Modelagem Viga Hibrida frp - Aço

See discussions stats and author profiles for this publication at httpswwwresearchgatenetpublication248879121 Structural Performances of Concrete Beams with Hybrid FiberReinforced PolymerSteel Reinforcements Article in Journal of Composites for Construction May 2002 DOI 101061ASCE10900268200262133 CITATIONS 78 READS 276 2 authors Some of the authors of this publication are also working on these related projects Cumulative damage of masonry infills caused by anthropogenic earthquakes International Exchange Scheme the Royal Society View project Thin Laminated CementBased Composites for Rehabilitation and Strengthening Existing Structures View project Maria Antonietta Aiello Università del Salento 167 PUBLICATIONS 2278 CITATIONS SEE PROFILE Luciano Ombres Università della Calabria 64 PUBLICATIONS 1263 CITATIONS SEE PROFILE All content following this page was uploaded by Luciano Ombres on 25 February 2019 The user has requested enhancement of the downloaded file Structural Performances of Concrete Beams with Hybrid FiberReinforced PolymerSteel Reinforcements Maria Antonietta Aiello1 and Luciano Ombres2 Abstract The paper analyzes the structural behavior of concrete beams reinforced with hybrid fiberreinforced polymer FRPsteel reinforcements The analysis refers to concrete beams reinforced with FRP rebars placed near the outer surface of the tensile zone with low cover thickness values and steel rebars placed at the inner level of the tensile zone with high cover thickness values able to protect the steel from the corrosion Such reinforcement allows one to optimize the structural behavior of beams and guarantees a good level of ductility and rigidity Results of an experimental and theoretical investigation are presented and discussed Significant features of the structural behavior regarding deflection curvature ductility crack width and spacing are pointed out Ultimate and serviceability conditions are examined highlighting the influence of mechanical and geometrical parameters affecting the behavior of hybrid reinforcedconcrete beams DOI 101061ASCE10900268200262133 CE Database keywords Concrete Beams Reinforcement Structural behavior Introduction Due to their advantageous properties ie light weight high strength and noncorrosive nature fiberreinforced polymers FRPs are becoming very promising candidates for reinforcing concrete structures FRP rebars are used as a reinforcement of concrete members in place of traditional steel rebars or as additional reinforcement in the rehabilitation or strengthening of existing steelreinforcedconcrete structures In both cases the noncorrosive nature of FRPs sensibly improves the durability of concrete structures However FRP rebars evidence linear behavior up to failure this property makes the structures behavior brittle and concrete becomes the ductile component of reinforcedconcrete structures The design criterion of flexural beams consequently has to be based on the achievement of concrete failure overreinforced beams providing a reinforcement percentage ratio higher than that corresponding to the balanced failure Besides the low elastic modulus of the FRPs involves high deformability the lack of ductility and high crack width as a consequence the design criterion of FRP reinforcedconcrete structures shifts to serviceability limit states that check the structural behavioral aspects instead of the strength to ensure functionality and safety during the expected life of the structures An improvement of the structural performances of concrete beams can be obtained utilizing a combination of FRP and steel reinforcements or alternatively FRP rebars manufactured combining two or more different reinforcing fibers hybrid FRP rebars In both cases it is possible to design beams with an adequate level of ductility ensuring good durability Hybrid FRP rebars present a bilinear ductile stressstrain behavior at present different types of hybrid FRP rebars are available Tepfers et al 1998 even if they have shown limited practical developments On the other hand a combination of FRP and steel reinforcements seems to be a practical and effective design solution for concrete beams Tan 1997 An optimal solution is obtained by placing the FRP rebars near the outer surface of the tensile zone with small cover thickness values and steel rebars at the inner level of the tensile zone After cracking the high values of the cover thickness protect the steel from aggressive agents Such a situation is also typical of a strengthening technique adopted for steelreinforced flexural beams based on gluing FRP rebars to the concrete near the external surfaces of the tensile zone near surface mounted rods technique Nanni and De Lorenzis 2000 From a static point of view the position of steel rebars within the cross section does not furnish a good contribution in terms of strength while its contribution is effective in terms of ductility and rigidity Besides the use of steel reinforcements allows one to design the beam as underreinforced with a limited amount of FRP reinforcements The behavior of a hybrid GFRPsteel reinforced beam was recently analyzed Newhook 2000 Obtained results evidence the benefits of this solution the yielding of the steel ensures the ductility and the strength of the GFRP increases the ultimate capacity after steel yielding In the present paper the behavior of flexural concrete beams reinforced with a combination of FRP and steel rebars is described as a result of a theoretical and experimental investigation Momentcurvature laws are defined by means of the traditional crosssectional approach they are used to predict the structural performances of beams with varying geometrical and mechanical parameters affecting the behavior of hybrid reinforcedconcrete elements steel and FRP reinforcement ratios mechanical properties of concrete and FRP rebars and cover thickness values JOURNAL OF COMPOSITES FOR CONSTRUCTION MAY 2002 133 Table 1 Details of Tested Beams Group Beam number Number of steel rebars Number of FRP rebars ds mm dr mm As mm2 Ar mm2 As mm2 ρr Ar As A A1 2 2 8 75 10048 8831 10048 08789 A2 2 2 8 10 10048 15700 10048 15625 A3 2 3 12 10 22608 23550 10048 10417 B B1 2 12 22608 10048 B2 2 75 8831 10048 C C1 2 2 8 75 10048 8831 10048 08789 Flexural tests are carried out on concrete beams reinforced with aramid FRP AFRP rebars and steel rebars the obtained results are compared with theoretical predictions Significant features of the structural behavior regarding deflection curvature ductility crack width and spacing are pointed out Some design model formulations for deflection and crack width calculation are examined and used in comparison with experimental and theoretical results Experimental Program The experimental investigation has been carried out on six concrete beamsone reinforced with only AFRP rebars one reinforced with only steel rebars and four reinforced with a combination of AFRP and steel rebars Tested Specimens Three groups of beams named A B and C have been made of 3000 mm length and with a rectangular cross section of 150 mm wide and 200 mm high Group A refers to beams with hybrid reinforcement steel and AFRP placed on two levels group B refers to beams with homogeneous reinforcement only steel or only FRP rebars and group C refers to beams reinforced with AFRP and steel rebars placed at the same level This last solution even if not effective from a durability point of view because it does not avoid the corrosion of steel rebars has been considered in order to analyze the influence of the cover thickness on the structural performances of the beams Two steel rebars of 8 mm diameter have been used as reinforcement at the compression side of the beams steel stirrups of 8 mm diameter and 100 mm spacing have been used as shear reinforcement More details about the tested beams are reported in Table 1 and Fig 1 Ar and As are the area of the AFRP and steel rebars respectively at the tensile side As is the area of the reinforcement in compression and dr and ds are the diameter of the AFRP and steel rebars Test Setup and Test Procedure Fourpoint flexural tests have been carried out using the arrangement shown in Fig 2 Beams have been instrumented with a linear variable differential transducer LVDT at midspan to measure deflections At the midspan strain gauges have been bonded to the compression surface at different levels they have been glued to the concrete with an epoxy resin after local sandblasting The concrete tensile surface has been instrumented with an electrical displacement transducer to measure deformations The load was gradually applied by means of a hydraulic jack and was measured by a load cell Crack formation and propagation were examined at each load step Beam deflections strains and load values have been monitored by means of a data acquisition system Materials The average concrete strength in compression was 457 MPa as evaluated by tests on three prismatic specimens 150 mm high The average tensile strength of the concrete determined by standard splitting tests on cylindrical specimens with 150 mm diameter and 300 mm high was 403 MPa The yield strength of the steel bars used as tensile shear and compressed reinforcement has been determined by standard tensile tests the average value was 465 MPa Tensile tests have been carried out to evaluate the tensile strength and tensile elastic modulus of the AFRP rebars In particular AFRP rebars manufactured by the Sireg Company Arcore Italy have been used for the tests the rebars were 75 mm and 10 mm in diameter and grain covered Average values of the mechanical properties obtained by the tests are reported in Table 2 Fig 1 Geometrical details of beam cross sections Fig 2 Test setup 134 JOURNAL OF COMPOSITES FOR CONSTRUCTION MAY 2002 Test Results Results obtained from the tests are presented and discussed in the following text Momentcurvature diagrams experimentally defined in the midspan section of the beams are drawn in Fig 3 Some considerations should be kept in mind when analyzing the results First it is evident that the rigidity of the control beam B2 reinforced only with FRP rebars is very low in comparison to the stiffness of the other beams mainly in cracked conditions For Table 2 Mechanical Properties of Aramid FiberReinforced Polymers Rods Rebar diameter mm Tensile strength MPa Elastic modulus GPa 75 1674 490 10 1366 501 Fig 3 Experimental momentcurvature diagrams Fig 4 Experimental loaddeflection curves Fig 5 Experimental crack spacing versus applied loads Fig 6 Experimental number of cracks versus applied loads hybrid beams A beams the rigidity is close to that of the B1 control beam only steel reinforcement before cracking while it becomes higher than that of B and C beams after cracking This result confirms the effectiveness of the hybrid reinforcement in terms of rigidity The comparison between diagrams corresponding to the A1 and C1 beams evidences the influence of the cover thickness values on the structural response In fact the two beams are reinforced with the same amount of steel and FRP rebars however in the A1 beam the cover thickness values of the steel rebars are twice those of the FRP rebars while the values for the C1 beam with steel and FRP rebars are at the same level Obtained results show that in service conditions load level up to 60 of the ultimate load the rigidity of the A1 beam is higher than that of the C1 beam and is very close to that of the B1 control beam On the contrary for a high level of applied loads cracked condition the C1 beam is more rigid than the A1 beam as expected Loaddeflection curves for all of the tested beams are drawn in Fig 4 Deflections have been measured at the midspan of the beams by means of LVDTs for each step of the applied load The analysis of the obtained results confirms the effectiveness of hybrid reinforcements in terms of rigidity of the beams as already evidenced from the analysis of the momentcurvature diagrams An improvement in terms of deformability and ductility can also be observed for all hybrid beams with respect to the B2 control beam In comparison with the B2 control beam in fact the A and C beams are less deformable mainly after cracking The cracking behavior of all of the tested beams is described in Figs 57 In Figs 5 and 6 diagrams pertaining to applied loads versus crack spacing and number of cracks respectively are drawn It is possible to observe that for beams with hybrid reinforcement the crack spacing is lower while the number of cracks is higher than in the case of the beam with only FRP reinforcement Fig 7 Experimental maximum crack width versus applied loads JOURNAL OF COMPOSITES FOR CONSTRUCTION MAY 2002 135 Fig 7 shows the maximum observed crack width versus the maximum applied loads for all tested beams Analyzing the results it appears that the presence of steel reinforcements reduces the crack widths In fact steel rebars in the tensile zone of the beams allow a decrease of the strain in the FRP reinforcement and consequently a reduction of crack widths that as well known are strongly dependent on the strain of the reinforcement By increasing the amount of steel reinforcements the crack widths drastically decrease as evidenced from the curves corresponding to the A beams and the control beam B2 The influence of the cover thickness values is outlined by the comparison between curves corresponding to the A1 and C1 beams with increasing load values the crack widths of the C1 beams are higher than those of the A1 beams Therefore the presence of steel reinforcement combined with the FRP reinforcement allows for the reduction of crack width and crack spacing even if the number of cracks is increasing this result is favorable from a serviceability point of view Theoretical Investigation The theoretical investigation has been carried out on the basis of the following hypotheses Planarity of the cross section Bernoulli hypothesis Perfect bond between concrete and reinforcement and Contribution of the concrete in tension tension stiffening effect In addition a nonlinear constitutive law has been adopted for the concrete in compression while linear elastic behavior has been assumed for the concrete and FRP in tension The momentcurvature law Mχ has been evaluated by means of a crosssectional approach in the Mχ plane a meaningful number of points is determined by a numerical procedure that allows one to evaluate the curvature values χi corresponding to the assigned bending moment Mi solving equilibrium conditions Aiello and Ombres 2000 In the analysis a trilinear momentcurvature law is adopted relevant points considered correspond to The attainment of the first cracking bending moment of the cross section Mcrχcr The attainment of the yield strength of the steel reinforcement Mysχys and The attainment of the ultimate bending moment of the cross section Muχu Analytical relationships of Mcr Mys and Mu for a cross section reinforced with hybrid FRPsteel reinforcement have been determined by equilibrium and compatibility conditions considering the contribution of the steel reinforcement in compression The momentcurvature law has been adopted for the evaluation of beam deflections Razaqpur and Burkan 2000 Design Models The behavior of hybrid reinforcedconcrete beams is also analyzed utilizing design model formulations at both the ultimate limit state USL and the serviceability limit state SLS conditions In regard to the ultimate conditions the ultimate bending moment is evaluated for the serviceability conditions the first cracking bending moment deflection ductility and crack widths are determined Referring to the USL the ultimate bending moment has been evaluated assuming for the concrete in compression the wellknown American Concrete Institute ACI stress block model ACI 1996a while no tensile strength for the concrete has been considered For the analysis of the SLS design models proposed for the determination of deflection and crack widths have been considered and are reported in the following sections Deflections Evaluation For deflections evaluation ACI 440R96 ACI 1996b suggests a modified version of Bransons formulation used for traditional steelreinforced beams Taking into account the tension stiffening effect the ACI formulation is found based on the introduction of an effective inertia Je for the whole beam expressed as Je βJg Mcr Mmax2 Jcr 1 Mcr Mmax3 1 where Mcr first cracking bending moment Mmax maximum moment Ig and Icr uncracked and cracked inertias respectively and β reduction factor equal to β α EFRP Esteel 1 where α bonddependent coefficient and EFRP and Esteel elastic modulus of FRP and steel respectively The α value must be determined for different types of FRP rebars however in the absence of specific information α 05 can be assumed In the analysis the Faza and GangaRao 1992 model also has been considered The model refers to simply supported FRP reinforced beams subjected to fourpoint loading it introduces a modified moment of inertia Jm to calculate deflections Based on such a model when the cracking moment is reached the moment of inertia between the point loads is assumed equal to the moment of inertia of the cracked section Jcr at the shear span the moment of inertia is considered equal to the effective moment of inertia of the beam Je loaded at its third point Je is obtained by Eq 1 assuming β 1 Crack Width According to experimental results different authors suggest a modified version of the wellknown GergelyLutz ACI 1996a equation for the evaluation of the crack width of FRP reinforcedconcrete beams Faza and GangaRao 1993 proposed the following relationship w 00112β Esteel EFRP fFRP3 dc A 103 mm 2 while the Gao model formulation ACI 1996b is w 00112 βkfJ FRP dc A 103 mm 3 In Eqs 2 and 3 A mm2 effective tension area of rebar β ratio between distance measured from reinforcement centroid to extreme tension fibers and neutral axis fFRP stress in FRP reinforcement MPa at load stage under consideration and dc mm thickness of concrete cover measured from extreme tension fiber to center of closest bar In Eq 3 kf modification coefficient that takes into account the specific behavior of FRP rebars expressed as kf kb Esteel EFRP 4 where kb bond properties of rebars The kb value has to be de Table 3 Values of Ultimate Moments Beam number Mu experimental kNm Mu theoretical kNm Mu ACI kNm A1 2514 2191 2150 A2 2841 2747 2700 A3 3555 3568 3578 B1 2545 2235 2358 B2 2021 1996 1807 C1 2514 2191 2267 termined by experimental tests for commercially available rebars if kb is unknown the value of 15 is suggested by the ACI to have safe results for deformed bars Comparison with Experimental Results Predictions of the theoretical model and design models were compared with experimental results in terms of flexural capacity ULS curvature deflection crack width and spacing Flexural Capacity Values of the ultimate bending moment for the tested beams are reported in Table 3 and are compared with those obtained by means of the theoretical model and by the ACI code model ACI 1996a In analyzing the results some considerations apply It is evident that the theoretical model and code model furnish results very similar to and in good agreement with those of the experimental model The design and theoretical models clearly show that the contribution of the steel reinforcement in terms of the strength of the concrete beams is little the maximum increase of the ultimate bending moment is lower than 15 even if the ratio between the tensile steel reinforcement and FRP reinforcement is high Both models adopted in the analysis confirm that the failure of the beams corresponds to the concrete crushing as experimentally evidenced Besides in all cases at the ultimate the strength of the tensile steel reinforcements reaches the yield strength while the stress of the FRP reinforcement reaches a small percentage of its ultimate value Curvature Momentcurvature diagrams of the beams obtained by means of the theoretical model are shown in Fig 8 and are compared with those of the experimental model Analyzing the results it appears that the theoretical predictions are in good agreement with the experimental results for the A beams while significant differences can be evidenced for the control beam B2 This result indicates that the theoretical model used in this analysis traditionally adopted in the analysis of steelreinforcedconcrete beams predicts very well the behavior of concrete beams with hybrid reinforcements At the same time it is evident that for a reliable analysis of FRP reinforcedconcrete beams a more accurate model is needed Aiello and Ombres 2000 Deflection The comparison between the loaddeflection diagrams for the examined beams is shown in Figs 9 and 10 For each tested beam curves describing the behavior up to failure and those corresponding to the serviceability state up to 50 of the ultimate load are drawn The comparison is made between the experimental curves those obtained by the design models ACI and FazaGangaRao and those theoretically predicted by means of the momentcurvature diagrams For each tested beam also drawn is a curve obtained by using an effective moment of inertia Jecal expressed as Jecal αcal Jg Mcr Mmax3 βcal Jcr 1 Mcr Mmax3 5 where parameters αcal and βcal have been calibrated by means of experimental results and are reported in Table 4 Fig 9 Experimental and theoretical results Load versus midspan deflection Eq 5 proposed curve th theoretical curve Comparisons indicate that for low load levels the ACI predictions are good only for hybrid reinforcedconcrete beams A and C beams For high load levels higher than 50 of the ultimate load the predictions of the ACI and FazaGangaRao models are sensibly different from the experimental results Predictions obtained using the theoretical model are close to the experimental results obtained for the hybrid reinforced concrete beams For the beams reinforced with only FRP rebars the theoretical and ACI predictions are similar and underestimate the deflections mainly at the serviceability state The use of the ACI model is thus appropriate for the analysis of hybrid reinforcedconcrete beams at the serviceability state while the use of the momentcurvature diagram is more effective for the analysis of beams up to failure In addition analyzing the results reported in Table 4 it seems that the code relationships reliable enough to determine the ef Fig 10 Experimental and theoretical results Load versus midspan deflection Eq 5 proposed curve th theoretical curve Table 4 Parameters of Calibrated Curve Beam number αcal βcal R2 A1 158 043 0999 A2 154 053 0994 A3 322 016 0992 B2 120 031 0997 C1 012 124 0995 effective moment of inertia for traditional steelreinforced beams and for FRP reinforced beams should be revised when a combination of FRP and steel rebars is utilized In particular the results suggest that the hybrid reinforcement involves a relevant increase of stiffness at the serviceability stage as indicated by the obtained α values α 1 reported in Table 4 for all hybrid reinforced beams Ductility Ductility of the beams is evaluated by means of the deformability factor DF defined as the ratio of the energy absorption at ultimate area under momentcurvature diagram to the energy calculated with respect to a limiting curvature a conventional value of 0005d radmm with d being the effective depth of the cross section is assumed Vijay and GangaRao 1996 Theoretical and experimental values are reported in Table 5 As expected by increasing the amount of steel reinforcement the deformability factors of the beams decrease Good agreement between the experimental values and theoretical predictions is obtained for the beams reinforced with hybrid reinforcements less accurate is the prediction for the control beam B2 reinforced with only FRP rebars Crack Width Experimental crack width values are compared with the theoretical values and those furnished by design models expressed by Eqs 2 and 3 Results of the comparison are drawn in Figs 11 and 12 Results of the comparison clearly show that the ACI formulation Gao Eq 3 is able to predict the crack widths of the hybrid reinforcedconcrete beams even if at the serviceability state they overestimate the crack width However predictions of the ACI relationships are strongly influenced by the kb factor that is dependent on the bond between the concrete and the FRP reinforcement and have to be determined for each type of FRP rebar The FazaGangaRao relationship furnishes good predictions for low values of applied loads while it underestimates the crack widths for high load levels Table 5 Deformability Factors of Beams Beam DFexp DFth DFthDFexp A1 1039 1168 1124 A2 753 822 1092 A3 395 389 0985 B2 1621 1136 0700 C1 699 840 1202 Fig 11 Experimental and theoretical crack widths for A1 beam Conclusions The behavior of concrete beams reinforced with FRP and steel rebars is analyzed in the paper The analysis has been carried out theoretically and experimentally at both the ultimate ULS and the serviceability SLS conditions On the basis of the obtained results the following conclusions can be drawn The use of steel reinforcement in combination with FRP reinforcement is advantageous from a deformability point of view An adequate amount of steel reinforcement within the cross section in fact allows for the reduction of the deformability of FRP reinforcedconcrete beams under service conditions Regarding strength because FRP beams are designed as overreinforced beams the contribution of steel reinforcement to the flexural capacity is low the increase of the ultimate bending moment obtained in this analysis has been less than 15 The increase of stiffness is more evident for beams reinforced with FRP rebars placed near the outer surface of the tensile zone and steel rebars placed at the inner level of the tensile zone In comparison with beams reinforced with only FRP rebars the presence of steel reinforcement reduces crack width and crack spacing values The behavior of concrete beams reinforced with steel and FRP rebars is accurately predicted by models found based on the use of the momentcurvature law determined supposing a perfect bond between the reinforcement and the concrete and considering the tension stiffening of the concrete At the serviceability stage the ACI code relationship furnishes good predictions of both deflections and crack width and Fig 12 Experimental and theoretical crack widths for B2 beam 139 JOURNAL OF COMPOSITES FOR CONSTRUCTION MAY 2002 Design model relationships reliable enough to determine the effective moment of inertia for steelreinforcedconcrete beams and for FRP reinforcedconcrete beams should be revised when a combination of FRP and steel rebars is utilized In the paper an expression for the effective moment of inertia calibrated by means of experimental results is proposed References Aiello M A and Ombres L 2000 Loaddeflection analysis of FRP reinforced concrete flexural members J Compos Constr 44 164171 American Concrete Institute ACI 1996a Building code requirements for reinforced concrete and commentary ACI 31895 Detroit American Concrete Institute ACI 1996b State of the art report on fiber reinforced plastic reinforcement for concrete structures ACI 440R96 Detroit Faza S S and GangaRao H V S 1992 Pre and postcracking deflection behavior of concrete beams reinforced with fiberreinforced plastic rebars Proc 1st Int Conf on Advanced Composite Materials in Bridges and Structures Canadian Society for Civil Engineering Montréal 129137 Faza S S and GangaRao H V S 1993 Theoretical and experimental correlation of behaviour of concrete beams reinforced with fiber reinforced plastic rebars Fiber reinforced plastic reinforcement for concrete structures SP138 American Concrete Institute Detroit 599614 Nanni A and De Lorenzis L 2000 Shear strengthening of RC beams with near surface mounted FRP rods ACI Struct J 981 6068 Newhook J P 2000 Design of underreinforced concrete Tsections with GFRP reinforcement Proc 3rd Int Conf on Advanced Composite Materials in Bridges and Structures J Humar and A G Razaqpur eds Canadian Society for Civil Engineering Montréal 153160 Razaqpur A G and Burkan I 2000 Methods for calculating deflection of FRP reinforced concrete structures Proc 3rd Int Conf on Advanced Composite Materials in Bridges and Structures J Humar and A G Razaqpur eds Canadian Society for Civil Engineering Montréal 371378 Tan KH 1997 Behaviour of hybrid FRPsteel reinforced concrete beams Proc 3rd Int Symposium FRPRCS3 487494 Tepfers R Apinis A Modniks J and Tamuzs V 1998 Ductility of hybrid fiber composite reinforcement FRP for concrete Proc ECCM8 European Conf on Composite Materials 8996 Vijay P V and GangaRao H V S 1996 A unified limit state approach using deformability factors in concrete beams reinforced with GFRP bars Proc 4th Materials Conf Materials for the new millennium 657665 140 JOURNAL OF COMPOSITES FOR CONSTRUCTION MAY 2002