TX_1~ABS:AT/ADD:TX_2~ABS:AT 81 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (2): 81-88 ReseaRch aRticle Study of Shear Transfer in Modified Push-off Members Using Finite Elements Method: A Comparative Study Sabih H. Muhodir Department of Architectural Engineering, Cihan University-Erbil, Kurdistan Region, Iraq ABSTRACT This paper aims to investigate numerically the behavior of modified push-off specimens under the action of direct shear stress. Based on the tow-dimensional finite element model developed in this research, the contribution of the aggregate interlock to resist the shear stress along the shear plane, the effect of existing of the compressive stress acting across the shear plane, the effect of the parallel reinforcement in resisting shear stress, the effect of the shear reinforcement parameter, the strains in the concrete and steel, and the actual distribution of the shear stress along the shear plane were studied. To verify the accuracy and applicability of the suggested finite element model, a comparison between the results obtained in this study and those obtained experimentally by other authors was carried out. Comparison showed that the finite element results were in good agreement with the experimental results. It has been found that, for modified push-off specimens of groups without shear reinforcement across the shear plane the diagonal tension crack within the shear plane occurred at the load level which is closely to the ultimate shear strength respectively, while for specimens with both shear and parallel reinforcement, the first crack formed at about (33.7–53.0%) of the ultimate strength, also the investigation showed that the presenting of the shear reinforcement normal to the shear plane are significantly increased the shear transfer stress for all levels of loading. Keywords: Shear, aggregate interlock, finite element method, interface, modified push-off INTRODUCTION Shear transfer may be of high importance in many types of reinforced concrete members including ordinary and deep beams, slabs, corbels and brackets, shear walls and shear diaphragms and containment vessels of various types. Shear transfer is generally considered as a major mechanism of load transfer along a concrete-to-concrete interface under the action of shear or under the combination effect of shear and normal force.[1-3] Although the mechanism of the shear transfer, the ACI-318-19 provisions[4] depends mainly on the relation between the shear transfer and the reinforcement crossing the shear plane (clamping force), as well as on the resistance generated from the friction between two sliding faces along the shear plane which is depending contact surface condition and on the coefficient of friction of the concrete used. To calculate the shear strength provided by the sear reinforcement perpendicular to the shear plane, the stress is assumed to have reached to its yield stress f y . This leads to the fact that the concrete contribution to resist the shear calculated using the ACI code equations increases compared to that provided by the shear reinforcement which is expressed as V n =μA v f y, where V n = nominal shear strength, A v is the area of reinforcement crossing the assumed shear plane to resist shear, and μ is the coefficient of friction.[5,6] Depending on the previously published test results Hsu[7-10] developed a formula to predict the shear transfer strength of reinforced concrete members: vu = 0.822(fc /)0.406(ρfy) c (1) Where: vu= unit Shear strength (MPa) c = 0.159(fcc /)0.33 (2) fcc /= concrete compressive strength of 150 mm cube and taken as fc / .0 85 To this end the present study is concerned with an attempt to verify the validity of the ACI shear friction provision and to investigate the influence of the direct shear stress acting parallel and transverse to the shear plane on the shear transfer strength using the finite element method (FEM) and to investigate their Corresponding Author: Sabih H. Muhodir, Department of Architectural Engineering, Cihan University-Erbil, Kurdistan Region, Iraq. E-mail: sabih.alzuhairy @cihanuniversity.edu.iq Received: June 05, 2022 Accepted: August 03, 2022 Published: August 27, 2022 DOI: 10.24086/cuesj.v6n2y2022.pp81-88 Copyright © 2022 Sabih H. Muhodir. This is an open-access article distributed under the Creative Commons Attribution License (CC BY-NC-ND 4.0). Cihan University-Erbil Scientific Journal (CUESJ) Muhodir: Study of Shear Transfer in Modified Push-off Members Using Finite Elements Method 82 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (2): 81-88 role in the influencing the strength and deformation using the typical and modified push-off specimens. The main objectives of this study are the following: 1. Study the contribution of the aggregate interlock to resist the shear stress along the shear plane 2. Study the effect of existing of the compressive stress acting across the shear plane 3. Study the effect of the parallel reinforcement in resisting shear stress 4. Study the effect of the shear reinforcement parameter 5. Investigating the strains in the concrete and steel and the actual distribution of the shear stress along the shear plane. FAILURE CRITERIA For formulation the failure criteria for concrete under combined states of stresses, one must agree on a proper definition of failure. Such criteria as yielding, initiation of cracking, load carrying capacity, and extent of deformation have been used to define failure.[11,12] In this study, failure is defined as first crack loading and load carrying capacity of the reinforced concrete element. In general, concrete failure can be divided into tensile and compressive types. With respect to the present definition of failure, tensile failure defined by the formation of major cracks and the loss of tensile strength in concrete normal to the crack direction, while in compressive failure many small cracks develop and the concrete element loses most of its strength. The Mohr-Coulomb criterion in the present study was used as a load carrying capacity criteria, this is dating from 1900 and states that the failure is governed by the relation.[13] |τ| = f(σ) (3) Where the limiting shearing stress τ is depending only on the normal stress (σ) in the same plane and at the same point, and where the equation (1) is the failure envelope for the corresponding Mohr-Circle.[9] The simplest form of equation (1) can be written as:[13] |τ|=C-σn.tan∅ (4) Where: τ: The shearing stress σn: The normal stress (tensile stress is positive) C: Cohesion ∅: The angle of internal friction (tan ∅ used in this study is equal to 1.4 –normal weight concrete).[14] In the principal –stress coordinate, the failure criterion (sliding criterion) given by equation (2) takes the form: [14] 1 2 1 1 2 1 01 3σ σ+( ) − −( ) − =sin sin C cos∅ ∅ ∅. (5) For σ1 ≥ σ2 ≥ σ3 [10] σ σ1 3 1 f ft c / / = = (6) In general, the Mohr-Coulomb criterion is a two-parameter model[13] where any combination of parameters, such as (∅, c), (fc /, ft /), experimentally observed will be adequate to characterized completely the material behavior, so it is sometimes convenient to use the parameters fc /and m, where m sin sin f f c t = + − = 1 1 ∅ ∅ / / (7) The coefficient m for concrete is considered to be 4.1,[13] then Equation (3) can be written as[14,15] m. σ1–σ3 = 2.C.√m=fc / (8) Where: m cos sin sin sin = − = + − [ ] ∅ ∅ ∅1 1 1 2 (9) and; f C cos sin ���������c / . .= − 2 1 ∅ ∅ (10) Therefore, the value of (C) used in equation (2) can be obtained using equation (10) in terms of fc /and angle of internal friction (∅). The failure criteria given by equation (4) holds for member with shear reinforcement by adding the contribution of the shear reinforcement which can be given by the reinforcement parameter (ρ.fy) to the normal stress (σn), therefore, |τ| = C – (σn – ρfy) tan∅ (11) MATERIAL AND SPECIMENS CHARACTERIZATION The dimension and reinforcement of the reinforced concrete members (modified push-of-specimens) were selected to be similar to those specimens, whose behavior being investigated experimentally by Al-Sharae.[15] The overall dimensions of the modified Push-off-specimens that were used in this study are of length (L = 650 mm) × width (B = 400 mm) × depth (D = 150 mm). The length of the shear Figure 1: Typical push-off-specimen Muhodir: Study of Shear Transfer in Modified Push-off Members Using Finite Elements Method 83 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (2): 81-88 plane remain constant for all specimens (i.e., the cross sectional area of the shear plane 150 mm × 300 mm) and the height of the slot is constant and equal to 25 mm as shown in [Figure 1]. In all specimens the shear reinforcement cross the shear plane at right angle. Additional reinforcement parallel to the shear plane is provided to prevent any failure other than along the specific shear plane. The specimens are loaded by concentrated (P), without moment. When the (p) applied concentrically in the modified push-off-specimen, the shear force along the shear plane will be (P. Cos Ѳ) and a compressive normal force (P. Sin Ѳ) across the shear plane. Five different values of (Ѳ) was used to maintain different values of shear stress and transverse compressive stress (Ѳ is the inclination of the upper point shear plane relative to the lower point). The details of specimens are summarized in [Table 1]. Therefore, the program of the shear transfer analysis is thus divided into the following three groups: • Group SC Group with plain concrete specimens. • Group SP Group reinforced with parallel to the shear plane reinforcement only as shown in [Table 1]. • Group SR (SR1, SR2, and SR3) Group with shear reinforcement placed at right angle to the shear plane as well as a parallel reinforcement is provided in the critical zone, [Table 1]. To study the effect of steel parameter (ρ.fy), different steel ratios were used by changing the diameter of the shear reinforcement crossing the shear plane. The detailing of all groups is summarized in [Table 1]. The properties of concrete and reinforcement used in this study are tabulated in [Tables 2 and 3] respectively. FINITE ELEMENT DESCRIPTION In the finite element formulation, the choice of a proper element is very important and effects on the accuracy of the final results of the analysis. In the current study a nine nodded Table 1: Details of specimens[15] Spec. identity Ѳo k-factor Parallel rein. Transvers rein. SC00 0 0 None None SC10 10 0.174 None None SC20 20 0.34 None None SC30 30 0.5 None None SC45 45 0.707 None None SP00 0 0 4φ12 None SP10 10 0.174 4φ12 None SP20 20 0.34 4φ12 None SP30 30 0.5 4φ12 None SP45 45 0.707 4φ12 None SR100 0 0 4φ12 6φ8 SR110 10 0.174 4φ12 6φ8 SR120 20 0.34 4φ12 6φ8 SR130 30 0.5 4φ12 6φ8 SR145 45 0.707 4φ12 6φ8 SR200 0 0 4φ12 6φ10 SR210 10 0.174 4φ12 6φ10 SR220 20 0.34 4φ12 6φ10 SR230 30 0.5 4φ12 6φ10 SR245 45 0.707 4φ12 6φ10 SR300 0 0 4φ12 6φ12 SR310 10 0.174 4φ12 6φ12 SR320 20 0.34 4φ12 6φ12 SR330 30 0.5 4φ12 6φ12 SR345 45 0.707 4φ12 6φ12 Table 3: Concrete properties[15] Spec. identity Cylinder compressive strength (MPa) Modulus of rupture (MPa) SC00 22.9 1.78 SC10 22.9 1.78 SC20 22.1 1.73 SC30 22.1 1.73 SC45 23.2 1.82 SP00 23.4 1.85 SP10 24.6 1.83 SP20 22.5 1.89 SP30 21.8 1.89 SP45 21.8 1.89 SR100 23.4 1.74 SR110 23.4 1.61 SR120 24.2 1.61 SR130 21.8 1.84 SR145 21.8 1.84 SR200 23.4 1.87 SR210 23.4 1.61 SR220 24.2 1.61 SR230 21.8 1.84 SR245 23.4 1.87 SR300 21.8 1.61 SR310 21.8 1.61 SR320 23.4 1.84 SR330 23.4 1.84 SR345 24.2 1.87 Table 2: Properties of bars used[15] Bar diameter φ (mm) Area (mm2) f y (MPa) Strain ε y 8 50.27 410 0.002 10 78.54 412 0.002 12 108.54 410 0.002 Muhodir: Study of Shear Transfer in Modified Push-off Members Using Finite Elements Method 84 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (2): 81-88 two-dimensional isoparametric quadrilateral elements with two degrees of freedom per node, as shown in [Figure 2], were used for all constituent materials (concrete and steel) in the modified push-off specimens’ analysis. In generating the finite element, mesh certain assumptions were made to simplify the complex geometry and to reduce the size of the mesh, such as, the interface between the concrete and steel was assumed. RESULTS AND DISCUSSION Cracking and Ultimate Strength Three groups of specimens (SC, SP, and SR) were analyzed using finite element model suggested in this paper to study the shear transfer strength in the modified push-off specimens. In this study, the modulus of rupture (f cr ) and the Mohr-Coulomb criterion were used as a first cracking and ultimate strength criteria, respectively. Using the finite element model, it was found that, the group (SP) behaved to same manner to the specimens of group (SC). Results of the finite element analysis are shown in [Table 4]. For specimens with both shear and parallel reinforcement (groups SR), the first crack formed at about (33.7–53.0%) of the ultimate strength. Depending on the first crack criterion, these cracks occurred first almost at mid-length of the shear plane approximately. As lad increased, more cracks began appear throughout the shear plane with rapid propagation away from the mid-length of the shear plane approximately. Furthermore, it can be seen that the ultimate strength is increased as the external compressive stress (σ nx ) and reinforcement parameter (ρf y ) are increased. In general, characterized failure for specimens with shear and parallel reinforcement is ductile failure. Al-Sharae,[15] in his experimental study found that, for modified push-off specimens with (Ф = 10 mm) as a main shear reinforcement, the diagonal tension crack within the shear plane occurred at about (51–55%) of the ultimate shear strength. Comparison of the results obtained in this study using FEM with those obtained experimentally by Al-Sharae[15] shows a good agreement as shown in [Table 4]. For specimens of groups (SC) and (SP), the first crack formed at about (87–95.02%) and (82.4–90.5%) of the ultimate strength, respectively, as shown in [Table 5]. Increasing in stiffness of group (SP) as compared with that of group (SC) can be attributed of the presenting of the parallel reinforcement within the critical zone. Al-Sharae,[15] in his experimental study found that, for modified push-off specimens of groups (SP and SC), the diagonal tension crack within the shear plane occurred Table 4: F.E.M results of the modified push-off-specimen Specimen’s Identity F.C.L* (KN) F.L** (KN) F.C.L/ F/L (%) SC00 143.18 154.0 93 SC10 162.1 170.4 95.36 SC20 185.13 193.0 95.28 SC30 210 227.32 93.2 SC45 267.6 307.76 87 SP00 147.58 163.05 90.5 SP10 165.32 187.6 88.12 SP20 196.3 218.0 90 SP30 219.74 250.2 87.83 SP45 273.43 331.45 82.4 SR100 122.34 256.3 47.78 SR110 145.70 318.63 45.72 SR120 183 368.0 49.73 SR130 210.8 412.02 44 SR145 254.37 480.49 53 SR200 128.5 312.84 41 SR210 160 400.0 40 SR220 225.63 469.3 48.1 SR230 247.2 538.8 46 SR245 322.35 656.81 49 SR300 136.55 406 33.7 SR310 184.84 533.0 34.6 SR320 248.9 631.7 39.4 SR330 309.3 741.63 41.71 SR345 395.34 869.7 45.5 F.C.L: First crack loading, **F.L: Failure loading Figure 3: Load – normal compressive stress curve- group (SC) Figure 2: Typical two-dimensional isoparametric element Muhodir: Study of Shear Transfer in Modified Push-off Members Using Finite Elements Method 85 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (2): 81-88 Table 5: First crack loading and failure loading using F.E.M. and the experimental results by Al-Sharea[15] Specimen’s Identity F.L (KN) EXP.[15] (1) F.L (KN) F.E.M (2) 1 2       F.C.L. (KN) EXP.[15] (3 F.C.L (KN) F.E.M (4) 3 4       SC00 154.0 166.77 0.92 143.18 156.96 0.91 SC10 170.4 181.84 0.94 162.1 169.71 0.95 SC20 193.0 201.12 0.91 185.13 180.5 1.03 SC30 227.32 220.72 1.03 210 194.5 1.08 SC45 307.76 249.30 1.06 267.6 255.06 1.05 SP00 163.05 183.44 0.88 147.58 179.52 O.82 SP10 187.6 220.72 0.85 165.32 215.82 0.76 SP20 218.0 245.25 0.88 196.3 235.44 0.83 SP30 250.2 274.68 0.91 219.74 259.96 0.84 SP45 331.45 333.54 0.99 273.43 311.95 0.87 SR200 312.84 284.49 1.10 128.5 147.15 0.87 SR210 400.0 372.78 1.08 160 196.2 0.81 SR220 469.3 451.26 1.04 225.63 245.25 0.91 SR230 538.8 549.36 0.98 247.2 294.3 0.84 SR245 656.81 608.22 1.09 322.35 333.45 0.96 σ n-1 =0.0849 σ n-1 =0.095 at about (76.0–95.0 %) and (93.0–98.0%) of the ultimate shear strength respectively, and this can be attributed to the absence of the shear reinforcement across the shear plane. [Table 5] shows the comparison of the results obtained by this study and those obtained experimentally by Al-Sharae.[15] In general, the agreement between the results is very good for some specimens and unstable for other specimens of groups (SP and SC). In general with help [Tables 4 and 5], it can be conclude that, the failure load increases with increase of the normal compressive stress (σ nx ) and reinforcement parameter (ρf y ) regardless of the specimen’s group. Furthermore, it can be concluded that, the reinforcement parallel to the shear plane has a little effect on the shear transfer strength. [Figures 3-7] show that the cracking loads versus normal compressive stress for groups (SC, SP, SR1, SR2, and SR3), respectively. From these figures, it can be noted that the reserve in strength after the formation of cracks is increased with increasing the external compressive stress (σ nx ). Furthermore, a large reserve in strength is obtained in the specimens reinforced with parallel and shear reinforcement, and is reduced a great deal when only plain concrete is present in the shear plane. The same behavior is obtained experimentally by Mattock and Hawkins[11] and Al-Sharae.[15] Comparisons of [Figures 3 and 4] show that the strength of specimens with the parallel reinforcement is higher than those of specimens made with the plain concrete only, but the reserve in strength is small, and in both groups failure occurred almost at a load closer to the first cracking load. Furthermore, it can be observed from [Figures 5-7] that the increase in strength with increase in (σ nx ) tends to stable for specimens in groups (SR). Figure 4: Load – normal compressive stress curve- group (SP) Figure 5: Load-normal compressive stress curve - group (SR1) Muhodir: Study of Shear Transfer in Modified Push-off Members Using Finite Elements Method 86 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (2): 81-88 In general, it can be concluded that the external compressive force will add clamping force, which resist the shear force; therefore, the shear transfer strength will increased with increasing this force. Effect of the Reinforcement Parameter (ρ.fy) The reinforcement parameter (ρ.f y ) can be changed by varying either the reinforcement ratio (ρ), the reinforcement yield strength (f y ) or both. If the area of the shear plane constant (as in this study), the reinforcement ratio (ρ) can be changed by changing the bar size and/or spacing between the bars crossing the shear plane. Mattock and Hawkins[9] stated that the way in which steel ratio chanced does not affect the relationship between shear stress and the reinforcement parameter (ρ.f y ). To study the effect of reinforcement parameter (ρ.f y ), three ratios of steel reinforcement have been used (2.75, 4.92, and 6.18) using three different bar diameters. (∅8 mm, ∅10 mm, and ∅12 mm). [Table 6 and Figure 8] presented the results of analysis using F.E.M of specimens of groups (SR1, SR2, and SR3). These results are studied and compared to determine the effect of this parameter. It was found that, for given values of (k = sinѲ), the specimens with higher reinforcement parameter had Figure 6: Load-normal compressive stress curve - group (SR2) Figure 7: Load-normal compressive stress curve-group (SR3) Figure 8: Effect of the reinforcement parameter (ρ.f y ) on the shear transfer stress (v u ) Figure 9: Max. shear stress-total normal compressive stress relationship (k=0) Figure 11: Max. Shear stress-total normal compressive stress relationship (k=0.34) Figure 10: Max. Shear stress-total normal compressive stress relationship (k=0.174) Muhodir: Study of Shear Transfer in Modified Push-off Members Using Finite Elements Method 87 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (2): 81-88 Table 6: Results of (vu) using finite element method Specimen’s Identity fc / (MPa) ρ.fy (MPa) σn (MPa) σn+ρ.fy (MPa) vu (MPa) SC00 22.9 None Zero Zero 3.10 SC10 22.9 None 0.592 0.592 3.41 SC20 22.1 None 1.31 1.31 3.83 SC30 22.1 None 2.25 2.25 4.49 SC45 23.2 None 4.32 4.32 6.10 SP00 23.4 None Zero Zero 3.85 SP10 24.6 None 0.82 0.82 4.69 SP20 22.5 None 1.86 1.86 5.43 SP30 21.8 None 3.20 3.20 6.39 SP45 21.8 None 5.41 5.41 7.65 SR100 23.4 2.75 Zero 2.75 4.53 SR110 23.4 2.75 1.02 3.77 5.88 SR120 24.2 2.75 2.25 5.00 6.58 SR130 21.8 2.75 3.75 6.50 7.50 SR145 21.8 2.75 6.30 9.05 8.90 SR200 23.4 4.29 Zero 4.29 5.40 SR210 23.4 4.29 1.24 5.53 7.10 SR220 24.2 4.29 2.77 7.06 8.09 SR230 21.8 4.29 4.58 8.87 9.16 SR245 23.4 4.29 7.97 12.26 11.27 SR300 21.8 6.18 Zero 6.18 6.80 SR310 21.8 6.18 1.55 7.73 8.95 SR320 23.4 6.18 3.61 7.79 10.55 SR330 23.4 6.18 6.19 12.37 12.37 SR345 24.2 6.18 10.3 16.48 14.57 higher shear strength than specimens without or with lower reinforcement parameter. Results presented by [Figure 8 and Table 6] show that the presenting of the shear reinforcement normal to the shear plane are significantly increased the shear transfer stress by (46.2%, 74.02%, and 119.4%) when groups (SR1, SR2, and SR3) are compared to the unreinforced specimens of group (SC) for k=0 (i.e., σnx =0). This increasing in the shear strength can be attributed to the clamping force which is developed in the reinforcing bars within the yield range when diagonal cracks appear. Effect of Total Normal Compressive Stress (σnx+ρfy) [Figures 9-13] and [Table 6] show the effect of total normal compressive stress (σnx+ρfy) on the shear transfer strength. Figure 13: Max. shear stress -total normal compressive stress relationship, (k=0.7070) Figure 12: Max. Shear stress-total normal compressive stress relationship (k=0.5) Muhodir: Study of Shear Transfer in Modified Push-off Members Using Finite Elements Method 88 http://journals.cihanuniversity.edu.iq/index.php/cuesj CUESJ 2022, 6 (2): 81-88 With reference to this figure, it can be noted that the presence of external normal compressive stress (σ nx ) and shear reinforcement within the shear plane enhanced dramatically the shear transfer strength of the specimens used when compared with the those without shear reinforcement or those include parallel reinforcement only. Furthermore, it can be concluded that the external normal compressive stress is additive to the reinforcement parameter (ρf y ) finally it can be concluded that, if a certain shear stress is to be resisted, the area of shear reinforcement can be reduced by an amount equal to the external compressive force (σ nx ) divided by (f y ). Efficiency of the FEM To verify the accuracy of the finite element model suggested in this study to the shear transfer analysis, the obtained results are compared with those obtained experimentally by Al-Sharae.[15] The experimental results obtained by Al-Sharae,[15] (v u, test ) and that obtained by the finite element, (v u, cal. ) are summarized in [Table 7]. The standard deviation value (σ_ (n-1)) for (v_ (u, Test)/v_ (F.E.M)) is 0.102, this indicates that the predicted shear strength using FEM is very effective and gave a clear picture about the behavior of the push-off specimens. CONCLUSIONS Based on the results presented in this study, the following conclusions can be stated. 1. The two dimensional isoparametric element used in the mesh of the FEM is quite efficient in idealizing the field of displacement and the state of stresses in the modified push-off specimens with and without shear reinforcement. 2. Specimens with shear reinforcement (i.e., group SR) ad a ductile failure, while the specimens without shear reinforcement (i.e., groups SC and SP) had a brittle failure. 3. The parallel reinforcement has a little or ignored effect on the shear transfer strength. 4. An externally applied compressive normal strength which acting transversely to the shear plane is additive to the reinforcement parameter (ρ.f y ) in the calculation of the shear strength. 5. Shear strength is increased with increasing the total compressive stress. (σ n + ρ.f y ). 6. FEM results showed a good agreement with those obtained experimentally by other authors. REFERENCES 1. L. Ahmed and A. Ansell. Direct shear strength of high strength fiber concrete. Magazine of Concrete Research, vol. 62, no. 5, pp. 379-390, 2010. 2. P. M. D. Santoa and E. N. B. Julio. A state-of-the-art review on shear friction. Engineering Structures, vol. 45, no. 1, pp. 435-448, 2012. 3. K. H. Yang, J. I. Sim, J. H. Kang and A. F. Ashour. Shear capacity of monolithic concrete joints without transverse reinforcement. Magazine of Concrete Research, vol. 64, no. 9, pp. 767-779, 2012. 4. K. A. Harries, G. Zeno and B. Shahrooz. Toward an improved understanding of shear-friction behavior. ACI Structural Journal, vol. 109, no. 6, pp. 835-844, 2012. 5. K. N. Rahal. Simplified design and capacity calculation of shear strength in reinforced concrete membrane elements. Engineering Structures, vol. 30, no. 10, pp. 2782-2791, 2008. 6. American Concrete Institute. ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary. American Concrete Institute, Farmington Hills, MI, USA, 2019. 7. T. T. C. Hsu. Unified approach to shear analysis and design. Cement and Concrete Composites, vol. 20, no. 89, pp. 419-435, 1998. 8. B. J. Al-Sulayvani and J. R. Al-Feel. Effect of direct compressive stress on the shear transfer strength of fibrous concrete. Al Rafidain Engineering, vol. 17, no. 2, pp. 65-75, 2009. 9. S. Mahmoodreza and B. E. Ross. Database evaluation of interface shear transfer in reinforced concrete members. ACI Structural Journal, vol. 114 no. 2, pp. 383-394, 2017. 10. M. Soltani, B. E. Ross and A. Khademi. A statistical approach to refine design codes for interface shear transfer in reinforced concrete members. ACI Structural Journal, vol. 115, no. 5, pp. 1341, 2018. 11. A. H. Mattock and N. M. Hawkins. Shear transfer in reinforced concrete-recent research. PCI Journal, vol.17, no. 2, pp. 55-75, 1972. 12. R. N. Khaldoun. Shear-transfer strength of reinforced concrete. ACI Structural Journal, vol. 107, no. 4, p. 346, 2010. 13. W. F. Chen. Plasticity in Reinforced Concrete. McGraw Hill, New York, 1982. 14. E. Hinton and D. R. J. Owen. Finite Element Programming. Vol. 90. Academic Press, Inc., Cambridge, p. 345, 1977. 15. A. J. Al-Sharae. Experimental and Analytical Study of Shear Transfer in Reinforced Concrete Members Made with Abu-Ghar Limestone as a Coarse Aggregate. M.Sc. Thesis, University of Basrah, Iraq, 1999. Table 7: Comparison of v u Using F.E.M and v u Experiment Specimen’s Identity v u , F.E.M. (MP) (1) v u , Experim[15] (MPa) (2) 2 1       SC00 3.10 3.69 1.19 SC10 3.41 3.98 1.17 SC20 3.83 4.46 1.16 SC30 4.49 4.87 1.09 SC45 6.10 6.54 1.08 SP00 3.85 4.06 1.05 SP10 4.69 4.84 1.03 SP20 5.43 5.45 1.01 SP30 6.39 6.04 0.94 SP45 7.65 7.34 0.96 SR200 5.40 6.26 1.16 SR210 7.10 7.91 1.12 SR220 8.09 9.76 1.22 SR230 9.16 11.92 1.30 SR245 11.27 13.52 1.21 σ n-1 =0.102