BOND CHARACTERISTICS OF VARIOUS FRP STRENGTHENING TECHNIQUES

Transcription

1 BOND CHARACTERISTICS OF VARIOUS STRENGTHENING TECHNIQUES S. H. RIZKALLA Distinguishe Proessor, Department o Civil Engineering, North Carolina State University Campus Box 7533, Raleigh, NC, USA T. HASSAN Assistant Proessor, Department o Civil Engineering, Ain-Shams University, Cairo, Egypt Strengthening o reinorce concrete struures using has emerge as a potential solution to the problems associate with civil inrastruure. Many researchers have reporte signiicant increases in strength an stiness o concrete struures strengthene with. Nevertheless, possible brittle ailures o the strengthene system ue to elamination o the strips an/or sheets coul limit the use o the ull eiciency o the system. This paper presents a bon ailure hypothesis or near surace mounte bars. Close-orm analytical solutions are propose to prei the interacial stresses or near surace mounte strips an externally bone sheets. The moels are calibrate by comparing the preie behavior to test results. Quantitative criteria governing interacial eboning ailure o near surace mounte bars, strips an externally bone sheets are establishe. NSM BARS Transer o stresses rom a eorme NSM ro to the concrete is mainly by mechanical interlocking o the lugs with the surrouning epoxy. The resultant orce exerte by the lug on the epoxy is incline at an angle β to the axis o the bar as shown in Figure, where /tan β is the coeicient o riion, µ between the bar an the ahesive. The raial component o the resultant orce creates zones o high tensile stresses at the -epoxy interace as well as at the concrete-epoxy interace. Finite element analysis was employe to provie in-epth unerstaning o the loa transer mechanism between NSM bars an concrete. Figure shows the mesh imensions use in moelling a portion o a concrete beam strengthene with a NSM bar. Groove imensions, bar location an properties o

2 concrete an epoxy were set ientical to the bon specimens teste by Rizkalla an Hassan, 00. Internal cracks Epoxy / µ Figure. Forces between a NSM bar an ahesive Bar Major crack Epoxy bar Raial pressure was applie at the bar location to simulate the bon stresses transerre rom the bar to the surrouning epoxy. Typical principal tensile stress istribution is shown in Figure 3. It shoul be note that the elastic moulus o the ahesive is generally less than that o the concrete. Such a phenomenon results in a stress iscontinuity at the concrete-epoxy interace as shown in Figure 3. Steel bar All imensions are in mm Concret Epox G 4 µ L 0 w Figure. Mesh imension or a portion Figure 3. Typical tensile stress istribution o a concrete beam strengthene aroun NSM bars with a NSM bar High tensile stresses are observe at the concrete-epoxy interace as well as at the -epoxy interace. Two ierent types o eboning ailures coul occur or NSM bars. The irst moe o ailure is ue to splitting o the epoxy cover as a result o high tensile stresses at the -epoxy interace, an is terme epoxy split ailure. Increasing the thickness o the epoxy β Force components on Concrete G G 4 µ L G Epox 4 µ L Force components on epoxy G / µ 4 µ L 4 µ L NSM Bar C

3 cover reuces the inuce tensile stresses signiicantly. Furthermore, using ahesives o high tensile strength elays epoxy split ailure. This type o eboning ailure orms with longituinal cracking through the epoxy cover. The secon moe o ailure is ue to cracking o the concrete surrouning the epoxy ahesive an is terme concrete split ailure. This moe o ailure will take place when the tensile stresses at the concrete-epoxy interace reach the tensile strength o the concrete. Wiening the groove minimizes the inuce tensile stresses at the concrete-epoxy interace an increases the eboning loas o NSM bars. Concrete split ailure was the governing moe o ailure or the bon specimens teste by the authors. Large epoxy cover an high tensile strength o the epoxy ahesive provie high resistance to epoxy split ailure an shite the ailure to occur at the concrete-epoxy interace. The tangential bon stress,, can be expresse as: = () 4 L where is the iameter o the bar, an L is the embement length neee to evelop a stress o in the NSM bar. I the coeicient o riion between the bar an the epoxy is µ, the raial stresses, σ raial, can be expresse as: σ = = () raial µ 4 µ L The tensile stresses at the concrete-epoxy interace, σ con-epoxy, an at the -epoxy interace, σ -epoxy, can be expresse in terms o the raial stress as ollows: σ = G (3) con epoxy 4 µ L σ = G or G (4) epoxy 4 µ L where G, G an G are coeicients etermine rom the inite element analysis base on a unit raial pressure applie at the bar location an using speciie groove imensions, concrete an ahesive properties. The maximum tensile stress at the -epoxy interace, σ -epoxy, epens on the coeicients G an G, whichever is greater as shown in Figure 3. Equating the tensile strength o concrete to Eq. (3), the minimum 3

4 4 embement length neee or NSM bars to prevent concrete split ailure can be expresse as: L = G (5) 4 µ Equating the tensile strength o the ahesive to Eq. (4), the minimum embement length neee or NSM bars to avoi epoxy split ailure shall not be less than: L = G or G (6) 4 µ epoxy where an epoxy are the tensile strength o concrete an epoxy, respeively. Increasing the ratio o the elastic moulus o the concrete to that o the ahesive generates high tensile stresses at the concrete-epoxy interace an low tensile stresses at the -epoxy interace. Praical values o the moular ratio coul vary between 5 an 40. This range covers various types o concrete an ahesives that are commonly use in concrete struures. Figure 4 shows the propose esign chart or the evelopment length o NSM bars. G w=.5 G w= G an/or G C/ or G an/or G curves Concrete Epoxy C w w= w= G an/or G 0.6 w= w= C/ or G curves To simulate Figure the 4. most Design critical chart conitions or the evelopment or esign purposes, length o NSM the coeicient bars G was evaluate or a moular ratio o 40. The coeicients, G an G were evaluate or a moular ratio 5 an the greater value was plotte in Figure 4. The chart covers a wie range o possible epoxy covers an 0.4

5 accounts or three ierent groove sizes. Using the propose esign chart, the coeicients G an the greater value o either G or G coul be evaluate or a given groove with, w, an using a speciie clear cover to bar iameter ratio (C/). The governing evelopment length or NSM bars coul be preie using the greater o Eqs. (5) an (6). The propose approach compare very well with the test results an overestimate the evelopment length o NSM C bars by less than 5 percent. 5 NSM STRIPS This seion presents a close-orm analytical solution to prei the interacial shear stresses or NSM strips. The moel is valiate by comparing the preie values with test results. The propose moel is base on the combine shear-bening moel or externally bone plates an is given in Figure 5. σ σ c σc σ + x σ c + x Cuto σ c + x x x x point 700 L L x x Concrete x 300 σ c Ahesive C strip σ Ahesive 300 Near surace mounte C strip 50 b Sec Concrete σ c Plan Figure 5. Analytical moel or NSM strips The moel is moiie to account or the ouble bone area o NSM strips. The moel accounts also or the continuous reuion in lexural stiness ue to cracking o the concrete. Deboning o NSM strips is assume to occur as a result o high shear stress concentration at cuto point. The erivation o the moel is reporte elsewhere. For simply supporte beams subjee to a concentrate loa, P, at mispan, the shear stress at the strip cuto point, can be expresse in terms o the eeive moment o inertia, I e, an the thickness o the C strip, t, as ollows:

6 6 t n P l = o y npy ω + (7) I I e e G E where, a ω = ; n = ; E is elastic moulus o the strip, E c t a t E Ec is elastic moulus o concrete, G a is the shear moulus o the ahesive, t a is the thickness o the ahesive, l o is the unbone length o the strip; y is the istance rom the strip to the neutral axis o the transorme seion an I e is the eeive moment o inertia o the transorme seion. Deboning will occur when the shear stress reaches a maximum value, which epens on the concrete properties. Premature eboning o NSM C strips is governe by the shear strength o the concrete. Other components o the system such as the ahesive an the C strips have superior strength an ahesion properties compare to concrete. Knowing the compressive an tensile strength o concrete, the Mohr-Coulomb line, which is tangential to both Mohr s circles or pure tension an pure compression, can be represente an the maximum critical shear stress or the pure shear circle can be expresse as: c max = (8) c + where c is the compressive strength o concrete ater 8 ays an is the splitting tensile strength o concrete. Equating the shear strength propose in Eq. (8) to the shear stress given in Eq. (7), eboning loas or NSM C strips can be etermine or simply supporte beams subjee to a concentrate loa at mispan. The evelopment length is highly epenent on the imensions o the strips, concrete properties, ahesive properties, internal steel reinorcement ratio, reinorcement coniguration, type o loaing, an groove with. The propose moel in Eqs. (7) an (8), can be use to estimate the evelopment length o NSM strips o any coniguration as ollows: a) Use the propose Eqs. (7) an (8) to etermine the eboning loa o the strip or ierent embement lengths as shown in Figure 6. The resulting curve represents a ailure envelope ue to eboning o the strip at cuto point.

7 b) Use a cracke seion analysis at seions o maximum inuce normal stresses an etermine the ultimate loa require to rupture the strip as shown in Figure 6. c) Determine the evelopment length at the interseion o the line corresponing to lexural ailure o the strip with the curve representing eboning ailure at cuto point. The calculate evelopment length will preclue brittle ailure ue to eboning o the strips an will ensure ull composite aion between the strip an concrete up to ailure. The propose approach compare very well with the experimental results. The preie eboning loas unerestimate the measure values by less than 6% Loa Rupture loa or the strips Failure envelope ue to eboning NSM strip Development length Embement length Figure 6. General proceures to etermine the evelopment length o NSM strips 7 EXTERNALLY BONDED SHEETS The propose approach moiies the analytical moel evelope by Malek et al., New expressions or the moment o inertia an the neutral axis epth o the concrete seion at cuto points are introuce. An eeive moment o inertia, I e an an eeive neutral axis epth, y e are propose to account or the continuous egraation in stiness as cracking progresses. Both expressions were originally evelope to prei the eleions o concrete members ater cracking 4. For simply supporte beams subjee to a concentrate loa at mi-span, the shear stress,, an the normal stress, σ n, at the ens o the externally bone reinorcement can be expresse by:

8 8 n P l o y e npy e = t + ω (9) I I e e k V + = n V c βm σ a n (0) E I E β 3 c I e npl where o y e npy e = + G V c V o b y e t ω ; ω = a ; I I e e t E a t 0.5 E a npl k n = ; o y npy e e k V = b t + t ω ; a I I e e 4 n b β = E I an t is the thickness o the sheets; t a is the thickness o the ahesive; n is ratio o the elastic moulus o the to that o the concrete; P is the applie concentrate loa; l o is the unbone length o the sheets; y e is the eeive istance rom the sheet to the neutral axis o the seion; I e is the eeive moment o inertia o the transorme seion; I is the moment o inertia o the sheets; E a, E c, E an are the moulus o elasticity o the ahesive, concrete an, respeively; G a is the shear moulus o the ahesive; b is the with o the reinorcement; M a is the applie moment on the concrete seion at cuto points; an V o is the shear orce in the concrete beam at the sheet cuto point. Delamination o externally bone reinorcement can be etermine using a critical combination o both normal an shear stresses at cuto points. The critical combination o these two stresses was establishe by using a elamination circle 5. The elamination circle provies a relationship between the shear strength, max, an the normal strength, σ nmax. This relationship can be expresse in terms o the concrete compressive strength, c an the concrete tensile strength, as ollows:

9 c max = c + c ( c + ) c ( c + ) σ n max ( c ) σ n max 9 () The maximum normal an shear stresses are evaluate or the bon specimens teste by the authors using the propose approach 4. Interacial eboning loas are preie using Mohr-Coulomb ailure criterion. The analysis is extene urther to inclue specimens F, C an G as well as specimens S.0, S. an S.4 teste by other researchers to examine the valiity o the propose approach 5,6. All the selee specimens experience concrete cracking with various intensities at the sheets cuto points prior to elamination. Figure 7 shows the preie elamination loas using the propose approach compare with the experimental results. The preie elamination loas using Malek s moel, as well as those preie using Brosens moel, are also shown or comparison. The igure clearly inicates that elamination loas can be preie with a suicient accuracy using the propose approach. Assuming uncracke concrete seions at the sheets cuto points overestimate the strength o the beams consierably an le to huge errors. Furthermore, using ully cracke concrete seions at cuto points provie very conservative elamination loas Delamination loa (kn) 00 Propose Approach Experimental Results Maleks Moel Brosens Moel C C C3 C4 C5 C6 F C G S S. S.4 Hassan 00 Brosens 00 Hearing an Test specimen Buyukozturk Figure 7. Experimental results compare with the propose approach

10 0 CONCLUSIONS (a) The eiciency o using C bars as NSM reinorcement is controlle primarily by the bon charaeristics o the bars as well as by the bon between the ahesive material an the concrete. (b) Two ierent types o interacial eboning ailures can occur or NSM bars: i- Epoxy split ailure ii- Concrete split ailure. (c) Increasing the groove with an/or using high strength concrete, increases the resistance to concrete split ailure. Using high strength ahesives an/or increasing the epoxy cover layer elays epoxy split ailure or NSM bars. () The propose analytical moels an ailure criteria or NSM strips as well as or externally bone sheets are capable o preiing the interacial shear stress istribution, ultimate loa carrying capacity an moe o ailure. REFERENCES. Rizkalla, S., an Hassan T., Eeiveness o techniques or strengthening concrete briges Journal o the International Association or Brige an Struure Engineering, (), 00.. Hassan, T., an Rizkalla, S., Investigation o bon in concrete struures strengthene with near surace mounte C strips. ASCE, Journal o Composites or Construion, 00, in press. 3. Malek, A., Saaatmanesh, H., an Ehsani, M., Preiion o ailure loa o R/C beams strengthene with plate ue to stress concentration at the plate en, ACI Struural Journal, 95(), 998, pp Hassan, T., Flexural behavior an bon charaeristics o strengthening techniques or concrete struures, Ph.D. Thesis, University o Manitoba, Canaa, 00, 304 p. 5. Brosens, K., Anchorage o externally bone steel plates an C laminates or the strengthening o concrete elements, Ph.D. Thesis, K. U. Leuven, Belg., 00, 5 p. 6. Hearing, B. an Buyukozturk, O., Delamination in reinorce concrete retroitte with ibre reinorce plastics, Ph.D. Thesis, MIT, 000, 87p.

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