STRENGTH OF REINFORCED CONCRETE CORBELS -A PARAMETRIC STUDY

International Journal of Civil Engineering and Technology (IJCIET) Volume 9, Issue 11, November 2018, pp. 2274–2288, Article ID: IJCIET_09_11_226 Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=9&IType=11 ISSN Print: 0976-6308 and ISSN Online: 0976-6316 © IAEME Publication Scopus Indexed STRENGTH OF REINFORCED CONCRETE CORBELS – A PARAMETRIC STUDY Asala Asaad Dawood M.Sc. Student/University of Diyala/College of Engineering/ Department of Civil Engineering Ali Kifah Kadhum Assistant Lecturer /University of AL-Mustansiriyah /College of Engineering/ Department of Civil Engineering Khattab Saleem Abdul-Razzaq Prof. Dr. /University of Diyala/College of Engineering, Department of Civil Engineering ABSTRACT Corbels are cantilever with small shear span to depth ratio (a/d) projected from columns or walls to support precast members like beams, girders or dapped end beams. Shear friction (SF) method is used to analyze and design reinforced concrete (RC) corbels. Because of the small value of a/d, corbels are treated as deep beams. Using strut and tie modeling (STM), they can be analyzed. In both SF and STM, there are many parameters that affect the behavior of the corbels such as a/d, width (b), compressive strength of concrete (f'c), yield strength of reinforcement (fy), and horizontal to vertical load ratio (H/V). In the current study, according to ACI 318-14 provisions, the effect of these parameters were investigated using both SF and STM. It was found that the shear capacity increases by about 32.6%, 26.3% and 31.2% for SF and by about 54.1%, 50.4% and 30.9% for STM with increasing width, compressive strength, and yield strength by about (100-300) %, (15-35) % and (400-600) %, respectively. Whereas, shear capacity decreases by about 58.54% and 48.7% for SF and about 59.4% and 33.2% for STM with increasing a/d and H/V by about (0.1-1.9)% and (0-1)%, respectively. It was also seen that the results obtained by STM is more reliable than SF when compared with experimental works that were taken from literature. Keywords: Reinforced Concrete, Corbels, STM, Shear friction, flexure, strength, Parameter. Cite this Article: Asala Asaad Dawood, Ali Kifah Kadhum, Khattab Saleem AbdulRazzaq, Strength of Reinforced Concrete Corbels – A Parametric Study, International Journal of Civil Engineering and Technology, 9(11), 2018, pp. 2274–2288 http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=9&IType=11 http://www.iaeme.com/IJCIET/index.asp 2274 [email protected] Asala Asaad Dawood, Ali Kifah Kadhum, Khattab Saleem Abdul-Razzaq 1. INTRODUCTION Brackets and corbels are short cantilevers that may fail by shearing along the interface between the column and the corbel, yielding of the tension tie, crushing or splitting of the compression strut, or localized bearing or shearing failure under the loading plate [1]. According to ACI 318-14 [2], there are two methods to analyze and design reinforced concrete corbels; SF, ACI 318-14, 22.9 and STM, ACI 318-14, chapter 23. SF method should be used for corbels with a/d ≤ 1.0 and H ≤ V, while STM can be used for corbels with a/d < 2 [3, 4]. In the current study, both SF and STM approaches are used to investigate the behavior of RC corbels with different values of a/d, b, f'c, fy, and H/V. 2. ANALYSIS OF CORBEL 2.1. Shear friction theory (SF) The shear friction analogy is familiar to most engineers in practice and to most researchers in investigations [5-7]. It is a valuable and simple tool which can be used to estimate the maximum shear force transmitted across a cracked plane in a reinforced concrete member, Fig.1. It is used for the design of short corbels wherein a control of the interface stresses is necessary to prevent a possible shear failure. More specifically, it is used with precast concrete structural connections for estimating the shear capacity of interfaces between precast members and castin-place concrete. In addition, it is used for calculating the residual shear capacity of cross sections which are weakened by cracking. Figure 1 Shear Friction Analogy Using SF can be summarized by the following steps: 1-Flexure reinforcement: Vn = *10 Where: Mn = As*fy*(d- )* 10 = ∗ . ∗ ∗ http://www.iaeme.com/IJCIET/index.asp 2275 [email protected] Strength of Reinforced Concrete Corbels – A Parametric Study = 2-Shear friction reinforcement: Vn = Avf fy 3-Minimum reinforcement: Vn = 0.04 (f'c /fy) (bd) 4- Check overall dimensions: Vn is minimum of: (a) For normal concrete, the minimum of the following values: 0.2* f'c *b*d ( 3.3+ 0.08 f'c) b*d 11bd (b) For high strength concrete, the minimum of the following values: 0.2 f'c*b*d 5.5bd 5- Check for bearing: Vn = 0.85 f'c*b*Lb 6- Find shear capacity by select minimum of Vn 2.2. Strut and tie modeling (STM) Strut and tie modeling is developed as one of the most beneficial design approaches for critical shear structures [8-12]. In STM, the RC member is converted into an equivalent truss, where the tension and compression zones are transformed into equivalent ties and struts connected at the nodes to form a truss that resists the loadings, Fig.2. Figure.2: Strut and Tie Modelling Using STM can be summarized by the following steps: 1- Find node dimension wt = 2*(h-d), ws = 0.8*wt jd = h-0.5*wt-0.5*ws http://www.iaeme.com/IJCIET/index.asp 2276 [email protected] Asala Asaad Dawood, Ali Kifah Kadhum, Khattab Saleem Abdul-Razzaq = ! " # $% & ' wsb =Ls sinθ+wt cosθ wst =Lb sinθ+ws cosθ 2- Find shear force at nodal zone A, CCT, Fig. 3-1. βs =0.8, fce = 0.85βs*f'c Vn,A1= fce*Ls*b Vn,A2= fce*wt*b*tanθ Vn,A3= fce*wsb*b*sinθ 3- Find shear force at nodal zone B, CCC, Fig. 3-2. βs = 1.0, fce = 0.85βs*f'c Vn,B1= fce*Lb*b Vn,B2= fce*ws*b*tanθ Vn,B3=fce*wst*b*sinθ 4- Find shear force at Strut AB, bottle shaped Q = ∑(Asi/bi*si)*sin)i, Fig. 3-3 If Q ≥ 0.03, βs = 0.75 If Q < 0.03, βs = 0.6λ λ = 1.8173( + , - ) − 0.0143 fce = 0.85βs*f'c weff = min(wst; wsb) Vn,AB=fce*weff*b*sinθ 4- Find shear force at Strut BC, prismatic shape βs = 1.0, fce = 0.85βs*f'c Vn,B2= fce*ws*b*tan 5- Find shear force at Tie AD Fn,AD = As fy Vn,AD = Fn,AD *tanθ 6- Find maximum nominal shear Vn. max =0.83*b*d*,2′4 Then Vn = min(Vn,B1; Vn,B2; Vn,B3; Vn,A1; Vn,A2; Vn,A3; Vn,AB; Vn,BC; Vn,AD; Vn. max) http://www.iaeme.com/IJCIET/index.asp 2277 [email protected] Strength of Reinforced Concrete Corbels – A Parametric Study Figure 3-1: Node A Figure. 3-2: Node B Figure. 3-3:secondry reinforcement Figure.3: STM details 3. DESCRIPTION OF THE SPECIMENS Double reinforced concrete corbel specimens to investigate the parameters that affect its shear capacity as shown in Fig.4, a=360.5mm, d=360.5mm, b=120mm, as=452.4mm2, Ah=226.2mm2, f'c=25MPa, fy=420MPa, Lb=90mm and Ls=90mm. The parameters that taken into considerations are a/d, b, f'c, fy and H/V. According to ACI 318-14 [1], SF and STM methods are used. Figure 4: Typical RC Corbel Specimen 4 PARAMETRIC STUDY 4.1. Effect of a/d The shear failure is mainly dependent on a/d ratio, therefor, it's considered the most important parameter. In the current study, a/d are ranged between 0.1 and 1.9 as shown in Table 1 and Fig. 5. http://www.iaeme.com/IJCIET/index.asp 2278 [email protected] Asala Asaad Dawood, Ali Kifah Kadhum, Khattab Saleem Abdul-Razzaq Table 1: Effect of a/d Shear capacity (kN) Shear Friction STM a/d Vn-SF Failure Vn-STM Failure kN mode kN mode 0.1 216.3 S 179.53 DS 0.2 216.3 S 179.53 DS 0.3 216.3 S 179.53 DS 0.4 216.3 S 179.53 DS 0.5 216.3 S 173.52 CS 0.6 216.3 S 164.39 CS 0.7 216.3 S 154.84 CS 0.8 212.96 F 145.32 CS 0.9 189.30 F 136.13 CS 1 170.37 F 127.44 CS 1.1 154.88 F 119.33 CS 1.2 141.98 F 110.98 CS 1.3 131.05 F 103.19 CS 1.4 121.69 F 96.43 CS 1.5 113.58 F 90.49 CS 1.6 106.48 F 85.25 CS 1.7 100.22 F 80.57 CS 1.8 94.65 F 76.39 CS 1.9 89.67 F 72.62 CS where S=shear, F = flexural, DS =diagonal shear and CS = strut compression 240 220 200 180 160 140 120 100 80 60 0 0.5 1 1.5 2 a/d Vn SF Vn STM Figure 5: The effect of a/d ratio on the shear capacity of RC corbels http://www.iaeme.com/IJCIET/index.asp 2279 [email protected] Strength of Reinforced Concrete Corbels – A Parametric Study 4.1.1. From the results of SF method: The failure mode for a/d ≤ 0.7 is shear failure with same value because the shear capacity calculated by using shear friction equation is not affected by a/d values. The effect of a/d appears when the failure mode of the specimen is flexural because the moment increases when a/d increases. Therefor SF method is limited for a/d less than unity only. In case of a/d ratio decreases from 0.1 to 1.9, the shear capacity of corbel increases by about 58.5% when using SF and 59.4% when using STM. 4.1.2. From STM method: The failure mode for a/d ≤ 0.4 is diagonal shear failure with same value because the shear capacity that calculated from maximum nominal shear equation is not affect by a/d values. By increasing a/d value, the failure mode changes to compression strut and the load capacity decreases with increasing a/d. The decrease in shear capacity is 59.43% when a/d value increases from 0.1 to 1.9. From the comparison between two methods above, it can be concluded that SF method couldn’t give accurate estimation for the corbel strength when a/d > 1. This is attributed to that fact that SF assumes flexural failure mode, while it is compression strut failure by STM assumption. 4.2. Effect of width: Twenty-one specimens are used to investigate the effect of corbel width on the strength of RC corbels, Table 2 and Figure (6). http://www.iaeme.com/IJCIET/index.asp 2280 [email protected] Asala Asaad Dawood, Ali Kifah Kadhum, Khattab Saleem Abdul-Razzaq Figure 6 The effect of width 4.2.1. From the result of SF method: The failure mode is shear for b ≤ 130 mm, but when the width increases, the corbel specimen will be controlled by flexural failure. It is seen that when the width increases from 100 mm to 300 mm, i.e. by about 66.67%, the shear capacity increases by about 32.58%. That takes place because when the width increases, the concrete becomes stronger, which transforms the failure from shear into flexural. 4.2.2. From STM method: The failure mode is strut compression failure for b ≤ 210 mm, but when the width increases, the corbel fails by yielding of tie reinforcement failure. It is found that when the width increases from 100 mm to 300 mm, i.e. by about 66.67%, the shear capacity increases by about 54%. This happens because when the width increases, the strut increases, so the failure transforms from strut into tie. It is worth to mention that when the effect of width is studied, main reinforcement had been taken 678.6 mm2, because the increase in width causes here an increase in section capacity. In other words, by using scarce reinforcement, the failure occurs in reinforcement and the effect of width increasing becomes unclear. 4.3. Effect of compressive strength: Compressive strength of concrete is considered the most important characteristic because concrete is a distinctive compressive material as shown in Table 3 and Fig. 7. http://www.iaeme.com/IJCIET/index.asp 2281 [email protected] Strength of Reinforced Concrete Corbels – A Parametric Study Figure 7 The effect of compressive strength 4.3.1. From the results of SF method: The failure mode is shear for f'c ≤ 19 MPa, but when f'c increases, the corbel specimen will be controlled by flexural failure. That happens because when f'c increases, the failure in compressive strut becomes difficult, so the flexural failure takes place. http://www.iaeme.com/IJCIET/index.asp 2282 [email protected] Asala Asaad Dawood, Ali Kifah Kadhum, Khattab Saleem Abdul-Razzaq 4.3.2. From STM method: The compressive strength is very important parameter because strut is a compression member that is affected mainly by f'c value. Therefore, the failure mode is strut compression for f'c ≤ 30 MPa, but when f'c increases, the corbel specimen will be controlled by tie failure. It was also seen that when f'c becomes greater than 30 MPa, normal and high strength concrete corbels have the same behavior. Finally, it is worth to mention that when f'c increases from 15 MPa to 35 MPa, i.e. 75.14%, the shear capacity increases by about 50.4%. 4.4. Effect of reinforcement yield strength: Since tie is a tensile member, it must be reinforced to resist tensile forces. Yield strength of steel reinforcement gives indication about reinforcement resistance to yielding failure as shown in Table 4 and Fig. 8. Table 4 Effect of reinforcemet yield strength fy (MPa) 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 Where Shear Friction STM Vn-SF Failure Vn-STM Failure (kN) mode (kN) mode 170.27 F 146.80 YT 174.26 F 150.47 YT 178.23 F 154.14 YT 182.18 F 157.81 YT 186.13 F 161.48 YT 190.05 F 165.15 YT 193.97 F 168.82 YT 197.87 F 172.49 YT 201.76 F 176.16 YT 205.64 F 179.83 YT 209.50 F 183.50 YT 213.35 F 187.17 YT 217.19 F 190.84 YT 221.01 F 194.51 YT 224.82 F 198.18 YT 228.62 F 201.85 YT 232.40 F 205.52 YT 236.17 F 209.19 YT 239.92 F 212.39 CS 243.67 F 212.39 CS 247.39 F 212.39 CS S = shear, F = flexure, CS = strut compression and YT= yield of tie http://www.iaeme.com/IJCIET/index.asp 2283 [email protected] Strength of Reinforced Concrete Corbels – A Parametric Study Shear capacity (kN) 260 240 220 200 180 160 140 120 350 400 450 500 550 600 650 Yield strength (MPa) Vn SF Vn STM Figure 8 The effect of yield strength 4.4.1. From the results of SF method: By increasing fy value from 400 MPa to 600 MPa, i.e. by 33.3%, the shear capacity increases by about 31.2% in conjunction with flexural failure. This failure mode takes place due to the increase of main reinforcement strength. 4.4.2. From STM method: The failure mode is reinforcement yielding of tie failure for fy ≤ 570 MPa, but when fy increases, the failure mode becomes compression strut. The increase of fy value from 400 MPa to 600 MPa, i.e. 33.3%, leads the shear capacity to increase by about 30.9%. It is worth to say here that the width had been taken 200 mm instead of 120 mm in order to clarify the effect of fy in a firmer way. 4.5. Effect of horizontal to vertical load ratio: The source of horizontal load in corbel is shrinkage, creep and temperature change of supported beam that causes direct tension on corbel main or tie reinforcement. In this study, different values of H/V are considered as shown in Table 5 and Fig. 9. Table 5 Effect of horizontal to vertical load ratio H/V 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Shear Friction Vn-SF Failure (kN) mode 170.37 F 162.97 F 156.14 F 149.81 F 143.93 F 138.46 F 133.37 F 128.62 F 124.18 F 120.02 F http://www.iaeme.com/IJCIET/index.asp 2284 STM Vn-STM Failure (kN) mode 127.44 CS 127.44 CS 127.44 CS 127.44 CS 127.44 CS 127.44 CS 123.95 YT 120.04 YT 116.36 YT 112.91 YT [email protected] Asala Asaad Dawood, Ali Kifah Kadhum, Khattab Saleem Abdul-Razzaq 0.5 116.12 F 109.65 YT 0.55 112.45 F 106.57 YT 0.6 108.99 F 103.67 YT 0.65 105.74 F 100.91 YT 0.7 102.67 F 98.30 YT 0.75 99.76 F 95.82 YT 0.8 97.02 F 93.47 YT 0.85 94.41 F 91.22 YT 0.9 91.90 F 89.08 YT 0.95 89.59 F 87.04 YT 1 87.35 F 85.09 YT Where S = shear, F = flexure, CS = strut compression and YT= yield of tie Shear capacity (kN) 180 160 140 120 100 80 0 0.2 0.4 0.6 0.8 1 1.2 Horizontal to vertical load ratio Vn SF Vn STM Figure 9 The effect of H/V ratio 4.5.1. From the results of SF method: The failure mode is flexural in different H/V values. Shear capacity decreases by about 48.7% when H/V increases from 0 to 1. This behavior takes place due to the effect of horizontal load on corbel main reinforcement that reduces the vertical load capacity. 4.5.2. From the results of STM method: The failure mode is strut compression failure for H/V ≤ 0.25, which means that there is no effect of horizontal load. Nonetheless, when increasing the H/V value, the failure converts into tie yielding. More specifically, the shear capacity decreases by about 33.2% when H/V increases from 0 to 1. This behavior occurs duo to tensile force effect of horizontal load on corbel tie reinforcement that reduces the vertical shear capacity. 5. COMPARISON BETWEEN SF AND STM IN TERMS OF THEIR RELIABILITY WITH EXPERIMENTAL RESULTS In order to verify the ratability of SF and STM methods, some experimental data were taken from the literature and compared with the theoretical solutions of the both methods, Table 6. http://www.iaeme.com/IJCIET/index.asp 2285 [email protected] Strength of Reinforced Concrete Corbels – A Parametric Study Table 6: Verification of SF and STM with experimental results Vn-test Vn-SF Vn-STM Vn-test/ Vn-test/ Vn-SF Vn-STM (kN) (kN) (kN) A2 158.3 175 130 0.9 1.22 A3 124.5 183.35 103.83 0.68 1.2 Mattock et B1 209.15 173 117.73 1.2 1.77 al. [7] B2 173 164.67 134.84 1.05 1.28 B3A 187.3 193.59 117.79 0.97 1.59 C1 796.2 470.4 370.37 1.692 2.15 Yong and C2 836.2 470.4 370.37 1.777 2.25 Balaguru D1 700.6 497 430.66 1.41 1.627 [13] D2 800.6 497 430.66 1.611 1.859 1.745 1.219 SC1-1 720 412.5 590.56 SC1-2 950 412.5 590.56 2.303 1.609 SC1-3 700 412.5 418.58 1.697 1.672 SC1-4 470 412.5 386.59 1.139 1.216 Foster et al. [14] SC2-1 980 412.5 490.16 2.376 1.999 SC2-2 700 412.5 490.16 1.697 1.428 1.406 1.500 SC2-3 580 412.5 386.6 SC2-4 490 412.5 386.6 1.188 1.267 C0 1426.2 1093.4 1105 1.304 1.29 Wilson et C1 1677.65 1093.4 1105 1.632 1.615 al. C2 1784.45 1093.4 1105 1.632 1.615 [15] C3 1544.15 1093.4 1105 1.412 1.397 where S=shear, F = flexural, DS =diagonal shear and YT= yield of tie From the above comparison shown in Table 6, SF method is more reliable than STM in relation with Mattock et al. [7] experimental results. That can be attributed to the fact that Mattock et al. relied on shear strength on the one hand, and on the other hand, relied on normal strength concrete in which the maximum average shear stress 5.5MPa is not involved. The other comparisons [13, 14, 15, 16, 17] show that STM is more reliable than SF because 1-The failure types that are defined by STM are more reliable because they contain diagonal crush, diagonal splitting or tie, i.e. not only shear friction or flexural like in SF method. 2-SF method can be used when a/d<1, otherwise, the corbel becomes cantilever. Whereas, STM deals with the corbel till a/d<2, because it becomes here deep corbel. 3-SF does not give accurate results when the high strength concrete is used. That is because the maximum average shear stress is limited to 5.5MPa or 0.2f'c, which is minimum. In other words, when f'c>27.5MPa, f'c value does not affect the results of SF. 4-The factor of safety in STM is more than that in SF that is why. STM is more favorable for the engineers. Author Specimens http://www.iaeme.com/IJCIET/index.asp 2286 [email protected] Asala Asaad Dawood, Ali Kifah Kadhum, Khattab Saleem Abdul-Razzaq 6. CONCLUSIONS 1. Comparing with the experimental data, the shear capacity calculated by SF method 2. 3. 4. 5. 6. 7. 8. 9. is greater than that calculated by STM method. The shear capacity of corbel increases by about 58.54% for SF and 59.43% STM when the a/d ratio decreases by about (0.1-1.9) %. The effect of a/d in SF method appears when the specimens fail by flexure because the moment increases when a/d increases. In STM method, a/d value is considered very effective on shear capacity. The increase of corbel width by about (100-300) % leads to increase shear capacity by about 32.58% for SF and 54.06% for STM. The increase of concrete compressive strength of corbel by about (15-35) % leads to increase load capacity by about 26.25% for SF and 50.42% for STM. The behavior of normal and high strength concrete corbel is the same because the corbel may fail by tension of main reinforcement or tension stress on strut itself. The load capacity of corbel increases by about 31.17% for SF and 30.88% for STM when the yield strength of the main reinforcement increases by about (400-600) %. The presence of horizontal force in corbel leads to decrease vertical load capacity. The failure mode in STM method is more accurate and virtual than SF method because it take in consideration strut and diagonal shear failure mode, which is very popular in RC corbel. LIST OF NOTATIONS As Total area of the primary reinforcement total area of the secondary reinforcement Ah Avf Total area of shear friction reinforcement a Shear span, mm b Width of the corbel, mm d Effective depth of the primary reinforcement at the face of the column, mm f'c compressive strength of the concrete), MPa fct Indirect tensile strength (splitting tensile strength), MPa fy yield strength of the primary reinforcement), MPa h Total depth of deep beam, mm Ls Length of support bearing block, mm Length of load bearing block, mm Lb Mn Nominal moment capacity at the column face Vn Nominal shear strength of the corbels, equal to half of the nominal load-carrying capacity of the specimens, kN ws Width of horizontal strut, mm wt Width of anchor tie, mm weff Effective width of strut, mm wsb width of inclined strut at support wst width of inclined strut at load βs Strut coefficient according to Table 23.4.3 in ACI 318-14 provisions θ Angle between the inclined strut and the tie ) Angle of inclination of reinforcement to the axis of the beam μ Coefficient of friction used in shear-friction calculations according to Table 22.9.4.2 in ACI 318-14 provisions http://www.iaeme.com/IJCIET/index.asp 2287 [email protected] Strength of Reinforced Concrete Corbels – A Parametric Study ; Modification factor reflecting the reduced mechanical properties of lightweight concrete REFERENCE [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] Elzanaty, A. 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M., “Behavior of Reinforced Concrete Continuous Deep Beams-Literature Review,” The Second Conference of Post Graduate Researches (CPGR'2017) College of Engineering, Al-Nahrain Univ., Baghdad, Iraq-4th. 2017. Abdul-Razzaq, Khattab Saleem, “Effect of Heating on Simply Supported Reinforced Concrete Deep Beams,” Diyala Journal of Engineering Sciences, 8(2), 2015, p.116-133. http://www.iaeme.com/IJCIET/index.asp 2288 [email protected]