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TÓM TẮT NHỮNG KẾT LUẬN MỚI CỦA LUẬN ÁN 1. Xây dựng phương pháp luận tính toán độ tin cậy chịu uốn của dầm BTCT được tăng cường bằng tấm CFRP dán ngoài trên cơ sở mô hình sức kháng theo ACI 440.2R08. 2. Xây dựng Chương trình 2TKN bằng ngôn ngữ lập trình VBA trên nền Microsoft Excel cho phép xác định chỉ số độ tin cậy, b, của mặt cắt chữ nhật dầm BTCT chịu uốn được tăng cường bằng tấm CFRP dán ngoài. 3. Các kết quả đạt được bằng thực nghiệm trong phòng và hiện trường: · Xác định các tham số thống kê do ảnh hưởng của phương pháp phân tích đến sức kháng uốn của dầm BTCT chịu uốn được tăng cường bằng tấm CFRP dán ngoài theo mô hình sức kháng của ACI 440.2R08: µP=1.14 và COVP=11.8% bằng thí nghiệm uốn phá hoại 8 dầm mặt cắt chữ nhật. · Xác định mô hình phân bố và giá trị của các tham số thống kê của: Chiều rộng và chiều cao mặt cắt ngang giữa nhịp; và cường độ chịu nén của bê tông dầm cầu Trần Hưng Đạo. Cường độ chảy cốt thép cầu cũ bằng thí nghiệm kéo mẫu thép lấy từ cầu Bông. Cường độ chịu nén bê tông tuổi 28 ngày và cường độ chảy của cốt thép của các mẫu bê tông và cốt thép lấy từ 8 dầm thí nghiệm. Cường độ chảy của cốt thép thông qua 410 mẫu thép tại các dự án ở Việt Nam. 4. Các kiến nghị khi phân tích bằng định lượng chỉ số độ tin cậy từ kết quả khảo sát bằng Chương trình 2TKN: · Chỉ nên sửa chữa tăng cường chịu uốn dầm BTCT có tỷ lệ hàm lượng cốt thép chịu kéo trên hàm lượng cốt thép cân bằng của mặt cắt nằm trong khoảng 0.2 đến 0.5. · Có thể dùng hệ số chiết giảm cường độ tấm CFRP bằng 0.9 cho tính toán mặt cắt dầm BTCT tăng cường bằng tấm sợi CFRP trong trường hợp tỷ lệ mô men hoạt tải trên tĩnh tải không lớn hơn 1.0.
1 INTRODUCTION Externally bonded fiber reinforce polyme, FRP, has been appeared for 30 years and promptly become one of effective methods in retrofitting old RC structures. This method would bring advantages comparing with traditional ones in term of less increasing dead load, unchanging general structures, increasing bending capacity, preventing the appearence of new cracks and widening old cracks in concrete, as well as easy and faster erection. FRP has high tension strength, light weight, good fatigue strength, high corrosion capacity and easily sticking on concrete surface, so that applying FRP in construction has been fast developed over last decades. Carbon fiber reinforce polyme, CFRP, receives all advantages of fiber reinforce polyme and has excellent fatigue capacity for retrofitting old bridges, especially RC bridges, more effectively than conventional methods as placing steeel bars in tension zone, externally postensioning cables, or externally bonded steel sheets. Reasons for thesis selection: CFRP sheets have been used in retrofitting and strengthening bridges in Vietnam; in contrast, current national code for bridges, 22TCN 272-05, has not been designed for CFRP material. Some bridges have been designed and erected using ACI 440.2R-08. Researches and calculations for retrofitting and strengthening by CFRP have mostly conducted in semi-reliability method, without considering all statistic behaviours of design parameters. Furthermore, other researchs on the world have been using reliability method in several fields. However, there is no reaserch completely evaluating the reliability of bending beams strengthened with externally bonded carbon fiber reinforced polymer sheets. Thus, reaserch of applying CFRP basing on reliability theory is a live problem in Vietnam and all over the world. This is the main reason for this thesis selection. Name of thesis: “Flexural reliability of RC Bridge girders strengthened with carbon fiber reinforced polymer sheets (CFRP)” Objectives of this study: to analyze and promote the factor of CFRP strength reduction and range of applying externally bonded carbon fiber reinforced polymer sheets in retrofitting and strengthening RC beams. Methods of this study: • Theory method: apply reliability theory with possible distributions and statistical parameters of random variables for determining reliability index of bending beams strengthened with externally bonded CFRP sheets. • Experiment method: carry out room and field experiments for getting possible distributions and statistical parameters of random variables in flexural resistance model in ACI 440.2R-08. Subjects and scopes: RC beams strengthened with externally bonded CFRP sheets. Range of study: 2 • Compute and evaluate reliability index of RC beams strengthened with externally bonded CFRP sheets. • Carry out room and field experiments for getting possible distributions and statistical parameters of random variables, icluding section geometry, concrete compressive strength, steel yield strength, and influence of analysis method to flexual resistance of RC beams strengthened with externally bonded CFRP sheets according to ACI 440.2R-08. Scientific and practical meaning of this study: • Theory: - Deriving a methodology for evaluating level of flexural reliability of RC Bridge girders strengthened with CFRP sheets, basing on reliability theory and flexural resistance model in ACI 440.2R-08. - Suggesting CFRP strength reduction factor and range of applying externally bonded carbon fiber reinforced polymer sheets in retrofitting and strengthening RC beams. • Experiment: define possible distributions and values of statistical parameters of random variables, icluding section geometry, concrete compressive strength, steel yield strength, and influence of analysis method to flexual resistance of RC beams strengthened with externally bonded CFRP sheets according to ACI 440.2R-08 basing on bending sample beams to rupture. Terms of rasearch include introduction, 4 chapters, and conclusions as following: Introduction: Introduction of CFRP sheets and name of thesis. • Chapter 1: General view of reaserchs about structures using FRP. • Chapter 2: Analyzed reliability index, β, of RC beams strengthened with externally bonded CFRP sheets according to bending resistance model in ACI 440.2R-08. • Chapter 3: Studying RC sample beams strengthened with externally bonded CFRP sheets throught bending to failure. • Chapter 4: Studying Trần Hưng Đạo bridge beams strengthened with externally bonded CFRP sheets under bending with calibrated loads Conclusions and suggestions: presenting results, suggestion, and proposed topics for future researches. 3 Chapter 1 GENERAL VIEW OF RESEARCH ABOUT STRUCTURES USING FRP 1.1. History of applying FRP in retrofitting and strengthening structures Reinforce concrete bridges are popular in Vietnam and all over the world. Nowadays, there are many serious deteriorations, however, there is not enough budget for replacing with new ones so retrofitting and strengthening bridges seem to be the best choice. Strengthening methods are varied depending on demand, structure, and e technical level. According to statistic, bridge strengthening is mainly using conventional methods as placing steeel bars in tension zone, externally postensioning cables, or externally bonded steel sheets. Externally bonded FRP has been appeared for 30 years and promptly become one of effective methods in retrofitting old RC structures. This method would bring advantages comparing with conventional ones in term of (1) less increasing dead load, (2) unchanging general structures, (3) increasing bending capacity, (4) preventing the appearence of new cracks and widening of old cracks in concrete, and (5) easy and fast erection. FRP has high tension strength, light weight, good fatigue strength, high corrosion capacity and easily sticking on concrete surface, so that applying FRP in construction has been fast develope over last decades. In 1980s, the first time FRP was applied for retrofitting RC columns in Japans. In Euro, as early as 1978, German researches had been mentioned the issue of using FRP in strengthening RC structures. Similarly, Switzer researchers had applied FRP for strengthening bridge beam in bending in 1987. In The USA, applying FRP was researched as early as 1930s, but the using of FRP in retrofitting and strengthening has been started in 1980s. In Vietnam, FRP has been applied in strengthening bridges as: Sài Gòn-HCM city; Trần Hưng Đạo - Phan Thiết city, Bình Thuận province; Trần Thị Lý- Đà Nẵng city, Gián Khẩu- Ninh Bình province, Tô Mậu - Yên Bái province. 1.2. FRP mechanical properties Unit weight of FRP is from 1.2 g/cm 3 to 2.1 g/cm 3 , about 1/4 to 1/6 that of steel. Unidirectional FRP has different thermal coefictions for longitudinal and transver directions depending on type of fibers, matrix, and volume of fiber. FRP in tension has linear relationship between stress and strain until rupture and this is truely a brittle material (Figure 1-1). FRP mechanical properties decrease under the impact of environment factors including: high temperature, humidity, and chemicals. Figure 1-1. Relationship between typical FRP stress and strain 4 1.3. FRP application Main FRP application includes: retrofitting and strengthening structures; reinforcing for RC; and constructing main frame. 1.4. Existing design manual for FRP 1.4.1 Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures Design bending RC section strengthening with externally bonded FRP base on beam theory with reinforce addition of FRP combining for tension. Acorrding to ACI 440.2R-08, flexural expression at limit state is as following: ∅൫M ୬ୱ +ψ M ୬ ൯≥γ ୈ M ୈ +γ M 1.4.2 Externally bonded FRP reinforcement for RC structures-FIB Bulletin No. 14 Design bending RC section strengthening with externally bonded FRP acorrding to FIB is similar to that of ACI: ܯ ோௗ = ܣ ௦ଵ ݂ ௬ௗ ሺ ݀−ߜ ீ ݔ ሻ +ܣ ܧ ߝ ሺ ℎ−ߜ ீ ݔ ሻ +ܣ ௦ଶ ܧ ௦ ߝ ௦ଶ ሺ ߜ ீ ݔ−݀ ଶ ሻ 1.4.3 Strengthening Reinforced Concrete Structures with Externally-Bonded Fibre Reinforced Polymers-ISIS Design Manual No. 4 ISIS' assumptions is similar to ACI's and added two more assumptions: perfect bond between concrete and FRP; and FRP are well anchored or extended enough to ensure the work of FRP to limit state. Flexural expression at limit state is as following: ܯ ோ =ܶ ௦ ቀ݀− ଶ ቁ+ܶ ቀℎ− ଶ ቁ 1.5. Structure Reliability 1.5.1. Basic of Reliability theory Probability of Stable, P s : P S = P{S<R | [0,T]} and probability of failure: P f = P{S>R | [0,T]} where P{S<R | [0,T]} is the probability for structure not break-down during operation time, T; P{S>R | [0,T]} is the probability for structure break-down during operation time, T. Checking expression: P S ≥[P S ] or P f ≤ [P f ], where ∫∫ > = RS f dSdRRfSfP )()( ∫∫ < = RS s dSdRRfSfP )()( This is a modern design method; taking into account for unstable and random characteristics of design variables. However, it is needed to get enough Possible Distributions and Statistical parameters of all variables. 5 1.5.2. Basic reliability theory for RC bending beams strengthening with externally bonded CFRP sheets 1.5.2.1 Methodology RC bending beams strengthening with externally bonded CFRP sheets have been evaluated in either two directions: Evaluating the reliability of RC structures being strengthened; or Designing strengthening RC structures with given reliability. Methodology for Evaluating the reliability of RC structures being strengthened base on basic reliability theory. Widely accepted model for design is beam theory with the addition of CFRP as part of tension material. For given reliability, β, probability of structure fail is defined. With analyzed model and design beam parameters specified, all demands of FRP are established. 1.5.2.2 Possible distributions and values of statistical parameters of random variables 1.5.2.3 Elements influencing to reliability of RC bending beams strengthening with externally bonded CFRP sheets Reliability of RC bending beams strengthening with externally bonded CFRP sheets depends on many elements such as: design standards, design level, construction technology, management and operation, loads, and environment. Evaluating the reliability of RC structures being strengthened with externally bonded CFRP sheets is only used to deal with random variables having specified statistical parameters and describing their influence to structure reliablity through state functions. 1.5.3. Reliability index, β ββ β 1.5.3.1 Definition of Reliability index, β ββ β Figure 1- 2. Diagram of state function for Resistance, R, Load effect, S, and safty reserve, G. Ratio of ߚ = ఓ ಸ ఙ ಸ is called Reliability index of structures. Reliability index is computed through means and standard deviations of Resistance, R, and Load effect, S as ߚ = ఓ ೃ ିఓ ೞ ට ఙ ೃ మ ିఙ ೞ మ Probability of structure fail is determined by standard normal distribution function: P =Φሺ−βሻ 1.5.3.2 Target Reliability index, β ββ β T 6 Target Reliability index selected depends on influence level to human-economy- social when structures are broken. Target Reliability index is different from new and strengthened structures. Research Andrzej S Nowak, Maria M Szerszen, and Allen; together with regulations of ASSHTO LRFD, EC, ACI 318- 05, Target Reliability index is proposed in this thesis as following: • β T = 3.75: multiple paths beam structures, strengthening age of 10 years. • β T = 3.5: multiple paths beam structures, strengthening age of 5 years. 1.5.3.3 Evaluating Reliability index using Rackwitz-Fiessler method This method is based on equivalent mean and standard deviation of variables with unnormal distribution. Susposing random variable, X, has mean of µ X; standard deviation of σ X; distribution function of F X (x) and density distribution function of f X (x). Equivalent mean of µ ଡ଼ ୣ and standard deviation of σ ଡ଼ ୣ is defined at point x* where values of F X (x) and f X (x) are repectively equal to those of distribution function and density distribution function of standard normal distribution. Point x* is on the limiting line or G=0. F ଡ଼ ሺ x ∗ ሻ = ߔ൬ ୶ ∗ ିµ σ ൰ f ଡ଼ ሺ x ∗ ሻ = ଵ σ φ൬ ୶ ∗ ିµ σ ൰ Where: Φ and φ are repectively distribution function and density distribution function of standard normal distribution (µ=0 và σ=1). ). Equivalent mean of µ ଡ଼ ୣ and standard deviation of σ ଡ଼ ୣ is defined as following: µ ଡ଼ ୣ =x ∗ −σ ଡ଼ ୣ ሾ ߔ ିଵ ሺ F ଡ଼ ሺx ∗ ሻ ሻ ሿ σ ଡ଼ ୣ = ଵ ሺ୶ ∗ ሻ φ ሾ ߔ ିଵ ሺ F ଡ଼ ሺx ∗ ሻ ሻ ሿ Iteration method is used for determining x* and β. 1.5.4. Analyis of statistic parameters 1.5.4.1. Defining minimum sample size Minimum sample size, min , of material, X, having covariance, COV X , approximate constant compared with mean, µ X , is defined as following: ୫୧୬ = ൫f ୮ COV /e൯ ଶ 1.5.4.2. Checking distribution functions of random variables Checking random variable, X, with a set of samples for appropriating with normal distribution includes: • Graphs (lines or colums for prbability distribution); • Checking synmetry value of Fisher, g 1 , and kurtosis value of Pearson, g 2 . • Using standard Shapiro-Wilk for sets of 3 to 20 samples; or extended Shapiro- Wilk with Royston algorithm for sets of 20 samples or more. 1.6. Analyze, evaluate research about beams strengthening with CFRP sheets In general, researches from all over the world to Vietnam have been studied beams strengthening with externally bonded CFRP sheets about many issues, including: 7 • Type of failure • Ultimate strength capacity • Section Stress Distribution • Advantages of FRP external bonded method for bending and shear • Model for evaluating peeling of CFRP sheets. • Finite Element Model for evaluating beams strengthening with externally bonded CFRP sheets • Using ductility index to evaluate beams strengthening with externally bonded CFRP sheets Terms of research are various but all of them are conducted in semi-reliability method, not implying all statistic behaviours of design parameters. 1.7. Analyze, evaluate researches about reliability theory In general, researches from all over the world to Vietnam have been applied reliability theory in many issues, including: • Avaluating beam element • Factors of loads and resistance • GFRP bar reinforcement for concrete • Beam with large ratio of reinforcement • Bridge deck at service limit state • Box-section RC beams These researches have been using reliability method in several fields. However, there is no reaserch completely evaluating the reliability of bending beams strengthened with externally bonded carbon fiber reinforced polymer sheets. 1.8. Objects of thesis Evaluating influences of materials, geometry, and analysis model of bending resistance to reliability of beams strengthening with externally bonded CFRP sheets. Evaluating and suggesting application range of strengthening with externally bonded CFRP sheets for single span beams and CFRP strength reduction factor. 1.9. Terms and Methods of this study Computing and evaluating reliability index of bending beams strengthened with externally bonded CFRP sheets; suggesting application range of strengthening with externally bonded CFRP sheets and CFRP strength reduction factor. Theory method: applying reliability theory with possible distributions and statistical parameters of random variables for determining reliability index of bending beams strengthened with externally bonded CFRP sheets. Experiment method: carrying out room and field experiments for getting possible distributions and statistical parameters of random variables in flexural resistance model in ACI 440.2R-08. 8 Chapter 2 EVALUATING FLEXURAL RELIABILITY INDEX OF RC BRIDGE GIRDERS STRENGTHENED WITH CFRP SHEETS BASING ON FLEXURAL RESISTANCE MODEL OF ACI 440.2R-08 • Reliability index, β, of bending sections of RC bridge girders strengthened with carbon fiber reinforced polymer (CFRP) sheets has been computed according to ultimate limit state (ULS) for flexural design suggested by the ACI 440.2R-08. 2880 strengthened RC beam- sections have been selected with reasonable sets of random variables (section dimensions, concrete compressive strength, steel strength, ultimate strength and ultimate relative strain of CFRP sheets) applying in analyzing model of nominal flexural resistance, M ୖ . Monte-Carlo simulations have been performed to determine the variability in material properties (M) and fabrication processes (F); whereas experimental data reported in the literature has been used to quatify the variability related to the analysis method (P). The reliability index, β, caculated using Rackwitz-Fiessler method with first order function. 2.1. Statistical properties of section geometry and materials • Geometrical properties: width of section, b, can be measured easily after construction, so that two extreme nominal values λ were selected 1.01 and 1.00; and two values COV were selected as 1.78% and 0.60%, respectively (Table 2-1). The effect of concrete vibrators to the positions of tension steel could hardly to measure after construction, thus two extreme nominal values λ of d were selected as 0.99 and 1.00, respectively; and two values COV of d were selected as 2.36% and 0.78%, respectively (Table 2-1). h values are proportionally related to d. Both b and d are assumed to have Normal distribution. • Concrete Compressive Strength, ݂ ′ , is closely related to construction level and curing. The bias at sites is usually smaller than in lab and the suggested value is 1.05. Two nominal values COV of grade 17 and 30 were selected: 15% and 13.5%, respectively. Compressive strength of concrete is assumed to be normally distributed. • Tensile Strength of steel bars, ݂ ௬ : two types of steel and their extreme nominal values of ݂ ௬ were considered in Table 2-1. Selected bias value is 1.10, near the lower limit; Selected COV value is 10%, near the upper limit. ݂ ௬ is assumed to be normally distributed. E ୱ =200000MPa. • Tension strength, f ୳ ∗ , and limit relative strain, ε ୳ ∗ , of CFRP is selected in Table 2-1. Selected bias values of them are 1.10, near the lower limit; Selected COV value of tension strength is 12% ,near the upper limit. Selected COV value of limit relative strain is 2.5% , near average value. These variables are assumed to agree with Weibull distribution. FRP modulus of elasticity: E = 230000MPa. 2.2. Design space 9 Resistance flexural model for Rectangle section RC beam strengthening by CFRP sheet is suggested by ACI 440.2R-08. Nominal values of b, d, f’ c , and f y as Table 2-1. Strengthening CFRP layers: ݊ ிோ = 1, 2, and 3. Steel reinforcement ratio: ߩ ௌ = 0.2, 0.3, 0.4, 0.5, 0.6ߩ , where ρ ୠ୪ =0.85β ଵ ౙ ′ ౯ க ౙ౫ க ౙ౫ ା ౯ ౩ ⁄ So that design space of section resistance includes 2 4 x 3 x 5 = 240 cases. Table 2-1. Statistical Properties of Main Variables Design Variable Minimum norminal Value (N) ߤ & ߪ Bias λ & COV (%) Maxnimum norminal Value (L) ߤ & ߪ Bias λ & COV (%) Probability Distribution b (x10 -3 m) ܾ ே =200 ߤ = ܾ ே +2.34 1.01 ܾ =500 ߤ = ܾ +2.34 1.00 Normal ߪ = 3.60 1.78 ߪ =3.60 0.60 d (x10 -3 m) ݀ ே = 0 . 9 ℎ ே =800 ߤ ௗ = ݀ ே − 4 . 41 0.99 ݀ =1500 ߤ ௗ = ݀ − 4 . 41 1.00 Normal ߪ =11.70 2.36 ߪ =11.70 0.78 ݂ ′ (MPa) 17 ߤ ′ = 17.9 1.05 30 ߤ ′ =31.5 1.05 Normal ߪ =2.7 15.00 ߪ =4.3 13.50 ݂ ௬ (MPa) 275 ߤ =302.50 1.10 420 ߤ =462.0 1.10 Normal ߪ =30.25 10.00 ߪ =46.20 10.00 ݂ ௨ ∗ (MPa) 3000 ߤ ೠ ∗ =3300 1.10 E=230000N/mm 2 Weibull ߪ =360 12.00 ߝ ௨ ∗ (mm/mm) 0.015 ߝ ೠ ∗ =0.0165 1.10 Weibull ߪ =0.000375 2.50 2.3. Influenced factors for flexural resistance: Flexural resistance, M R , is a random variable and according to Ellingwood, 2003 [9], the factors influenced to flexural resistance random characteristic include: • Material properties (M): strength, modulus of elasticity, relative strain… • Fabrication (F): dimensions and their effects to geometric properties. • Analysis method (P): accurate level of selected method in ACI 440.2R-08. M, F and P are assumed to be independent variables. Effects of M and F are evaluated together through values of λ MF and COV MF . These values are computed by randomly generated variables of material properties and fabrication as Monte Carlo simulation. Effects of P is evaluated by comparing experimental values of the flexural capacity available in literature, ܯ ௨,்௦௧ with the corresponding analytical value ܯ ூ , derived using the analysis method proposed by ACI 440.2R-08 (Table 2-2).The following values were chosen: ࣅ ࡼ = . and ࡻࢂ ࡼ =% Table 2-2. Statistical Properties of P N 0 Source Sample No. ߣ ܥܱܸ 1 P. Alagusundaramoorthy et al.[116] 12 1.69 13.1% 2 G. Spadea et. al.[57] 8 1.43 3.8% 3 J.G. Dai [65] 6 1.12 19.8% 2.4. Load model 10 Dead load (D) and live load (L) are the two load categories considered in this study. The dead load considered in the design is the gravity load due to the self weight of the structure. It is normally treated as a Normal random variables in literature (Cardoso et.al,2007, Nowak 1993-1995-1999 and Project No. NCHRP 20-7/187 - ASSHTO 2007); because of the control over construction materials, it is assumed that the accuracy to estimate dead loads is higher compared to that of live loads. The works in this study induced to adopt a bias ࣅ ࡰ = .ܽ݊݀ࡻࢂ ࡰ =% for dead load. In this study, live load is HL 93 and its statistical properties are available in Project No. NCHRP 20-7/187 - ASSHTO 2007. Live load is assumed to agree with Gumbel distribution. In this study, ૃ ۺ =1.20 and COV L =18% are selected. 2.5. Evaluating reliability index 2.5.1. State function: State function to determine flexural reliability index β based on ACI 440.2R-08 concludes 3 random variables: flexural resistace, M R , dead load moment, M D , and live load moment, M L : G ሺ M ୖ ,M ୈ ,M , ሻ = M ୖ −ሺM ୈ +M ሻ Assuming ratio of live load moment to dead load moment at specific section is n ୈ = ై ీ . In this study, investigated values of n MLD are 0.25; 0.50; 0.75 and 1.00. In addition, assuming the section is at limit state or γ ୈ M ୈ +γ M =∅M ୬ , so thatM ୈ = ై ୬ ైీ = ∅ γ ీ ାγ ై ୬ ైీ Thus establishing reliability level of function G ሺ M ୖ ,M ୈ ,M , ሻ = M ୖ −ሺM ୈ +M ሻ is completely defined. This is an linear function of three random variables: M ୖ ,M ୈ , normal distribution, and M , Gumbel distribution. Rackwitz-Fiessler method is applied to find reliability index β. 2.5.2. Computer aided software Figure 2- 1. Program Figure 2- 2. Block CI [...]... model (P) basing on testing utimate moment (Mu,test) and resistance moment deriving from ACI 440.2R 08 (MACI) 2 Approximating distribution functions of concrete compression strength and steel yield strength 3 Investigating behaviour of bending beams with different area of tension steel, compressive strength of concrete, and layer of CFRP sheets 4 Investigating beam deflection 5 Evaluating efficiency of... ሺ1.64 x 15.70%/0.1ሻଶ = 6.63 mẫu Selecting 13 samples of CFRP sheets and getting fp=2.29 and p=0.989 3.4 Geometric propertis of sample beams Minimum size of sample number, min, is defined as equation (1.47) with p=0.90, fp=1.64, e=0.1 và COV0= (13.1%+3.8%+19.8%)=12.23% Thus, ୫୧୬ = ሺ1.64 x 12.23%/0.1ሻଶ = 4.02 samples Selecting 8 sample beams (including 2 control beams) and getting fp=2.003 and p=0.957 Beam... Strengthening Strengthening objective is increasing permitted load to 15T-18T vehicle: • Strenghtening main beams with externally bonded CFRP sheets; • Retrofitting piers by concrete jacket 4.5 Cablirating bridge after strengthening Calibarting results show that after strengthening the bridge could be safely operated with 18T vehicle 4.6 Parameters for calculation 4.6.1 Section geometry dimensions... literature are used for calculating P effect The reliability 23 indexs, β, are calculated using Rackwitz-Fiessler method with first order function 2TKN propramme has been developed for computing β Lab and field experiments have been carried out for possible distribution and statistical parameters of random variables 1 Contributions a Deriving a methodology for evaluating level of flexural reliability... distribution of section height and width, concrete compressive strength, and steel yield strength 2 Determining and evaluating section reliability index of simple-span RC beams strengthening with externally bonded CFRP sheets 4.2 Experimantal places a Construction material – Cablirating LAB: LAS-XD 225 Content of experiment: • Compressing to failure of 12 concrete samples from Trần Hưng Đạo bridge beams... City- Bình Thuận province Content of experiment: • Measuring geometry dimensions of main beams • Addresing the percentage of tension reinforcement deterioration 20 • Cablirating bridge after strengthening Date: June 2012 4.3 Bridge existing condition before strengthening Trần Hưng Đạo bridge, across Cà Ty River, had been constructed before 1975, at Km1704+300 of former 1A high way, which is now Trần Hưng... sample number Minimum size of sample number, min, is defined with p=0.9, fp=1.64, e=0.1 và COV0= (5.85%+8.8%+7.7%)=7.45% Thus, ୫୧୬ = ሺ1.64 x 7.45%/0.1ሻଶ =1.49 samples Selecting 3 samples of D12 steel and 3 samples of D16 steel and getting fp=2.325 and p=0.975 b Results Distribution functions of steel yield strength are agrred with normal distribution through Shapiro-Wilk checking 3.3.3 CFRP sheets a Minimum... statistical parameters are used those values in Chapter 2 4.7 Determing and evaluating flexural reliability index of middle-span section There are 18 cases of flexural reliability index of middle-span section (3 load levels x 3 levels of steel deterioration x 2 cases fore before and after strengthening) Results computing by 2TKN is showed in Table 4-2 with the asumption of transversal distribution... Materials 3.3.1 Concrete a Minimum size of sample number Minimum size of sample number, min, is defined as equation (1.47), where COV0= (10%+7%+6%+9.1%+9.1%+9.1%)/6=8.38% Selecting 6 samples of C21 concrete and 6 samples of C25 and getting fp=2.923 and p=0.998 b Results Distribution functions of C21 and C25 concrete compressive strength are agrred with normal distribution through Shapiro-Wilk checking 3.3.2... Shapiro-Wilk Test is applied for every single section with ten sets of 5000 samples All 6 sections have p greater than 0.05 and the asumption of normal distribution of MR is accepted (Figure 2-7) 2.5.3.4 Evaluating group cases in investigated region 2.5.3.4.1 Influence of tension steel ratio to β Average reliability index of 2660 cases as Figure 2-8 The graphs of ψ = 0.85 and ψ = 0.90 are slightly different . with carbon fiber reinforced polymer sheets (CFRP) Objectives of this study: to analyze and promote the factor of CFRP strength reduction and range of applying externally bonded carbon. reaserch completely evaluating the reliability of bending beams strengthened with externally bonded carbon fiber reinforced polymer sheets. 1.8. Objects of thesis Evaluating influences of materials,. CFRP strength reduction factor and range of applying externally bonded carbon fiber reinforced polymer sheets in retrofitting and strengthening RC beams. • Experiment: define possible distributions