SUBJECT: AASHTO LRFD Guide Specifications for Design of Concrete-Filled FRP Tubes for Flexural and Axial Members

Transcription

1 2012 AASHTO BRIDGE COMMITTEE AGENDA ITEM: 43 SUBJECT: AASHTO LRFD Guide Speiiations or Design o Conrete-Filled FRP Tubes or Flexural and Axial Members TECHNICAL COMMITTEE: T-6 Fiber Reinored Polymer Composites REVISION ADDITION NEW DOCUMENT DESIGN SPEC CONSTRUCTION SPEC MOVABLE SPEC MANUAL FOR BRIDGE SEISMIC GUIDE SPEC COASTAL GUIDE SPEC EVALUATION OTHER DATE PREPARED: 2/14/12 DATE REVISED: AGENDA ITEM: AASHTO LRFD Guide Speiiations or Design o Conrete-Filled FRP Tubes or Flexural and Axial Members See Attahment B OTHER AFFECTED ARTICLES: None BACKGROUND: Guide Speiiations were developed in onjuntion with the AASHTO TIG initiative or onrete-illed FRP tube type strutures. ANTICIPATED EFFECT ON BRIDGES: Provides or an alternate type o onstrution or bridges and ulverts. REFERENCES: None OTHER: None 352

2 ATTACHMENT B 2012 AGENDA ITEM 43 - T-6 AASHTO LRFD GUIDE SPECIFICATIONS FOR DESIGN OF CONCRETE-FILLED FRP TUBES FOR FLEXURAL AND AXIAL MEMBERS 353

3 TABLE OF CONTENTS SECTION 1: INTRODUCTION 1.1 SCOPE DEFINITIONS LIMITATIONS DESIGN PHILOSOPHY REFERENCES... 3 Setion CONCRETE-FILLED FRP TUBES (CFFTs) SCOPE DEFINITIONS NOTATION LIMITATIONS MATERIAL PROPERTIES FRP Tube General Tensile and Compressive Ultimate Strengths and Strains Modulus o Elastiity LIMIT STATES Servie Limit State Fatigue and Creep Rupture Limit State Strength Limit State General Resistane Fators Stability Extreme Event Limit State DESIGN CONSIDERATIONS General Eet o Imposed Deormation DESIGN FOR FLEXURE WITH NO AXIAL COMPRESSION General Assumptions

4 General Servie and Fatigue and Creep Rupture Limit States Strength and Extreme Event Limit States Minimum Longitudinal Tension Reinorement Minimum Reinorement in the Transverse or Hoop Diretion Fatored Flexural Resistane General Method Simpliied Method Deormation Control o Craking Stress Limit or Conrete DESIGN FOR AXIAL COMPRESSION General Assumptions Fatored Axial Compressive Resistane Minimum Reinorement in the Hoop Diretion Stress Limit or Conrete DESIGN FOR COMBINED FLEXURE AND AXIAL COMPRESSION General Assumptions Fatored Resistane General Method Simpliied Method Evaluation o Slenderness Eets Minimum Reinorement Deormation Control o Craking Stress Limit or Conrete DESIGN FOR SHEAR EFFECTS General Nominal Shear Resistane Minimum Shear Reinorement CONNECTIONS

5 2.13 REFERENCES Setion SCOPE DEFINITIONS NON-STANDARD DOCUMENTS MATERIAL AND MANUFACTURE Fibers Matrix Resins Fillers and Additives Manuaturing Proess PHYSICAL PROPERITES Fiber Content Glass Transition Temperature Longitudinal and Transverse Coeiients o Thermal Expansion (CTE) MECHANICAL PROPERITES Tensile Strength Tensile Modulus o Elastiity Ultimate Tensile Strain Compressive Strength Ultimate Compressive Strain DURABILITY PROPERTIES Moisture Absorption Resistane to Alkaline Environment SAMPLING Sampling Frequeny and Number o Speimens Rejetion CERTIFICATION Douments QC/QA Produt Certiiation Markings REFERENCES

6 Setion 1 INTRODUCTION 1.1 SCOPE These Speiiations present provisions or the analysis and design o onrete-illed iber reinored polymer (FRP) tubes (CFFT) or use as strutural omponents in bridges. Design methodology presented in this speiiation allows CFFTs to be designed as lexural members, axial ompression members, or members subjeted to ombined lexural and axial ompression, in addition to shear. CFFT bridge omponents may inlude beams, arhes, olumns and piles. These Speiiations are not intended to supplant proper training or the exerise o judgment by the Design Proessional, and state only the minimum requirements neessary to provide publi saety. The Owner or the Design Proessional may require the sophistiation o the design and/or the quality o materials and onstrution to be higher than the minimum requirements. C1.1 FRP materials have emerged as an alternative material to steel reinorement or onrete strutures. They oer advantages over steel reinorement due to their nonorrosive nature and nonondutive behavior. FRP is a also a versatile material that an be produed in many orms suh as reinoring bars, grids, rigid plates, lexible sheets and several strutural shapes, inluding tubes. This speiiation is oused on one appliation o FRP in the orm o tubes used as strutural stay-in-plae orms illed with onrete [Fardis and Khalili (1981), Nanni and Bradord (1995), Mirmiran and Shahawy (1996), Davol (1998), Burgueño (1999), Fam (2000), Fam and Rizkalla (2001), Fam and Rizkalla (2002)]. Due to dierenes in the physial and mehanial behavior o FRP materials as opposed to steel, partiularly when used as stay-in-plae strutural orms, unique guidane on the engineering and onstrution o bridge omponents using this tehnology is needed. The Design Proessional shall be amiliar with the provisions o the AASHTO LRFD Bridge Design Speiiations, 6 th Ed. (AASHTO LRFD) and the latest interim revisions, as well as with the design o onventional reinored onrete strutures and strutures exposed to earth loading. The ommentary direts attention to other douments that provide suggestions or arrying out the requirements and intent o these Speiiations. However, those douments and this ommentary are not intended to be a part o these Speiiations. 357

7 1.2 DEFINITIONS Composite Ation - A ondition in whih two or more elements or omponents are made to at together by eliminating relative movements at their interae. Design Proessional - The arhitet, engineer, arhitetural irm, or engineering irm responsible or the design o the bridge and issuing Contrat Douments or administering the Work under Contrat Douments, or both. Fiber - Any ine thread-like natural or syntheti objet o mineral or organi origin. Note: This term is generally used or materials whose length is at least 100 times its diameter. Fiber, Aramid - Highly oriented organi iber derived rom polyamide inorporating an aromati ring struture. Fiber, Carbon - Fiber produed by heating organi preursor materials ontaining a substantial amount o arbon, suh as rayon, polyarylonitrile (PAN), or pith in an inert environment. Fiber, Glass - Fiber drawn rom an inorgani produt o usion that has ooled without rystallizing. 1.3 LIMITATIONS Composite ation between the onrete ore and FRP tube is required or a CFFT member to develop it s stiness and strength as deined in these speiiations. CFFT s whih do not have suiient bond between the onrete ore and FRP tube to ensure omposite ation are not addressed in these Speiiations. C1.3 Bond may be ahieved by shear interlok mehanism, suh as a roughened inner surae o the FRP tube and/or rition, whih an be urther enhaned by the use o low-shrinkage or expansive onrete. It is the responsibility o the engineer to ensure bond is suiient or the loading requirements, design lie, and exposure onditions o the speii appliation. The assumed ailure mehanism o CFFTs used as lexural members shall not be based on the ormation o plasti hinges. Moment redistribution in ontinuous members shall not be onsidered or CFFTs without internal steel reinorement. FRP materials demonstrate a linear-elasti behavior up to ailure and do not demonstrate yielding, whih is the basis or plasti hinge ormation and moment redistribution. 1.4 DESIGN PHILOSOPHY These Speiiations are based on limit state design priniples where strutural omponents shall be proportioned to satisy the requirements at all appropriate servie, atigue and reep rupture, strength and extreme event limit states. In many instanes, servieability or C1.4 The limit states speiied herein are intended to provide or a buildable, servieable bridge, apable o saely arrying design loads or a speiied lietime. 358

8 atigue and reep rupture limits may ontrol the design. Provisions related to limit states analyses, general design and loation eatures, loads and load ators, and strutural analysis and evaluation shall be in ompliane with the AASHTO LRFD. 1.5 REFERENCES AASHTO. (2012). AASHTO LRFD Bridge Design Speiiations, 6 th Edition with Interims. Washington DC: Amerian Assoiation o State Highway and Transportation Oiials. Burgueño, R. (1999). System Charaterization and Design o Modular Fiber Reinored Polymer (FRP) Short- and Medium-Span Bridges. (Dotoral dissertation, University o Caliornia, San Diego, 1999). (UMI No ) Davol, A. (1998). Strutural Charaterization o Conrete Filled Fiber Reinored Shells. (Dotoral dissertation, University o Caliornia, San Diego, 1998). Fam, A. (2000). Conrete-Filled Fibre-Reinored Polymer Tubes or Axial and Flexural Strutural Members. (Dotoral dissertation, Univeristy o Manitoba, 2000). Fam, A. & Rizkalla, S. (2001). Coninement Model or Axially Loaded Conrete Conined by Cirular Fiber- Reinored Polymer Tubes. ACI Strutural Journal 98(4), Fam, A. & Rizkalla, S. (2002). Flexural Behavior o Conrete-Filled Fiber-Reinored Polymer Cirular Tubes. Journal o Composites or Constrution. 6(2), Fardis, M. N. and Khalili, H. Conrete Enased in Fibreglass-Reinored Plasti, ACI Strutural Journal, Title No , Nov.-De. 1981, pp Mirmiran, A. & Shahawy, M. (1996) A new onrete-illed hollow FRP omposite olumn. Composites Part B: Engineering. Speial Issue on Inrastruture. Elsevier Siene Ltd., 27B(3-4), Nanni, A., & Bradord, N. (1995) FRP Jaketed Conrete Under Uniaxial Compression. Constrution and Building Materials. 9(2)

9 Setion 2 CONCRETE-FILLED FRP TUBES (CFFTs) 2.1 SCOPE This setion ontains the provisions or the design o onrete-illed FRP tubes (CFFTs) or use as omponents o a bridge struture. 2.2 DEFINITIONS Component - A onstituent part o a struture. Composite Ation - A ondition in whih two or more elements or omponents are made to at together by eliminating relative movements at their interae. Creep - Time-dependent plasti strain in a material subjeted to sustained stress. Creep Rupture - The gradual, time-dependent redution o tensile strength due to permanent loading that leads to a premature ailure o the setion. Dynami Load Allowane - An inrease in the applied stati ore eets to aount or the dynami interation between the bridge and moving vehiles. Speiied Strength o Conrete - The nominal ompressive strength o onrete speiied or the work and assumed or design and analysis o new strutures. Stay-in-Plae Form - A permanent orm or the onrete that remains in plae ater onstrution is inished. 2.3 NOTATION A = eetive onrete area (in 2 ) C E = environmental redution ator d v = eetive shear depth (in) D = average diameter o irular FRP tube (in) D i = inner diameter o irular FRP tube (in) D o = outer diameter o irular FRP tube (in) E = elasti modulus o onrete (ksi) E h = elasti modulus o the tube laminate in the hoop diretion (ksi) E l = elasti modulus o the tube laminate in the longitudinal diretion (ksi) E s = elasti modulus o steel (ksi) 360

10 EI = lexural stiness o onrete-illed FRP tube (kip-in 2 ) = unonined onrete design ompressive strength (ksi) = onined onrete design ompressive strength (ksi) u = design ompressive strength o FRP laminate in longitudinal diretion onsidering redutions or servie environment (ksi) * u = ompressive strength o FRP laminate in longitudinal diretion or produt ertiiation as reported by manuaturers (ksi) e = tensile hoop stress in the tube laminate (ksi) uh = design tensile strength o FRP laminate in hoop diretion onsidering redutions or servie environment (ksi) * uh = tensile strength o FRP laminate in hoop diretion or produt ertiiation as reported by manuaturers (ksi) ul = design tensile strength o FRP laminate in longitudinal diretion onsidering redutions or servie environment (ksi) * ul = tensile strength o FRP laminate in longitudinal diretion or produt ertiiation as reported by manuaturer (ksi) l = maximum oninement pressure (ksi) r = modulus o rupture (ksi) I l = moment o inertia o the FRP tube (in 4 ) I s = moment o inertia o a steel tube (in 4 ) M r = raking moment (kip-in) M n = nominal lexural resistane (kip-in) M nb = nominal lexural resistane orresponding to the balane point (kip-in) M r = atored lexural resistane (kip-in) n = modular ratio = E l /E P e = Euler bukling load (kip) P n = nominal axial ompressive resistane (kip) P nb = nominal axial ompressive resistane orresponding to the balane point (kip) P' n = axial ompressive resistane (kip) P r = atored axial ompressive resistane (kip) S = setion modulus o the extreme iber o the omposite setion where tensile stress is aused by externally applied loads (in 3 ) t = eetive strutural thikness o FRP tube (in) V = nominal shear resistane provided by the onrete (kip) V = nominal shear resistane provided by the FRP shell (kip) V n = nominal shear resistane (kip) V r = atored shear resistane (kip) V s = nominal shear resistane provided by steel reinorement (kip) X = embedment length o a CFFT member into a reinored onrete ooting, pile ap or beam (in) ε u = maximum onined longitudinal ompressive strain (in/in) ε e = tensile strain in the hoop diretion o the FRP tube (in/in) ε u = design ultimate ompressive strain o the FRP laminate in the longitudinal diretion onsidering redutions or servie environment (in/in) ε * u = ultimate ompressive strain o FRP laminate in longitudinal diretion or produt ertiiation as reported by manuaturers (in/in) ε uh = design ultimate tensile strain o the FRP laminate in the hoop diretion onsidering redutions or servie environment (in/in) ε * uh = ultimate tensile strain o FRP laminate in hoop diretion or produt ertiiation as reported by manuaturers (in/in) 361

11 ε ul = design ultimate strain o the FRP laminate in the longitudinal diretion onsidering redutions or servie environment (in/in) ε * ul = ultimate tensile strain o FRP laminate in longitudinal diretion or produt ertiiation as reported by manuaturers (in/in) ε v = hoop strain resulting rom shear (in/in) ρ = reinorement ratio ρ b = reinorement ratio produing balaned strain onditions in bending without axial load φ = resistane ator ψ = FRP system redution ator or lexural resistane 2.4 LIMITATIONS Seismi design is not addressed in this doument. However, where appliable, it shall be onsidered as one o the loading ases. Design provisions in the ollowing setions should not be applied to CFFTs with tubes having ibers in the longitudinal diretion only. These provisions shall not be applied to CFFT members with unonined onrete strength exeeding 10 ksi (70 MPa). C2.4 Seismi design may require providing internal steel reinorement in the viinity o moment onnetions to develop the neessary plasti hinges. Tubes with ibers oriented only in the longitudinal diretion tend to ail prematurely under horizontal shear by splitting in a plane parallel to the ibers (Fam 2000) beore developing their ull lexural strength. Perormane o that type must be veriied by tests. Strength enhanement due to oninement in CFFT ompression members with onrete strength exeeding 10 ksi (70 MPa) has not been experimentally veriied (ACI 440.2R-08). Further experimental evidene show that oninement eetiveness using FRP jakets is redued as the onrete strength inreases (Mandal et al 2005). 2.5 MATERIAL PROPERTIES FRP Tube General The FRP tube shall onorm to the material speiiations reported in Setion 3, and omply with the appliable requirements o Artiles 1.3 and Tensile and Compressive Ultimate C

12 Strengths and Strains The design ultimate tensile strength o the FRP tube material in the longitudinal diretion, ul, and the transverse or hoop diretion, uh, shall be taken as: = C ul = C uh E E * ul * uh ( ) ( ) The design ultimate ompressive strength o the FRP tube material in the longitudinal diretion, u shall be taken as: = C u E * u ( ) The strength values as reported by manuaturers provide a perent probability that the indiated values are exeeded by similar FRP oupons provided that the number o tested speimens omplies with the provisions o Artile The manuaturer should provide a desription o the method used to obtain the reported strength. The material properties provided by the manuaturers are onsidered as initial properties that do not inlude the eets o long term exposure to the environment. Beause long term exposure to various environments may redue the tensile strength and reep rupture and atigue endurane o FRP tubes, the material properties used in all design equations are redued based on type and level o environmental exposure. The design ultimate tensile strain o the FRP tube material in the longitudinal diretion, ε, and the transverse or hoop diretion, ε uh ul, shall be taken as: ε = C ε ul E * ul ( ) ε = C ε uh E * uh ( ) The design ultimate ompressive strain o the FRP tube material in the longitudinal diretion, ε shall be taken as: u ε = C ε u E * u ( ) In Equations through , C E shall be taken as 0.85 or a arbon-based FRP, 0.65 or glass, and 0.75 or aramid. I the bridge is exposed to aggressive environments, C E shall be taken as 0.5 or glass and 0.7 or aramid. The quantities * * * * * ul, uh, u, ul, ε uh ε, and ε * u are the ultimate tensile strengths and strains in the longitudinal and hoop diretions and the ultimate ompressive strength and strain in the longitudinal 363

13 diretion or produt ertiiation as reported by the manuaturer and shall be deined as the average value alulated or a requeny and number o speimens as speiied in Artile minus three times the standard deviation. In hybrid tubes, where dierent types o ibers are used in the longitudinal and transverse or hoop diretions, dierent C E shall be used in the two diretions aording to the type o ibers Modulus o Elastiity The FRP tube material shall be treated as linearly elasti in tension and ompression. The modulus o elastiity in the longitudinal diretion, E l, and the transverse or hoop diretion, E h, shall be alulated as: E l = ε ( ) ul ul E h = ε ( ) uh uh 2.6 LIMIT STATES Servie Limit State Under servies loads, CFFT members shall be analyzed as ully elasti strutures. Cheks to be perormed at servie limit state shall be related to deormations, raking and onrete stresses as speiied in Artiles 2.8.6, and or CFFT lexural members and Artiles , and or CFFT members under lexure and axial ompression. The FRP tube stresses at servie are addressed in Artile The loads to be onsidered in this analysis shall be as deined in Setion 3 o AASHTO LRFD Fatigue and Creep Rupture Limit State The maximum longitudinal tensile stress in the FRP tube under all sustained loads plus atigue loading l,s shall not exeed the ollowing limits: C2.6.2 To prevent reep-rupture o the FRP tube under sustained stress or ailure due to yli stresses and atigue, the longitudinal stress level in the tube under these stress onditions should be limited. Beause 364

14 For arbon-based FRP: 0.55 ul (longitudinal) For glass-based FRP: 0.20 ul (longitudinal) For aramid-based FRP: 0.30 ul (longitudinal) these stress levels will be within the the elasti range o the CFFT member, the stress an be omputed through an elasti analysis o the raked transormed CFFT setion. The loads to be onsidered in this analysis onsist o all permanent loads, and the atigue load as deined in Artile o AASHTO LRFD. The load ators or DC and DW, EV, and EH shall be 1.0, and the load ator or the atigue vehile plus impat shall be Hoop diretion stresses shall be heked or atigue and sustained loads when the FRP tube is relied upon or oninement o the onrete ore and i the onrete ompressive stress level under atigue and sustained loads is higher than 0.65 in aordane with Artile I the axial stress in CFFT members exeeds 0.65, radial raking ours and the FRP tube is loaded in the irumerential diretion. In this ase, reep rupture and atigue should also be heked Strength Limit State General The strength limit states to be onsidered shall be those o strength and stability. Fatored resistane shall be the produt o nominal resistane as determined in aordane with the appliable provisions o Artiles 2.7, 2.8, 2.9, 2.10 and 2.11 unless another limit state is speiially identiied, and the resistane ator as speiied in Artile The loads to be onsidered in this analysis shall be as deined in Setion 3 o AASHTO LRFD Resistane Fators The ratio o the ross-setional area o the FRP tube to the ross-setional area o the onrete ore is deined as C Tension ailure o CFFT lexural and axial-lexural members is typially by rupture o the tube on the 365

15 the reinorement ratio ρ. In CFFT members subjeted to lexure without axial ompression loads, the balaned reinorement ratio ρ b is deined as the reinorement ratio whih results in tensile rupture and ompressive rushing o the FRP tube under longitudinal stresses ourring simultaneously, in aordane with the assumptions in Artile The resistane ator φ or lexure shall be omputed as ollows. φ = 0.55 i ρ ρ b φ = 0.65 i ρ 1. 4ρ b ρ φ = i ρ b ρ 1. 4ρ b ρ b in whih: ( ) 4t ρ b b = D ( ) and the balaned tube thikness t b is: t b α D = 4π ( ) ( 2 θ Sin (2 θ )) ul ( θ in radian) u θ = a os 1 2β α β = ul u + u ε u = ε ε u ε ( ) ( ) ( ) ( ) tension side under longitudinal tensile stresses (i.e. a uniaxial state o stress). Compression ailure o CFFT lexural and axial-lexural members is not by onrete rushing as in onventional reinored onrete members but is triggered primarily by ailure o the tube, whih is immediately ollowed by rushing o onrete as a seondary ailure. For CFFT lexural members it is predominantly governed by ompression ailure o the tube under longitudinal ompressive stresses, where the hoop tensile stresses (i.e. oninement eet is insigniiant). On the other hand, or CFFT axial and axial-lexural members, ompression ailure is governed by ailure o the tube on the ompression side under a bi-axial state o stress involving longitudinal ompressive and hoop tensile (i.e. oninement eet) stresses. The resistane ators proposed here are essentially the same as those used in FRP-reinored onrete strutures governed by FRP rupture or tension ailure and lassi onrete rushing or ompression ailure (AASHTO 2012). As stated above, ompression ailure o CFFT members is dierent. Until urther reliability analysis is arried out and new ators are established, it is reommended to use the urrent ators. In pure bending, without axial loads, there is a unique tube thikness that provides the balaned ondition when the extreme tension and ompression ibers o the FRP tube reah the respetive ultimate longitudinal strengths, simultaneously. Equations to have been established based on an equivalent onrete stress blok with parameters and β. These parameters have the onventionally known deinition and have been established or a large range o onrete ompressive strengths o 3 to 15 ksi and ultimate longitudinal ompressive strain o the FRP tube ranging rom 2 to 10 times the onrete ompressive strain that orresponds to the peak strength. It is to be noted that the onrete ore in CFFT under pure bending is assumed to be represented by an unonined stress-strain urve in ompression, with an extended strain sotening that is limited by the tube ultimate longitudinal ompressive strain. The two onditions used to establish and β are: i) the area under the non-linear stress-strain urve is equal to the retangular stress area, and ii) the loation o the entroid o the area under the nonlinear urve is the 366

16 in whih: ε n = E n 1 ; ( ) n = ; ( ) 0 same as that o the retangular stress distribution. While this tehnique onventionally applies to retangular setions, is adopted here or the irular setion or simpliity. Both AASHTO LRFD (2012) and ACI 318 (2008a) also use the same and β or any ross-setion geometry. E = ( ) where: = the onrete ompressive strength (ksi) ul = the longitudinal ultimate tensile strength o the FRP tube (ksi) u = the longitudinal ultimate ompressive strength o the FRP tube (ksi) The ollowing limits shall apply: ( ) ul u ( ) ε u 2 10 ε ( 3ksi 15ksi) ; ( ) ( ) In CFFT members subjeted to ombined bending and axial loads and governed by ailure on the tension side by rupture o the tube under longitudinal stresses, the resistane ator φ shall be taken as

17 In CFFT members subjeted to ombined bending and axial loads and governed by ailure on the ompression side and when ρ is greater than 1.4 ρ, the resistane ator φ shall be taken as b In CFFT members subjeted to pure axial loads, the resistane ator φ shall be taken as Members an be onsidered to be subjeted to pure axial load i the eentriity is less than 0.1D. Resistane ator φ or shear shall be taken as Stability The struture onsisting o CFFT members as a whole and its omponents shall be designed to resist sliding, overturning, and uplit. Eet o eentriity o loads shall be onsidered in the analysis and design Extreme Event Limit State The struture onsisting o CFFT members as a whole and its omponents shall be proportioned to resist ollapse due to extreme events, speiied in Table o AASHTO LRFD, as may be appropriate to the site and appliation. 2.7 DESIGN CONSIDERATIONS General Components and onnetions shall be designed to resist load ombinations as speiied in Setion 3 o AASHTO LRFD, at all stages during the lie o the struture, inluding those during onstrution. Load ators shall be as speiied in Setion 3 o AASHTO LRFD, with additional permanent load ators as deined in Artile or the atigue and reep rupture limit state. As speiied in Setion 4 o AASHTO LRFD, equilibrium and strain ompatibility shall be maintained 368

18 in the analysis Eet o Imposed Deormation The eet o imposed deormations due to shrinkage, temperature hange, reep, and vertial and/or horizontal movements o supports shall be investigated. 2.8 DESIGN FOR FLEXURE WITH NO AXIAL COMPRESSION General The CFFT shall be detailed, abriated and onstruted suh that ull omposite ation is ahieved between the tube and onrete. The onrete shall be suiiently onsolidated to ahieve the levels o strength, stiness and dutility assumed in the design. C2.8.1 Consolidation o onrete within the FRP tube may be ahieved by internal or external vibration, or through the use o sel-onsolidating onrete (SCC). Seletion o a onsolidation method should onsider stability o the onrete and, i mehanial vibration is perormed, the ability o the FRP tube to withstand vibration-indued deormations and stresses without loss o strutural integrity Assumptions General The ollowing assumptions may be used to determine the lexural resistane o CFFT s at the limit states indiated: Servie and Fatigue and Creep Rupture Limit States Suiient bond exists between onrete and the FRP tube to produe omposite ation. The longitudinal strains in the onrete vary linearly over the depth o the member and are proportional to the distane rom the neutral axis, exept in omponents or regions o omponents or whih onventional strength o materials is inappropriate. 369

19 The tensile strength o the onrete is negleted. The modular ratio, n = E l /E is rounded to the nearest integer; or permanent loads, a modular ratio o 2n shall apply Strength and Extreme Event Limit States Suiient bond exists between onrete and the FRP tube to produe omposite ation. The longitudinal strains in the onrete vary linearly over the depth o the member and are proportional to the distane rom the neutral axis, exept in omponents or regions o omponents or whih onventional strength o materials is inappropriate. The tensile strength o the onrete is negleted. The FRP tube is sturdy enough to ontribute longitudinally in ompression. Conrete is partially onined when irular tubes are used. The FRP tube ontrols ailure, whether in tension or ompression. As suh, the onrete longitudinal ompressive strain at ailure may exeed Tension ailure is deined by tensile rupture o the FRP tube under uniaxial longitudinal stresses, while ompression ailure is deined by rushing o the FRP tube under uniaxial longitudinal stresses. Coninement in lexure is not signiiant enough to weaken the tube under longitudinal ompression or longitudinal tension. The onrete stress-strain relationship proposed by Popovis (1973), with an extended strain sotening beyond the usual ultimate ompressive strain o 0.003, may be used in alulating the ultimate moment apaity based on equilibrium and strain ompatibility in Artile The stress-strain relationships o the FRP tube in tension and ompression shall be taken as linear elasti as speiied in Artile Minimum Longitudinal Tension Reinorement At any setion o a lexural CFFT omponent, the FRP reinorement shall be adequate to develop a atored 370

20 lexural resistane M r equal to the lesser o 1.2M r or 1.33 times the atored moment required by the appliable strength load ombinations speiied in Artile o AASHTO LRFD, where: M = S r r ( ) In whih: r = ' 0.37 or normal-weight onrete where: S = the setion modulus o the extreme iber o the omposite setion where tensile stress is aused by externally applied loads (in 3 ) Minimum Reinorement in the Transverse or Hoop Diretion At any ross-setion, the FRP tube shall provide suiient oninement to the onrete ore to justiy the use o the onrete stress-strain relationship employed or the strength analysis. In addition, the minimum transverse shear reinorement requirement o Artile shall be satisied Fatored Flexural Resistane The atored lexural resistane o a setion M r shall be taken as: M = φ r M n ( ) where: M n = the nominal moment apaity determined either by the general method in Artile or the simpliied method in Artile General Method 371

21 The nominal moment apaity M n shall be alulated based on a rigorous ross-setional analysis that satisies equilibrium and strain ompatibility, and utilizes appropriate material onstitutive relationships or the onrete and FRP, and ailure modes, satisying the provisions o Artile Simpliied Method For tension ailure-ontrolled irular CFFT members, and in lieu o the rigorous equilibrium and strain ompatibility approah, M n may be alulated as ollows: M n D 3 o 4t 100 Do ul = ( ) C Equation is an empirial ormula developed by best itting o experimental data and inite element model results o a parametri study. Both the experimental and numerial data overed a wide range o CFFT geometri and mehanial properties (Fam and Son, 2008). where: t = the strutural wall thikness o the tube (in) D o = the outer diameter (in) ul = the design tensile strength o FRP laminate in the longitudinal diretion (ksi) = the onrete unonined ompressive strength (ksi) Deormation Control o deletions shall be onsidered in aordane with AASHTO LRFD Control o Craking Crak width shall be ontrolled by limiting the tensile stress level in the FRP tube in aordane with Artile C2.8.7 Crak width is indiretly limited by ontrolling the stress level in the FRP tube under servie load or reep rupture and atigue ailure. Also, raking in CFFT members is invisible beause o the tube and does not pose aestheti or durability onerns Stress Limit or Conrete C

22 Compression stresses in the onrete shall be investigated at the Servie Limit State Load Combination I speiied in Table o AASHTO LRFD. The stress limitation o 0.45 shall apply to onrete in ompression. This provision is to ontrol the eets o onrete reep, inluding exessive deormation with time. Note that the unonined onrete strength is used, given the insigniiant oninement eets in CFFTs under lexure. 2.9 DESIGN FOR AXIAL COMPRESSION General Design o CFFT members with FRP tubes having suiient strength and stiness in the hoop diretion, in aordane with Artile 2.9.4, may inlude the eet o oninement that leads to inreasing the onrete ore ompressive strength rom to Assumptions The ollowing assumptions may be used to determine axial resistane o CFFT s: Axial load is applied over the entire ross-setion o the onrete ore and FRP tube The onrete ore and the FRP tube are ully bonded. As suh, the axial shortening is equal in both the tube and onrete. The FRP tube is sturdy enough to ontribute longitudinally in ompression. The tube ats as a bi-axially loaded membrane subjeted to hoop tensile and longitudinal ompressive stresses. The longitudinal stress weakens the tube in the hoop diretion. The unonined onrete ompressive strength does not exeed 10 ksi. Failure, and hene the ultimate axial load, our when the FRP tube ratures under the bi-axial state o stress Fatored Axial Compressive Resistane The atored axial ompressive resistane o a nonprestressed setion P r shall be taken as: C2.9.3 Several models that simulate the stress-strain behavior o FRP-onined onrete ompression members are available in the literature, inluding ully empirial models suh as Samaan et al (1998) and Lam and Teng (2003) or semi empirial models with some 373

23 P = φ r P n in whih: P n is the nominal axial resistane determined as: P = n ' 0.85P n ( ) ( ) ' P n is the axial ompressive resistane and is determined or irular CFFT members rom: rational mehanis basis suh as Spoelstra and Monti (1999) and Fam and Rizkalla (2001). The stress-strain model developed by Lam and Teng (2003) has been adopted in the ACI440.2R-08 design guide and is reommended to be used or CFFT members in this doument due to its simpliity ombined with its reasonable auray. The FRP tube shares some o the axial loading apaity in the longitudinal diretion, hene, the seond term in Eq P ' n π D 2 = i π Dt E l ε u ( ) in whih: is the onrete onined strength alulated as: = +3.3ψ ( ) l l is the maximum oninement pressure alulated as: l = min( l1, l2) ( ) l 2E h tε D e 1 = ( ) l 2 = ' ε 12 ' ε ε ' e 0.45 ( ) where: D i = the inner diameter o the FRP tube (in) D = the average diameter o the FRP tube (in) 374

24 E l = the design longitudinal modulus o the tube (ksi) ψ = a redution ator equal to 0.95 ε e = the eetive hoop strain level in the tube at the ultimate ompressive apaity o the CFFT. ε e shall be taken as 0.55 ε uh ε uh = the design ultimate tensile strain o the tube in the hoop diretion. E h = the design modulus o the tube in the hoop diretion. Where the onining pressure, l is governed by the limiting value l2 obtained using ( ), shall be alulated as: The eetive hoop strain level in the tube at ultimate is redued rom the ultimate value by a ator taken here as This is attributed to several ators that may inlude (a) the multiaxial state o stress in the tube, in whih the longitudinal ompressive stresses weaken the tube in the irumerential diretion in aordane to Tsai-Wu ailure riteria (Daniel and Ishai, 1994) and (b) stress onentration regions aused by raking o onrete as it dilates. ( ) = E 2 in whih: E ' * 2 = εu ( ) * = + 3.3ψ l 1 ( ) In presene o a shear ore ating on the setion, ε e shall be replaed by ( ) e ε v ε as per setion In the presene o shear, the tube resists additional irumerential tensile stresses. As suh, the ull tensile apaity may not be available or oninement. The maximum longitudinal ompressive strain ε u shall be determined as: 0.45 ε l e ε u = ε ( ) ε in whih: n ε = ( ) E n 1 375

25 n = ( ) 2.5 E ( ) = Minimum Reinorement in the Hoop Diretion The FRP tube shall have suiient thikness and stiness to produe a oninement pressure l alulated aording to equation o not less than 0.08 times the unonined onrete strength. C2.9.4 Based on the tests by Lam and Teng (2003), the ratio o oninement pressure to unonined onrete strength should not be less than This is the minimum level o oninement required to assure a nondesending seond branh in the stress-strain urve Stress Limit or Conrete At servie limit states, the axial ompressive stress in onrete shall not exeed C2.9.5 To ensure that radial raking o onrete will not our under servie loads, the transverse strain in onrete shall remain below its raking strain at servie load levels. This orresponds to limiting the ompressive stress in the onrete to 0.65 (ACI 440.2R-08). By maintaining the speiied stress in the onrete at servie, the stress in the FRP tube will be relatively low. Servie load tensile stress in the tube should never exeed the reep-rupture stress limit DESIGN FOR COMBINED FLEXURE AND AXIAL COMPRESSION General The CFFT shall be detailed, abriated and onstruted suh that ull omposite ation is ahieved between the tube and onrete. The onrete shall be suiiently onsolidated to ahieve the levels o strength, stiness and dutility assumed in the design. Flexure may be indued by an eentri axial load and/or by transverse loading. Design o CFFT members with FRP tubes having suiient strength and stiness in the hoop diretion, in aordane with Artile 2.9.4, may inlude the eet o oninement that may lead to inreasing the onrete ore ompressive strength rom to, depending on the C Fam et al (2003) have demonstrated experimentally and analytially that the eet o onrete oninement is redued as the eentriity o axial load (or the ratio o moment to axial load) is inreased. The extreme limits are ull oninement at onentri loading and partial oninement at pure bending, where it is hypothesized that the peak onrete strength remains at the unonined level o but the material experienes an extended strain sotening beyond the typial rushing strain o In this ase ailure in ompression is governed by rushing o the tube under longitudinal ompressive stresses. 376

26 eentriity e, where e is the ratio o the applied moment M u, inluding slenderness eet, to the ompression load P u Assumptions The ollowing assumptions may be used in determining the resistane o CFFT s to ombined axial and lexural loading: Suiient bond exists between onrete and the FRP tube to produe omposite ation. The longitudinal strains in the onrete vary linearly over the depth o the member and are proportional to the distane rom the neutral axis, exept in omponents or regions o omponents or whih onventional strength o materials is inappropriate. The tensile strength o the onrete is negleted. The FRP tube has suiient strength and stiness to ontribute longitudinally in ompression. Depending on the eentriity, onrete experienes dierent levels o oninement when irular tubes are used. The FRP tube ontrols ailure, whether in tension or ompression. As suh, the onrete longitudinal ompressive strain at ailure may exeed The tube ats as a bi-axially loaded membrane on the ompression side subjeted to hoop tensile and longitudinal ompressive stresses. The longitudinal stress weakens the tube in the hoop diretion. Tension ailure is deined by tensile rupture o the FRP tube under uniaxial longitudinal stresses, while ompression ailure ours when the FRP tube ratures under the bi-axial state o stress. In the general method in Artile , the onrete stress-strain relationship based on the variable oninement model o Fam et al (2003) shall be used in alulating the ultimate moment and axial load based on equilibrium and strain ompatibility. For eah eentriity, a dierent stress-strain urve with a dierent ultimate longitudinal ompressive strain is used. In the simpliied method in Artile , a single onrete stress-strain relationship based on 377

27 ull oninement under onentri ompression shall be used or all ranges o eentriity between onentri ompression and the balaned point. The model by Lam and Teng (2003) in Artile may be used. The stress-strain relationships o the FRP tube in tension and ompression shall be taken as linear elasti as speiied in Artile Fatored Resistane The designer shall use one o the two methods stated below to establish atored resistane under ombined bending and axial ompression. C Either the rigorous method o Artile or the more onservative simpliied method o Artile may be used to determine the interation diagram or ombined ompression and bending General Method The nominal moment and axial load apaity (φ P n, φ M n ) shall be alulated based on a rigorous ross-setional analysis that satisies equilibrium and strain ompatibility, and utilizes appropriate material onstitutive relationships or the onrete and FRP, and ailure modes, satisying the provisions o Artile Simpliied Method In lieu o the general method in Artile , the nominal moment and axial load (φ P n, φ M n ) interation resistane envelope may onservatively be simpliied as a bi-linear urve between the pure axial load point (φ P n, 0), the balaned point(φ P nb, φ M nb ) and the pure bending point (0, φ M n ). Where the equations o this setion alulate a balaned axial load less than 0 (i.e. axial tension) the interation diagram shall be approximated using a straight line between the pure axial load point and pure bending point. C This simpliied method is approximate and is based on an equivalent retangular approximation o the onined onrete stress distribution. The pure axial ompression resistane P n shall be alulated in aordane with Artile The pure lexural resistane M n shall be alulated in aordane with Artile The balaned point resistane shall be alulated as ollows: 378

28 P nb π Dt = E lε 2 u 2 Di (2 D) + α1 (2θ a Sin2θ a ) 8 ( ) M nb = D t 8 D 12 π 3 3 i E lε u + α Sin 3 1 θ a ( ) in whih: t ε u = ( Do ) ( ) 2 ε u + ε ul 2β1 θa = ArCos( 1 ) ( ) D i where: α = β = ε u is alulated using equation Evaluation o Slenderness Eets Evaluation o member slenderness and moment magniiation shall ollow the provisions o the AASHTO LRFD as appliable to reinored onrete members. The value o EI or use in determining P e shall be alulated using E l and I l in plae o E s and I s, respetively when applying provisions o the AASHTO LRFD, where I l is the moment o inertia o the ross-setion o the FRP tube Minimum Reinorement At any ross-setion o the CFFT member, the FRP tube shall provide suiient oninement to the onrete ore to justiy the use o the onrete stress-strain relationship employed or the strength analysis. The 379

29 provisions o artile shall apply. Also, the minimum transverse shear reinorement requirement o Artile shall be satisied. At any ross-setion o the CFFT member, the FRP tube shall be adequate to develop a atored lexural resistane φ M n equal to the lesser o 1.2M r or 1.33 times the atored moment required by the appliable strength load ombinations speiied in the AASHTO LRFD. M r shall be alulated taking into onsideration the presene o the atored axial load φ P n Deormation Control o deletions shall be onsidered in aordane with AASHTO LRFD Control o Craking Crak width is indiretly ontrolled by limiting the tensile stress level in the FRP tube in aordane with Artile C Craking in CFFT members is not visible and does not ause aestheti or durability onerns Stress Limit or Conrete Compression stresses in the onrete shall be investigated at the Servie Limit State Load Combination I speiied in Table o AASHTO LRFD. The stress limitation o 0.45 shall apply to CFFT members governed by tension ailure and 0.65 shall apply to CFFT members governed by ompression ailure in aordane with Artile DESIGN FOR SHEAR EFFECTS General The ritial setion or shear near a support in a CFFT member shall be determined in aordane with the provisions o AASHTO LRFD or reinored onrete C In CFFT members, longitudinal and transverse (shear) reinorement are integral and oupled in the orm o the same FRP tube. As suh, ombined shear 380

30 members. In lieu o the methods speiied herein, the resistane o members in shear may be determined by satisying the onditions o equilibrium and ompatibility o strains and by using experimentally veriied stress-strain relationships or the transverse reinorement provided by the FRP tube and or diagonally raked onrete. and lexure or shear and axial loading plaes the tube in a state o bi-axial stresses Nominal Shear Resistane The atored shear resistane o a setion V r shall be taken as: V = φ r V n ( ) The nominal shear resistane, V n, shall be determined as: V = V + V + V n s ( ) When no longitudinal steel reinorement is used in the CFFT member, the onrete shear strength, V (kip), shall be taken as: C Compared with a steel-reinored setion, with equal areas o longitudinal reinorement, a ross setion reinored with FRP lexural reinorement ater raking has a smaller depth to the neutral axis beause o the lower modulus o FRP reinorement. As a result, the shear resistane provided by both aggregate interlok and ompressed onrete is redued. Furthermore, the ontribution o the FRP lexural reinorement by dowel ation is less than steel reinorement beause o their lower strength and stiness in the transverse diretion (ACI 440.1R-06). In ase o CFFTs, the shear resistane o the FRP tube is simpliied to a irumerential tensile stress. V = ' A ( ) where: A = eetive onrete area, whih is the area o the ompression zone o the raked transormed setion under servie axial load and moment ating on the setion o interest based on the assumption o linearly elasti material response. In lieu o the detailed setional analysis, and assuming no axial ompression ore is ating on the setion, A may be alulated based on a neutral axis depth o 0.3D o (in 2 ) ' = unonined onrete ompressive strength (ksi) I internal longitudinal steel reinorement is used, V, 381

31 shall be taken as deined in AASHTO LRFD. The FRP tube shear strength, V, shall be taken as: V = 2td v e ( ) where: t = the strutural wall thikness o the FRP tube (in) d v = the eetive depth, taken as 0.8 D o (in) The tensile hoop stress in the FRP tube, e, shall be limited to: e = E h where: ( ) E h = the elasti modulus o the tube laminate in the hoop diretion (ksi) The ombined eets o shear and oninement on the hoop strain level in the FRP tube shall be onsidered in heking the ultimate strain in the tube. This may be ahieved by deduting the hoop strain due to shear ore and limiting the total hoop strain to to ensure shear integrity o the onined onrete ore, in both the general and simpliied methods. In the simpliied method, this may be ahieved by substituting the eetive hoop strain ε in Eq and by ( ) e ε where the e ε v hoop strain resulting rom shear at the same setion is alulated as ollows: The hoop tensile strain in the FRP tube under shear is limited to to ontrol shear rak width and maintain shear integrity in the onrete. The eetive Young s modulus o the tube laminate in the irumerential diretion, E h, is used along with the total strutural wall thikness t o the tube to determine its shear ontribution. Alternatively, in the speial ase o [0/90] ross-ply laminates, the thikness and modulus o the ombined [90] hoop layers only ould be used. The hoop tensile strain in the FRP tube due to shear redues the apaity o the tube or oninement under axial ompression loads. This must be aounted or. = V V u ε v ( ) 2td v E h subjet to the limitation: ( ε e ε ) v ( ) where: 382

32 V u = the atored shear ore ating on the setion o interest (kip) I axial ompression load is applied with shear, the strain in Eq shall be redued by the amount o hoop strain in the tube due to oninement under the applied atored axial ompression load I internal transverse steel reinorement is used, V s, shall be taken as deined in AASHTO LRFD Minimum Shear Reinorement V Transverse shear reinorement is required where: 0.5φ u V ( ) The minimum tube thikness t min to satisy minimum shear reinorement shall be taken as: C The minimum requirements or transverse reinorement area is to prevent or restrain shear ailure in members where the sudden ormation o raks an lead to exessive distress (joint ACI-ASCE Committee 426 (1974)). In the ase o CFFT, the minimum reinorement is releted in terms o a minimum thikness o the FRP tube t ' = D min o uh ( ) where: uh = the design ultimate tensile strength o the tube in the hoop diretion (ksi), alulated rom Equation D o = the outer diameter o the FRP tube (in) 2.12 CONNECTIONS CFFT members subjeted to lexure, shear and/or axial loads may be onneted to other reinored onrete (RC) strutural omponents o adequate size suh as ootings, pile aps or beams by diret embedment o the CFFT into the RC member without the use o additional reinorement. C2.12 CFFT members seured into onrete ootings, pile aps or ap beams o adequate size an develop their ull lexural apaity beore a premature bond-slip ailure ours, provided that the embedment length is suiient. Equations and are based on the work by Sadeghian and Fam (2010), inluding a 1.5 saety ator, where the resistane is provided by a 383