Student (Ph.D.), 2 Professor, Department of Applied Mechanics, S.V.N.I.T., Surat , Gujarat, India.

Transcription

1 Amerian International Journal o Researh in Siene, Tehnology, Engineering & Mathematis Available online at ISSN (Print): , ISSN (Online): , ISSN (CD-ROM): AIJRSTEM is a reereed, indexed, peer-reviewed, multidisiplinary and open aess journal published by International Assoiation o Sientii Innovation and Researh (IASIR), USA (An Assoiation Uniying the Sienes, Engineering, and Applied Researh) A Comparative Study o the Flexural Beam Design with Externally Bonded FRP Material Using ACI 440 2r-08, ISIS Canada And FIB-14 Bulletin Mr. Aditya N.Contrator 1, Dr. S.A. Vasanwala 2. 1 Student (Ph.D.), 2 Proessor, Department o Applied Mehanis, S.V.N.I.T., Surat , Gujarat, India. Abstrat: To enhane the quantitative load arrying apaity o strutural elements, externally bonded ibre reinored polymer (FRP) omposite materials have suessully been applied to reinored onrete beam elements. The guidelines or the proposed designing methods suh as ACI 440 2R-08, ISIS CANADA and FIB- 14or an externally bonded FRP material are beam elements. These methods are based on approximately the same philosophy. Taking only shear rak eet into onsideration, ib Bulletin 14 was the irst to publish guidelines or externally bonded FRP reinorement or RC strutures. Shear raks in onrete elements are inlined and may result in debonding. In ISIS ode, the design strain is not limited up to debonding ailure and existing substrate strain is not deduted or eetive strain o iber. The strength redution ators are also dierent than ACI method to ind out the ompressive strength o beam elements. Thereore, an eort has been made in hand work to ompare the design steps and resisting moment o FRP materials on beam elements by all the three methods. The lexural apaity in guidelines omes rom three parts: onrete, steel and FRP. However, detail o eah ode is dierent rom one another. Keywords: FRP omposite material, Flexural, Substrate Strain, ACI 440 2R-08, ISIS, FIB -14, debonding ailure, shear raks I. Introdution Conrete is one o the most ommon building materials and is used or Reinored Conrete (RC) strutures. Typially, onrete strutures are very durable, but need to be strengthened with time. The reasons may be raking due to environmental eets, new building odes or damage resulting rom earthquakes. Though onrete an withstand ompressive loads very well, it is sensitive to tensile ores. Thereore, onrete strutures are typially reinored by asting steel bars in areas where tension an arise. This annot be done aterwards, and one strengthening method, is thereore to glue reinorement on the exterior o the struture in the areas exposed to tension, inreasing both the strength and stiness o the beam elements. Fibre omposite an be used in reinoring onrete strutures externally. Fibre omposite materials have several advantages like low density, ormability, ease o abriation and bonding, orrosion resistane, light weight. They an be easily installed and are easy to ut to length on site. Thereore, ibre omposite as external reinorement or onrete strutures has beome very attrative and popular around the world in the ield o retroitting design. To assure good bond between FRP omposite material and onrete surae, it must be leaned or sandblasted down to aggregate. Then omposite materials an be made rom a variety o resins/glue and ibres depending upon desired physial, mehanial properties and eonomi onsideration. (Malek and Saadatmanesh 1996). I FRP is loaded in ibre diretion, then FRP will generally behave linearly elastially to ailure. I one study the behaviour o RC beams strengthened with FRP laminations then dierent modes o ailure have been reported by (Saadatmanesh & Ehsani in 1991). Rupture o the plate or ompression o onrete ontrols the strength o the beam. At the end o the beam i the beam ails loally then it may lead to premature ailure o the strengthened beam. The main reasons or the ailure are the lexural raks and shear and normal stress onentration at the ut-o point. There are dierent types o design steps laimed by dierent ountries to ind out the lexural strength having same philosophy. To ompare and to ind the inal output dierent to that method some guidelines are not mentioned or avoided. This doument mentions the steps & the methods to ompare the lexural elements i.e. ACI 440 2R-08, ISIS and FIB-14. II. ACI Method A. Environment Redution Fator (CE ) Environmental onditions aet the ibers and resins o various types o FRP system. Environmental ators namely alkalinity, salt water, high humidity and reeze-thaw yle are responsible or degrading FRP system.tensile strength, ultimate tensile strength & Elasti modulus are the mehanial properties. AIJRSTEM ; 2016, AIJRSTEM All Rights Reserved Page 162

2 Sr. No. Table 1: Environment Redution Fator For Various FRP System And Exposure Condition. Exposure Conditions Fiber Type Environmental redution ator CE 1. Interior exposure Carbon 0.95 Glass 0.75 Aramid Exterior exposure (Bridges, piers and unenlosed parking garages 3. Aggressive environment (hemial plants and wastewater treatment plant) Carbon 0.85 Glass 0.85 Aramid 0.65 Carbon 0.85 Glass 0.50 Aramid 0.70 B. Strength Redution Fator To redue the dutility o original member, externally bonded FRP reinorement to strength the lexural is used. Loss o dutility an be avoided in some ases. But the setions experiening signiiant loss o dutility should not be overlooked. The level o strain in steel whih is at ultimate limit state should be heked in order to maintain a signiiant degree o dutility. To ahieve an appropriate dutility or reinored onrete members having nonprestressed steel reinorements, the strain in the steel at the point o onrete rushing o ailure o the FRP should inlude delamination or debonding values o at least or t 0.25( ) t sy 0.65 or sy t sy 0.65 or t sy Where in above equation Ɛ t is the net tensile strain in extreme tension steel at nominal strength. So, ɸ = 0.9 or dutile & ɸ =0.65 or brittle setion, where the steel does not yield. An additional strength redution ator or FRP ψ is applied to the lexural strength ontribution o the FRP reinorement. The reommended value o ψ =0.85. C. Failure Modes The potential lexural ailure modes or externally strengthened reinored onrete lexural members are as ollows:- 1. Conrete rushing beore yielding o the reinoring steel 2. Steel yielding ollowed by onrete rushing. 3. Steel yielding ollowed by FRP rupture. 4. Debonding o the FRP reinorement at the FRP/onrete interae. D. Design Eetive Strain Cover delamination o FRP debonding an our i the ores in the FRP annot be sustained by the Substrate; suh behaviour is known as debonding. A ailure ontrolled by FRP debonding may govern i it is away rom the setion where externally bonded FRP laminates. To avoid an intermediate rak-indued debonding ailure mode, the eetive strain in FRP reinorement should be limited toɛ d, as per SIunits is d ' nt E Fig. 1. Internal stress and strain distribution o member under lexure by ultimate limit state as per ACI method b u a d h s1 rp A rp AIJRSTEM ; 2016, AIJRSTEM All Rights Reserved Page 163

3 E. Existing Substrate Strain It is applied at the tension side o the beam at the time o laminating. There is some strain existing due to sel weight and any pre-stressing ores and other load dead load, the substrate to whih the FRP is applied will be strained. These strains should be taken into aount as initial strains and should be removed rom the strain in the FRP. The initial strain level on the bonded substrate; Ɛ bi, an be examined rom an elasti analysis. The elasti analysis o the existing member should be based on raked setion properties. Where, M DL= moment due to dead load on the beam. I r= raked moment o inertia. E = Modulus o elastiity o onrete. F. Servieability The stress in the steel reinorement under servie load should be limited to 80% o the yield strength, s,s= 0.8 y And the stress in onrete should be,s= 0.8 III. ISIS Method A. Environment Redution Fator The strength redution ators are high ompared to ACI method and so it is mostly ompensated. Table 2: Strength Redution Fator Material redution ator For building For bridges ϕ Φ s ϕ rp arbon ϕ rp glass Generally the ɸ rp arbon = 0.75 and ɸ rp glass= 0.5 is onsidered or the alulation. B. Failure Modes Failure modes are same as given in ACI method. An assumption is to be made and the ailure mode should be heked as it is not lear regarding whih type o ailure it will be. I the assumption results inorret then a dierent ailure mode is assumed and the analysis is repeated. In this method it is assumed that the ourth ailure mode FRP debonding will not our and an be ignored (in pratie this assumption is assured through the use o speialized anhorage tehnique). C. Design o Flexural Beam By using the amiliar onept o strain ompatibility, design o lexural element an be arried out, the strain and stress distribution over the ross setion at ailure an be desribed as shown in igure below. Now the equilibrium o internal ores required are the three stress resultants (onrete in ompression, steel in tension T s, and FRP in tension T rp) sum to zero. C = T s+ T rp The stress resultant an be determined as C= Φ α 1 β 1b Fig.2. ISIS assumed stress blok b ' Neutral axis d h d- h- e =E e e =E e Fig. 3. Stress-strain blok at ultimate ailure by onrete rushing AIJRSTEM ; 2016, AIJRSTEM All Rights Reserved Page 164

4 ' Neutral axis d- h- e =E e T s= ϕ s A s s with s y T rp=ϕ rp A rp E rp ε rp with ε rp ε rpu And the inal lexure moment is alulated by M r = T s (d-(β 1 )/2) +T rp (h-(β 1 )/2) IV. FIB method A. Failure modes In this method ailure modes an be divided into two setions :- 1) unless the onrete reahes rushing in ompression or FRP ails in tension, the ull omposite ation o onrete and FRP will be maintained. 2) Composite ation will be lost beore setions Fig.4.FIB Stress Blok N s2 N.A. d A 2 s2 x e N d h d 1 Table 3: Comparison o Flexural Design or Beam Step No. ACI method ISIS method FIB-14 Method Step 1 u = ultimate tensile strength Step 2 Step 3 ε u = ultimate breaking or rupture strain E = Modulus o elastiity o FRP Design material properties (take ɛ = 0.95 or interior exposure) u = ε u ε u = ε ε u Multiply above terms with environmental redution ator. Preliminary alulationsuh as area o steel reinorement and area o ibre laminate. u = ultimate tensile strength ε u = ultimate breaking or rupture strain E = Modulus o elastiity o FRP Environment redution ator not inluded in ISIS method. Preliminary alulation Stress blok ator β 1 = A = n t w 1 = E = 5700 ' E = Modulus o elastiity o FRP Environment redution ator not inluded in FIB method. Preliminary alulation A= n t b AIJRSTEM ; 2016, AIJRSTEM All Rights Reserved Page 165

5 Step 4 Existing substrate strain The existing state o strain is alulated assuming the beam is raked and only loads ating on the beam at the time o the FRP installation are dead loads k= Step 5 ε bi = M DL (h kd) I r E Determine the design strain This design strain is alulated to prevent against debonding ailure ε d = ε n t E u Existing substrate strain this is assumed as zero in ISIS method beause the variation due to existing substrate strain is very less Determine the design strain In ISIS method debonding ailure mode is not aounted beause by using speial anhorage system it an be prevented. Initial strains at extreme ibres Compression ɛ o= M o x o / E I o Tension ɛo = ɛ oh - x 0 / x 0 ɛ s2 = ɛ u ((X-d 2)/X) Mo = moment during strengthening Io = moment o inertia o the raked setion Determination o ailure model 0.85 Ѱ db x + A s2e sɛ s2 A s1 yd+ A E ɛ I this ondition satisy then ollow step 6, This should be less than rupture strain to ontrol the debonding ailure Step 6 Eetive strain in FRP Find neutral axis depth As per ore equilibrium Step 7 Step 8 ε e = ( h ) - ε i ε d 0.9 ε u Calulate the stress level in the reinoring steel and FRP ε s = (ε e + ε bi )( d h ) Calulate steel level in reinoring & FRP s = E s ε s y e = E ε e C = T s + T rp the stress resultant an be determined as C = α 1 β 1 b T s = s A s y With s y T rp = rp A rp E rp ε rp With ε Eetive strain in FRP rp ε rpu This means that strain in the ompression ibre o the ross-setion is the assumed ailure strain or onrete in ompression. One neutral axis depth is known rom strain ompatibility strain is hek out ε u = should be less than rupture strain ε rpu I above ondition satisy than go to step 7 I above ondition not satisy than go to step 8 Fatored moment o resistane an be obtained by ε rp = ε u ( h ) > ε rpu M r = s A s y (d β 1 ) + 2 To avoid rp sudden A rp Eand rp brittle ε rp (h ailure β 1 o ) 2 the externally strengthenedmember, we ensure that the internal steel has yielded ε rp ε s > ε y to seure dutil d ε s = ε u ( ) > ε y And i this not satisy than redue the amount o FRP laminate and regulate until steel yielded in inal design Again assume that the ailure ours by tensile ailure o FRP, ε rp = ε rpu this means that and the strain in onrete in ompression is less than ε u = Where, C = T s + T rp I this ondition not satisy than go to step no 7 Failure FRP rupture ɛ= ɛd,ɛ, ɛs2,ɛs1 Stress blok oeiients Ѱ = Ѱ(ɛ), δ = (δ ) φ = δ G = 1000 ε ( ε ) or ε ε ε { or 4 ( ε ) ε Failure - onrete rushing ɛ= ɛu, ɛ, ɛs2, ɛs1 Stress blok oeiient Ѱ = 0.8, δg= 0.4 The neutral axis depth or ε ε (3000 ε 4) ε (3000 ε 2 ) { or ε Ѱ b x d+ A s2 σ s2 As 1 yd- A σ = 0 Step 9 Calulate the internal ore resultant and hek equilibrium 1 = 3ε 2 ε ε 3β 1 ε 2 β 1 = 4ε ε 6ε 2ε T s = s A s y C = 1 β 1 b T rp = rp A rp ε rp E rp Veriy that the strain in extreme ompression ibre is than ε = ε rpu h < ε u Calulate atored moment o resistane o setion using ε rp = ε rpu M r = s y A s (d β 1 2 ) + Flexural apaity ater strengthening M Rd = A s1 yd (d δg X) + A E ɛ (h-δg X) +A s2 E s ɛ s2 (δg X - d 2) AIJRSTEM ; 2016, AIJRSTEM All Rights Reserved Page 166 rp E rp A rp ε rp (h β 1 2 )

6 Step10 Where, ε = 1.5 Fore equilibrium is veriied E by heking the initial estimate o with = A s s+ A e Calulate moment 1 o βresistane 1 b A s s (d β 1 MN = [ 2 ) where, + φ A (d β ] 1 φ 2 ) = 0.85 V. Design Data The reinored onrete beam as shown in Figure no.4 is singly reinored and is strengthened in lexure with externally bonded arbon FRP on its tension ae or bottom o a beam. Beam dimension and material properties are given below. Calulate the atored moment apaity o the beam. Conrete strength, =30 MPa Internal steel reinorement = 4 x 12 mm bars Area o steel, A s=453 mm 2 Yield strength o steel, y=415 MPa Modulus o Elastiity o steel, E s=200 GPa Carbon FRP properties A rp=a = 120 mm 2,Ɛ u = 1.55% = 186 GPa Length o beam = 5 m Working dead load = 16 kn/m. Figure 4: Beam Bounded With FRP Laminates 230mm 375mm 400mm 4-12mm bar 120 VI. Results For dierent grade o onrete ( ) and remaining data are same onsider or omparison o lexural strength o using FRP laminate. Table-5 Sr. No. Conrete strength (in N/mm 2.) Variation In Flexural Moment In kn-m. ISIS method (Moment o resistane) ACI method (Negleting existing substrate strain) (Moment o resistane) FIB method (Flexural apaity ater strengthening) VII. Conlusion From the above result it is onluded that FIB method gives higher strength rom amongst the given methods. However, the FIB does not take into signiiant onsideration, the strength redution ators. The ACI method is AIJRSTEM ; 2016, AIJRSTEM All Rights Reserved Page 167

7 addition to strength redution ator, as also appliable to ISIS Canadian method also takes in to aount the environmental redution ators. The ailure modes are learly deined in ACI method, however in other methods the trial and error is resorted to get the ailure modes. In ISIS Canadian Method debonding ailure modes are not aounted. With the inrease in the grade o onrete the moment o resistane do not inrease signiiantly. Reerenes [1]. Täljsten, B. (2002):.Strengthening o existing onrete strutures with externally bonded Fibre Reinored Polymers. Design and exeution. Tehnial report. Luleå University o Tehnology, Division o strutural engineering. [2]. L.A.Bisby,(2004): An Introdution to FRP Strengthening o onrete strutures ISIS Eduation [3]. Module-4, CANADA, Department o Civil Engineering, Queen s University. [4]. ACI 440 2R-(2008) Guide or the design and onstrution o externally bonded FRP system or strengthening onrete strutures ACI ommittee, Farmington Hills, U.S.A. [5]. Neale KW. And Labossiére P., (1997),.State-o-the-art report on retroitting and strengthening by ontinuous ibre in Canada., Non-Metalli (FRP) Reinorement or Conrete Strutures, Japan Conrete Institute, [6]. Tehnial Report on the Design and Use o Externally Bonded FRP Reinorement or Reinored Conrete Strutures, ib Bulletin 14, TG 9.3, [7]. ISIS CANADA - Design Manual No. 4, September2001, Strengthening Reinored Conrete Strutureswith Externally-Bonded Fibre Reinored Polymers. [8]. Bhunga, Murad M. and Arora, N.K. (2012). Comparative Studyo ER-FRP Laminated Beam Design with ACI 440.2R-08 and ISISCANADA method. International Journal o AdvanedEngineering Researh and Studies. [9]. Hussain, M., Shari, A., Basunbul, I. A., Baluh, M. H., and AlSulaimani,G. J. (1995), Flexural Behavior o PrerakedReinored Conrete Beams Strengthened Externally by SteelPlates, ACI Strutural Journal, vol. 92, No. 1, pp [10]. Saadatmanesh and Ehsani, 1991, RC beams strengthened with GFRP plates - Part - I and Part-II, ASCE Journal o Strutural Engineering, 117 (11) (1991), pp [11]. Malek, A.M., and Saadatmanesh, H. (1996). Physial and mehanial properties o typial ibers and resins. Pro. 1st Con. on Compos. In Inrastruture, Tuson Ariz., AIJRSTEM ; 2016, AIJRSTEM All Rights Reserved Page 168