Nghiên cứu ứng xử cắt của dầm bê tông cường độ cao cốt sợi thép TT TIENG ANH

MINISTRY OF EDUCATION AND TRAINING UNIVERSITY OF TRANSPORT AND COMMUNICATIONS TRAN THI LY RESEARCH ON SHEAR BEHAVIOR OF HIGH STRENGTH FIBER REINFORCED CONCRETE BEAMS Field of study: Transport Construction engineering Code : 9580206 Major: Technical technology Construction of special works SUMMARY OF DOCTORAL THESIS HANOI - 2022 download by : skknchat@gmail.com This research is completed at: UNIVERSITY OF TRANSPORT AND COMMUNICATIONS Supervisors: Assoc Prof Pham Duy Anh Assoc Dao Văn Dinh Reviewer 1: Prof.Dr.Sc Reviewer 2: Prof Reviewer 3: Assoc Prof This thesis will be defended before Doctoral-Level Evaluation Council at University of Transport and Communications at … hours……Day……Month……Year…… The thesis can be found at: - Vietnam National Library - Library of University of Transport and Communications download by : skknchat@gmail.com INTRODUCTORY Question High-strength concrete (HSC) has a large compressive strength, but the tensile strength is still very small In addition to increasing the compressive strength, the tensile strength of concrete also needs to be improved to increase the bearing capacity of concrete and reinforced concrete structures To increase the tensile strength of concrete, it is common to use dispersed fiber reinforcement as a component of the aggregate in the concrete mix Steel fiber reinforcement (SFR) is one of the most commonly used types of fiber reinforcement Steel fiber reinforcement has the role of increasing tensile strength for concrete and high strength concrete Thereby increasing the contribution of the tensile region to the shear strength of the reinforced concrete beams In order to increase the shear strength of reinforced concrete beams, in addition to using traditional stirrups, oblique reinforcement, reinforcement made from new materials such as composite reinforcement, carbon fiber reinforcement, carbon stickers plate … were also applied The reinforcement bars enhance the shear resistance for beams significantly, however, using steel bars to reinforce shear resistance for beams will face some problems such as: Only increase the bearing capacity in the direction of the reinforcement; When using large diameter, the adhesion is not good, the distance of the reinforcement bars is too close, leading to difficulty in construction and erection, difficult to pour concrete, expensive production costs, etc., so using dispersed steel fibers to be inserted into the base phase of the project SFR increasing shear strength for beams is a new trend Research on shear behavior of steel fiber reinforced concrete beams (SFRC) has been interested by many scientists around the world Shear behavior of steel fiber reinforced concrete beams is always a complicated issue Shear failure is derived from inclined cracks caused not only by the shear force but also by the combination of shear force with bending moment, torque and axial force Shear failure depends on many factors such as size, geometrical characteristics, load effects and structural properties of the structural materials The comprehensive study of the shear behavior of SFRC beams helps scientists to come up with a more accurate calculation model In particular, the study of the shear behavior of SFRC beams using stirrups is a complicated topic that has not been studied much The topic of shear behavior of SFRC beams download by : skknchat@gmail.com needs more attention Stemming from that fact, the thesis proposed and implemented a topic called: "Study on shear behavior of high-strength steel fiber reinforcement concrete beams" Ressearch purposes - Research on the theory of shear behavior of SFRC beams and reinforced concrete beams in particular, thereby selecting a semiempirical model suitable for the calculation of shearing for reinforced concrete beams with reinforced concrete - Research and develop a formula for predicting the shear resistance of Hight strength SFRC beams, survey the factors affecting the shear resistance of Hight strength SFRC beams - Provide the shear design sequence for the SFRC beams subjected to the design load in the Standard of Road Bridge Design TCVN 118232017 - Experimental study to verify the proposed formula, study the types of shear failure in the Hight strength SFRC beams and study the deformation in the longitudinal reinforcement, the stirrups and in the concrete in the compression domain of the simple Hight strength SFRC beam Object and scope of the study Shear behavior of simple SFRC girder The design compressive strength is 70MPa The content of fiber reinforcement ranges from 0.5%-2% Dramix steel fibers, double crochet hook with variable length Dramix steel fiber reinforcement is a common type of steel fiber and has been applied to reinforced concrete structures in Vietnam Research Methods Method of combining theory and experiment in the room Scientific and practical significance The research results of the thesis contribute more to a model to calculate the shear resistance for high-strength concrete beams with steel fiber reinforcement, which helps researchers and designers to refer to their work The structure of the topic The thesis topic includes an introduction, main chapters, conclusions, recommendations and directions for further research, list of references and appendices download by : skknchat@gmail.com Chapter1 OVERVIEW OF STEEL FIBER REINFORCED CONCRETE AND STEEL-REFIED CONCRETE CONSTRUCTION BEAM CUTTING BEHAVIOR 1.1 Development history of reinforced concrete Around the world, from the period of Egypt and Babylon, people have used fibers or animal hair to strengthen bricks, plaster walls, plaster With Portland cement mortar, people use asbestos fibers The first studies on dispersed steel fibers were by Romualdi, Batson, Mandel Subsequent research was carried out by Shah and Swamy and several others in the US, UK and Russia In the 1960s, SFRC began to be used in pavement structures In the years 1989 - 1999, the standards of ACI 544 on fiber reinforced concrete were born, including volumes: 1R overview, 2R properties, 3R technology introduction, 4R-99 guide design guidelines for SFRC Up to now, there has been a set of 9R- forecasting based on measuring mechanical properties of rigid fiber reinforced concrete The standards have included the calculation content of SFRC structures such as ACI, DIN, AASHTO, EHE, Fib from 1988 to present In Vietnam, research on manufacturing fiber-reinforced concrete, steel fiber as well as studies on properties of steel-reinforced concrete by authors such as Tran Ba Viet, Nguyen Thanh Binh and Pham Duy Anh has been carried out, published in prestigious journals of the Industry Researches on fabricating fiber-reinforced concrete based on local materials by Ho Chi Minh City University of Science and Technology and for Traffic works by the Institute of Transport Science and Technology have also contributed to the development of this material in Vietnam The issues of ecological construction were initially interested and published in 2003 with the book "Steel fiber Reinforced concrete" edited by author Nguyen Viet Trung Researches on the mechanical properties and behavior of SFRC structure have also been studied by the authors in their doctoral thesis from 2000 up to now 1.2 Mechanical Features of SFRC Steel fiber reinforced concrete is a composite material, which improves the behavior of ordinary concrete after cracking The properties of concrete after cracking depend greatly on the adhesion force between the fiber reinforcement and the concrete The main role of steel fiber reinforcement is to stitch cracks, limit crack expansion, download by : skknchat@gmail.com make SFRC more flexible and absorb more energy than ordinary concrete Steel fiber reinforcement increases the tensile strength of concrete The greater the adhesion force between the steel fiber and the concrete, the greater the tensile strength of the reinforced concrete because the reinforcement is difficult to pull out of the concrete According to Lim et al The tensile strength of fiber-reinforced concrete is 2-3 times greater than the tensile strength of the sample without steel fiber when the fiber content is 1% and 1.5% The compressive strength of concrete does not increase significantly when using dispersed steel fiber reinforcement The research results at the University of Transport on the reinforced concrete beam structure show that the tensile strength when bending increases by 15-20% Lim et al confirmed that with steel fiber content from 0%-2%, the shear strength of reinforced concrete increases to 100% compared to normal concrete 1.3 Overview about researh on shear behavior of SFRC beams in the world and Vietnam In the world, from the 80s of the 20th century up to now, there have been many researches on the shear behavior of fiber reinforced concrete beams (SFRC) in general and SFRC slabs in particular In which, SFRC beams have been interested by many scientists around the world The research method on shearing of SFRC beams in the world today is mainly theoretical research combined with experiment or research based on the shear resistance calculation equations in the current standards Some studies are completely experimental to provide a model to calculate the shear resistance of reinforced concrete beams *) Researching method for calculating shear resistance of SFRC beams in current standards in the world: The equation in the current standards are based on experimental or semi-empirical studies by previous scientists To calculate the shear resistance of SFRC beams according to the models calculated in the current standards, a lot of input test parameters are needed In the RILEM TC62 TDF standard to calculate the shear strength SFRC beams needs the input parameters which are the characteristic flexural tensile strengths through the beam sample bending test In the ACI standard 544-4R 88, to be able to calculate the shear resistance of the SFRC beams, it is necessary to have the tensile strength parameters directly or indirectly through testing… The experimental parameters download by : skknchat@gmail.com are sometimes not available, so it is difficult to meet the requirements Many difficulties for predicting the shear strength of SFRC beams, especially when experimental data are not available  Theoretical and experimental study of shear behavior of reinforced concrete beams without using reinforcement The initial studies on shearing of SFRC beams focused on investigating the influence of factors such as fiber shape, fiber content and the ratio between the distance of the force application to the effective height of the beam (referred to as the ratio for short cutting span and effective height) Some studies, based on theoretical and experimental methods, have proposed formulas for calculating average shear stress on beam cross-section (νu) Previous studies have shown that steel fiber reinforcement contributes greatly to the shear strength of SFRC beams The authors study on the influence of content and other factors on shear resistance such as: Sharma, Narayanan and Darwish, Naaman et al., Lim and Oh, K S Elliott, C H Peaston and K A Paine; Joaquim A.O Barros and Lucio A.P.Lourenỗo Simao P.F Santos; Yoon Keunt Kwak, Mack O Eberhard, Woo-Suk Kim, and Jubum Kim; Two Palaces; Gustavo J Parra-Montesinos, M.ASCE and James K Wight suggested that the average shear stress in the SFRC beam is 0.33√f'c (MPa) when the reinforcement content is 0.75% - 1.5 % Experimental research on building models of shear resistance by authors such as Narayanan and Darwish; Yoon Keunt Kwak, Mack O Eberhard, Woo-Suk Kim, and Jubum Kim used the test results from the collected 139 SFRC beams to develop a formula for calculating the mean shear stress of the SFRC beam The authors Emma Slater, Moniruzzaman Moni, M Shahria Alam experimentally studied 222 fiber-reinforced concrete beams without reinforcement The authors have built a formula to calculate the average shear strength of beams by linear and non-linear regression methods for reinforced concrete and reinforced concrete beams In the calculation model, a quantity that needs to be determined through experiment is the adhesion force between the steel fiber reinforcement and the concrete The adhesion force between steel fiber reinforcement and concrete is a parameter that depends on fiber shape, fiber length as well as concrete grade It would be difficult without experimental data on this parameter  Theoretical and experimental study of the behavior of SFRC download by : skknchat@gmail.com beams using stirrups Around the world, there have been a number of authors studying the behavior of reinforced concrete beams using stirrups Studies often use computational models available in current standards Esefanía Cuenca in her thesis in 2014, used the shear resistance calculation model in EHE-08 standard and proved that steel fiber reinforcement can replace all or part of the reinforcement in beams The study of fiber reinforcement content, assessment of the contribution of fiber in SFRC beams and the behavior of beams using stirrups is very large However, the author does not research only for high-strength steel fiber concrete (HS SFRC) beams and also does not build a computational model for HS SFRC beams The authors all have the same conclusion that in girders with stirrups, steel fiber reinforcement increases shear resistance more than girders without reinforcement when having the same fiber reinforcement content Daniel de Lima Araújo, Fernanda Gabrielle Tibúrcio Nunes, Romildo Dias Toledo Filho and Moacir Alexandre Souza de Andrade have compared two types of fiber-reinforced concrete beams without stirrups and with low stirrups content (0.21%) Fibered content from 1% to 2% The authors used control beams without fiber reinforcement The results show that, when increasing the amount of fiber in the girder without reinforcement, the critical shear force increases less than when using the girder with reinforcement Meda, Minelli and Plizzari have experimentally studied on prestressed reinforced concrete beams with large I-section (real beam size), I-section with 0.64% fiber content Using reinforcement, it has been shown that fiber reinforcement significantly increases the shear resistance of beams In addition to considering the contribution of steel fiber reinforcement, the authors also believe that steel fiber reinforcement can replace the minimum reinforcement From the review of shear behavior studies in the world, it is shown that there are not many studies on high-strength concrete beams with steel fiber reinforcement Very few studies have built a model to calculate the shear resistance for only reinforced concrete beams with steel fibers, especially girders using stirrups From the above analysis, the thesis focuses on solving the following issues: Studying the mechanical properties of HS SFRC, especially the tensile behavior of the HS SFRC because it will serve to calculate the shear resistance of the HS SFRC beams Studying experimental models, theoretical models and standard models in the world, from which to choose a suitable model for SFRC download by : skknchat@gmail.com girders; Experimental study to determine the relationship formula between tensile stress after cracking of HS SFRC with fiber content and other parameters, thereby finding out the contribution of steel fiber reinforcement to tensile stress after the concrete is cracked; Research and propose formula for predicting shear resistance for HS SFRC beams; Research on beams of design dimensions to verify the formula in the proposed thesis; thereby evaluating some behaviors of the HS SFRC beams such as evaluating the force relationship and deflection between spans; the behavior in concrete in the compression domain, deformation in the main longitudinal reinforcement and the reinforcement by connecting the output device Research and propose the design sequence of shearing for SFRC beams under the effect of road bridge loads Chapter RESEARCH AND BUILDING MODEL FOR FORECASTING SHEAR RESISTANCE OF SFRC BEAMS 2.1 Destruction and shear force components of SFRC beams 2.1.1 Destruction of SFRC beams For SFRC beams that not use stirrups, fiber reinforcement acts as the stirrups in the beam Steel fiber reinforcement can redistribute the tensile stress in the beam, slow down the propagation and widen the inclined crack Prevents concrete splitting along the main longitudinal reinforcement bar The fiber reinforcement controls the crack width and promotes the formation of microcracks With that clear role, the deformation stiffness and bearing capacity of the beam are enhanced The analysis of shear strength in reinforced reinforced concrete beams faces many challenges The most important issue related to the reinforcement of fiber reinforcement is their proper distribution to form uniform mechanical properties In addition, the widening of the inclined crack in the SFRC beams is caused by the steel fiber reinforcement being pulled instead of the ductile reinforcement in the conventional reinforced concrete beams 2.1.2 Participating components are subjected to shear forces The components participating in the shear stress of the reinforced concrete beam include: The transmission of shear forces in the uncracked concrete area of the beam (Vcc); The transmission of surface shear forces due to the interlocking of aggregates and the roughness of the surface along the fracture inclined cracking (Va); Transmission of download by : skknchat@gmail.com shear force through the dowel effect of longitudinal reinforcement (Dowel Action) (Vd); Transmission of shear through residual tensile stresses in inclined cracks (Vcr); The transmission of shear forces through the shear reinforcement (Vs); Vertical component of the prestress force (Vp) For SFRC beams, in addition to the above components, there is also the participation of shear force transmission of steel fiber reinforcement (Vf) 2.1.3 Factors affecting the shear resistance of SFRC beams There are many factors affecting the shear resistance of SFRC beams such as: the ratio between the distance from the point of application of the force to the bearing and the effective height (ratio a/d); Effect of beam size; Effect of compressive strength of SFRC (fc'); Effect of steel fiber reinforcement content; Effect of longitudinal reinforcement content (ρ); Effect of fiber shape and size In which the steel fiber content is the factor that has the greatest influence on the shear resistance of the reinforced concrete beams 2.2 Models for predicting shear resistance of SFRC beams Models in the current standards In which, some standards have proposed to calculate the shear resistance of beams according to experimental models, others based on theoretical and experimental models Models in standards such as: ACI 544-4R88, RILEM TC 162, fib MODEL CODE 2010, EHE-08, DIN1045-1, MC2010… have proposed formulas for predicting shear resistance of SFRC beams with or without reinforcement Experimental model: There are many authors in the world who have experimentally researched and built predictive models of shear resistance SFRC beams, but the empirical models are often very simple and ignore a number of secondary factors One of the models that simply predicts the shear resistance of normal strength SFRC beams without reinforcement is proposed by Sharma However, it is necessary to more fully evaluate the factors affecting the shear resistance It is very expensive to build such a model purely experimentally because of the extremely large number of test samples Semi-empirical model Semi-empirical models such as: Modified compression field theory (MCFT), fixed angle soft truss model (FA-STM) and Rotating Angle Softened Truss Model (RA-STM), Sliding crack model (Crack Sliding download by : skknchat@gmail.com 11 The experimental results were analyzed statistically, the probability density function of the test samples corresponding to the cases of no fiber, short fiber and long fiber with different fiber content is shown in Figure 2.27, Figure 2.28 and Figure 2.29 StDev 0.8135 0.3259 0.5231 0.6115 N 15 15 12 12 0.6 0.6 Mean 5.679 8.484 9.401 11.39 0.5 0.4 StDev 0.8135 0.6956 0.5639 1.184 N 15 15 12 12 Variable N-0 % N-1% N-1.5 % D-0 % D-1% D-1.5 % 1.2 1.0 0.8 M ật độ Mean 5.679 6.929 8.201 10.15 0.8 Variable 0% D-0 % D-1% D-1.5 % 0.7 M ật độ 1.0 M ật độ 0.8 Vari abl e Không sợi N-0 % N-1% N-1.5 % 1.2 Mean 6.929 8.201 10.15 8.484 9.401 11.39 0.6 0.3 0.4 0.4 StDev 0.3259 0.5231 0.6115 0.6956 0.5639 1.184 N 15 12 12 15 12 12 0.2 0.2 0.2 0.1 0.0 10 11 Cường độ é p chẻ (M Pa) Figure 2.27 Normal distribution function of split compressive strength of fiberless and short fiber samples 0.0 10 12 0.0 14 Cường độ é p chẻ (M Pa) 10 12 14 Cường độ é p chẻ (M Pa) Figure 2.28 Normal distribution function of split compressive strength of fiberless and long fiber samples Figure 2.29 Normal distribution function of split compressive strength of short and long fiber samples Regression results found that the coefficients A and B for the two cases of reinforcing steel fibers are short fibers (Lf/Df = 63.63) and long fibers (Lf/Df = 80) shown in Figure 2.30 and Figure 2.30 2.31 The equations with the large R2 correlation coefficient are R2 = 86.3% (short fiber), R2 = 86.0% (long fiber) respectively, and these values are all greater than 80% This shows that the regression models are suitable and completely statistically significant fsp=5.426+2.950Vf Figure 2.30 Data processing results of samples using short fibers (lf/df=63.63) fsp=5.813+3.755Vf Figure 2.31 Data processing results of samples using long fibers (Lf/Df=80) Add the remaining parameters such as concrete strength, fiber size download by : skknchat@gmail.com 12 ratio into the regression equation, the post-cracking tensile strength of the reinforced concrete for both cases according to the proposed thesis as shown in equation (2 - 81) L (2-82)  f  0.37 f  f f 'c Df The model for calculating the shear resistance of the proposed SFRC beams From the experimental results to determine the residual tensile strength (after cracking) of the high-grade concrete as equation (2-82), replace this equation in (2 68) and (2 69), the thesis gives the formula forecast shear resistance of reinforced concrete beams of CST as (2-85) To take into account the effects of beam and arch effects, if the ratio a/d < 2.5, the formula is multiplied by 2.5d/a as shown in equation (2-86) L Vn  ( fc '  0.37 f f fc ' cot    z f szcr cot  )bv dv , a/d ≥ (2 85) Df Vn  2.5d / a( fc '  0.37 f Lf Df fc ' cot    z f szcr cot  )bv dv a/d < 2.5; (2-86) CONCLUSION CHAPTER Selecting a semi-empirical model to predict the shear resistance of SFRC beams is very important The semi-empirical model needs to predict relatively accurately the shear resistance of SFRC beams and the reinforced concrete beams Therefore, the Modified Compression Field model simply was chosed because of its suitability - In the simple modified compression field model, the quantity participating in the formula for calculating the shear resistance of SFRC beams is the main tensile stress (f1) Contribution to the main tensile stress consists of two components: the component due to concrete and the contribution of steel fiber reinforcement - The factors affecting the post-cracking tensile strength of reinforced concrete are fiber content, fiber shape, fiber length and concrete grade In which, fiber content is an important factor that greatly affects the tensile strength of SFRC Therefore, building a function of tensile strength depending on fiber content and other parameters to evaluate the contribution of steel fiber reinforcement to shear strength was performed Due to the difficulty of pulling the SFRC sample directly, the standard cylindrical compression test was performed - Postgraduate uses types of fibers as described above, with download by : skknchat@gmail.com 13 variable fiber content, to design the composition for 70MPa highstrength concrete mix Adjust the composition for SFRC mixes and cast 105 samples for splitting and 21 samples to test the compressive strength of each calculated grade - Based on the experimental results of split compression with 105 samples of HS SFRC, has built a formula to calculate the tensile strength of HS SFRC after cracking as formula (2- 82) - Combined with the model to calculate the shear resistance of SFRC beams selected in section 2.2.3, the researcher has built a formula to calculate the shear resistance HS SFRC beams for cases a/d ≥ 2.5 and a/d < 2.5 as in (2 85) (2 86) Chapter EXPERIMENTAL RESEARCH SHEAR BEHAVIOR OF SFRC BEAM 3.1 Experiment target Chapter conducts an experimental study on the shear behavior of reinforced concrete beams of the design size to verify the model proposed by the researcher and evaluate the behavior in the HS SFRC beams including cracking angle, deformation in compacted concrete, and deformation form in longitudinal reinforcement and stirrups under load until failure The girder size is selected to match the jacking capacity and design standards The 4-point bend beam model used for testing the reference beam according to ASTM C78 [39] 3.2 Design of experimental beams Beam size The beam structure must be designed so that only shear failure is not caused by bending (Figure 3.2) The girder size is selected so that the device can bend and break the beam The beam bending test was carried out at the Engineering Experiment Center Figure 3.2 Arrangement of reinforcement and measuring of the University of Transport positions for strain and deflection when bending the HS SFRC download by : skknchat@gmail.com 14 3.3 Calculate the shear resistance of the test beams according to the proposed model and investigate the influencing factors Forecasting shear strength of reinforced concrete beams and surveying fiber content Using the proposed model, calculate the shear resistance of HS SFRC beams Calculation of shear resistance for beam h=400mm Investigate the shear resistance of HS SFRC beams with dimensions as mentioned in the above section Using Dramix fiiber Lf/Df=35/0.55=63,636, with fiber content of: 0%, 0.63%, 1%, 1.5%, respectively The results show that the shear strength of beams increases greatly with increasing fiber content (Table 3.3) The fiber length has an influence on the shear strength of SFRC beams, according to the survey of large fiber lengths, the shear resistance of HS SFRC beams increases as shown in Figure 3.4 3.4 Calculation of test Figure 3.4 70MPa SFRC beam shear load resistance when using short fibers Calculation of test loads for (65/35) the purpose of predicting beam breaking loads due to shea r From there, consider the jacking capacity of the beam bending device From there, it is decided to choose equipment with suitable capacity to destroy the test beam Calculation results as in table 3.5 download by : skknchat@gmail.com 15 3.5 Conduct testing Fabrication of beams Figure 3.5 Construction of formwork for casting HS SFRC beams Conduct beam bending The beam bending device must have a jacking capacity greater than the maximum internal load causing shear failure as shown in table 3.6 Equipment at the University of Transport meets the Figure 3.7 Construction of formwork for casting SFRC beams Conduct beam bending above requirements Use a jacking device with a capacity of 100T to increase the load To measure the load acting on the beam, a load cell placed on the top of the beam is used as shown in Figure 3.8 The deflection sensor head is mounted in the middle of the span, the front of the beam and connected to the dosing device The strain gauges in concrete, longitudinal reinforcement and belt as shown in Figure 3.2 are connected to the measuring device Beams are loaded according to each download by : skknchat@gmail.com 16 level Loading rate according to the relationship of load (P) and strain 3.6 Results and analysis of results Shear resistance of test beam Table 3.7 is the data of the load measured when the beam fails and the experimental shear resistance, compared with the shear resistance calculated according to the model proposed in chapter The results show that the experimental beam shear resistance is higher than that of the shear strength with calculation However, it is not too large The results show that there is a similarity between theory and experiment The beam failure model is also expected Inclined cracks usually begin to crack from the middle or from the tension zone, grow to the compression zone, and then the beam breaks Use the ACI standard 544R88 for further control comparison Comparison results as in table 3.6  Analysis of destructive patterns All beams show inclined cracks and failure due to shear bending For reinforced concrete beams without steel fiber reinforcement, only main inclined cracks appear, when failure at that crack, the crack width is larger In addition to the main crack, many inclined cracks of smaller width appear near the main crack The angle of inclination of the crack is smaller than that of the beam crack without reinforcement download by : skknchat@gmail.com 17 Figure 3.9 Crack model in beam bending Beam B-0-300-6-300 Figure 3.10 Crack model in beam bending Beam B-0.63-300-6-300short fiber Figure 3.11 Crack model in beam bending Beam B-1-300-6-300- short fiber Figure 3.12 Crack model in beam bending Beam B-0.63-300-6-300-long fiber Figure 3.13 Crack model in beam bending Beam A-0-300-6-300 Figure 3.14 Crack model in beam bending Beam B-0.63-300-6-300short fiber  Analysis of load relationship and deflection between spans Figure 3.15 Graph of relationship between load and deflection between beam span H400mm download by : skknchat@gmail.com 18 Analysis of load relationship and deformation of concrete under compression Figure 3.16 Graph of internal load and deformation in concrete in compression beam H400mm Remarks, the graphs are relatively linear, concrete works in the elastic period Using steel fiber reinforcement with higher content, the greater the plasticity in compressive strength of reinforced concrete and the larger plastic deformation in concrete in the compression domain at failure Result of strain measurement in longitudinal reinforcement The graphs in Figure 3.17 and Figure 3.18 show that, because beams B0-300-6-300 not use steel fiber reinforcement, the main longitudinal reinforcement quickly melts when the load is very small The remaining beams when using steel fiber reinforcement, the content of steel fiber reinforcement increases, the main longitudinal reinforcement is plasticized more slowly, when the load is much larger The internal load capacity in longitudinal reinforcement increases when combined with fiber reinforcement because steel fiber reinforcement participates in tensile strength and limits the crack width Result of strain measurement in longitudinal reinforcement download by : skknchat@gmail.com 19 Result of strain measurement in longitudinal reinforcement at position T1(Figure 3.19) and T2 position as shown in Figure 3.20 The strain gauge graph also shows that the rebar flows more slowly in the beams with steel fiber reinforcement Non-boiled girder girder (B0300-6-300) is flexible at very small loads In contrast, the reinforcement in beams with high fiber content such as beams B0.63-300-6-300-SD and B1-300-6-300-SN only flows when the force is many times larger than that of the beam no steel reinforcement 3.8 Conclusion of chapter After building a model to calculate shear resistance for High strength SFRC beams, the model is verified by testing on beams with length 2.4m, height h=45cm and 40cm - Survey of the main quantities shows that the fiber content greatly affects the shear resistance With a fiber content of only 1% by volume, the cutting resistance is increased by 120% - The same fiber content, fiber shape, if the fiber has a larger size, according to the proposed model, it shows greater shear resistance - The angle of inclination of the main tensile stress of reinforced concrete beams is usually less than 45 degree - The results of the measurement of the critical shear force of the test beam show that the thesis model has relatively accurately predicted the shear strength of SFRC beam The results of bending the High strength SFRC beams are similar to the results calculated according to the model Thesis uses the formula in ACI 544-4R 88 standard for comparison, the results are also very similar - The destructive cracks also show that the cracks have an angle of inclination less than 45 degrees, consistent with the forecast of the proposed formula download by : skknchat@gmail.com 20 - Failure mode of HS SFRC beams according to shear and bending shear The inclined cracks of the HS SFRC beams appear more, the cracks are smaller and the gap is smaller for the steel fibers, which increases the ductility of the SFRC beams when subjected to shear Chapter RESEARCH APPLICATION OF CALCULATIONS CUTTING FOR ROAD BRIDGE HIGH STRENGTH BEAM USING STEEL REINFORCED 4.1 Overview In the world, many standards have introduced cutting calculation methods for SFRC beams such as: RILEM TC162 TDF, ACI 544-4R18, Fib Model code 2010, AASHTO LRFD 2017 In Vietnam, standards The road bridge design TCVN 11823-2017 has used a shear calculation model based on simple modified compressive field theory for reinforced concrete beams, but there is no calculation SFRC beams Proposing a cutting design method for the bridge girders of SFRC as well as reinforced concrete is very necessary when the project increasingly requires quality and longevity, it is necessary to use advanced materials such as steel fiber Therefore, the researcher proposes a shear design method for the SFRC girders for road bridge girders, with actual load HL93 The method can be a reference for engineers when designing for cutting 4.2 Shear design solution for road bridge girders using SFRC In the AASHTO standard, the improved compressed field model as analyzed above is applied In the calculation of shear resistance, the load and resistance factors are used The tensile stresses in cracked concrete constitute a very significant shear strength Modified compressive field theory (MCFT) considers the effect of primary tensile stress on shear behavior of reinforced concrete beams after crack formation The balanced equations for the modified compressive field theory (MCFT) can be obtained in a similar way to the compressive field theory (CFT) with the principal tensile stress in the concrete added For reinforced concrete beams, the mean main tensile stress after f1 cracking, suggested by Collins and Mitchell (1991) is as follows: f1  f cr  500 (psi) In the thesis, the average main tensile stress in the SFRC beams is proposed as follows: download by : skknchat@gmail.com 21 f1  0.33 f c '  5001 (1  v f )   f In which: σf - determined through practice, proposed in the thesis  f  0.37 lf df f f 'c Sequence of design With the theoretical analysis presented on the thesis proposed steps to shear design the SFRC beams with adjustment in the process of calculating the relevant quantities Calculation example Calculation of arrangement of stirrups for SFRC beams cross section T Load HL93 is specified according to standard TCVN11823-2017 *The size of the beam is as shown in the figure 4.5 Figure 4.5 Beam size Calculation results Calculation results of belt reinforcement for high strength concrete bridge girders with concrete grade 70MPa Using Dramix 3D 80/60 BG fiber reinforcement as described in Table 4.1 Calculation results of belt reinforcement for high strength concrete bridge girders with concrete grade 70MPa Using Dramix 3D 65/35 BG fiber is described in Table 4.2 download by : skknchat@gmail.com 22 Table 4.2 Calculation results of reinforcement for reinforced concrete beams when using short fibers Conclusion Chapter Chapter has given the design sequence of the high-strength concrete bridge girders using steel fiber reinforcement and traditional girders and bearing the design load HL93 according to the standard TCVN118232017 [1] - If the beam size is kept the same, using a very small amount of steel fiber reinforcement (νf