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1 G Journal of the Korea Concrete Institute Vol. 19, No. 6, pp. 763~771, December, 2007 FRP w w gj p 1) *Áw 2) Á 1) 1) w w œw 2) w w ey l Behaviour of One-Way Concrete Slabs Reinforced with Fiber Reinforced Polymer (FRP) Bars Dae-Won Seo 1) *, Byum-Seok Han 2), and Sung-Woo Shin 1) 1) Dept. of Architectural Engineering, Hanyang University, Ansan , Korea 2) Sustainable Building Research Center, Hanyang University, Ansan , Korea ABSTRACT Over the last few decades, many researches have been conducted in order to find solution to the problem of corrosion in steel reinforced concrete. As a result, methods such as the use of stainless steel bars, epoxy coatings, and concrete additives, etc., have been tried. While effective in some situations, such remedies may still be unable to completely eliminate the problems of steel corrosion. Fiber reinforced polymer (FRP) elements are appealing as reinforcement due to some material properties such as high tensile strength, low density, and noncorrosive. However, due to the generally lower modulus of elasticity of FRP in comparison with the steel and the linear behavior of FRP, certain aspects of the structural behavior of RC members reinforced with FRP may be substantially different from similar elements reinforced with steel reinforcement. This paper presents the flexural behavior of one-way concrete slabs reinforced with FRP bars. They were simply supported and tested in the laboratory under static loading conditions to investigate their crack pattern and width, deflections, strains and mode of failure. The experimental results shows that behavior of the FRP reinforced slabs was bilinearly elastic until failure. Also, the results show that the FRP overreinforced concrete beams in this study can be safe for design in terms of deformability. Keywords : reinforced concrete, fiber reinforced polymers (FRP), one-way concrete slabs, structural behavior, FRP bars 1. FRP (fiber reinforced polymer) w ü w w w y p w, FRP w w w ƒ» w j {ü w. ù FRP w wš p (sheet) xk w š, ü. w šƒ š, w w š q w w p w û k w w ƒ». w w FRP w» w FRP w w yw wƒ v w. w w *Corresponding author Received June 11, 2007, Accepted September, by Korea Concrete Institute FRP w» w q p w, ü ³ q,, x p sƒw. 2. FRP w p 2.1 FRP p Fig. 1» FRP GFRP(glass fiber reinforced polymer) CFRP(carboiber reinforced polymer) - x w v 1). w z j x ùkü FRP w x w q ùkü. w GFRP w û k. 2.2 FRP w w gj p 763

2 Fig. 1 Material characteristics of FRP and steel reinforcement 1) gj p ƒ w» w w w. w y w wš, q z ùkü. ù FRP Fig. 1 w FRP w w ³x, w ³x w q x w ³x «2). (1) ACI 440.1R wš FRP w { ³x.» { FRP k š w xk. ρ fb 0.5βf ck f u 0.003E f E f + f u β f 27.6 ck w w Fig. 2 ùkü, w ³x w 1/7 ~1/9 û ³x. FRP w û ³x» gj p w. ³x «, w w. ACI 440 z wš FRP { Fig. 3. Fig. (1) (2) 2 Balanced reinforcement ratios for flexural sections reinforced with GFRP and steel Fig. 3 Strength reductioactor as a function of the reinforcement ratio 2) 3.1 x z 3. x FRP w w, x FRP bar w w sƒ w GFRP w x w. ³x w x ³x x zw. Ì ü» 3) š w w Ì (l/20) 150 mm ISIS Canada 4) w FRP w Ì w (3) w 200 mm zw. l n h --- frp l n --- h», l n ¼ (mm), h Ì (mm) ε k x x α d, ƒx 0.5 FRP w x w» w» x w SS150-, SS200- q w» w 0.3ρ b w, FRP w w» w 0.5~2.5ρ fb ¾ 5 x w. Table 1 ùkü (steel, FRP), FRP (ρ fb ) Ì (h) x z w, x Fig ε s s ε frp α d gj p» 30 MPa pgj p w, 2 x 36 MPa, k 25 GPa ùkü. (3) 764 w gj pwz 19«6y (2007)

3 Parameters Specimens SS150- FS150-3 FS150-6 FS150- FS FS SS200- FS200-4 FS200- FS FS FS Table 1 Fig. 4 of tested slabs Dimension (b d l) Reinforcement material Steel 1, ,000 ck GFRP 30 Steel 1, ,000 GFRP 5) Fig. 6 ρ /ρ b Test setup 크리트의 변형은 압축측 단면에 4개의 스트레인게이지 를 부착하여 측정하였다. 실험체 설치 및 가력 4. 실험체의 설치는 Fig. 6과 같이 실험체를 단순지지 하 였으며, 1,000 mm의 가력 지점 간에 순수휨만 작용하도 록 2점 가력 방식으로 하였으며, 가력은,000 kn UTM 을 사용하여 초기균열까지 하중제어 후에 변위 제어 방 식으로 실험을 수행하였다. 실험중의 데이터 측정은 하중 의 증가에 따른 슬래브 중앙의 변위를 측정하기 위하여 mm 변위계를 설치하였다. 보강근의 변형은 인장측 주보강근에 스트레인게이지를 부착하여 측정하였으며, 게 이지는 전체 인장근의 중앙, 1/4 위치에 부착하였다. 콘 Fig. 5 Reinforcement ratio (ρ, %) Details of tested slabs 근에 사용된 FRP 보강근은 국내에서 개발된 것으로서 인장강도는 철근에 비해 40% 이상 큰 705 MPa인데 비 하여 탄성계수는 25% 수준인 44 GPa이었다. 보강근의 형상은 Fig. 5와 같이 부착강도 확보를 위해 나선형 표 면을 가진 형태이며, 부착강도는 17 MPa을 나타내었으 며, 보강근으로 사용된 철근과 FRP 보강근의 재료 역 학적 성질은 Table 2에 나타내었다. 3.3 f (MPa) Glass FRP bars (D13 mm) 4.1 실험 결과 및 분석 균열 및 파괴 양상 각 실험체의 최대하중, 최대 변위 및 파괴 양상을 Table 3에 정리하였으며, Fig. 7은 실험 종료 후 휨파괴, 전단 파괴 및 압축파괴 등의 파괴 양상별 최종 파괴를 나타 내고 있다. FS150-6,, 11, 14 실험체들은 최대처짐이 국 내 콘크리트 설계기준의 허용처짐의 20배 이상이 발생 하여 최종 파괴시까지 실험을 하지 못하고 종료하였다. 슬래브 두께 150 mm (a/d.0)실험체에서는 철근콘크리 트 실험체는 순수휨 구간에 균열이 주로 발생하였으며, 최종 파괴시까지 휨균열만이 발견되었다. FRP 보강근을 사용한 실험체는 균형보강비 이하의 실험체들은 휨 구간 내에서 균열이 주로 발생하였으나, 균형보강비 이상의 실 험체들에서는 중앙부에 균열발생 이후에 균열발생 구간 이 철근콘크리트 실험체보다 넓게 발생하였다. Table 4 Characteristics of reinforcement Reinforcement Diameter (mm) Section area (mm ) Modulus of elasticity (GPa) Yield strength (MPa) Tensile strength (MPa) Steel GFRP Table 2 2 FRP 보강근을 주근으로 사용한 일방향 콘크리트 슬래브의 거동 765

4 Table 3 Experimental results Specimens SS150- FS150-3 FS150-6 FS150- FS FS SS200- FS200-4 FS200- FS FS FS Max. load (kn) Max. deflection (mm) Failure mode Flexural failure FRP rupture Flexural failure FRP rupture FRP rupture Shear-compressive failure Shear-compressive failure Shear-compressive failure Crack characteristics Average crack Number of cracks spacing (mm) between point loads Specimens ρ/ρb 30% Mu 90% Mu 30% Mu 90% Mu SS FS FS FS FS FS SS FS FS FS FS FS Table 4 Fig. 7 Typical crack patterns and failures of specimen 에 나타낸 바와 같이 휨 구간 내에서의 균열발생 구간 이나 균열의 간격은 보강비에 따라 큰 차이를 나타내지 않았으나 균형보강비 이하의 실험체들이 상대적으로 균 열수가 적게 나타났다. 이는 저보강 실험체들은 초기에 발생한 균열의 폭이 커지면서, FRP의 파단으로 최종파 괴가 발생하였으나, 균형보강비 이상의 실험체들은 처짐 이 매우 크게 발생하면서 균열이 진전되었기 때문으로 판단된다. 슬래브 두께 200 mm 실험체 (a/d 5.)에서는 철근콘 크리트 부재에서는 150 mm 실험체와 유사한 균열 및 파 766 한국콘크리트학회 논문집 제19권 제6호 (2007) 괴 양상을 나타내었다. FRP 보강근을 사용한 슬래브의 경우 균형보강비 이하의 실험체에서는 Fig. 과 같은 FRP 보강근의 파단에 의한 급격한 파괴가 발생하였다. 균형 보강비 이상의 과보강된 실험체에서는 Fig. 9와 같이 가 력점 주위에서 콘크리트의 압축파괴가 발생하였으며, 이 후에 사인장균열과 주보강근의 길이 방향으로 발생한 균 열이 크게 진전되며 취성적인 전단파괴를 나타내었다. 균 열의 발생 구간은 두께 150 mm 슬래브와 마찬가지로 철 근콘크리트 슬래브보다 균열의 발생 구간이 더 넓게 나 Fig. Rupture of main reinforcing FRP bars (FS200-4)

5 Fig. 9 Concrete crushing (FS200-16) kû, ³ j w ùkû. q ƒ ù ³x x q gj p q m w q z dw. 4.2 { ACI 440.1R-01 FRP w gj p œe{ FRP w - x w, (4), (5) wš. FRP š w x k ³x (4), ³x w (5) w. M n ρ f f f ρ f f f bd 2 f ck M n 0.A f f fu d β c », ρ f FRP, f f , A f d( 1 k 3 ) k ( ρ f ) 2 + 2ρ f ρ f, f ck gj p (MPa) f fu FRP (MPa), β 1 c ƒ ¾ Fig. x (4), (5) w w { w. ³x w FS150-3, FS200-4 w x M (4) (5) x { ƒ j ùkû. Fig. 3 w, 1.5~2.5 ¾ x { sƒw ùkû. ù FRP w w ƒ ƒ, x ùe, wz ƒ q y w yw v w š q. 4.3 ³ s gj p ³» w ƒ. ù FRP w gj p FRP p w ³ s j ƒ. ù FRP gj p ³ mw v ƒ. Fig. 11 ƒ x x d ³ s ƒ ùk ü, x w FRP w ³ s w j w ƒ ³ s z ƒ. Table 5 w w ³ sƒw, Ì 150 mm x FRP ³ s ƒ ù x ƒ ü gj p» ww x ³ s (0.4 mm) 2~5 w. Ì 200 mm x ³x Fig. Comparison between predicted and experimental flexural capacities Fig. 11 Moment versus crack width FRP w w gj p 767

6 Table 5 Responses of slabs Specimens FS (2.06 ρ fb ), FS (2.60ρ fb ) x» w. ƒ FRP w gj p ³ s z q. Fig. 12 ACI 440 ³ s w FS200 w v. (6),» Gergely-Lutz FRP w x w xk 2). w βk b f 3 f E f Under service load* Crack width (mm) Deflection (mm) Load at deflection limit** (kn) FS FS FS FS FS FS FS FS FS FS *Service load is considered as approximately 50% of the ultimate load of the control specimens reinforced with steel **Defined as l/360, where l is the length of clear span between the supports of the slab, in accordance with KBC 2005 d c A (mm) (6)», w ³ s (mm), E f FRP k (MPa), f f FRP ü, β w ¾ ¾ ù, d c ƒ¾ ¾, A z, k b FRP ( x FRP 1.2) Fig. 12 w x ³ s sƒw ùkû ù, w ³ dw ùkû, w ü w ùkû. ³ j ³ s ƒ j ùkù w FRP x ƒw gj p w w q. 4.4 Fig. 13 ƒ x w ùkü. x w z w j ƒ ƒ ƒw x ùkü. ù FRP w x» ³ ƒ w z x x ¾ ùkü. FRP w gj p gj p w û k w w j w, ƒ w. Table 5 FRP w x w w x w ùkû,» gj p w Ì w» FRP w w» q. FRP w gj p d w m w. ACI 440 z d w z p FRP û k FRP p w wš. Fig. 12 Comparison of crack width between analysis and experimental results (FS200-20) Fig. 13 Load-deflection relationship of tested slabs 76 w gj pwz 19«6y (2007)

7 I e M cr β d I g I cr I g M a M cr 3 M a (7)», kn m, α b , M cr 2f r I g h ( ) β d,,, E f E s bd 3 α b :0.5 I cr k 3 + A f d 2 1 k 3 ( ) 2 k 2ρ f + ρ f ρ f, f ck ( ) 2 f r 0.62 (MPa) -----, E f :FRP k, E s : k ISIS Canada design manual () z p w. (7) w x l w x, () CEB-FIP gj p. I e I g I cr I cr M cr I g I cr (7), () w 2 ƒ x (9) w, Fig. 15 ACI 440 ISIS Canada w x w ùkü. 3L 2 4a ( ) 2 ( ) M a Pa E c I e Fig. 14 FS x ACI 440, ISIS Canada w w wš, x w ü w ùkü ù, w ƒw ƒ j ùkû. d yw w Fig. 15 x ACI 440.1R ISIS Canada z p I e yw E f E c () (9) Fig. 14 Comparison of load-deflection relationship between analysis and experiment(fs200-20) w. ISIS Canada ³ w z p I e ACI 440.1R sƒw w ùk ü» ƒ w q. ƒ ƒw ƒ ùkù ³x d zw q ù, ³x w d ƒ j w ùkû. 4.5 gj p x w w d gj p x Fig. 16 ùkü. w gj p x w gj p x j w. gj p x x w z x w ùkü, gj p x wì x ùkü ù, FRP w x ³ z gj pƒ w x ùkü. FRP x ³ z Fig. 15 Effect of the FRP ratio FRP w w gj p 769

8 Table 6 Deformability of specimens Specimens Moment factor Deflectioactor Deformability FS FS FS FS FS FS FS FS FS FS Fig. 16 Strain variations in concrete and reinforcement j ƒw gj p w w, FRP x w, FRP w e w k w w. 4.6 gj p sƒw t. gj p w (š ) w (š ) w. ù FRP w q ¾ x w» w w, FRP gj p w ƒ v w. Jaeger w x (deformability factor) w FRP w w sƒw. x (). DF φ m ()» φ m p (moment factor), (deflectioactor) ùkü, ƒƒ (11), (12) w w. φ m M u M u (11) (12)», M u w p M gj p x p u w k gj p x Table 6 () w ƒ x x sƒw ùkü, Ì 150 mm x 14.2~2.3, Ì 200 mm x 6.0~17.3 x ùkü.» 4 w, w j w x ùkü q. w w w ƒ, FRP w» w x sƒ wì mƒ w w ƒ w ƒ. 5. FRP w w gj p 2 ƒ x ww, p sƒwš,» sƒw. w. 1) FRP w w gj p ³ z wƒ j ùkû, q ¾ x w. 2) FRP ƒ ü ƒ z ù, q w. ù x w FRP y ³ w, ƒ w q. 3) FRP w ³ s gj p w j w, ƒ ³ ³ 770 w gj pwz 19«6y (2007)

9 j w e. ³ s w x» ³x x w, ƒ ³ s z. 4) FRP w w gj p x» w ùkü gj p w Ì» FRP w w w», Ì» v w š q. ACI 440, ISIS Canada z p w ³ s w w w y w d ùkü. œœ» z 2005 FRP w y w gj p» w» l w (R ),. š x 1. Abdalla, H. A., Evaluation of Deflection in Concrete Members Reinforced with Fibre Reinforced Polymer (FRP) Bars, Composite Structures, Vol.56, 2002, 64pp. 2. ACI Commitee 440, ACI 440.1R-03, Design and Construction of Concrete Reinforced with FRP Bars, American Concrete Institute, 2001, 1pp. 3. w wz t» z, FRP w y w gj p», w wz, 2005, 197pp. 4. ISIS Canada, Reinforcing Concrete Structures with Fibre Reinforced Polymers, 2001, 75pp. 5. w», FRP w y w gj p»,» š (3 ), Jeager, L. G. and Mufti, A., Balanced Section Ductility and Deformability in Concrete with Reinforcement, Research Report No , Industry's Center for Computer Aided Engineering, Technical University of Nova Scotia, Halifax, Canada, 1995, 29pp. gj p ü x w j, ƒ ƒ. w w v Ì ƒ, š gj p, s gq ù w w wš. w w» w š FRP (fiber reinforced polymer) w w. ù û k w gj p w ƒ v w y. FRP w w x mw gj p p w. ³ q,, sƒ mw ƒ sƒw, w w ³ d w sƒw. w : gj p, FRP w, w, FRP, { FRP w w gj p 771

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