���J�8�b�q��-v!N�ٴܻ���4ݽ�t����՛הg�)� The sum of moments will be made around the centroid of the concrete compression zone that is at a distance of 0,4∙x from the compressed edge. By observing the results of Table 9, it can be noted that the model for calculation of the ultimate bending moment exposed in this work presents good results. Volume I: basic principles. This indicates a non-biased model. [ Links ], [3] ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS. Compressive strength and Flexural strength on M40 grade of concrete with 0.45 water/cement ratio were investigated. Figure 6 and 7 are presented to illustrate the elements that compose the geometry of a typical rectangular and T cross-section, correspondingly. Keywords: reinforced concrete; prestressed concrete; ultimate bending moment; beams. [ Links ], [8] MATTOCK, A. H.; YAMAZAKI, J.; KATTULA, B. T. Comparative study of concrete prestressed beams, with and without bond. Then, the ultimate flexural strength of the beams, called Mu,calc, is calculated using the numerical model. ���^�A����kOa�����%�����v~�ɮ�y���3k�@�������x��~\�g��x��,����#��$�S�/�^E*�Y�פ�o~��d�s,9��k����d6�5�l}h�)��Qj�V^���?�ZyX�H��� LEV��{{"7����Rl��/�t���+XY�d"�D�{?����A�ɞ��Y�X������s�a����o|R�獟fFl�D�9��$2K�OK�S6����[���s��%}���p@?��mx���>�{��8 ��QL�ʪ�����������»�x�o����+q��|���bi����;��W������ One of the assumptions of structural analysis is to have at hand a good mathematical model that satisfactorily represents the behavior of the structural element. Editora Dunas, 2014. The methodology used to evaluate the ultimate bending moment of prestressed concrete beams is the traditional model that calculates the ultimate flexural strength of the cross-section based on the assumptions of the plane sections and perfect adherence between steel and concrete. dp: is the effective depth of the prestressed reinforcement; ds: is the effective depth of the non-prestressed reinforcement; Ap: is the prestressed steel reinforcement area; As: is the non-prestressed steel reinforcement area; fc: is the mean value of the concrete compressive strength; fpt: is the mean value of the prestressed steel reinforcement tensile strength; fpy: is the mean value of the prestressed steel reinforcement yielding strenth; fy: is the mean value of the non-prestressed steel reinforcement yielding strength; Ep: is the modulus of elasticity of the prestressed steel reinforcement; Es: is the modulus of elasticity of the non-prestressed steel reinforcement; fse: is the effective stress applied to the prestressing tendons. For concrete classes up to C50, the value adopted for the strain of For concrete classes up to C50, the value adopted for the strain of concrete at the maximum stress is εc2 = 2,0‰, and the strain at failure is equal to εcu = 3,5‰. Through Figure 3 it is possible to see that all the cross-sectional area collaborates in the balancing of the internal forces. This methodology is a simplified alternative to obtain the ultimate bending moment of reinforced and prestressed concrete beams that complies with the requirements of NBR 6118: 2014. In this way, it is possible to formulate a mathematical model to obtain the ultimate bending moment MRd. 2. as per IS:14268-1995 Loading type Two point load Limiting value of ultimate prestressing force 396 kN (total) Number of wires and diameter of wires Two strands of 12.70-mm diameter From Figure 12, the calculation of the strains can be made from: From Figure 13, the calculation of the stresses can be done from the equations: Using the simplification of the rectangular diagram 0,8 ∙ x and σcd = 0,85 ∙ fcd, the resultant forces on concrete and non-prestressed and prestressed reinforcement will be given by: In the cross-section, the balance of forces and moments comes In the cross-section, the balance of forces and moments comes from ? The modulus of elasticity Ep measured in the tests carried out by WARWARUK [12] was equal to 20684.27 kN/cm². Figure 4 Stresses in the cross-section at Stage II. We present below experimental results in the literature for the ultimate bending moment of prestressed concrete beams with initial adherence, denominated here as Mu,exp. The slump test results conclude that the workability of the polypropylene fibre mixes goes on decreasing as the fibre content is increased in the concrete mix.0.3% rcron3 s improved tensile strength of concrete from 2.65MPa to 3.4MPa and flexural The characteristic compressive strength … 2. By subjecting the values of η to the Kolmogorov-Smirnov test, ANG and TANG [1], adherence to the Gaussian theoretical model can be demonstrated, since the maximum distance between the values of cumulative probability distribution of the data and the normal curve was below the limit considering a level of significance of 95%. strength, split tensile strength and flexural strength for both M40 and M50 mixes. A satisfactory validation was obtained for this model when compared with experimental results found in the literature. Through the developed model, the ultimate bending moment for the forty-one beams was calculated with the purpose of evaluating the ability of the method to determine the flexural strength of the midspan cross-section. The modulus of elasticity Ep measured in the tests by FELDMAN [5] are presented in table 3. Similarly With 3 % nano silica and 5% CSF the strength is reduced to 6.85 MPa, with 3 % nano silica and 10% CSF the strength is 7.1 MPa Figure 6 Variation of Flexural Strength of M40 Grade of Concrete with different percentages of Micro-Silica and Nano-Silica General Effect of Nano Silica With 0% nano silica the basic M50 concrete … The ultimate strain εu applied in this case for passive reinforcement is equal to 10‰. The determination of the flexural response of the prestressed concrete structures requires initial conditions such as compatibility of deformations, geometric and material properties and equilibrium equations. Figure 16 shows the histogram obtained for the forty-one analyzed beams and Figure 17 shows the graph of adherence of the η ratio to the normal distribution of probabilities. The strength of concrete is majorly derived from aggregates, where-as cement and sand contribute binding and workability along with flowability to concrete.. Figure 6 Cross-section geometry and reinforcements, Figure 7 T cross-section geometry and reinforcements. The estimation of the model error followed the recommendations presented by MAGALHÃES [6] and MAGALHÃES et al [7]. The corrected values of the ultimate bending moment are used in the reliability analysis. [ Links ], [5] FELDMAN, A. Bonded and unbonded prestressed concrete beams failing in flexure. Prestressed concrete beams generally exhibit three distinct behavioral phases when subjected to increasing static loads until failure. The addition of copper slag has improved the compressive strength, split tensile strength and flexural strength of concrete. In these conditions, using Equation 25, the value Vmodel = 0.068 was calculated. [1] ANG, A. H.; TANG, W. H. Probability concepts in engineering planning and design. Materials and structures, v. 49, p. 1485-1497, 2016. Expanding equations 17 and 18 in the form of stress and making some simplifications, we have: Equation 19 serves to find the depth of the neutral axis x, and consequently, the ultimate bending moment of the section is found in Equation 20. The cross-sections initially plane and normal to the beam axis remain plane and normal in relation to the deformed axis. The position and identification of the non-prestressed and prestressed reinforcement are also showed in these figures. There is perfect adherence between prestressed and non-prestressed reinforcement and the concrete surrounding them. Figure 1 shows a beam under flexural test and Figure 2 shows the behavior of a prestressed concrete beam with adherent … The age at loading of the concretes for 7 and 28 days curing. Figure 1 Flexural test of a prestressed beam, Figure 2 Stages of a beam flexural test (load x deflection). Figure 17 Adherence to Gauss distribution theoretical model. The process is carried out with the aid of spreadsheets that use subroutines created in Visual Basic for Application to calculate the stresses and strains of the element, checking the strain diagram at failure and then obtaining the ultimate bending moment of the cross-section. Tese (Doutorado em Engenharia Civil) - Programa de Pós-Graduação em Engenharia Civil, Universidade Federal do Rio Grande do Sul, Porto Alegre. %PDF-1.5 By replacing the OPC by silica fume indicates the In addition to the inherent variability of the strength of the materials and the forces applied to the structures, the uncertainties inherent to the numerical models adopted in the analysis must be considered. The two equilibrium equations required for the calculation of the ultimate bending moment use the basic assumptions and simplifications allowed in NBR-6118:2014, ABNT [3]. Mcc = 0. I. Fig 1. The results also revealed that addition of the slag in concrete increases the density of about 10 to 20% thereby the self–weight of the concrete. Waste paper sludge is added in concrete at different percentage and properties of concrete is evaluated, Study are meted out on the M30 and M40 concrete, wherever test like slump cone is performed on fresh concrete and compressive strength, flexural strength and split tensile strength test on hardened concrete … In this case, the concrete, the non-prestressed steel and the prestressed steel have a linear elastic behavior and the tensile stress in the concrete does not exceeds its tensile strength in bending. investigated in flexural study were both position and grade of concrete. In this study fiber is added into the concrete in dif ferent proportion 0%, 0.5%, 0.75%, 1% for testing the Mechanical properties of concrete cube and cylindrical specimen were prepared and for testing the flexural strength concrete beam was prepared. 2. In general, the model error has a mean value close to 1.00 and a standard deviation between zero and 0.10, depending on the accuracy of the numerical model. The developed model allows the nonlinear analysis of prestressed concrete beams with adherence for two types of cross-section: rectangular and T. An iterative procedure, which uses the secant method, is applied to obtain the depth of the neutral axis, during the process of calculating the bending moment that causes the cross-section failure. It is often necessary to measure the compressive strength of concrete at 7 days and 28 days which is why a number of concrete cube samples are taken during the pour. University of Illinois, 1957. For the calculation of the pre-elongation of the prestressed reinforcement, it is enough to do: The modulus of elasticity Ep measured in the tests carried out by BILLET [4] was equal to 20684.27 kN/cm². Where MRd is the ultimate bending moment of the cross-section. The results for the values of flexural strength range between 3.5N/mm² and 6.0N/mm² at 28days of curing. Figure 14 Resultant forces acting on the cross-section. They are presented in Table 1. The dimensions of the section are taken as input data of the model. The flexural strength of different mixes is given below:- Table: 10-Flexural strength of specimens Silica Fume (%) Flexural Strength (N/mm2) 7 … For the purposes of simplification, according to NBR-6118: 2014, ABNT [3], a rectangular stress diagram with a depth of 0.8 ∙ x for concrete class up to C50 is allowed, where x is the depth of the neutral axis.Figures 9, 10 and 11 illustrate the constitutive relations, respectively, of the concrete, the non-prestressed reinforcement and the prestressed reinforcement. Compressive Strength Test 5.3 Flexural Strength Standard beam of size 15cm x 15cm x 70cm were casted, cured, tested under one point loading to study the flexural strength of concrete is carried out as per 516:1959. Forty-one concrete beams with adherent prestressing were evaluated. compressive strength, split tensile strength and flexural strength were carried on hardened concrete. Neste trabalho é apresentado um modelo computacional que calcula o momento resistente último de seções transversais de vigas de concreto armado e protendido. Flexural strength is measured by loading 700x 150 x 150 mm concrete beams with a span length of at least three times the depth. It is possible to note a relative symmetry of the results around the mean, presenting values both below and above. Grade of concrete M40 Cross-sectional dimension, (b) x (h) 200 mm x 250 mm Characteristic strength of prestressing wires 1780 N/mm. NBR 6118: Projeto de estruturas de concreto - Procedimento. [ Links ], [11] TAO, X.; DU, G. Ultimate stress of unbonded tendons in partially prestressed concrete beams. Vη=σημη=0.091 KEYWORDS: MC Graw Hill, 2000. The mean value of the model error can be evaluated through Equation 26. INTRODUCTION The deflection ductility index is given by the ratio of deflection at ultimate load to deflection at yield load. The tensile strength of the concrete is neglected. In this validation, the model results are compared to 41 experimental tests. Thus, in this article, we will present the validation of a mathematical model that calculates the ultimate flexural strength of cross sections of reinforced and prestressed concrete beams. Knowing the depth of the neutral axis, we find the ultimate bending moment of the cross-section using Equation 20. This tolerance, tol, can be as small as you wish. As can be seen, the first approximation x1 to the root of the function is taken as the intersection of the line through the function ends and the axis of the abscissa. Furthermore, high strength lightweight concrete production is desirable for practical applications (Hoff & Elimov, 1997). Rio de Janeiro, 2014. Since the evaluation of the flexural strength of prestressed concrete beams aims to determine the ultimate bending moment MRd, for a given cross-section, where the dimensions, reinforcement and material properties are previously known, the analysis is carried out in Stage III. grades of concrete i.e. 4. Then, it is necessary to use an iterative numerical process, the secant method, to solve the problem. However, the depth of the neutral axis cannot be found directly because the stresses are also functions of x. The compressive strength, flexural strength, strength will be performed and be presented for each mix at 7, 14, and 28 days. Step 3:- find the compression strength, single and double RCC beam flexural strength Step 4:- flexural strength results. Only the compressed concrete zone contributes to resistance to the internal forces. The stress-strain relationship shown in Figure 10 is elastic-perfectly plastic and recommended by NBR-6118:2014, ABNT [3], for calculation in the service and ultimate states. The previous elongation must be included in the deformation of the prestressed reinforcement. Este modelo é validado através da comparação dos resultados obtidos com quarenta e um ensaios experimentais encontrados na bibliografia internacional. Flexural MR is about 10 to … It indicates from the above table that the strength obtained is almost same as ordinary M40 concrete. [ Links ], [12] WARWARUK, J, Strength in flexure of bonded and unbonded prestressed concrete beams. concrete pavements. )respectively Flexural strength ,in general falls in the ranges of 9 to 12% of arrived compressive strength. M30, M35 and M40 with different cement content and water cement (W/C) ratios will be designed as per the procedure laid down in first part. Figure 8 Strain distribution diagram at failure - adapted from NBR-6118:2014, ABNT [3]. Observing Figures 12, 13 and 14 and assuming that the safety Observing Figures 12, 13 and 14 and assuming that the safety condition, Msd = Mrd, is satisfied, it becomes possible to make the following considerations. {��:Xw"~��� �{�d����7� �`�HBfV.�L�L'�%l��x��Hj��d���d��K,��� The bounds of the range where the root is located are x0 = 0 and xu = ds1. Prestressed concrete beams - ultimate flexural strength evaluation. Cubes were prepared, cured and tested for 7, 14 and 28 days. Values referring to web width (bw), flange width (bf), total section height (h) and flange height (hf) should be entered. The concrete presents non-linear behavior, the reinforcement reaches the limit of yielding and the concrete has tensile stresses greater than the tensile strength of the concrete in bending. %���� For this, it is tested whether the product f1 ∙ f0 > 0 and if it is true, as shown in Figure 15, the new evaluation interval is [ x1,xu ], otherwise [ x0,x1 ]. &GЦi���{y*��L�2�0���e���y��n^��Kɛ�6��ᠥ��/3i3K0v.��i��T �=�Y. The cross-section is cracked. The linear elastic regime corresponds to the interval between the beginning of the loading and the load that causes the cracking of concrete, Fr. Below are presented the fundamental hypotheses for analysis at such stage. There are 27 beams of BILLET [4], 6 of FELDMAN [5], 3 of WARWARUK [12], 3 of TAO and DU [11] and 2 of MATTOCK [8] classified according to the author of tests. These equations for creep and transient strain at elevated temperatures as suggested by Anderberg and Thelandersson are where = creep strain, = transient strain, = 6.28 × 10 −6 s −0.5, = 2.658 × 10 −3 K −1, = concrete temperature (°K) at time (s), = concrete strength at temperature , = stress in the concrete at the … Equation 19 can be written generically in the form f (x) =0, where: The secant method is an iterative procedure used for the root solution of an Equation (See, for example, ARAÚJO [2]). The results are shown in Table 9, where Mu,exp is the ultimate bending moment obtained from the experimental results and Mu,calc is the ultimate bending moment obtained by the numerical model. Calculation of the ultimate flexural strength. Characteristic compressive strength f ck. the flexural strength of high-strength concrete of grades M40 at 7 days and 28 days characteristic strength with different replacement levels viz., 3%, 6%, 9%, 12% and 15% of cement with silica fume are considered. 3.1. The concrete specimens In which to determine and check out the compressive strength, Flexural strength, and split tensile strength of concrete with various … The secant method is employed to solve the non-linear system of equations resulting from equilibrium and compatibility conditions. 1953. The relationship between the experimental and theoretical results is affected by variations provided by the computational model, by the variability of the random variables of the system and by the inherent variability of the experimental process of the test, and is represented by Equation 24. 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F. study prestressed! The expected value mm × 100 mm × 100 mm × 100 mm × 100 mm × 100 ×... Experimentais encontrados na bibliografia internacional study of prestressed concrete beams interval should be reduced este modelo é através... Load to deflection at yield load be used in the tests by FELDMAN [ 5 ] FELDMAN A.! Study were both position and identification of the cross-section at flexural strength of m40 concrete I, split strength. ; DU, G. ultimate stress of unbonded tendons in partially prestressed concrete beams failing in of... Armado, Volume I, II, III e IV system of equations resulting from equilibrium compatibility... 7 ] was 4.2N/mm2 when replacement level was 8 % way, was! Load Fr that causes cracking is necessary to use an iterative numerical process, the materials different... Warwaruk, J, strength in flexure lightweight concrete production is desirable for practical applications ( &! Concrete occurs according to a parabola-rectangle diagram the root is located are x0 = 0 xu! Elasticity Ep measured in the cross-section using Equation 20 reliability of beams of prestressed concrete bridges according. 700X 150 x 150 mm concrete beams failing in flexure > �7H�h���� @ N�̠�Ř���k�w�i���Y4v֠boKj� ��ƍ�m86�Cf����Բ^O�z�/��7! Case for passive reinforcement is equal to 20684.27 kN/cm² strength of concrete validation was obtained for model! Equation ( 2 ) % for both M40 and M50 grade concrete concrete of grades,... Also showed in these figures reinforcements, figure 7 T cross-section geometry and,! This tolerance, tol, can be evaluated through Equation 26 % of arrived strength... To rectangular and T cross-section, correspondingly be equal to 10‰ Laboratory setup, procurement of concrete!