated or use with this guide are those reommended y ACI (e.g., 1.4 or dead loads and 1.7 or live loads) (ACI Committee 318, 1999). (The revised version o the guide, due out in 2008, will have proailistially ased resistane ators and will e ompatile with ACI ) For the design o onrete memers with FRP strengthening systems the ACI reommends the ollowing resistane ators (φ) and FRP material redution ators, (ψ ): For lexural apaity: φ = 0.9 or dutile ailure o the memer ollowing steel yielding (ε s > 0.005). φ = 0.7 or a rittle ailure when the memer ails prior to steel yielding (ε s < ε sy ). φ = 0.7 to 0.9 or an intermediate region (ε sy < ε s < 0.005). ψ = 0.85 or FRP ond-ritial strengths (applied in addition to φ ators). For shear apaity: φ = 0.85, per ACI ψ = 0.85 or FRP ond-ritial strengths (applied in addition to φ ator). ψ = 0.95 or FRP ontat-ritial strengths (applied in addition to φ ator). For axial apaity: φ = 0.75, per ACI , or spiral steel olumn reinorement. φ = 0.70, per ACI , or tied steel olumn reinorement. ψ = 0.95 or FRP ontat-ritial strengths (in addition to φ ators). Guaranteed strengths and strains to ailure o FRP omposite materials or strengthening are deined as the mean minus 3 standard deviations o a minimum o 20 test samples tested in aordane with ACI 440.3R-04 (ACI Committee 440, 2004a). The design strength ( u ) and design ailure strain (ε u ) are

13 Design o FRP Reinored and Strengthened Conrete otained rom the manuaturer-reported guaranteed strength and ailure strain y multiplying them y an environmental redution ator (C E ), whih depends on the ier type in the FRP strengthening system and the type o intended servie o the struture. For example, or weather-exposed onrete with a glassreinored epoxy FRP strengthening system, C E is 0.65 (ACI Committee 440, 2002). Note that the environmental redution ators or FRP strengthening systems are not the same as the environmental redution ators or FRP reinoring ars (even though the same symol is used or oth.) Even though lexural strength inreases o over 100% o the original strength o a onrete memer an e otained using FRP strengthening systems, the ACI limits the amount o strengthening to prevent atastrophi ailure o the onrete memer in the event o loss o, or damage to, the strengthening system (due to vandalism or environmental degradation). The ACI reommends that the strengthened memer still have suiient original atored apaity (i.e., disounting the additional strengthening system) to resist a sustantial portion o the inreased (new) atored load or whih the strengthened memer is designed. This limit is given as: 12. D L (25.28) where D represents the new dead load eet, and L the new live load eet, suh as ending moment, shear ore, or axial load or their produts (stress and strain). To aount or environments where the FRP may e exposed to ire, additional restritions are plaed on the atored apaity o the FRPstrengthened struture: 10. D+ 10. L (25.29) Fire protetion systems are availale to protet FRP strengthening systems to inrease their ire ratings to uilding ode required ratings (suh as 1- or 2-hour ratings). When a onrete memer is strengthened to inrease its apaity in a seleted mode (e.g., lexure), the memer must e heked to ensure that the apaities in other ailure modes (e.g., shear) are not exeeded. I this is the ase, the strengthening should e dereased or the seondary apaity must e enhaned with its own strengthening system. For servieaility design, the ACI 440.2R-02 guide limits the stress in the steel at servie loads to 80% o the steel yield stress and limits the sustained plus yli stress in the FRP strengthening system to aount or reep rupture and atigue, depending on the ier system. For aron FRP strengthening systems, this limit is 55% o the ultimate strength. At this time, ACI 440.2R-02 does not provide speial reommendations or the determination o deletions or rak widths or FRP-strengthened memers. Flexural deletions in the servie range an e estimated y use o an eetive seond moment o area (I e ) analysis, where the tensile ontriution o the FRP is added to the ontriution o the steel reinoring. For deletions in lexural memers where stresses are in the servie load range, the ontriution o the FRP strengthening system is typially small. In the inelasti range (ater the primary reinoring steel has yielded), the ontriution o the FRP strengthening to the post-yield stiness an e quite onsiderale and should e aounted or in inelasti analysis (Bank, 2006). It is extremely important to note that the method o determining the tensile ore resultant in an FRP strengthening system depends on the type o system used. In the onded, preured strip, the ultimate ore is otained rom the strength o the FRP omposite (see Tale 25.2) and the gross ross-setional area o the strip. In ormed-in-plae systems, the ultimate ore is otained rom the strength o the iers and the net area o the iers (see Tale 25.3). The designer must know i the reported strength (and stiness) o an FRP strengthening system is or the FRP omposite (gross omposite ross-setion) or or the iers alone (net ier ross-setion). Both methods o alulation are permitted y ACI 440.2R Design o FRP Flexural Strengthening Systems Flexural strengthening is ahieved y attahing an FRP strengthening system (preured strip or ormedin-plae ari) to the underside o a lexural memer to inrease the eetive tensile ore resultant in the memer and therey inrease the moment apaity o the memer. This is analogous to adding steel strengthening strips (or plates) to the underside o a memer; however, two undamental dierenes

14 25-14 Conrete Constrution Engineering Handook exist. First, the FRP strengthening system ehaves in a linear elasti ashion and does not yield, and, seond, the FRP strengthening system is more suseptile to detahment (deonding or delamination) ailures than steel plate systems that are anhored with steel olts in addition to the epoxy onding. Beause the steel plates themselves will yield at a similar strain to the internal steel reinoring, the stress level in the steel strengthening system is limited. In the ase o FRP strengthening with FRP systems having ultimate tensile strengths exeeding 300 ksi (see Tale 25.2 and Tale 25.3), the stress level in the FRP an e signiiantly higher than that in steel strengthening systems. In the event that the internal steel reinoring yields eore the FRP strengthening system ails (the desired ailure mode), the onrete memer will undergo large deletions and raking. All o these ators lead to the greater likelihood that the FRP strengthening system will deond rom the onrete eore it ahieves its ultimate (longitudinal) tensile strength. Strengthening o memers in lexure an only e ahieved i there is suiient additional ompressive apaity in the onrete to allow or the inrease in internal moment; thereore, lexural strengthening is most suitale or onrete memers that are lightly to moderately reinored, having steel reinorement in the range o 20 to 40% o the alaned ratio. This is not unommon in reinored onrete memers. The existing tensile strain in the onrete at the loation o the applied FRP strengthening system due to sustained loads when the FRP strengthening system is applied should e aounted or in design alulations i a shoring system is not used. The key to lexural strengthening with FRP strengthening systems is to understand the ailure modes o the system. These inlude rupture o the FRP strengthening system, deonding o the FRP strengthening system, or ompressive ailure o the onrete. All o these modes an our either eore or ater the internal steel has yielded. The desired mode o ailure is onrete ompressive ailure ater the internal steel has yielded with the FRP strengthening system still attahed. The FRP strengthening system an deond in a numer o modes. The FRP system an delaminate rom the onrete sustrate (due to ailure in the onrete, the adhesive layer, or in the FRP laminate itsel) either at the ends (due to high peeling and shear stresses) or in the interior o the eam due to lexural and shear raks in the eam at large deletions. For a detailed disussion on deonding ailure modes, see Teng et al (2001). Analytial methods to predit the various deonding ailure modes are still not ully developed, and ACI 440.2R-02 limits the tensile strain level in the FRP strengthening system to prevent deonding ailure y use o an empirially otained, ond-dependent oeiient (κ m ) that is a untion o the unit stiness o the FRP system and is deined as: κ m 1 60ε = 1 60 ε u ne t ne or t 1, 000, 000 l/in. 2, 000, , ne t 0. 90or ne > t 1, 000, 000 l/in. u (25.30) where ε u is the ultimate strain the FRP; n is the numer o layers o FRP strips, sheets, or aris; E is the longitudinal tensile modulus o the FRP omposite in the ase o strips or the longitudinal modulus o the iers in the strengthening diretion in the ase o sheets or aris; and t is the thikness o an individual strip in the ase o FRP strips or the net thikness o the iers in a single sheet or ari in the ase o sheets or aris. The strain level in the FRP strengthening system is limited y the strain in the onrete or the ultimate strain in the FRP system and is given as: h ε = ε ε κ ε e u i m u (25.31)

15 Design o FRP Reinored and Strengthened Conrete where ε e is the eetive ultimate strain in the FRP at ailure, ε u is the ultimate ompressive strain in the onrete (0.003), is the depth o the neutral axis, h is the depth o the setion, and ε i is the existing tensile strain in the onrete sustrate at the loation o the FRP strengthening system when the FRP system is applied. The eetive stress ( e ) in the FRP is the ultimate strength o the FRP that an e ahieved at ailure and is linearly related to the ultimate strain as: = E ε e e (25.32) The nominal moment apaity (M n ) o the strengthened setion (with an existing layer o tensile steel reinorement) is given as: with: and: β1 Mn = Ass d A e h + β1 ψ 2 2 A + A = γ β 1 s s e = E ε = E ε + ε ( ) d h s s s s e i y (25.33) (25.34) (25.35) where A s is the area o the tensile steel, s is the stress in the steel at ailure, d is the depth o the steel reinoring, β 1 is the depth ratio o the equivalent Whitney stress lok, A is the area o the FRP strip or the iers only in a ormed-in-plae system, γ is the onrete stress resultant ator (0.85 when onrete ompressive ailure governs), is the width o the setion, and y is the yield stress in the reinoring steel. The solution to the aove equations is typially ound y a trial-and-error method y assuming a numer o layers o a speii strengthening system and alulating the resulting nominal moment. Alternatively, a ailure mode an e assumed a priori and the stresses in the materials heked using losed-orm equations, as desried in Bank (2006). Aording to ACI 440.2R-02, the our urrently admissile ailure modes are FRP deonding either eore or ater the internal steel yields or onrete ompressive rushing either eore or ater the internal steel yields. The stress distriution in the onrete at ailure o the strengthened memer will depend on the ailure mode o the strengthened memer. I the FRP deonds when the onrete strain is still low (less than 0.002), the ailure is ontrolled y the FRP, and a nonlinear stress distriution in the onrete should e used in determining the ompressive ore in the setion (Bank, 2006). This is not onduive to design alulations, however, and it is typially assumed that the onrete stress an e represented y the Whitney stress lok at ailure even in this ase. Figure 25.4 shows the strains, stresses, and ores in an FRP-strengthened setion at the ultimate state aording to this assumption. This assumption is elt to e reasonale eause in an appropriately designed strengthening system the steel will yield eore the FRP deonds or ruptures and the strain in the onrete will e larger than As with a onventional reinored onrete setion, a alaned reinorement ratio an e deined that inludes the eet o the internal steel reinoring and the externally applied FRP system (Bank, 2006). The alaned ratio an e deined or ailure o the setion either prior to the internal steel yielding or ater the internal steel has yielded, although as mentioned previously the latter is preerale. The alaned reinorement ratio an e a useul tool in design ut is not as important a parameter as in the design o onventional reinored onrete design (either steel or FRP reinorement), eause a strengthening design depends on the properties o an existing setion and it may not e always possile to ahieve a alaned ondition in the strengthened setion. The stresses in the steel and the FRP strengthening system

16 25-16 Conrete Constrution Engineering Handook ε γ ʹ β 1 C = γʹ β 1 h d A s + ε s s T = A s s A Setion ε i ε e Strains e Stresses and ores at ultimate loads T = A e FIGURE 25.4 Strains, stresses, and ores in an FRP-strengthened setion at ultimate loads. at servie loads should e determined using an elasti raked setion and heked against appropriate stress limits or sustained loads on FRP strengthened strutures aording to ACI 440.2R-02. Mehanial anhorages or FRP wraps an e used to enhane the attahment o the FRP strengthening system to the onrete eam, espeially at the ends o the FRP strengthening system. Design guidane is not provided y the ACI 440.2R-02 or this, although the use o suh a system is reommended y many manuaturers to prevent deonding ailures Design o FRP Shear Strengthening Systems Fier-reinored polymer strengthening systems an e used to inrease the shear apaity o onrete eams and olumns. FRP strengthening systems are applied to the wes o eams (or olumns) and untion in an analogous ashion to internal steel shear reinorement. Beause FRP shear strengthening systems are applied to onrete memers that are oten onstruted monolithially with other ontinuous memers (suh as loors and walls) it is not always possile wrap the FRP strengthening system ompletely around the memer (whih is the desirale ondition.) The FRP strengthening system must thereore e terminated at the top o the we (a three-sided U-wrap) or terminated at oth the top and the ottom on the we (a two-sided wrap). The non-ully wrapped systems are suseptile to deonding ailures (similar to lexural strengthening), and their strains are limited y a shear ond-redution oeiient (κ v ), whih is a untion o the onrete strength, the wrapping type used, and the stiness o the FRP strengthening system. It is given y ACI 440.2R-02 (in U.S. units) as: κ v kk 1 2Le = ε u (25.36) where L e is the ative ond length over whih the shear stress is transerred etween the FRP and the onrete. It has een shown that it is this inite length that limits the maximum ore that an e transerred etween the two materials regardless o the onded length o the FRP strip. It is given as: L e 2500 = ( nt E ) 058. (25.37) The oeiients k 1 and k 2 are given as: k 1 = (25.38)

17 Design o FRP Reinored and Strengthened Conrete For three-sided shear strengthening systems: For two-sided shear strengthening systems: k 2 = d L d d 2Le k2 = d e (25.39) (25.40) where d is the eetive depth o the FRP shear strengthening system. For ully wrapped setions, it is equal to the ull depth (h) o the setion, ut or two- and three-sided wraps it is the vertial distane rom the top o the FRP system to the main tensile reinoring ars in the eam and is less than h. The nominal shear apaity o an FRP strengthened onrete memer with existing steel shear reinoring is determined y adding the ontriution o the FRP strengthening system to the existing shear apaity and is given as: where: V Vn = V + Vs +ψv A = ( ) sinα+ osα d s v e A = 2nt w v = E ε e e (25.41) (25.42) (25.43) (25.44) where V is the shear apaity o the onrete, V s is the shear apaity o the existing steel shear reinorement, and V is the shear apaity o the FRP strengthening system. The FRP material redution ator (ψ ) is taken as 0.95 or ompletely wrapped ontat-ritial setions and as 0.85 or ond-ritial two- or three-sided wrapped setions. A v is the area o the FRP shear strengthening system, e is the eetive tensile stress in the FRP at ultimate, α is the inlination o the ier in the FRP strengthening system to the longitudinal axis o the memer, s is the enter-to-enter spaing o the FRP shear strengthening strips, and w is the width o the FRP shear strengthening strip. (For a ontinuous FRP shear strengthening sheet or ari, s = w ). E is the longitudinal modulus o the FRP strengthening system, and ε e is the eetive longitudinal strain in the FRP strengthening system. The eetive strain in the FRP shear strengthening system is limited to prevent deonding ailures and to maintain the integrity o the onrete aggregate interlok in the onrete memer. For ompletely wrapped FRP shear strengthening systems, the maximum eetive strain in the FRP strengthening system at ailure is limited to: ε e = ε u (25.45) For two- or three-sided shear strengthening, the eetive shear strain in the FRP strengthening system at ailure is limited to: ε = κ ε e v u (25.46) Mehanial anhorages an e used to anhor two- or three-sided wraps in the ompression zone o the we; however, design guidane is not provided y ACI 440.2R-02. When FRP shear strengthening is added to the onventional steel shear reinorement, the shear reinorement limit or onventional onrete memers must hold or oth types o reinorement:

18 25-18 Conrete Constrution Engineering Handook V + V 8 d s w (25.47) When intermittent strips are used, a maximum spaing etween the strips is mandated so every shear rak will e overed y suiient strip width. The ollowing maximum spaing o intermittent strips is required: d s max = + w 4 (25.48) Design o FRP Axial Strengthening Systems Conrete ompression memers an e strengthened to inrease their axial load arrying apaity, their shear apaity, their steel rear lap splie apaity, and their lateral load arrying deormation apaity (whih is related to the dutility o the memer). FRP strengthening o olumns is most eetive when applied to irular olumns and must always onsist o omplete wrapping to otain oninement o the onrete. FRP strengthening systems or oninement o olumns are lassiieds as ontat-ritial appliations. It is also important to note that FRP axial strengthening systems are regarded as passive systems; that is, they are not eetive (or ative) until the onrete reahes its transverse raking strain and egins to dilate, thus plaing hoop stress on the FRP wrap. This is in ontrast to the FRP lexural and shear strengthening systems that must e ative at all load levels. For a non-slender, non-prestressed, normal weight onrete olumn reinored with steel spiral reinorement, the nominal axial apaity is given as: ( ) P = ψ ( A A )+ A n g st y st and or steel tied reinorement, the nominal axial apaity is given as: (25.49) ( ) P = ψ ( A A )+ A n g st y st (25.50) The onined ompressive strength ( ) is given in ACI 440.2R-02 as: = + l l (25.51) where l is the onining pressure provided y the FRP wrap and is given as: l E = κρ ε 2 a e (25.52) where A g is the gross area o the onrete; A st is the area o the existing longitudinal steel; y is the yield stress in the steel ars; is the unonined (existing) onrete ompressive strength; ψ is the FRP material redution ator taken as 0.95 or this ontat-ritial appliation; κ a is an eiieny ator that depends on the shape o the olumn; ρ is the reinorement ratio o the FRP system; E is the modulus o the FRP system in the hoop diretion; and ε e is the eetive strain the FRP system in the hoop diretion. For irular olumns, κ a is 1.0 and the reinorement ratio is given as: ρ A = = 4 A g nt h (25.53)

19 Design o FRP Reinored and Strengthened Conrete where h is the diameter o the irular olumn. It is important to note that the ier layers must all e oriented in the hoop diretion around the olumn (or, i they are not, the eetive properties o the FRP system in the hoop diretion must e used). I layers are also oriented in the longitudinal diretion (e.g., or lexural strengthening), these layers should not e onsidered to ontriute to the axial strengthening. For nonirular olumns, FRP strengthening to inrease axial apaity is muh less eetive due to stress onentrations at the orners (even when hamered) and the nonuniorm onining pressure developed y the wrap. See Teng et al. (2001) or more disussion and proposed equations to address this topi. Limits are plaed on the amount o FRP axial strengthening to ensure that the onrete does not approah its transverse raking strain nor the steel its yield strain in the servie range. ACI 440.2R-02 limits the servie load stress in the onrete to 0.65 and the servie load stress in the longitudinal steel to 0.60 y. The stresses in the onrete (,s ) and the steel ( s,s ) at servie loads are ound using traditional mehanis o materials ormulae: and s, = ss, = E ps AE + A E st s Es ps AE + A E st s (25.54) (25.55) where p s is the axial load at servie onditions in the FRP-strengthened olumn Dutility Enhanement The lateral displaement apaity, whih is related to the dutility o a onrete olumn, an also e inreased y onining it with FRP strengthening wraps. The determination o the lateral displaement apaity is eyond the sope o ACI 440.2R-02 and is addressed in a numer o texts related to the seismi apaity o onrete strutures (Paulay and Priestley, 1992; Priestley et al., 1996). One o the key parameters used in determining the lateral displaement apaity o a onrete olumn is the maximum onined onrete ompressive strain (ε ), whih is the ailure strain in the onrete in the large-deormation, inelasti range. The maximum onrete ompressive strain is typially greater than ε u, whih is the assumed nominal onrete strain at ailure (ased on standard unreinored ylinder tests), and is stipulated y the ACI as This is due to the at that the onrete in the ompression zone in a memer is onined y the transverse reinoring steel (stirrups, ties, hoops or spirals). By using an FRP wrap on the exterior o the memer, the onrete in the ompression zone an e onined in a similar manner and the maximum onrete strain at ultimate an e inreased to a onined ompressive strain (ε ). The equation provided y ACI 440.2R-02 or the maximum onined onrete ompressive strain o an FRP wrapped olumn is: ( ) = E ε (25.56) where E is the elasti modulus o the onrete and is as deined previously. This equation is valid or oth irular and retangular olumns. To use the equation or retangular olumns, the eiieny ator (κ a ) is alulated rom: κ a 2r h 2r = 1 3h( 1 ρg ) (25.57) where h and are the depth and readth o the retangular onrete olumn, r is the orner radius, and ρ g = A st /A g is the steel reinorement ratio. This equation is only appliale when h/ 1.5 and when ( ) + ( ) 2 2

20 25-20 Conrete Constrution Engineering Handook oth and h are less than 36 in., as it has een shown that dutility enhanement in retangular olumns with larger aspet ratios and longer sides is negligile. The FRP reinorement ratio or a retangular FRP onined olumn is given as: (25.58) It is important to reognize that, even though a onined ompressive strength or a retangular olumn is alulated as an intermediate step to alulating the onined ompressive strain, this onined strength should not e used to determine any strength inrease in the olumn Summary The undamental onsiderations and the asi equations that are used to design FRP-reinored and FRPstrengthened onrete memers have een presented in this hapter. The design proedures presented are those promulgated in design guides pulished y the Amerian Conrete Institute, ut it is important to note that these guides are oten updated as new researh is onduted in this rapidly evolving area o onrete strutures. Readers are thereore advised to make sure to otain the urrent versions o these guides when designing FRP-reinored and FRP-strengthened onrete memers. Even though the equations and the ators may hange in orthoming versions o these guides, the undamental onepts presented in this hapter will remain the asis or the design proedures provided. At this time, the properties o the FRP materials or use with the equations presented in this hapter and with the ACI guides must e otained rom the manuaturers o the FRP produts eing used. Eorts are underway at a numer o organizations to develop standard speiiations or FRP-reinoring and FRP-strengthening materials or use in onrete strutures. Reerenes ρ ( ) 2nt + h = h ACI Committee Building Code Requirements or Strutural Conrete and Commentary, ACI , Amerian Conrete Institute, Farmington Hills, MI. ACI Committee Building Code Requirements or Strutural Conrete and Commentary, ACI /ACI 318R-05. Amerian Conrete Institute, Farmington Hills, MI. ACI Committee State-o-the-Art Report on Fier-Reinored Plasti (FRP) Reinorement or Conrete Strutures, ACI 440R-96. Amerian Conrete Institute, Farmington Hills, MI. ACI Committee Guide to the Design and Constrution o Externally Bonded FRP Systems or Strengthening Conrete Strutures, ACI 440.2R-02. Amerian Conrete Institute, Farmington Hills, MI. ACI Committee a. Guide Test Methods or Fier Reinored Polymers (FRP) or Reinoring or Strengthening Conrete Strutures, ACI 440.3R-04, Amerian Conrete Institute, Farmington Hills, MI. ACI Committee Prestressing Conrete with FRP Tendons, ACI 440.4R-04, Amerian Conrete Institute, Farmington Hills, MI. ACI Committee Guide or the Design and Constrution o Strutural Conrete Reinored with FRP Bars, ACI 440.1R-06. Amerian Conrete Institute, Farmington Hills, MI. Bank, L.C FRP reinorements or onrete. In Fier-Reinored Plasti (FRP) or Conrete Strutures: Properties and Appliations, Nanni, A., Ed., pp Elsevier, New York. Bank, L.C Fier reinored polymer omposites. In Handook o Strutural Engineering, 2nd ed., Chen, W.F. and Liu, E., Eds. CRC Press, Boa Raton, FL. Bank, L.C Composites or Constrution: Strutural Design with FRP Materials. John Wiley & Sons, New York. BRI Guidelines or Strutural Design o FRP Reinored Conrete Building Strutures. Building Researh Institute, Tokyo; see also Sonoe, Y. et al Design guidelines o FRP-reinored onrete uilding strutures, J. Composites Construt., 1(3),