AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 176 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. NON-LINEAR ANALYSIS OF REACTIVE POWDER CONCRETE (RPC) DEEP BEAMS WITH OPENINGS STRENGTHENED BY CFRP Asst. Prof .Dr .Ragheed Fatehi Makki kufa University , Civil Engineering Department,Najaf ,Iraq E mail: Ragheed.Almutwali@uokufa.edu.iq Asst.Prof.Dr.Ali Talib Jassem kufa University , Civil Engineering Department,Najaf ,Iraq E mail: alit.albozwaida@uokufa.edu.iq Hayder Abd Al-latef Jassem kufa University , Civil Engineering Department,Najaf ,Iraq E mail: hayderaliqabi1992@gmail.com Abstract: This paper mainly uses ANSYS V.15 , the finite element analysis software, to make nonlinear analysis of reactive powder concrete deep beams . The models simulating the test process were established, the calculation results of ANSYS are compared with the experimental results. Data of eight RPC deep beams tested by researchers were used for comparison with ANSYS models .Furthermore three parametric studies were carried out by changing the size of opening , location of openings and CFRP systems configuration . The comparison shows that ANSYS analysis results are similar to experimental results (the maximum difference in the ultimate load was less than 7.5 %), which indicates ANSYS analysis software can be used to simulate the mechanical property of reactive powder concrete structures. Keywords: Non-linear analysis , Finite Element, RPC deep beams , opening , CFRP 1. INTRODUCTION ANSYS (ANalysis SYStem) is a comprehensive general-purpose finite element computer program that contains over 100,000 lines of code and more than (180) different elements. It is capable of performing static, dynamic, heat transfer, fluid flow, and electromagnetism analysis. It can be used in many engineering fields, including structures, aerospace, electronic and nuclear problems. In 1971, the earliest version of ANSYS program was released for the first time [1]. One of the main advantages of ANSYS is the integration of the three phases of finite element analysis: preprocessing, solution and postprocessing. Pre-processing routines in ANSYS define the model, boundary conditions, and loadings. Displays may be created interactively on a graphics terminal as the data are input to assist the model verification. Postprocessing routines may be used to retrieve analysis results in a mailto:Ragheed.Almutwali@uokufa.edu.iq mailto:alit.albozwaida@uokufa.edu.iq mailto:hayderaliqabi1992@gmail.com AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 177 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. variety of ways. Plots of the structure’s deformed shape and stress or strain contours can be obtained in the post processing stage. According to the ACI code Provisions for shear , deep beams are members with length of clear span measured face to face of supports(ℓn) not exceeding four times total depth (h) (ℓn ≤ 4h ) or region of beams with concentrated loads within a distance (a) two times the total depth measured from the support (a ≤ 2h) that is loaded on one face and supported on the opposite face [2]. The presence of the web openings in the deep beams is because many ducts and pipes are necessary to accommodate essential services like air-conditioning, water supply , sewage, telephone, computer network and electricity .The depth of ducts or piping may range from a couples of centimeter to as much as half a meter[3] . Reactive powder concrete is an ultra-high-strength and high ductility composite material with advanced mechanical properties. It is produced from ordinary materials (cement, very fine aggregate "0.15-0.6"mm, low water-cement ratio) , in addition to other materials (Silica Fume, Superplasticiser, steel fibers). The maximum particle size of materials is (0.6)mm, an optimization of the dry fine powder packing has to be managed for getting very dense matrix[4] . In the present work, a finite element analysis has been conducted using ANSYS V.15 for eight beams deep with and without openings ,with and without CFRP strengthening tested experimentally by researchers in 2017 . A comparison of results has been made to calibrate to material models adopted in this study. And also three parametric studies were carried out by changing the size of opening , location of openings and CFRP systems configuration. 2.GEOMETRY OF TESTED RPC DEEP BEAMS Eight simply supported RPC deep beams with and without web openings having a total span (L)of 1400 mm, overall depth (h) 400mm, and width 150 mm, with shear span to overall depth ratio (a/h),1 and clear span to depth ratio (ℓn/h), 3 .Seven beams had two square openings (150*150 mm) symmetrically about the center of specimens. The distance between the opening center and the beam centerline for all beams was equal to 400mm. The center of opening of all beams set at the shear span center, which is the critical load path. All beams tested under two points top loading .Two Ø 16 mm deformed bar were used as longitudinal tension reinforcement ,Table (1) showed the properties of steel bars. Table (1) Properties of Steel Bars RPC deep beams are divided into two group ,group one represents the beams (two beams) without strengthening ,group two represents the beams (six beams) strengthening by different patterns of CFRP strips. Figure (1) showed the details of RPC deep beams. Nominal Bar Diameter (mm) Bar Area (mm2) Yield Stress (MPa) Ultimate Stress (MPa) Elongation at Ultimate Stress (%) 16 201 612 727.9 6 AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 178 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure (1) Detail and Geometry of Beams (All Dimensions in mm) 3. MECHANICAL PROPERTIES OF RPC The results of laboratory tests has been adopted for compressive strength, tensile strength and modulus of elasticity ,as shown in Table (2).Furthermore, the strain-stress curve in Figure (2) was drawn by the data of modulus of elasticity test . Group One Group Two AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 179 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Table (2) Mechanical Properties of RPC Compressive Strength Of Cylinder (MPa) Splitting Tensile Strength (MPa) Modulus of Rupture (MPa) Modulus of Elasticity (GPa) 83.44 5.35 10.38 39.2 Figure (2) Strain-Stress Curve of RPC 4. FINITE ELEMENT MODELING 4.1 ELEMENTS TYPE The elements adopted in the present study were:  solid 65 used to simulate concrete.  solid 185 used to simulate loading and supporting plates.  link180 used to represent all steel bars.  shell 41 used to represent CFRP strips . 4.2 REAL CONSTANT The real constant for any element required specific data to work .The Table (3) shows the real constant data that used for all element except the Solid 185 (plate element) ,it has no real constant. 0 10 20 30 40 50 60 70 80 90 100 0 0.001 0.002 0.003 0.004 0.005 S tr e s s Strain AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 180 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Table (3) Elements Real Constant *When symmetry Asb =Asb/2 ** Depends on the CFRP direction 4.3 MATERIAL PROPERTIES There was a material properties for each element ,where material model number 1 indicated to Solid 65 (concrete element). The requirement of this element are linear isotropic , multi-linear isotropic and concrete parameters . The Table (4) shows material properties for RPC that used in the analysis. Material model number 2 indicated to longitudinal reinforcement (Link 180). The requirement of this element are linear isotropic and bilinear isotropic properties, as shown in Table (5). Material model number 3 indicated to steel plate (Solid 185) at loading and supporting points. The input data are shown in Table (6). Material number 4 suggests to the Shell 41 element ( CFRP strips) .The CFRP is assumed to be orthotropic material , where the properties of the CFRP composites are the same in any direction perpendicular to the fibers. The modulus of elasticity was taken to be 230 GPa and the Poisson's ratio was assumed to be equal to zero [6] .Table (7) shows the CFRP properties entered in the present work. Element Type Real Constant Value Adopted Solid65 (Concrete) Material No. 0 Volume Ratio Orientation Angle (THETA) Orientation Angle (PHI) Link180 (steel bar Ø16) Cross-sectional Area (mm2) 201* Initial Strain 0 Shell41 (CFRP sheet) Shell thickness at node I,j,k,l 0.167 Element axis rotation theta ** Elastic foundation stiffness 0 Added area (mass/unit) 0 AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 181 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Table (4) Material Model for Concrete Table (5) Material Model for Steel Reinforcement Table (6) Material Model for Steel Plates Material Properties for Element Solid 65 Linear Isotropic Modulus of elasticity, MPa EX 39300 Poisson's ratio PRXY 0.2 Multi Linear Isotropic Points Number Strain Stress ,MPa 1 0.000288 11.317 2 0.000582 22.635 3 0.000950 33.953 4 0.001287 45.271 5 0.001688 56.589 6 0.002217 67.906 7 0.003173 79.224 8 0.004243 83.7 Concrete Parameters Shear transfer coefficients for an open crack ShrCf-Op 0.1 Shear transfer coefficients for a close crack ShrCf-Cl 0.15 Uniaxial tensile cracking stress, MPa. UnTensSt 5.35 Uniaxial crushing stress (positive), MPa. UnCompSt 83.44 Material Properties for Element Link 180 Bilinear Isotropic Modulus of elasticity, MPa EX 200000 Poisson's ratio PRXY 0.3 Bilinear Isotropic Yield stress, MPa Yield Stss 640 Tangent Modulus, MPa Tang Mod 6000 Material Properties for Element Solid 185 Linear Isotopic Modulus of elasticity, MPa EX 200000 Poisson's ratio PRXY 0.3 AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 182 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Table (7) Material Model for CFRP Strips 4.4 GEOMETRY In the finite element analysis, tested RPC beams experimentally, modeled by taking the benefit of the symmetry of the deep beams supports and loadings. The finite element mesh for quarter of the beam is shown in Figure (3) to simulate the RPC deep beams . In this study, perfect bond between materials is assumed .Discrete representation (Link 180) was used to model steel reinforcement . The beam and plates were modeled as 8 node elements, while the steel bars were modeled as a straight elements, also the 4 node shell is used for modeling CFRP strips. the Figure (4) shows details of elements modeling. Figure (3) Geometry of the Numerical Model Material Properties for Element Shell 41 Linear orthotropic EX 230000 EY 1 EZ 1 PRXY 0 PRYZ 0 PRXZ 0 GXY 1 GYZ 1 GXZ 1 AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 183 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure (4) Details of Elements Modeling 4.5 LOADS AND BOUNDARY CONDITIONS In ANSYS, the applied load was represented by dividing the total distributed load on the top nodes according to the area surrounded by each node to represent the distributed load in ANSYS program as shown in Figure (5). The supports were approximately as similar as in the experimental work. Figure (5) Details of Applied Load and Boundary Conditions AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 184 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. 5. RESULTS OF FINITE ELEMENT ANALYSIS The results of finite element analysis using ANSYS program were compared with the experimental results for all tested beams. The numerical failure was similar to the failure mode of each beam that occurred in experimental work. ANSYS results including ultimate load, load-deflection response and crack patterns where a close to the experimental results. 5.1 NUMERICAL ULTIMATE LOAD The comparison between the ultimate load from the experimental results and numerical models from finite element analysis of the analyzed beams are listed in Table (8) . The difference between the experimental ultimate load and that obtained by finite element analysis is not more than (7.5) %. Table (8) Comparison Between the Experimental and Numerical Ultimate Loads Beam Ultimate Load(KN) [[ 𝑝𝑢)𝐴𝑁𝑆𝑌𝑆 − 𝑝𝑢)𝐸𝑋𝑃.] /𝑝𝑢)𝐸𝑋𝑃.] % 𝑝𝑢)𝐸𝑋𝑃. KN 𝑝𝑢)𝐴𝑁𝑆𝑌𝑆 KN CBS 594 622 4.71 CBO 177 182 2.83 BSE1 197 201 2.03 BSE2 240 258 7.5 BSE3 249 254 2.01 BSE4 315 329 4.44 BSE5 220 229 4.09 BSE6 268 274 2.24 5.2 LOAD-DEFLECTION CURVES The load-deflection curve for each beam obtained from the finite element analysis together with the experimental curves are presented and compared in Figures from (6) to (13). In general, all these figures show a good agreement between the experimental and F.E.A curves. AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 185 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure (6) Experimental and Numerical Load-Deflection Curves for Beam CBS 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 0 1 2 3 4 5 6 7 8 Lo a d ( K N ) Mid span deflection(mm) Numerical Experimental 0 50 100 150 200 250 0 1 2 3 Lo a d ( K N ) Mid span deflection(mm) Numerical Experimental AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 186 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure (7) Experimental and Numerical Load-Deflection Curves for Beam CBO Figure (8) Experimental and Numerical Load-Deflection Curves for Beam BSE1 0 50 100 150 200 250 0 1 2 3 Lo a d ( K N ) Mid span deflection(mm) Experimental Numerical AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 187 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure (9) Experimental and Numerical Load-Deflection Curves for Beam BSE2 Figure (10) Experimental and Numerical Load-Deflection Curves for Beam BSE3 0 50 100 150 200 250 300 0 1 2 3 4 Lo a d ( K N ) Mid span deflection(mm) Experimental Numerical 0 50 100 150 200 250 300 0 1 2 3 4 Lo a d ( K N ) Mid span deflection(mm) Experimental Numerical AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 188 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure (11) Experimental and Numerical Load-Deflection Curves for Beam BSE4 Figure (12) Experimental and Numerical Load-Deflection Curves for Beam BSE5 0 50 100 150 200 250 300 350 0 1 2 3 4 5 Lo a d ( K N ) Mid span deflection(mm) Experimental Numerical 0 50 100 150 200 250 0 1 2 3 4 Lo a d ( K N ) Mid span deflection(mm) Experimental Numerical AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 189 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure (13) Experimental and Numerical Load-Deflection Curves for Beam BSE6 5.3 CRACK PATTERNS The numerical-model painted the cracks at all stages of loading. Cracking-patterns in the beams was obtained using the Crack/Crushing plot option in ANSYS V.15. According to ANSYS program, the first crack which represented slight crack is symbolized by a red circle outline at an integration point, the second crack which represents moderate crack is symbolized by a green circle outline, and the third crack which represents failure crack is symbolized by a blue circle outline. The results showed a good agreement in crack patterns and failure mode between numerical and experimental tested beams as shown in Figure(14) and Figure(15) . 0 50 100 150 200 250 300 0 1 2 3 4 5 Lo a d ( K N ) Mid span deflection(mm) Experimental Numerical AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 190 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure (14) Crack Pattern for Beam CBO at Failure Load Figure (15) Crack Pattern for Beam SBE1 at Failure Load 6. NUMERICAL PARAMETRIC STUDY In the present work, an important factors were studied by using numerical models to investigate their influence on the behavior RPC deep beam with openings .The considered parameters are the size of opening , location of openings and CFRP systems configuration . AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 191 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. 6.1 OPENINGS LOCATION The first assumption in this parameter was change the horizontally location of the opening with respect to the shear span . Five models with different distances from the support center to the opening center as 175 ,225 ,250 , 275 and 300 mm were used in this assumption as shown Figure (16). The results showed that when the location of opening was changed horizontally from the critical location at the center of shear span , the strength of beam was increased significantly , whenever was opening Located further away from critical location toward middle of span . as shown in Figure (17) . The second assumption in this parameter was change the vertically location of the opening with respect to the shear span . Two models with different distances from the bottom face of beam to the opening center as 125 and 275 mm were used in this assumption as shown in Figure(18). The results showed that when the location of the opening changed vertically from the critical location at the center of the shear span ,the strength of beam was increased significantly as shown in Figure (19) . The reason of increase the strength in the two assumptions due to the opening moving from the critical location at shear span that deals with the previous study. Figure (16) Horizontal Changes in Locations of the Opening AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 192 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure (17) Load-Deflection Curves of first Assumption Figure (18) Vertical Changes in Locations of The Opening 0 50 100 150 200 250 300 350 400 0 1 2 3 4 Lo a d ( K N ) Mid span deflection(mm) 300 275 250 225 175 200 (CBO) AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 193 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure (19) Load-Deflection Curves of Second Assumption 6.2 OPENINGS SIZE To explain the effect of opening size on the behavior of RPC deep beam with openings ,four sizes of opening were provided (50x50 , 100x100 , 200x200 and 250x250 mm ) at the center of shear span .Figure (20) shows the load deflection curves of several cases of deep beams which have different opening sizes compared with numerical beams ( CBS and CBO). The results showed that the ultimate load was decreased with increasing the opening size . The strength of beam was decreased Significantly compared with solid beam , Table (9) shows the reduction in strength due to existence of different opening sizes compared with numerical solid beam .The explain of decreasing the strength with increasing the size of opening due to the diagonal cracks at corner along a line joining the support and load points cracks crossing minimum distances to occur the failure. 0 50 100 150 200 250 300 0 1 2 3 Lo a d ( K N ) Mid span deflection(mm) 125 275 200 (CBO) 0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 0 1 2 3 4 5 6 7 8 Lo a d ( K N ) Mid span deflection(mm) CBS 50X50 100X100 150X150 (CBO) 200X200 250X250 AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 194 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure (20) Load-Deflection Curves of Several Cases of Deep Beams with different opening sizes Table(9) The Strength Reduction in Deep Beams Due to Existence of Different opening sizes Model Ultimate Strength (KN) Strength Reduction Respect to Solid Beam % Beam without Opening (Solid) 623 _______ Beam with Opening (50x50) 524 15.89 Beam with Opening (100x100) 339 45.59 Beam with Opening (150x150) 182 70.79 Beam with Opening (200x200) 97 84.43 Beam with Opening (250x250) 42 93.26 6.3 CFRP SYSTEMS CONFIGURATION To study the effect of these three system on the strengthening process of RPC deep beam with openings ,three model (full warp , U-wrap and two sides wraps) were used by taking CFRP strips patterns of BSE2 as a case study .The models were have the same system shape in front view as shown in Figure (21) . According to results of ANSYS as shown in Figure (22) , the ultimate load and the mid span deflection of three systems were very close and the difference was not noticeable . The explain of that behavior is the failure of deep beam with opening (which located at the load path) occurs at the corners of opening , because that was no difference among the three configuration Systems. Figure (21) Front and Side View of Full warp, U-wrap and Two sides wraps Models AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 195 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. Figure(22) Load –Deflection curves of Full Warp, U-Wrap and Two Sides Warps Models 7. CONCLUSIONS 1- The comparison between the F.E.A and the experimental results asserted the validity of the numerical analysis and the methodology developed. The maximum difference in the ultimate load was less than 7.5 %. 2-From the comparison between the numerical models (full warp),(U-warp) and (two sides warps), it can be observed that there is no significant effect for the vertical anchorage warp if it used for the deep beam with openings. 3- The presence of opening in deep beam (at critical location of shear span) decrease the strength and increase the deflection , and that effect become higher with increasing the size of opening .When the opening size were (50x50 ,100x100 ,150x150 ,200x200 and 250x250) mm the ultimate load decreased about (15.89 ,45.59 , 70.79 , 84.43 , 93.26) % respectively. 4- When the location of opening was changed horizontally from the critical location at the center of shear span , the strength of beam was increased significantly about (12 - 80 )% . 5-When the location of the opening changed vertically from the critical location at the center of the shear span ,the strength of beam was increased significantly about (41 - 57)% . 6- The crack patterns at the final load from the finite element model had a good match with the noticed failure of the experimental results. 0 50 100 150 200 250 300 0 1 2 3 4 5 Lo a d ( K N ) Mid span deflection(mm) Full warp U warp Two sides warps AL-QADISIYAH JOURNAL FOR ENGINEERING SCIENCES Vol. 11, No. 2 ISSN: 1998-4456 Page 196 Copyright  2018 Al-Qadisiyah Journal For Engineering Sciences. All rights reserved. REFRENCES 1-AL-Shimmari I,Kh. , Hamad N.T. and Waryosh W.A. Investigation of the Behavior for Reinforced Concrete Beam Using Non-Linear Three-Dimensional Finite Elements Model .Engineering College, University of Al- Mustansiriya/Baghdad ,Eng. & Tech. Journal, 29(10) ,2011, pp.1870-1885 . 2-ACI Committee .Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary(ACI 318R-14), American Concrete Institute, Farmington Hills, MI, 519 pp. 3-Mansur MA, Tan KH. Concrete beams with openings: Analysis and design. CRC Press; 1999 Jan 29. 4- Maroliya MK. State of Art-on Development of Reactive Powder Concrete. International Journal of Innovative Research and Development. 2012 Oct 1;1(8):493-503 5-ANSYS Help V 15.0 . A finite element computer software theory and user manual for nonlinear structural analysis . 6-Al-Habbobi ,A.M .The Use of CFRP for Shear Strengthening of Reactive Powder Concrete Beams. Phd Thesis, Al- Basrah University , 2014, pp.204.