Mechanics, Materials Science & Engineering, September 2016
ISSN 2412-5954
Determination of Bond Capacity in Reinforced Concrete Beam and Its Influence on the Flexural Strength Mohammad Rashidi1, Hana Takhtfiroozeh2 1
Department of Civil Engineering, Sharif University of Technology, Tehran, Iran
2
Department of Civil Engineering, Building and Housing Research Centre, Tehran, Iran DOI 10.13140/RG.2.2.18300.95361
Keywords: flexural strength, bond capacity, tensile bars, reinforced concrete beam, compressive strength
ABSTRACT. This paper presents results of an experimental investigation of actual performance of the reinforced concrete beam in bond under flexure, when reinforced with tension steel is going to consider. In this experiment four specimens of beam and a bar in the middle of the width of the beam has been used and 2.5 cm of concrete cover has been considered from the center of the bar. In addition, transverse bars have been used to reassure lack of shear yield at the two ends of the beam. Flexural bar has been put in the middle of the beam symmetrically and the length of the flexural bar in each of the samples shall be: 15, 20, 30 and 40 cm. Three cylindrical samples were made in order to determine f'c and were examined at 28 days and the compressive strength of concrete used in this study was about 35 MPa. The beam samples were examined after 28 days via two-point loading system. Based on the results, increasing the length of bar causes increase of flexural strength. The presence of longitudinal rebar resulted in the ultimate momentum to be more than the crack momentum of the cross-section in parts which have broken at the point of longitudinal bar cut.
Introduction. Concrete is of a lot of use in constructions due to availability, appropriate compressive strength and ease of implementation; although, its weakness in traction has resulted in not being able to use this material solely in construction. In order to eliminate the weak traction of concrete, usually bar is used in the tensile area of the concrete. The goal of this experiment is to determine the bond strength between steel reinforcing bars and concrete. The main parameters that influence this bond strength are well documented in the technical literature. Important among these parameters include development/splice length, diameter of the reinforcing bar, and concrete compressive strength [1, 2, 3, 4]. The type of cracking leading to failure has been investigated using deformed bars in tension by injecting ink around the bars [5, 6]. The bond strength of rebars in concrete decreases as the embedment length increases, and decreases with increasing the bar diameter [7]. The previous investigations proved that the bond strength of rebars in concrete is influenced by the development length rather than the bar diameter [8]. The ultimate bond strength seems to be a function of c f 'c when other parameters are constant, since the bond strength is related to the tensile strength of concrete. Studies on understanding the nature of bond, modes of failure and factors influencing the failure, bar spacing and beam width, end anchorage, flexural bond and anchorage bond with high strength ribbed bars have been reported [9]. The slip of deformed bars is due to (i) splitting of concrete by wedge action, and (ii) crushing of concrete in front of the ribs [9]. Nilson [10] used slope of steel strain curve to evaluate the bond stress at a given load in reinforcing bar, and a new test method was adopted to study the local slip, secondary cracking and strain distribution in concrete [11]. A bond stress-slip model has been proposed to predict the load end slip and anchorage length of bars extended from adjoining beams in to exterior columns under large nonlinear actions [12]. Effect of bar diameter, confinement and strength of concrete on the bond behaviour of bar hooks in exterior beam-column joints has been reported [13]. The bond strength decreases as the bar diameter increases. The post-peak bond-slip response was not influenced by the bar diameter [14], while confinement has direct influence on the local bond stress [15]. A new bond MMSE Journal. Open Access www.mmse.xyz
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Mechanics, Materials Science & Engineering, September 2016
ISSN 2412-5954
stress-slip response has been simulated recently by Abrishami and Mitchel [16]. However, consistent bond stress-slip response was obtained on short embedment length [17]. A mathematical model for bond stress-slip response of a reinforcing bar due to cyclic load has been reported [19]. Other models to predict the tensile strength of concrete from the pullout load has been reported [20]. Confinement by ordinary steel reinforcement has improved the bond strength with significant ductility [21]. Several studies on bond in normal strength concrete (NSC) have been reported [22]. In high strength concrete (HSC), increasing the development length does not seem to increase the bond strength of deformed bars when the concrete cover is relatively small. A minimum confinement reinforcement needs to be provided over the splice length in RC members when HSC is used [23]. An expression has been proposed to estimate the extra confinement reinforcement [24]. Also more general information on the local bond can be seen in CEB-FIP Report [25]. This paper studies bond capacity in reinforced concrete beam and its influence on the flexural strength. Firstly it introduces materials and test methods. Then it presents the comparison of the results of the experiment with the existing theories. Materials and methods. In this experiment four specimens of beam and a bar in the middle of the width of the beam has been used and 2.5 cm of concrete cover has been considered from the center of the bar. Also, transverse bars have been used to reassure lack of shear yield at the two ends of the beam. Flexural bar has been put in the middle of the beam symmetrically and the length of the flexural bar in each of the samples shall be: 15, 20, 30 and 40 cm. Three cylindrical specimens were made in order to determine f 'c and were examined at 28 days and the compressive strength of concrete used in this study was about 35 MPa. The beam samples were examined after 28 days via two-point loading system. The considered mix for the samples has been shown in table 1 below. According to the instructions, coarse aggregates have been sieved via a 2-cm sieve. Also, the samples considered in construction are three cylindrical samples in 30 15 cm dimensions and four beams samples in 60 10 10 cm dimensions. Due to the fact that the goal of this experiment is to determine the capacity of sliding bar from within the beam; therefore, bars with different lengths in each bar have been applied. Longitudinal bars are of for observing this space, spacer has been used. The existing spacers in the laboratory were of more height; therefore, in order to convert this height to 2.5 cm, we cut them. All the beams have the same shear bar and their design was conducted as over design. Shear bars were placed 5 cm from the bar up to 20 cm with the distance of 5 cm between according to Fig.s 1 to 4. Table 1. The considered mix for the samples. Part
Weight Ratio (kg/m3)
Cement
500
Sand
800
Gravel
800
Water
220
Total
2320
With regard to the fact, that the goal of this experiment was determination of the bond strength between steel reinforcing bars and concrete, 4 produced beam samples during the length of the main bar are different and the flexural bar shall be placed symmetrically from the middle of the beam in a manner, that the length of the flexural bar in each of the samples is: 15, 20, 30, 40 cm.
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Mechanics, Materials Science & Engineering, September 2016
ISSN 2412-5954
After reinforcement of samples according to Fig.s 1 to 4, the stages of concreting and curing of concrete shall be conducted and then the samples shall be examined after 28 days of curing. Dimensions of cylindrical samples and beam samples are also shown in table 2 and 3 respectively.
Fig.1. Samples No. 1, longitudinal bar of 40 cm.
Fig.2. Samples No. 2, longitudinal bar of 30 cm.
Fig.3. Samples No. 3, longitudinal bar of 20 cm.
Fig.4. Samples No. 4, longitudinal bar of 15 cm. Table 2. Dimensions of Cylindrical Samples. Sample No. 1 2 3
The Average Diameter (Cm) The Average Height (Cm) 15.2 30.4 15.2 30.3 15.2 30.6
Table 3. Dimensions of the Beam Samples. Sample No. 1 2 3 4
Length (Cm) 60.20 60.30 60.20 60.25
Width (Cm) 9.95 10.25 10.1 9.95
Height (Cm) 10.10 10.15 10.02 10.25
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Mechanics, Materials Science & Engineering, September 2016
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It should be noted that the compressive strength test of the samples shall be conducted after cappingthe goal of which is to create a flat surface on the sample. All the beams which were experimented on were 60 centimetres long they were placed on a 55centimetre- wide support and were loaded and tested. Two concentrated symmetrical loads which were 25 centimetres away from each other were used for loading purposes. The weight of the rods which are placed on the beam was 37.8 kg. The used bars in this experiment are of type A2 and the current strength of 300 mpa. The loading model of the beams can be seen in Fig. 5.
Fig. 5. The loading model of the beam. With regard to the suggested relationship in the regulations, the amount of modulus of elasticity of concrete is: (1)
Table 4. The Result Modulus of Elasticity of Concrete for the Samples Sample No.
Compressive force KN
Stress Mpa
Ec
1
706.0
39.95
31603
2
730.0
41.30
32132
3
511.6
28.15
26530
Average
649.2
34.46
29351
Discussion of test results. In the flexural load of the reinforced beam, at the beginning of loading due to the lowness in the amount of tensile and compressive stress in concrete, the part operates in an elastic and linear manner. The linear behavior continues until when the stress in the last warp of the tensile area of the crossof the bar is known as the elastic stage. In order to calculate the crack momentum of the concrete cross-sections (meaning the least of flexural momentum which causes the fraction of the cross-section), an approximate but simple method, which is based on the distribution of linear stress and applying module of rupture of concrete, is used. Until the time when the most tensile stress in one flexural cross- section does now exceed the tensile strength of the concrete, the cross- section will remain in the elastic mode. In this mode, the crossMMSE Journal. Open Access www.mmse.xyz
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Mechanics, Materials Science & Engineering, September 2016
ISSN 2412-5954
section will remain uncracked and distribution of stress is linear. Therefore, in order to determine the stress, it is possible to use the classic relations of material strength. Another matter which is discussed in relation to the elastic stage is the calculation of crack momentum. A simple and practical method which is applied for this calculation, is the use of the order of the relation of determining crack momentum of a tensile cross- section is according to equation 2:
(2)
- section in relation to the neutral axis and It is worth mentioning that in the regulations, for the ease of calculation, a simpler relation is suggested instead of the above relation:
(3)
In which Ig is the moment of inertia of the whole cross- section in relation to the central axis of the cross- section without taking steel into account and yt is the distance of the furthest tensile warp from the central axis of this cross- section. According to the regulations, the module of rupture for concretes with normal weight is kg/ cm2:
(4) The results of the experiment for different samples of beam are as follows: As can be seen in Fig. 6, the crack has begun precisely from under the load in Sample number 1 in a flexural manner and by increasing the load, the crack progressed and ended at the point of applying the load and the beam failed completely.
Fig. 6. Failure of beam No. 1 MMSE Journal. Open Access www.mmse.xyz
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Mechanics, Materials Science & Engineering, September 2016
ISSN 2412-5954
For sample number 2 according to Fig. 7, the flexural crack was established at the point of cutting the longitudinal bar and developed through increasing the load and caused the beam to break.
Fig. 7. Failure of beam No. 2 Based on Fig.s 8 and 9 for sample number 3 and 4 respectively, the flexural crack was established at the point of cutting the longitudinal bar and developed through increasing the load and caused the beam to break.
Fig. 8. Failure of beam No. 3
Fig. 9. Failure of beam No. 4. MMSE Journal. Open Access www.mmse.xyz
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Mechanics, Materials Science & Engineering, September 2016
ISSN 2412-5954
With regard to the existing methods in the discussion of traction of the parts of the reinforced concrete, in order to calculate crack momentum of the cross- section and the ultimate momentum of the crosssection, the following equations can be applied. While the required equation for calculation the ultimate momentum of the cross- section, with regard to the ultimate compressive force which was tolerated by the cross- section is mentioned below Crack momentum:
(5)
The ultimate momentum of the cross- section via the Whitney rectangle method:
(6)
The ultimate momentum on the cross- section:
(7)
The created momentum in the x distance from the base to the concentrated load:
(8)
Considering the above- mentioned equations and the results of the experiment, the below table can be established and it is possible to compare the results of the experiment with the applied theories in the concrete lesson and conduct the required analysis. Table 5. Comparison of the Results of the Experiment with the Existing Theories. Sample No.
Compressive Crack Ultimate Momentum force (KN) Momentum of the Cross- Section (t.m.)
Maximum of Created Momentum at the CrossSection (t.m.)
Created Momentum at the Rupture of the Cross- Section (t.m.)
1
26.0
0.065
1.52
0.1950
0.1950
2
12.4
0.065
1.54
0.0930
0.0775
3
11.8
0.062
1.50
0.0885
0.0885
4
10.8
0.064
1.55
0.0810
0.0810
In beams number 3 and 4 the crack was at the place of bar cut and because in this beams the length of the tensile bar was less than the distance between the two point forces, the momentum which caused the beam to break is the maximum momentum forced on the beam which was almost 40% more than the crack momentum of the cross- section. In beam number 2, the tolerated momentum MMSE Journal. Open Access www.mmse.xyz
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Mechanics, Materials Science & Engineering, September 2016
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was 5% more than beam number 3 and 15% more than beam number 4 which is in accordance with the existing theories and in beam number 2 the momentum is less than the tolerated maximum momentum at the place of the crack which indicates the fact that the length of the applied bar was shorter that what could prevent the beam from breaking. The results show that increasing the length of the bar results in increase of tolerable momentum by the cross- section. Even in beams number 3 and 4, where the crack was between the two forced loads and occurred at the bar cut, the tolerated momentum in beam number 3 was almost 10% more than beam number 4; whereas, according to the existing methods, the tolerated momentum should be equal at the two cross- sections. While the tolerated momentum in beam number 4 was 8% more than the experimented samples in the flexural experiment of the simple concrete samples, which carries the point that the presence of longitudinal bar influenced the increase in the capacity of the freight of the cross- section. Through comparing the tolerated momentum by the cross- section and the crack momentum and the ultimate momentum which resulted from the theory, we can reach the conclusion that the momentum which caused the crack in the cross- sections without longitudinal bar (breaking at the longitudinal bar cut) is more than the crack momentum; whereas, it should be equal to the crack momentum. Although this increase in strength can be due to the safety factors used in the equations and applying these factors is because of problems which exist in performance, such as less strength of concrete compared to the calculated amount. But in this experiment, due to thoroughness in performance and application of compressive strength which resulted from the experiment, the existing error is insignificant and has caused the tolerated momentum to be more than the crack momentum. In beam number 1 the crack was at the point where the bar was longitudinal but the tolerated momentum was far less than the ultimate momentum calculated by the Whitney rectangle method and is in no accordance with the above theory. Summary. The purpose of this study was to make an effort to determinate bond capacity in reinforced concrete beam and its influence on the flexural strength. The result gained from this study are as follows: In beams that the length of the tensile bar was less than the distance between the two point forces, the crack took place at bar cut place and because in this beams, the momentum which caused the beam to break is the maximum momentum forced on the beam which was almost 40% more than the crack momentum of the cross- section. In beam number 2 (the flexural bar of 30cm), the tolerated momentum was 5% more than beam number 3 (the flexural bar of 20cm) and 15% more than beam number 4 (the flexural bar of 15cm) which is in accordance with the existing theories and in beam number 2 the momentum is less than the tolerated maximum momentum at the place of the crack which indicates the fact that the length of the applied bar was shorter that what could prevent the beam from breaking. Increasing the length of the bar results in increase of tolerable momentum by the cross- section. The momentum which caused the crack in the cross-sections without longitudinal bar (breaking at the longitudinal bar cut) is more than the crack momentum; whereas, it should be equal to the crack momentum. Although this increase in strength can be due to the safety factors used in the equations and applying these factors is because of problems, which exist in performance, such as less strength of concrete compared to the calculated amount. References [1] Darwin, D., Zuo, J., Tholen, M.L., and Idun, E.K., Develpomnet length criteria for conventional and high relative rib area reinforcing bars, ACI Structural Journal, No. 3, 93, 347-359, 1993. [2] Orangun, C.O., and Breen, J. E., Strength of anchored bars: A re-evaluation of test data on development length and splices, Research Report No. 154-3F, Center for Highway Research, University of texas at Austin, Austin, Tex., 78, 1975. MMSE Journal. Open Access www.mmse.xyz
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[3] Orangun, C. O., and Breen, J. E., Reevaluation of test data on development length and splices, ACI Journal, Proceedings, No. 3, 74, 114-122, 1977. [4] Zuo, J., and Darwin, D., Splice strength of conventional and high relative rib area bars and high strength concrete, ACI Structural Journal, No. 4, 97, 630-641, 2000. [5] Rehm G, Uber die grundlagen des verbudzwischen stahl undbeton, Heft 138, Deutscher Ausschuss fur Stahlbeton, Berlin, 1961. [6] Goto Y., Cracks formed in concrete around deformed bars in concrete. ACI Journal 68(2) 244251, 1971. [7] Mathey RG and W Watstein D, Investigation of bond in beam and pull out specimens with high yield strength deformed bars. ACI Journal T. No.57-50 1071-1089, 1961. [8] Ferguson PM, Robert I and Thompson JN, Development length of high strength reinforcing bars in bond. ACI Journal T. No.59-17 887-922, 1962. [9] Lutz LA and Gergely P, Mechanics of bond and slip of deformed bars in concrete. ACI Materials Journal T. No. 64-62 711-721, 1967. [10] Nilson AH, Internal measurement of bond slips. ACI Journal 69(7) 439-441, 1972. [11] Jiang DH, Shah SP and Andonian AT. Study of the transfer of tensile forces by bond. ACI Journal T. No.81-24 251-258, 1984. [12] Ueda T, Lin I and Hawkins NM, Beam bar anchorage in exterior column-beam connections. ACI Structural Journal T. No. 83-41 412-422, 1986. [13] Soroushian P, Pull out behavior of hooked bars in exterior beam-column connections. ACI Structural Journal 85 269-276, 1988. [14] Soroushian P and Choi KB, Local bond of deformed bars with different diameters in confined concrete. ACI Structural Journal 86(02) 217-222, 1989. [15] Soroushian P, Choi KB, Park GH and Aslani F, Bond of deformed bars to concrete: effects of confinement and strength of concrete. ACI Materials Journal 88(3) 227-232, 1991. [16] Abrishami HH and Mitchel D, Simulation of uniform bond stress. ACI Materials Journal T. No. 89-M18 89(2) 161-168, 1992. [17] Malvar LJ, Bond of reinforcement under controlled confinement. ACI Materials Journal 89(6) 593-601, 1992. [18] Yankelevsky DZ, Adin MA and Farhey DN, Mathematical mode0l for bond slip behavior under cyclic loading. ACI Structural Journal 89(6) 692-698, 1992. [19] Bortolotti , Strength of concrete subjected to pull out load. ASCE Materials Journal 15(5) 491495, 2003. [20] Harajli MH, Hamad BS and Rteil AA, Effect of confinement on bond strength between steel bars and concrete. ACI Structural Journal 101(5) 595-603, 2004. DOI: 10.14359/13381 [21] Somayaji S and Shah SP, Bond stress versus slip relationship and cracking response of tension members. ACI Journal 78(3) 217 225, 1981. [22] Azizinamini A, Stark M, Roller JJ and Ghosk SK, Bond performance of reinforcing bars embedded in HSC. ACI Structural Journal 90(5) 554 561, 1993. [23] Azizinamini A, Pavel R, Hatfield E and Ghosh SK, Behavior of spliced reinforcing bars embedded in HSC. ACI Structural Journal 96(5) 826 835, 1999a.
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[24] Azizinamini A, Darwin D, Eligehausen R, Pavel R and Ghosh SK, Proposed modification to ACI 318-95 tension development and lap splice for high strength concrete. ACI Structural Journal 96(6) 922 926, 1999b. CEB-FIP Report, Bond of reinforcement in concrete: state of the art report. FIB Bulletin-10, Switzerland, 2000. Cite the paper Mohammad Rashidi & Hana Takhtfiroozeh (2016). Determination of Bond Capacity in Reinforced Concrete Beam and Its Influence on the Flexural Strength. Mechanics, Materials Science & Engineering Vol.6, doi: 10.13140/RG.2.2.18300.95361
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