Finite Element Analysis Of Concrete Beams Reinforced With Fibre .
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12, 2019 (Special Issue) Research India Publications. http://www.ripublication.comFinite Element Analysis of Concrete Beams Reinforcedwith Fibre Reinforced Polymer BarsShigna JagadishMtech student, Dept. of Civil EngineeringVimal Jyothi Engineering CollegeKannur, Kerala, IndiaRona P Maria JamesAssistant Professor, Department of Civil EngineeringVimal Jyothi Engineering CollegeKannur, Kerala, IndiaAbstract—Fibre reinforced polymer (FRP) bars have becomecommercially available as reinforcement for concrete over the lastdecades. These bars have several important advantages overconventional reinforcing steel such as high tensile strength, lightweight, non-corrosiveness, anti-fatigue, non-magnetic, electricalinsulation, small creep deformation and specific gravity. All theseadvantages are the main reasons of their incorporation into the civilengineering structures. The FRP bars are generally made of glass,carbon and aramid fiber reinforced composites can be readilyformed into complex shapes through the pultrusion manufacturingprocess in order to increase the strength. In this project behavior ofconcrete beams reinforced with Glass fibre reinforced polymer(GFRP) bars and carbon fibre reinforced polymer (CFRP) bars ofdifferent surface configurations by varying the reinforcement ratioare analyzed using non linear finite element analysis in ANSYSworkbench 16.1. CFRP bars and GFRP bars of three differentcross-sections are considered. Circular section without longitudinalribs and with two and four longitudinal ribs. Total twenty eightbeams of M25 grade concrete is modeled. Also found the ultimateload carrying capacity and deformation and studied the loaddeflection behavior of all the beams and comparison is donebetween the reinforced concrete beams. From ANSYS result, it isfound that beam reinforced with CFRP bar of circular section withfour longitudinal ribs of 4% reinforcement ratio increases theultimate strength of the beam.Keywords—concrete beams; GFRP bars; CFRP bars; Finite elementanalysis; ANSYSI.INTRODUCTIONAn important feature of fibre reinforced polymer composites(FRP) is their extremely high corrosion resistance. This makesthem suitable for use in structures subjected to severeenvironmental exposure. Applications for FRP bars as internalreinforcement in concrete structural members include parkinggarages, multi-storey buildings and industrial structures. In manyof these applications provision of appropriate fire resistance isone of the major design requirements. Similar to other materials,the properties of Fiber Reinforced Polymer composite materialsdeteriorate when exposed to fire. One of the major concerns withusing FRP reinforcing bars in building construction is their earlyloss of strength and stiffness at elevated temperatures. There isvery little information in literature on the variation of strengthand stiffness of FRP with temperature. Fiber reinforced polymer(FRP) reinforcement in the form of longitudinal and transversereinforcement, are currently being developed for use in newbuildings and bridges. The major driving force behind thisdevelopment is the superior performance of FRPs in corrosiveenvironments. FRP reinforcement has high strength-to-weightratio, favorable fatigue strength, electro-magnetic transparencylow relaxation characteristics when compared with steelreinforcement, offering a structurally sound alternative in mostapplications. However, FRP reinforcement shows linear stressstrain characteristics up to failure, without any ductility. Thisposes serious concerns about their applicability to earthquakeresistant structures, where seismic energy is expected to bedissipated by inelasticity in members. Reinforced Concrete is avery common building material for the construction of facilitiesand structures. As complement to concrete's very limited tensilestrength, steel reinforcement bar has been an effective and costefficient reinforcement. However, insufficient concrete cover,poor design or workmanship, and presence of large amounts ofaggressive agents including environmental factors all can lead tocracking of the concrete and corrosion of the steel rebar. Formany years, there have been many studies on this corrosionissue, and the interest in FRP (Fiber Reinforced Polymer) hasarisen recently as prospective substitute for steel. Usingpultrusion process FRP bars can be deformed into differentshapes. Surface configurations of FRP bars effect the strength ofconcrete beams.II.LITERATURE REVIEWNasr Z. Hassan.et.al (2017)[11]Finite element analysis has beenused in order to study this problem. Fifty-seven beams analyzedusing finite element program ANSYS V12. The analysis resultscompared with fifteen experimental beams had been done byIbrahim. Study beams have opening width and height ofdimensions 200x100 mm and 300x100 mm. The centerline ofthe opening is at distance of 225, 300, 350 and 400 mm from thenear support. Strengthening of all beams with opening came outto six types of different scheme around the opening using fiberreinforced polymer (FRP). Scheme 1 is vertical and horizontalcarbon fiber sheets around the opening, scheme 2 is inclined at45 carbon fiber sheets around the opening in addition tohorizontal one, schemes 3 and 4 are same of schemes 1 and 2respectively but with glass fiber sheets, while schemes 5 and 6are same as schemes 3 and 4 respectively but with an additionalstrengthening at flexural area at the middle of the beam with Ushape. The reinforced concrete beams were modeled in ‘ANSYSV12’ Program under statical load. The failure loads, crackpattern, strain progress, mode of failure and energy absorptionwere analyzed here in this study.Ibrahim M. Metwally et.al (2015)[4] presents numericalinvestigation of twelve large scale concrete deep beamsinternally reinforced with GFRP bars without web reinforcementfailed in shear which were experimentally tested and collectedfrom literature. The collected specimens cover severalparameters which usually influenced strength and behavior ofPage 100 of 107
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12, 2019 (Special Issue) Research India Publications. http://www.ripublication.comdeep beams as shear span/depth ratio, the reinforcement ratio,the effective depth, and the concrete strength. Concrete deepbeams are generally analyzed using conventional methods suchas empirical equations or strut and tie models. These methodshowever do not take into account the redistribution of forcesresulting from non-linear materials’ behaviors. To address thisissue, non-linear finite element analysis that incorporates nonlinear material behavior as ABAQUS package is used.Maher A. Adam et.al (2015)[5] presents an experimental,numerical and analytical study of the flexural behavior ofconcrete beams reinforced with locally produced glass fiberreinforced polymers (GFRP) bars. A total of ten beams,measuring 120 mm wide 300 mm deep and 2800 mm long, werecast and tested up to failure under four-point bending. The mainparameters were reinforcement material type (GFRP and steel),concrete compressive strength and reinforcement ratio. The midspan deflection, crack width and GFRP reinforcement strains ofthe tested beams were recorded and compared. The test resultsrevealed that the crack widths and mid-span deflection weresignificantly decreased by increasing the reinforcement ratio.The ultimate load increased by 47% and 97% as thereinforcement ratio increases. The recorded strain of GFRPreinforcement reached to 90% of the ultimate strains. A nonlinear finite element analysis (NLFEA) was constructed tosimulate the flexural behavior of tested beams, in terms of crackpattern and load deflection behavior. It can be considered a goodagreement between the experimental and numerical results wasachieved.III.METHODOLOGYThis project is carried out on beams reinforced with FRP bars todetermine the total deformation, and ultimate load obtained inthe structure analytically using ANSYS workbench softwarepackage.A.Review of LiteratureVarious literatures were studied and reviewed and the researchgap was identified.B.Research Gap IdentificationIn all the reviewed literatures concrete beams are reinforced withGFRP bars. Many research have been carried out related to FRPbars. Here, in this project, non-linear finite element methodusing the software ANSYS workbench is used to determinedeformation and ultimate load capacity of twenty eight concretebeams of size 1500x200x250 mm reinforced with steel bars ofcircular cross section, glass fiber reinforced polymer (GFRP)bars and carbon fibre reinforced bars (CFRP) of circular section,circular section with two longitudinal ribs and circular sectionwith four longitudinal ribs and with and without longitudinal ribsby varying reinforcement ratio (0.5%, 1%, 1.5% and 2%) will bemodeled and analyzed using ANSYS software to determine thetotal deformation and ultimate load carrying capacity developedin the reinforced concrete beam and load deflection behavior ofthe different concrete beams modeled and is then comparedamong themselves to find the best cross section of bar to be usedfor reinforcement.C.ValidationThe validation on the referred paper, "Analytical andexperimental flexural behavior of concrete beams reinforcedwith glass fiber reinforced polymers bars" is done.D.ModelingANSYS Workbench 16.1 is used to model the concrete beamsand 28 different models are considered. Concrete beamsreinforced with reinforced with steel bars of circular crosssection, glass fiber reinforced polymer (GFRP) bars and carbonfibre reinforced bars (CFRP) of circular section, circular sectionwith two longitudinal ribs and circular section with fourlongitudinal ribs by varying the reinforcement ratio by 0.5%,1%, 1.5% and 2% are modeled.E.AnalysisAfter the modeling, analysis is carried out in ANSYSWorkbench. Non-linear static analysis is carried out.F.Comparison of parametersThe parameters such as ultimate load carrying capacity andcorresponding deflection of different concrete beam models arecompared.G.Results and discussionsUltimate load carrying capacity and deformation obtained for allthe concrete beams are analyzed and discussed.IV.MODELING AND ANALYSISFinite element analysis (FEA) includes modeling the beam,defining the element type for materials, real constant, materialproperties, meshing loading and boundary conditions. In order toaccurately simulate the actual behavior of the concernedconcrete beams, all its components such as concrete beam, steelbars, FRP bars and stirrups have to be modeled properly.Meanwhile, choosing the element types and mesh size areimportant as well in building the model to provide accurateresults with reasonable computational time.A.Finite element analysisFinite element analysis is a numerical method for analyzingcomplex structural and thermal problems. Like homogeneousmaterials, composite materials can also be analyzed using preand post-processor facilities of ANSYS to study its behaviorunder different load condition. The displacements of theconcrete structures are small compared to the dimensions of thestructure and hence in the present study geometric nonlinearity isneglected. Since the concrete is a non-homogeneous material andbehaves linearly over a small percentage of its strength, materialnon linearity is considered. With the aid of nonlinear finiteelement analysis, it is possible to study the behavior of concretestructures up to the ultimate load range. This leads to theoptimum design of the concrete structures. The load deformation relationships can be used to forecast the behavior ofthe structures.Page 101 of 107
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12, 2019 (Special Issue) Research India Publications. http://www.ripublication.comB.Finite element analysisThe finite element approach a numerical method for solvingdifferential equation generated by theories of mechanics suchelasticity theory and strength of materials .The basis of a finiteelement method is the representation of the body or a structureby an assemblage of subdivisions called finite elements. This isusual done using numerical approximation in structural analysisis the finite element method(FEM). FEM is best understoodfrom is practical application known as finite elementanalysis(FEA). FEA as applied in engineering is a computationaltool for performing engineering analysis. Non linear analysisgives enhanced data of serviceability and ultimate strength.C.ANSYSANSYS Workbench is used for modeling. ANSYS Workbenchis a software environment for performing structural, thermal andelectromagnetic analyses. For modeling concrete, ANSYSprovides an element which replicates the behavior of concrete.The element also takes into account the non linear materialproperties of concrete as well as the non-linearity of largedeflections. It also allows for the modeling of reinforcementwithin the elements. This capability is used to model the mesh.Concrete is modeled using 3 dimensional 8 noded solid elementSOLID 65. Reinforcing bar is modeled using beam elementBEAM 188. All calculations were made with FEM by creationof a friction interface between the composite rebar and concrete.D.ModelingTABLE 1 TWENTY EIGHT MODELS CONSIDERED IN THIS PROJECTNo. ofType ofSectionReinforcemeModelsbarnt ratio1Steel0.5%2Steel1%Circular section3Steel1.5%4Steel2%5GFRP0.5%6GFRP1%Circular section7GFRP1.5%8GFRP2%9CFRP0.5%10CFRP1%Circular section11CFRP1.5%12CFRP2%13GFRPCircular section with 20.5%longitudinal ribs14GFRP1%15GFRP1.5%16GFRP2%17CFRPCircular section with 20.5%longitudinal ribs18CFRP1%19CFRP1.5%20CFRP2%21GFRPCircular section with 40.5%longitudinal ribs22GFRP1%23GFRP1.5%24GFRP2%25CFRPCircular section with 40.5%longitudinal ribs26CFRP1%27CFRP1.5%28CFRP2%E.Details of the specimenThe model of 1500mm long with a cross section of 200 mmx250mm is studied. Finite element model of the beam is shown in fig1. Concrete beams reinforced with steel bar of circular section,GFRP bar of circular section with 2 and 4 longitudinal ribs andCFRP bar of circular section with 2 and 4 longitudinal ribs withreinforcement ratio 0.5%, 1%, 1.5% and 2% are modeled andanalyzed using ANSYS workbench 16.1.Beam of size 1500x200x250mm is modeled. Flexuralreinforcing bar is 6mm diameter and is spaced a 110mm c/c.1)Material modelingThe material properties of the components considered aredetailed in table 2, table 3 and table 4. In all cases, the ultimatestrain of the concrete at failure was taken as 0.0035 and thePoisson’s ratio of concrete taken is 0.15. A multi-linear isotropicstress-strain relation is used for modeling concrete material incompression. The Poisson’s ratio was assumed to be 0.3 for steelreinforcement. For stirrups and loading plates, the stress-strainrelation was considered linear.a) ConcreteFor concrete, ANSYS requires input data for material propertiesas shown in table 5.1 below. The grade of concrete (fck) is M25and Fe415 grade of steel (fy) is used.TABLE 2. PROPERTIES OF CONCRETEPropertiesConcreteFig. 1.ANSYS model of beamTwenty eight models of concrete beams reinforced with steel barof circular section, GFRP bar and CFRP bar of circular sectionwith 2 and 4 longitudinal ribs with reinforcement ratio 0.5%,1%, 1.5% and 2%considered are shown in table 1.Modulus of elasticity, Ec25000 MPaPoisson's ratio, µ0.15b) Fibre reinforced polymer barsThe material properties assigned for the FRP materials- CFRPand GFRP bars used for the study.Page 102 of 107
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12, 2019 (Special Issue) Research India Publications. http://www.ripublication.comTABLE 3. PROPERTIES OF CFRP AND GFRPPropertiesCFRPGFRPModulus of elasticity165000 MPa21000 MPaTensile strength2300 MPa510 MPaPoison's ratio, µ0.30.26supported beam is taken for analysis. Loading and supports areshown in fig 3.c)Steel reinforcementElastic modulus and poisson's ratio for the steel reinforcementused in this FEM study are given in table 4.TABLE 4. PROPERTIES OF STEELPropertiesSteelYoung's modulus200000 MPaPoisson's ratio, µ0.3Steel plates were added at support locations and loading pointsin the finite element models to provide a more even stressdistribution. An elastic modulus equal to 200,000 MPa andPoisson’s ratio of 0.3 were used for the plates. The steel plateswere assumed to be linear elastic materials. Structural steelgrade of Fe250 is used.2) Finite element type and meshTo obtain an accurate simulation of the actual behavior of theconcrete beam, the elements composing the finite element modelhad to be chosen properly. The mesh size is carefully selected toobtain high accuracy of results with reasonable computationaltime. Meshed view is shown in fig. 2. The aspect ratio of theused solid elements was kept as possible within therecommended range between 1 and 3. Both material andgeometric non- linearity were considered in the analysis.Concrete is modeled using 3 dimensional 8 noded solid element65. Reinforcing bar is modeled using beam element BEAM 188.Fig. 3.Loading and supportsF. Modeling of concrete beams reinforced with CFRP andGFRP bars of circular section with two longitudinal ribs.Concrete beams reinforced with steel bar of circular section,GFRP bar of circular section with 2 longitudinal ribs and CFRPbar of circular section with 2 longitudinal ribs withreinforcement ratio 0.5%, 1%, 1.5% and 2% . Reinforcementratio is the ratio of the area of bar provided to the area of sectionof beam. Bar modeled with two longitudinal ribs is shown in fig.4. Both CFRP and GFRP bar are modeled with four longitudinalribs. Height of the rib provided is 4mm and width is 2.5mm.Fig. 4.Bar of circular section with 2 longitudinal ribsG. Modeling of concrete beams reinforced with CFRP andGFRP bars of circular section with four longitudinal ribs.Fig. 2.Meshed view3) Loading and boundary conditionTwo point loading is applied to the concretebeam. Modeling of boundary condition are must in ANSYSanalysis and the most critical aspect in achieving sensible,reliable data from a finite element method. Therefore simplyConcrete beams reinforced with steel bar of circular section,GFRP bar of circular section with 4 longitudinal ribs and CFRPbar of circular section with 4 longitudinal ribs withreinforcement ratio 0.5%, 1%, 1.5% and 2% . Bar modeled withfour longitudinal ribs is shown in fig. 5. Both CFRP and GFRPbar are modeled with four longitudinal ribs. Height of the ribprovided is 4mm and width is 2.5mm.Page 103 of 107
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12, 2019 (Special Issue) Research India Publications. http://www.ripublication.comFig. 7.Deformation developed in concrete beam reinforced with GFRP bar ofcircular cross section with 4 ribs of reinforcement ratio 2%.Fig. 5.Bar of circular section with 4 longitudinal ribs.H. AnalysisThe structure is modeled using ANSYS workbench16.1. ANSYS Workbench provides superior CAD connectivity,meshing and an easy framework to perform design optimization.After analysis, the results are drawn and graphs have been pottedin Microsoft Excel using chart tools option.Analysis of concrete beam reinforced with CFRP bar of circularcross section with 4 ribs of reinforcement ratio 2% is done.When the load is applied, the obtained deflected shape of theconcrete beam is showed in fig. 8.V.RESULT AND DISCUSSIONAnalysis of concrete beams reinforced with steel bar of circularsection with reinforcement ratio 2% is done. When the load isapplied, the obtained deflected shape of the concrete beam isshown in fig. 6.Fig 8.Deformation developed in concrete beam reinforced with CFRP bar ofcircular cross section with 4 ribs of reinforcement ratio 2%.The load v/s deflection graph plotted for the beams reinforcedwith steel bars of 0.5%, 1%, 1.5% and 2% is shown in fig. 9.LOAD -DEFLECTION CURVE180160STEEL CSA 0.5%reinforcementratio.140Fig. 6.Deformation developed in concrete beam reinforced with steel bar ofcircular section with reinforcement ratio 2%.Analysis of concrete beams reinforced with GFRP bar of circularcross section with 4 ribs of reinforcement ratio 2% is done.When the load is applied, the obtained deflected shape of theconcrete beam is shown in fig. 7.Load (KN).120100STEEL CSA 1% reinforcementratio.80604020002468Deflection (mm)Fig. 9.load v/s deflectionPage 104 of 107STEEL CSA 1.5%reinforcementratio.
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12, 2019 (Special Issue) Research India Publications. http://www.ripublication.comFrom figure 9 it is clear that beam reinforced with steel bar of2% reinforcement ratio undergoes less deflection compared tobeams reinforced with steel bar of reinforcement ratio 0.5%, 1%and 1.5%.The load v/s deflection graph is plotted for the beam reinforcedwith GFRP bar of circular cross section with 4 ribs ofreinforcement ratio 0.5%, 1%, 1.5% and 2% is shown in fig 10.A. Comparison of resultsComparison of ultimate load obtained the concrete beamsreinforced with steel bar of circular section and the concretebeams reinforced with GFRP and CFRP bars of circular section,circular section with 2 longiudinal ribs and circular section with4 longiudinal ribs of reinforcement ratio 0.5%, 1%, 1.5% and2% is shown in table 5.TABLE 5 ULTIMATE LOAD COMPARISON BETWEEN THE CONCRETE BEAMSType ofbarLOAD -DEFLECTION CURVE200180160GFRP CSA 0.5% reinforcementratio-4 RIBSLoad (KN)140120GFRP CSA 1%reinforcementratio.4 RIBS10080GFRP CSA 1.5% reinforcementratio.4 RIBS6040GFRP CSA 2 %reinforcementratio.4 ction (mm)Fig. 10.load v/s deflectionCFRPbarFrom figure 10 it is clear that beam reinforced wih GFRP bar ofcross section with 4 longitudinal ribs of reinforcement ratio 2%undergoes less deflection compared to other beams.The load v/s deflection graph is plotted for the beam reinforcedwith CFRP bar of circular cross section with 4 ribs ofreinforcement ratio 0.5%, 1%, 1.5% and 2% is shown in fig. 11.GFRPbarCFRPbarLOAD -DEFLECTION ateload (N)94177138080151920167110133620Circular sectionCircular sectionwith 2 ribsCircular sectionwith 4 ribs0.5%1%1.5%2%% increasein r section159070250Circular sectionwith 2 ribsCFRP CSA 0.5% reinforcementratio-4 RIBS200Load (KN)Section of bar150GFRPbar2%Circular sectionwith 4 ribsCircular sectionCFRP CSA 1%reinforcementratio.4 RIBS100CFRP CSA 1.5% reinforcementratio.4 RIBS50001020306.6518626017.09194710Circular sectionwith 2 ribsCFRPbar2%2024603.9821542010.64Circular sectionwith 4 ribsCFRP CSA 2% reinforcementratio.4 RIBSCircular section159070GFRPbarDeflection (mm)1696502%Circular sectionwith 2 ribsCircular section1696506.65194710Fig. 11.load v/s deflectionFrom figure 11 it is clear that beam reinforced wih CFRP bar ofcross section with 4 longitudinal ribs of reinforcement ratio 2%undergoes less deflection compared to other beams.CFRPbarGFRPbarCFRPbarPage 105 of 1072%Circular sectionwith 2 ribs2044602%Circular section1590701947105.0122.4
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12, 2019 (Special Issue) Research India Publications. FRPbar2%Circular sectionwith 2 ribs1696502044602%Circular sectionwith 4 ribs20.5218626021542015.65Deflectionv/s reinforcement ratio is plotted for the concretebeams reinforced with GFRP bars of circular section, circularsection with 2 longitudinal ribs and 4 longitudinal ribs is shownin figure 12.From figure 13 it is clear that as the reinforcement ratioincreases, there is increase in ultimate load carrying capacity ofconcrete beams. Concrete beams reinforced with GFRP bars ofcircular section with 4 longitudinal ribs of 2% reinforcementratio has higher ultimate load carrying capacity compared toother beams.Deflection v/s reinforcement ratio is plotted for the concretebeams reinforced with CFRP bars of circular section, circularsection with 2 longitudinal ribs and 4 longitudinal ribs is shownin figure 14.DEFLECTION COMPARISON CHARTDEFLECTION COMPARISON CHART1025Deflection (mm)15Circular section2 ribs104 ribsDeflection (mm)82056circular section2 ribs44 ribs200.5%00.5%1%1.5%Reinforcement ratio1%1.5%Reinforcement ratio2%2%Fig. 12.Deflection comparison chart for concrete beams reinforced with GFRPbars of circular section, circular section with 2 longitudinal ribs and 4longitudinal ribs.From figure 12 it is clear that as the reinforcement ratioincreases, there is decrease in deflection. Concrete beamsreinforced with GFRP bars of circular section with 4longitudinal ribs with 2% reinforcement ratio has less deflecioncompared to other beams.Ultimate load v/s reinforcement ratio is plotted for the concretebeams reinforced with GFRP bars of circular section, circularsection with 2 longitudinal ribs and 4 longitudinal ribs is shownin figure 13.Fig. 14.Deflection comparison chart for concrete beams reinforced with CFRPbars of circular section, circular section with 2 longitudinal ribs and 4longitudinal ribs.From figure 14 it is clear that as the reinforcement ratioincreases, there is decrease in deflection. Concrete beamsreinforced with CFRP bars of circular section with 4 longitudinalribs with 2% reinforcement ratio undergoes less deflectioncompared to other beams.Ultimate load v/s reinforcement ratio is plotted for the concretebeams reinforced with CFRP bars of circular section, circularsection with 2 longitudinal ribs and 4 longitudinal ribs is shownin figure 15.ULTIMATE LOAD COMPARISON CHART250000ULTIMATE LOAD COMPARISON CHARTload(N)150000circular section1000002 ribs4 ribs50000UltimateUltimate load(N)200000200000150000circular section2 ribs1000004 ribs50000000.5% 1%1.5%2%Reinforcement ratio0.5% 1% 1.5% 2%Reinforcement RatioFig. 13.Ultimate load comparison chart for concrete beams reinforced withGFRP bars of circular section, circular section with 2 longitudinal ribs and 4longitudinal ribs.Fig. 15.Ultimate load comparison chart for concrete beams reinforced withCFRP bars of circular section, circular section with 2 longitudinal ribs and 4longitudinal ribs.Page 106 of 107
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 14, Number 12, 2019 (Special Issue) Research India Publications. http://www.ripublication.comFrom figure 15 it is clear that as the reinforcement ratioincreases, there is increase in ultimate load carrying capacity ofconcrete beams. Concrete beams reinforced with CFRP bars ofcircular section with 4 longitudinal ribs with 2% reinforcementratio has higher ultimate load carrying capacity.VI.CONCLUSIONS[3][4]Fares Jnaid and Riyad Aboutaha (2015)," Nonlinear Finite ElementModeling of Unbonded Steel Reinforced Concrete Beams", InternationalJournal of Civil and Environmental Engineering, Vol.9, No.3.Hsuan-Teh Hu, Fu-Ming Lin and Yih-Yuan Jan (2014),"Nonlinear finiteelement analysis of reinforced concrete beams strengthened by fiberreinforced plastics", Science Direct composite structures, 63, 271–281.[5]Ibrahim M. Metwally (2015),"Three-dimensional nonlinear finite elementanalysis of concrete deep beam reinforced with GFRP bars", Science DirectHBRC Journal, 13, 25-38[6]Maher A. Adam, Mohamed Said, Ahmed A. Mahmoud and Ali S. Shanour(2015),"Analytical and experimental flexural behavior of concrete beamsreinforced with glass fiber reinforced polymers bars", Science DirectConstruction and Building Materials, 84, 354–366.[7]M.A. Hossain, I. Saifullah , M. Nasir-uz-zaman , S.M.K. Uddin and M.H.Rashid (2015), "Experimental and Analytical Investigation of FlexuralBehavior of Reinforced Concrete Beam", International Journal ofEngineering & Technology, Vol. 11, No. 1.M. A. Musmar, M. I. Rjoub and M. A. Abdel Hadi (2014), "Nonlinearfinite element analysis of shallow reinforced concrete beams using solid65element", APRN Journal of Engineering and Applied Sciences, Vol. 9, No.2.Mazen Musmar (2018), "Nonlinear Finite Element Flexural Analysis of RCBeams", International Journal of Applied Engineering Research, Vol. 13,No. 4, pg 2014-2020.M. Kh Hind (2016), "Nonlinear Finite Element Analysis of ReinforcedConcrete Beams Retrofitted with Fiber Reinforced Polymers", Journal ofAdvanced Research in Applied Mechanics, Vol. 12, No. 2.Nasr Z. Hassan, Alaa G. Sherif, Amal H. Zamarawy (2017), "Finiteelement analysis of reinforced concrete beams with opening strengthenedusing FRP", Science Direct Ain Shams Engineering Journal, 8, 531-537.Richa Pateriya, Dr. Saleem Akhtar and Prof. Nita Rajvaidya (2015), "Analysis of Compressive Strength of Columns Reinforced with Steel &FRP Bars", International Journal of Recent Development in Engineeringand Technology, Vol.4.T.S. Thandavamoorthy and C. Selin Ravikumar (2013), " Glass FibreConcrete: Investigation on Strength and Fire Resistant Properties", IOSRJournal of Mechanical and Civil Engineering (IOSR-JMCE), Vol.9, 3, 2125.Y.C. Wang a, P.M.H. Wong and V. Kodur (2016), "An experimentalstudy of the mechanical properties of fibre reinforced polymer (FRP)and steel reinforcing bars at elevated temperatures", Science DirectComposite structure, 80, 131-140.IS 456-2000 Indian Standard Plain And Reinforced Concrete-Code forPractice.IS 800-2007 Indian Standard General Construction in Steel-Code ofPractice.The following conclusions are obtained.1. As the reinforcement ratio increases from 0.5% to 2%,ultimate load carrying capacity increases and deflectiondecreases.2. Beam reinforced with CFRP bar of circular section with 4 ribsof 2% reinforcement ra
experimental flexural behavior of concrete beams reinforced with glass fiber reinforced polymers bars" is done. D.Modeling . ANSYS Workbench 16.1 is used to model the concrete beams and 28 different models are considered. Concrete beams reinforced with reinforced with steel bars of circular cross
Finite element analysis DNV GL AS 1.7 Finite element types All calculation methods described in this class guideline are based on linear finite element analysis of three dimensional structural models. The general types of finite elements to be used in the finite element analysis are given in Table 2. Table 2 Types of finite element Type of .
Figure 3.5. Baseline finite element mesh for C-141 analysis 3-8 Figure 3.6. Baseline finite element mesh for B-727 analysis 3-9 Figure 3.7. Baseline finite element mesh for F-15 analysis 3-9 Figure 3.8. Uniform bias finite element mesh for C-141 analysis 3-14 Figure 3.9. Uniform bias finite element mesh for B-727 analysis 3-15 Figure 3.10.
Finite Element Analysis of Concrete Fracture Specimens I May 1984 . -----·-----7. AutMor(s) . Finite Element Model of Notched Beam Nonlinear Portion of Finite Element Grid Effect of Assumed Concrete Tensile Response on Load-Deflection Curves
1 Overview of Finite Element Method 3 1.1 Basic Concept 3 1.2 Historical Background 3 1.3 General Applicability of the Method 7 1.4 Engineering Applications of the Finite Element Method 10 1.5 General Description of the Finite Element Method 10 1.6 Comparison of Finite Element Method with Other Methods of Analysis
2.7 The solution of the finite element equation 35 2.8 Time for solution 37 2.9 The finite element software systems 37 2.9.1 Selection of the finite element softwaresystem 38 2.9.2 Training 38 2.9.3 LUSAS finite element system 39 CHAPTER 3: THEORETICAL PREDICTION OF THE DESIGN ANALYSIS OF THE HYDRAULIC PRESS MACHINE 3.1 Introduction 52
Finite Element Method Partial Differential Equations arise in the mathematical modelling of many engineering problems Analytical solution or exact solution is very complicated Alternative: Numerical Solution – Finite element method, finite difference method, finite volume method, boundary element method, discrete element method, etc. 9
3.2 Finite Element Equations 23 3.3 Stiffness Matrix of a Triangular Element 26 3.4 Assembly of the Global Equation System 27 3.5 Example of the Global Matrix Assembly 29 Problems 30 4 Finite Element Program 33 4.1 Object-oriented Approach to Finite Element Programming 33 4.2 Requirements for the Finite Element Application 34 4.2.1 Overall .
The Finite Element Method: Linear Static and Dynamic Finite Element Analysis by T. J. R. Hughes, Dover Publications, 2000 The Finite Element Method Vol. 2 Solid Mechanics by O.C. Zienkiewicz and R.L. Taylor, Oxford : Butterworth Heinemann, 2000 Institute of Structural Engineering Method of Finite Elements II 2
