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MINISTRY OF EDUCATION AND TRAINNING THE UNIVERSITY OF TRANSPORT AND COMMUNICATIONS BUI NGOC TINH ANALYSIS OF MECHANICAL BEHAVIOR OF REINFORCED CONCRETE BOX GIRDER IN ONE-PLANE CABLE STAYED BRIDGE Domain: Transport Construction Engineering Code: 9580205 SUMMARY OF DOCTORAL THESIS Hanoi - 2020 INTRODUCTION The necessity of the thesis Cable stayed bridge was firstly built in Vietnam since 1998 (My Thuan bridge) Sofar, a number of cable stayed bridges were designed and constructed Many of them using two planes of cables as well as the I and Π type cross section with incline webs to ensure the aerodynamic stability, enhance the lateral rigidity and therefore is able to pass over long span In comparison to two-plane cable stayed bridge, the one-plane cable stayed bridge help to separate two traffic flows on the bridge by location the plane of cable in the middle of the cross-section; open the better view for transportation and also brings better aesthetic feeling However, since the cable is vertically located in the middle of the cross –section; they subject to only the vertical bending of the girder and not contribute to the torsional strength of the cross-section That is the reason why the box-type of cross-section (which has high torsional rigidity and aerodynamic stability) is normally used for one-plane cable stayed bridge In Vietnam, there are two one-plane cable stayed bridges, they are Bai Chay bridge and Nga ba Hue bridge In which, Bai Chay bridge ranked the first among the list of longest span one-plane cable stayed bridge in the world at the time of construction (2006) In the design of one plane cable stayed bridge, the cables are located in the middle of the top slab of the cross section; therefore the top slab has to subjected to rather large pull-out loading in out-of-plane direction This type of loading result in the compression in the slab (due to the incline of cable), the bending effect in the girder and also the local pull-out loading on the slab; the combination of these effects lead to a complicated stress-strain condition in the slab Because of this reason, othotropic steel decks or composite deck solution is used in many oneplane cable stayed bridges, such as the Rama VIII bridge pass over Chao Phraya river in Bangkor Reinforced concrete box girder can avoid the fatigue, vibration and large deformation problem as can be happened in steel box girder However, there is no guidelines for calculation of reinforced concrete slab subjected to the local pull-out loading combine with overall compression and bending as explained above In order to avoid the local damage on the slab, the design solution in Bai Chay bridge is using the tension pipe connecting the top slab to two bottom edge of the cross-section in order to transfer the pull-out loading in the top slab to the bottom of webs This is an acceptable solution in term of loading capacity, but leading to many difficulties in construction; and the effect of the solution will be limited at the position where the incline angle of the cable is small and nearly perpendicular to the vertical pipe Therefore, we decided to carry out the doctoral thesis namely “Analysis of mechanical behavior of reinforced concrete box girder in one-plane cable stayed bridge” in order to propose the theoretical analysis model, validated by experimental study, to analyse the mechanical behavior of reinforced concrete girder in one-plane cable stayed bridge Also, base on the proposed model, analyse the effectiveness of the strengthening method using vertical pipe as used in Bai Chay bridge The Aims, Objectives and Scope of research as summarized as follows: Aims - Analyse and select the appropriate calculation model for analysing the local behavior of reinforced concrete slab subjected to out-of-plane loading; - Perform experiments to validate the proposed theoretical model; -Using the proposed model in analysing, evaluating the mechanical behavior of reinforced concrete box girder in oneplane cable stayed bridge - Compare and conclude on the effective solution for strengthening the concrete box girder subjected to cable force in term of loading capacity Objectives and the Scope of study Structure: Reinforced concrete box girder subjected to pull out loading in the middle of the top slab; Material: Reinforced concrete box girder, taking into account the non-linear behavior of steel and concrete Loading: limited to static loadings Methodology - Literature review, determine the problem to be studied - Experimental study; - Numerical modeling Novel contributions of the study - Scientific contributions: Non-linear material model is employed for numerical modeling the behavior of concrete box girder of one-plane cable stayed bridge Number of experimental experiments were tested to validate the numerical result - Application contribution: the thesis results can be applied in modeling the practical concrete box girder one-plane cable stayed bridge; contributes in design and evaluation of cable stayed bridge - Main contributions: Propose the “total strain crack” model in analyse the local behavior of concrete box girder in one-plane cabale stayed bridge Propose the experimental speciments and tests to validate the theoretical model in this type of structure Numerical analysis of the mechanical behavior of reinforced concrete box girder bridge of one-plane cable stayed bridge subjected to local pull-out loading of cable forces, which will help to evaluate the effectiveness of the strengthening methods Structure of thesis The thesis consists of the Introduction, four main chapters and the Conclusion and Perpectives Introduction Chapter 1: Problem statement; Chapter 2: Study on the mathematical model for analyse the stress-strain condition of reinforced concrete box type girder of oneplane cable stayed bridge; Chapter 3: Experimental study for validating the “total strain crack” model for reinforced concrete slab subjected to out-of-plane inclined loading and the Publication list of the Author CHAPTER PROBLEM STATEMENT Cable stayed bridge was introduced in the 16th century and was widely applied from 19th century Some initial cable stayed bridges were the combinations of cable stayed bridge and suspension bridge (Brooklyn bridge, for example) In the development of cable stayed bridge, people used the two-plane, three-plane and also four-plane of cables The two-plane cable type were mostly used, however the inconvenience of this type of bridge was the aesthetics and the difficulty in lanes arrangement One-plane cable type is more beautiful and helps to reduce the dimension of the substructure However, the most unfavourable problem for one-plane cable stayed bridge is that the cable system can not support the main girder to againts twisting, aerodynamic unstability and vibration In order to enhance the twisting capability and aerodynamic stability, box-type girder was normally employed For steel box girder, the weight of girder, the thickness of slab is relative small sothat for long span bridge, the girder is usually vibrate with high frequency and leading to the damage on the Asphalt cover layer (happened in Rama VII bridge with the span length equals to 450m) For concrete box girder bridge, one-plane cable leads to a reinforced concrete slab subjected to out-of-plane pull out loading This problem will be the central question to be solved in this thesis At the moment (2020), there are two one-plane cable stayed bridges have been built in Vietnam They are Bai Chay and Tran Thi Ly bridge In this type of bridge, a clear design of load transfer path from cable to the girder is necessary At the moment, there is not many researches or studies in this issue, especially the local behavior of the slab on the anchorage zone The literature review showed that it is necessary to continue the research on the connection between cable and the slab of reinforced concrete box girder The bridge design specifications of Vietnam has not directly mentioned on the analysis of reinforced concrete slab subjected to local pull-out loading The stress-strain condition in the local anchorage zone of the cable is not similar with the local anchorage zone of tendons in prestress concrete; since it is the combination the overall bending, the overall compression of the slab and the local pull-out at the anchorage region In this thesis, the author focus on both theoretical aspect and experimental aspect of this problem CHAPTER THEORETICAL MODEL OF REINFORCED CONCRETE BOX GIRDER SUBJECTED TO CABLE FORCE IN ONE-PLANE CABLE STAYED BRIDGE 2.1 The current status of the problem Cable stayed bridge is designed due to the national design specications and standard In Vietnam, bridge design specifications TCVN 11823:2017 is not enough to design the cable stayed bridge, sothat people needs to refer to other specifications/standards which take into account the aerodynamics stability of bridge under wind load The problem of reinforced concrete slab subjected to the tensile force of cable, is the combination of three loading condition: reinforced concrete slab subjected to compression, to bending and the local pull-out loading Vietnameses design specifications and standards have not mentioned on this combination of loadings 2.2 Propose the “total strain crack” model for analysing the behavior of reinforced concrete slab subjected to cable force in one-plane cable stayed bridge Reinforced concrete slab subjected to incline out-of-plane loading is a common type of structure widely used in bridge and other construction For bridges, this type of structure is applied in the slab of one-plane cable stayed bridge or in the hollow tower with the anchorage located inside This type of structure subjects to overall bending, inplane compresion, local out-of-plane loading and was studied in both modeling and experimental aspects In numerical modeling aspect, the “multi-layer method” was introduced, in which the slab is divided into many layer, each layer is assumed to have uniforme tension or compression stress perpendicular to the layer In this type of approach, the reinforcement and concrete is modeled as a “layer”, and can help to estimate the stress-strain condition in the slab direction However, this method can not take into acount the effect of the stress perpendicular to the slab direction, for example the shear stress Also, this type of method cannot take into account the contribution of local reinforcement, which normally located perpendicular to the loading direction In order to solve this problem, Hrynuk and Vecchio proposed the “multi-layer method” but taking into acount the shear effect The method of Hrynuk and Vecchio helps to solve the reinforced concrete slab subjected to vertical loading However, can not modeling the effect of incline loading and cannot estimate the forming and the development of local cracks In order to modeling the happen and development of cracks in reinforced concrete structure; there are two approaches They are the “discrete” model and the “smeared crack” model In “discrete” model, the discontinuity in the displacement field is used to model the crack Extended finite element method (X-FEM, ED-FEM) is employed for numerical modeling and the “discontinuity” in displacement is taken into account by an additional shape function for the displacement (see Ibrahimbegovic, Armero, ) It is difficult to apply this type of approach for three-dimensional reinforced concrete structure; since it is needed to have the contact relation equation between concrete, reinforcement and bonding in all three dimensions, and will require a huge computational work The second approach is so-called the smeared crack model In which, the displacement field is still assumed to be continuous field after crack In term of finite element method, the crack is modeled as a displacement inside the finite element, but not in the nodes The “smeared crack” model was studied by many authors, but initialy proposed by Vecchio and then developed by Selby for threedimensional element, namely “total strain crack” model The “total strain crack” model theoretically can model the forming and development of crack in three-dimensional refion, therefore can be applied in such type of structure like deep beam, or the anchorage zone of prestressed concrete construction The application of “total strain crack” model in modeling the reinforced concrete slab subjected to perperdicular compression was performed by Ngekpe and Barisua and give reasonable results However, this model have not been applied in modeling the reinforced concrete slab subjected to out-of-plane incline compression or tension In the experimental aspect, there is only few reports on the reinforced concrete subjected to vertical loading, but not many research on the reinforced concrete slab subjected to incline loading In this thesis, the author will also carry out experimental research on this issue In the “total strain crack” model, the direction of principal stress is assumed to be same with the direction of principal strain Figure Stress-strain condition Since this model apply for reinforced concrete material then the technical properties of concrete and reinforcement is necessary, including: young modulus, Poission ratio, tensile strength, compressive strength and the fracture energy For fracture energy (Gf), one can refers to the value from CEB-FIP 1990 as shown in equation and table G f G fo f cm f cm o (1) In which, fcm is the average compressive strength of concrete, f cm0 is the reference compressive strength, equals to 10 MPa The value of reference fracture energy (Gf0) is selected due to the maximum aggregation dimension (Dmax) as shown in Table 1: Table Reference fracture energy Gfo vs Dmax Dmax (mm) 16 32 Gf0 (J/m2) 25 30 58 The stress-strain relation of concrete under compression and tension of reinforced concrete in principal direction is shown in figure Figure Relation between stress-strain of reinforced concrete in principal direction in compression and tension There are a number of mathematical models were proposed for the stress-strain relation of concrete under compression and tension Equation introduces the equation of Thorenfeldt for compression and Equation introdues the equation of Vecchio and Collins for tension Theorenfeldt equation: i f fp p n 1 In which: n n i p nk (2) nÕu p , k fcc 17 nÕu p 62 fcc Vecchio and Collins equation for compression: f c1 E c ' ft 200 cr (3) cr The shear stress – shear strain behavior of concrete is assumed to be linear, with a reduction factor β G cr G (4) reinforcement layer of the slab An incline compression (P) was put on the middle-top of the slab The compression P increases with time until the slab is failure; strain in concrete and reinforcement, deflection in the slab are measured during compression 3.2 Modeling results The experimental slabs are numerical modeled using “total strain crack” model; the input parameter of material are showed in the table Table Material parameters No Parameter Symbol Reinforcement CB400V Yield strength fy Young modulus Es Concrete C40 Compressive strength f'c Young modulus Ec Poisson ratio v Value Unit 400 20000 MPa MPa 40 31975 0.2 MPa MPa From the above parameters, the stress-strain relation curve of reinforced concrete is made The reinforced concrete slab is modeled by finite element method (3d brick element for concrete, 1d element for steel bar) (see figure 4) Figure Reinforced concrete slab model The compression force P increases in 11 levels (with Pu is the ultimate load of compression), which the specific value in the Table 11 Table Values of compression force (P) Level of compression Level Level Level Level Level Level Level Level Level Level 10 Level 11 Pi/Pu =25° 12 24 36 48 60 72 84 96 108 120 132 0,1Pu 0,2 Pu 0,3 Pu 0,4 Pu 0,5 Pu 0,6 Pu 0,7 Pu 0,8 Pu 0,9 Pu Pu 1.1 Pu Value kN) =45° 16 24 32 40 48 56 64 72 80 88 =70° 6.5 13 19.5 26 32.5 39 45.5 52 58.5 65 71.5 The calculated deflection of the slab, stress in the reinforcement of the slab with different incline angle is shown in the Table and Figure In the figure 5, the dashed lines show the result at 20cm from the central point of the slab while the normal lines show the result at the central point of the slab Table Calculation results Deflection (mm) Stress in steel bar (MPa) Loading level α=25 0.17 0.17 0.19 0.32 0.35 0.56 ° α =45° α =70° 0.5 3.4 7.1 0.41 8.1 7.8 15.9 0.58 0.8 15.8 18.1 45.8 0.91 1.13 1.44 46.1 59.6 97.5 1.42 1.86 2.13 91.9 111.3 133 2.03 2.58 2.93 142.8 172.5 183.8 2.7 3.31 3.75 198.7 221 236.6 3.39 4.16 5.7 257.3 273.9 297.9 α =45 ° α =70 12 ° α=25° 5.58 5.09 7.17 326.4 332.7 343.6 10 7.61 6.17 9.18 400 400 400 11 10.81 9.24 12.16 400 400 400 Figure Relation between compression loading and deflection, stress in the reinforcement of three incline slabs due to calculation results Figure shows the overall deformation of the slab and the distribution of stress in concrete at the ultimate loading P u (level 10) for different incline slabs 13 α = 70° P=65 kN α = 45° P=80kN α=25° P = 120 kN Figure Deformation and stress in reinforcement at ultimate loading level (level 10) Table and figure shows the tensile stress in reinforcement reaches the yield strength (400 MPa) at level 10, so-called the ultimate level of loading The ultimate loading for 25°, 45° and 70° reinforced concrete slab is 120kN, 80kN and 65kN, respectively 3.3 Comparison between the calculation results and the experimental results Due to experiment, the deflection and loading at the ultimate level for each incline slab is shown in Table Table Defection of slab and the ultimate loading due to experimentals results Experimental results No of Specimens Specimens Specimens Distance to the central point of the slab (cm) R=0 R=20 R=0 Specimens 250 Deflection (mm) 7.22 6.27 7.04 Specimens 450 Ultimate load (kN) 142 141.1 14 Deflection (mm) 9.94 7.20 9.08 Ultimate load (kN) 100.2 92.8 Specimens 700 Deflection (mm) 12.72 8.48 12.20 Ultimate load (kN) 79.6 79.85 Specimens R=20 R=0 R=20 6.02 7.32 6.25 6.68 9.28 7.25 140 97.32 8.39 12.01 9.08 80.39 The experimental results showed that the ultimate loading for 25°, 45° and 70° is 141kN, 96kN and 80kN, about 15% to 20% higher than the calculated ultimated values (120kN, 80kN and 60kN) The differences come from the higher compressive of concrete (normally higher than the design value = 40Mpa) and the contribution of bonding between steel bar and concrete Figure Comparison between calculation and experimental results 15 The crack patterns from the modeling result is similar to the visible cracks in the specimens (figure 8) Those cracks include the cracks due to overall bending and due to local failure at anchorage zone Figure Failure in specimens and due to modeling Figure clearly shows that the crack patterns due to modeling and due to experiment is similar 2.3 Conclusion of Chapter Experimental results show that the “total strain” crack model capable of modeling the behavior of reinforced concrete slab subjected to incline loading, both in term of deformation, deflection, ultimate loading as well as the failure type, with resonable accuracy for practical design CHAPTER APPLICATION OF THE „TOTAL STRAIN CRACK“ MODEL FOR ANALYSING OF A REINFORCED CONCRETE BOX GIRDER IN ONE-PLANE CALBE STAYED BRIDGE 4.1 Selection of the calculation structure In order to prove the capability of the total strain crack model, one need to apply this model into a specific problem of one-plane cable stayed bridge For that reason, the typical cross-section of Bai Chay bridge was selected In this calculation, stress-strain condition of reinforced concrete slab is modeled for different incline of cables, and with the cable force ranging from 0.2fpy to 0.7fpy) Two type of crosssections, with and without steel pipi enhencement, are considered 16 Calculation result also help to evaluate the effectiveness of using steel pipe in strenthening the one-plane cable stayed bridge box-girder slab The calculation is limited for the serviceability state 4.2 Analysis results In order to simplify the model, a segment of girder was taken into account, separated from other part of the girder at the middle point between two adjacent cable Figure The finite element model for a segment of box girder Table Dimension of the box girder No Dimensions Value Unit Depth of the girder 3,70 m Width of the top slab 25,00 m Width of the bottom slab 8,00 m Thickness of the top slab 0,25 m Thickness of the bottom slab 0,20 m Thickness of the web 0,35 m Material parameters Compressive strength of concrete f’c 17 = 45 MPa Density of concrete kg/m3 yc = 2400 Tesile limitation [σk] = 3,354 MPa Compressive limitation [σn] = 27 MPa Yield limite fy = 390 MPa Young modulus Es = 205000 Lateral reinforcement d1 = 22 mm Longitudinal reinforcement d2 = 16 mm Stress limitation for concrete Reinforcement MPa In reality, the cross-section between two adjacent boundary is considered to be fix boundary Figure 10 Boundary condition The loading acting on the bridge include: selfweight of the main girder, deadload of the superimposed structures, live-load and other special loadings such as wind load or earth-quake These load are normally transfer to the cable force, then from the cable to the tower Theredore, we can only concentrate on analysis the box-girder subjected to cable forces 18 Figure 11 Detail of anchorage zone from cable to box girder The cable consists of 61 tendons, diameter of each tendon is 15,2mm The cable force transfer to the concrete box girder at the slab as show in the figure Due to the detail of anchorage reinforcement, the cable force can be assumed to be uniformly distributed on the anchorage plate The incline angle of cable ranges from 25° to 70° and results in different stress-strain condition in the top slab of the girder Due to the design of the cable, the stress in the cable is normally between 0.3fpy and 0.6fpy When the girder subjected to wind load, the stress in the cable can increase a little bit to 0,65fpy Therefore, in this thesis, we calculate the box girder subjected to cable force ranging from 0.5fpy to 0.7fpy Figure 12 to Figure 16 shows the stress-strain condition for reinforced concrete box girder subjected to 50o incline loading equals to 0.5fpy 19 Figure 12 Displacement in z direction Figure 13 Displacement in X direction 20 Figure 14 Displacement in Y direction 21 Figure 15 Stress in reinforcement and in pipe Figure 16 Crack region Table Stress-strain and deformation condition of box-girder when using and not using the pipe enhancement 0.5fpy Loading Withou t pipe 0.6fpy With pipe 22 Withou t pipe With pipe 0.7fpy Withou t pipe With pipe Vertical displacement (mm) tensi X on Maxi dire mum ctio com pres stress n sion in conc tensi Y rte on dire (MP com ctio a) pres n sion tensi on Stress in reinforcedm com ent (MPa) pres sion Crack width (mm) 1.898 1.693 2.479 2.161 3.098 2.666 3.35 3.35 3.35 3.35 3.35 3.35 -16.90 -19.44 -20.88 -23.77 -24.972 -28.249 3.35 3.35 3.35 3.35 3.35 3.35 -21.22 -20.72 -25.76 -25.17 -30.198 -29.61 138.31 119.99 194.16 158.34 246.72 197.73 -122.6 -141.0 -156.3 -179.9 -192.72 -221.77 0.203 0.173 0.297 0.237 0.385 0.300 In Table 7, when stress exceeds the tensile limitation, we write the tensile value 4.3 Conclusion of chapter In the chapter 4, the author applied the “total strain crack” model which has been proposed in chapter and validated in chapter 3, to analyse the mechanical behavior of a typical reinforced concrete box girder for one-plane cable stayed bridge The calculation result clearly showed the stress-strain condition at reinforced concrete box slab, stress in reinforcement, and especially, indicated the local crack zone around the anchorage zone as well as the maximum crack width Theses results are important, especially to the bridge located in the corrosion environment (eg near by the sea) such as Bai Chay bridge The calculation result for different incline angle of cable, and different cable force also clearly explain the effectiveness of using steel pipe enhancement system for reinforced concrete box girder (like in Bai Chay bridge) The calculation result shows that the pipe enhacement system is reasonable, especially to the big angle cable, but not really useful for small angle cable 23 CONCLUSION AND PERPECTIVES In this thesis, the author has studied on the theoretical aspect, experimental aspect of reinforced concrete box girder in one-plane cable stayed bridge The literature review carried out in Chapter showed that the remaining problem to be considered in mechanical behavior of reinforced concrete box girder in one-place cable stayed bridge is to propose a suitable mathematical analysis model, which allows to calculate, evaluate the local stress-strain condition in the reinforced concrete slab of the girder, at the position near by the anchorage zone The position where the slab has to subjected to the local pull-out loading, overall bending, overall compression simultaneously Based on the literature review in chapter 1, in chapter 2, the author has studied on different models of reinforced concrete and propose to use the “total strain crack” model to modeling the behavior of reinforced concrete box girder in one-plane cable stayed bridge The proposed “total strain crack” model is then validated in chapter and applied to modeling a practical reinforced concrete box girder and clearly indicate the capability of this model for such type of problem This is also be the main and new scientic results of the thesis In chapter 4, the author applied the total strain crack model in modeling the stress-strain condition in a typical cross-section of reinforced concrete box girder subjected to incline cable force The calculation results show the effectiveness of the design enhancement solution The propose model in this thesis can be developed for analyzing the cable force which taking into account the impact loading (due to vibration of cable or break down of cable), fatigue analysis of reinforced concrete at anchorage zone of cable The propose model can also be applied to pre-calculate the effectiveness of enhancement solution at local anchorage zone of box girder, which are: - Directly anchorage to bottom face of top slab, - Using diagram; - Using pipe system; in order to choose the appropriate solution for each section, each girder This is also the direction for the next research of the author 24 PUBLICATIONS OF AUTHOR RELATED TO THE THESIS Bùi Ngọc Tình, Nguyễn Ngọc Long, Nguyễn Viết Trung, Ngơ Văn Minh: “Phân tích trạng thái ứng suất - biến dạng mặt cầu hiệu hệ tăng cường cầu dây văng mặt phẳng dây”, Tạp chí Khoa học Giao thơng Vận tải, số 56, (tháng 2/2017) Bùi Ngọc Tình, Nguyễn Ngọc Long, Nguyễn Viết Trung, Ngô Văn Minh: “Ứng dụng mơ hình nứt theo tổng biến dạng phân tích ứng xử phi tuyến bê tông cốt thép chịu lực nén xiên”, Tạp chí Khoa học Giao thơng Vận tải, số 72, 2019 ... Long, Nguyễn Viết Trung, Ngơ Văn Minh: ? ?Phân tích trạng thái ứng suất - biến dạng mặt cầu hiệu hệ tăng cường cầu dây văng mặt phẳng dây? ??, Tạp chí Khoa học Giao thơng Vận tải, số 56, (tháng 2/2017)... Long, Nguyễn Viết Trung, Ngô Văn Minh: ? ?Ứng dụng mô hình nứt theo tổng biến dạng phân tích ứng xử phi tuyến bê tông cốt thép chịu lực nén xiên”, Tạp chí Khoa học Giao thơng Vận tải, số 72, 2019 ... the girder 3,70 m Width of the top slab 25,00 m Width of the bottom slab 8,00 m Thickness of the top slab 0,25 m Thickness of the bottom slab 0,20 m Thickness of the web 0,35 m Material parameters
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