Pushover Analysis Of A Reinforced Concrete Building .

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2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania.Pushover Analysis of a Reinforced Concrete Building According to VariousHinge ModelsBurak Yön1, Yusuf Calayır21Department of Civil Engineering, Fırat University, Turkey2Department of Civil Engineering, Fırat University, TurkeyABSTRACTIn this study, behavior of a multi-story reinforced concrete frame building designed as three baysand six stories is investigated. Pushover analyses of the selected building are performedaccording to various lateral load patterns and hinge models. Uniform and inverted triangularshapes are selected for the load patterns while lumped and spread hinge (fiber hinge) models areused for hinge models. Analyses are performed by Sap2000 and Seismostruct programs.Capacity curves and interstory drifts of the building are compared with each other for variouslateral load patterns and hinge models, and obtained results are evaluated.INTRODUCTIONStatic pushover analysis which shows nonlinear static behavior of buildings subjected to lateralloads has been used in structural engineering due to simplicity. This analysis method is a practiceprocedure for estimating the structural capacity of buildings in the post-elastic range. Capacitycurve of a building shows the relationship between the base shear force and the roofdisplacement. For obtaining the capacity curve, lateral forces monotonically are increased until acertain level of deformation at the top of building is reached. While structural elements reachultimate moment capacity, plastic hinges occur at the end of elements and sections betweenplastic hinges remain elastic [1-4].The other plastic hinge type is fiber hinge which used in nonlinear analysis. In this hinge model,cross-sections of structural member are divided into fibers which monitor confined concretesection, unconfined concrete cover, and reinforcement. This plastic hinge approach allowsprediction of the spread of inelasticity within the element cross-section and along the elementlength.

2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania.The first spread plasticity models date from the work of Bazant [5]. The concept of fiberelement which considered a discretization of the element section to include the differentconstitutive materials was introduced in 1984 [6]. Later, the model was improved and importantchanges have been incorporated [7,8].Many researchers performed structural analyses by using fiber hinge model. Mwafy and Elnashai[9], in their study named as static pushover versus dynamic collapse analysis in reinforcedconcrete buildings, used spread hinge approach for the nonlinear analysis. Dides and Llera [10]compared plasticity models which include fiber hinge model in dynamic analysis of buildings.Mwafy [11] assessed seismic design response factors of concrete wall buildings. For this study,five reference structures, varying in height from 20 to 60 stories, were selected. Analyses ofstructures were performed according to fiber hinge modeling. Kunnath and Kalkan [12]evaluated the seismic deformation demands of multistory steel and concrete moment framesusing non-linear procedures based on spread hinge assumption. Duan and Hueste [13]investigated the seismic performance of a multi-story reinforced concrete frame building whichdesigned according to the provisions of the Chinese seismic code. They used fiber hinge modelfor analyses. Kwon and Kim [14] studied a RC building which damaged during the 2007 PiscoChincha earthquake. They performed nonlinear analysis of this building by considering spreadhinge model. Hankok and Bommer [15] investigated inelastic structural response using spectralmatched records. They used fiber hinge approach in the numerical study. Kadid et al. [16]assessed behavior of reinforced concrete buildings under simultaneous horizontal and verticalground motions considering fiber hinge model. Thomos and Trezos [17] generated amethodology to obtain pushover curves of reinforced concrete frames, taking into account therandomness of the basic variables. They used fiber hinge model in numerical studies. Sarno andManfredi performed pushover and dynamic response history analyses for both built andretrofitted structures to investigate the efficiency of buckling restrained braces. They used fiberelement model in nonlinear analysis [18].In this study, static pushover analyses of a selected reinforced concrete building subjected tovarious lateral loads patterns are performed by using lumped and fiber hinge models. To obtainthe capacity curves and interstory drifts of the selected building, SAP2000 [19] and SeismoStruct[20] programs which can simulate the inelastic response of structural systems subjected to staticand dynamic loads are used. Obtained results are compared with each other for various lateralload patterns and hinge models.Fiber Hinge ModelThe fiber hinge model accounts distributed plasticity along structural element. In this model, thestructural element is divided in three types of fibers: some fibers are used for modeling oflongitudinal steel reinforcing bars; some of fibers are used to define nonlinear behavior ofconfined concrete which consists of core concrete; and other fibers are defined for unconfinedconcrete which includes cover concrete. Also, for each fiber, the stress/strain field is determined

2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania.in the nonlinear range by using constitutive laws according to defined materials. Figure1and 2 show fiber modeling of a RC beam and typical fiber model section of a RC element,respectively.Figure 1 Fiber modeling of a reinforced concrete beam [20]RC elementUnconfinedconcrete fibersConfinedconcrete fibersSteel fibersFigure 2 Typical fiber model of a RC elementNUMERICAL APPLICATIONIn this study, behavior of a multi-story reinforced concrete frame building which designed asthree bays and six stories are investigated. The total height of building is 19.0 m. In thisbuilding, height of first story is 4.0 m and height of other stories is 3.0 m. The elevation view ofthe building and the cross section properties of a typical column and beam including reinforcingbars are shown in Fig. 3. The cross sectional properties of all columns and beams are assumed tobe same, respectively. Reinforcements of structural members are selected according to minimum

2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania.requirements of Turkish Seismic Code (TSC). In this building, the slab thickness is 14 cm. Thecompressive strength of the concrete is 20 N/mm2, and the yield strength of the reinforcementbars is 420 MPa. It is assumed that the building is located in Seismic zone 1 and Z3 local siteclass which defined in TSC.30 kN/mØ12Triangular60Uniform50Ø1630 cm50 cm6.0 m4.06.0Figure 3 Selected building and, cross section properties of a typical column and beamSelected material constitutive models for steel and concrete are shown as in Fig. 4. Thebilinear elastic–plastic material model with kinematic strain-hardening is used for the steelreinforcement, and the concrete material is defined by the uniaxial constant confined model. Thematerial model properties of concrete and steel are given in Table 1. The confinement effect istaken into account using the model proposed by Mander et al.[23].

2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania.Stress Stress EyfcEStrain ftcoStrain(Steel)(Concrete)Figure 4 Material constitutive models [20]Table 2 Material model parameters used in numerical solutionsConcreteParametersSteelUnconfined Confined Longitudinal&Concrete Concrete Transversef c (Compressive Strength)20 Mpa23 Mpa-f t (Tensile Strength)2.0 Mpa2.3 Mpa- co ( Maximum Strain)0.002-Ec (Concrete Elasticity Module)28500 Mpa- (Strain Hardening Coefficient)--0.02Es (Steel Elasticity Module)--2e5 MpaTransverse Spacing--0.10 mSap2000 and Seismostruct structural analysis programs are used for numerical solutions.Pushover analyses of the building are performed according to various lateral load patterns and

2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania.hinge models. Two load shapes are used in the analyses. The first load pattern is a uniformdistribution, representing lateral forces that are proportional with the mass. The second one is aninverted triangular distribution which represents the first mode shape. In these analyses, lumpedand spread hinge (fiber hinge) approaches are used for hinge models.Figure 5 shows capacity curves of the building. The uniform load pattern yields higher initialstiffness and base shear capacity according to the triangular load pattern, in cases both lumpedand spread hinge models. In other words, the uniform load pattern gives lower roof displacementwith respect to the triangular one for the same base shear force in cases two hinge models. It isnoted that the uniformly distributed load gives a better prediction of the ultimate strength ofstructures influenced by higher modes compared with the inverted triangular load [11].500000.10.20.30.4Displacement (m)Fiber hinge (Triangular)Total Base Shear (kN)Total Base Shear (kN)Comparison of capacity curves of the building according to various hinge models for same loadpatterns is given in Figure 6. Although, for two load patterns, the lumped hinge model yieldshigher initial stiffness according to the fiber hinge model, the base shear capacity is to be sameapproximately in case two hinge models.500000.10.20.30.4Displacement (m)Lumped hinge (Triangular)Fiber hinge (uniform)Lumped hinge (uniform)a)Fiber hinge modelb) Lumped hinge model500000.10.20.3Displacement (m)Fiber hinge (triangular)Lumped hinge (triangular)0.4Total Base Shear (kN)Total Base Shear (kN)Figure 5 Capacity curves of the building according to various load patterns and hinge models500000.10.20.3Displacement (m)Fiber hinge (uniform)Lumped hinge (uniform)0.4

2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania.Figure 6 Comparison of capacity curves of the building according to various hinge models forsame load patterns87664Story levelStory levelInterstory drifts of the building are shown in Figure 7 and 8 for various hinge models andload patterns. The uniform load pattern yields higher interstory drifts at lower stories while thisload shape gives less interstory drifts at upper stories according to the triangular load pattern, incases both lumped and spread hinge models. This indicates the lower stories usually have thepotential to act large displacement under significant lateral demands for the uniform load pattern.It is clearly seen that from the Figure 8, the fiber hinge model yields higher interstory drifts atlower stories for triangular load pattern. However, this situation is not clear for the uniform loadshape.542300246Interstory drift (%)2100Fiber hinge (triangular)1Fiber hinge (uniform)a)Fiber hinge model234Lumped hinge (triangular)Interstory drift (%)Lumped hinge (uniform)5b) Lumped hinge model8866Story levelStory levelFigure 7 Interstory drifts of the building according to various load patterns and hinge models420420024Interstory drift (%)6024Interstory drift (%)Fiber hinge (triangular)Fiber hinge (uniform)Lumped hinge (triangular)Lumped hinge (uniform)6

2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania.Figure 8 Comparison of interstory drifts of the building according to various hinge models forsame load patternsCONCLUSIONIn this study, static pushover analyses of a selected reinforced concrete building subjected tovarious lateral loads patterns (inverted triangular and uniform shapes) are performed by usinglumped and fiber hinge models.Obtained results show that the uniform load pattern yields higher initial stiffness and base shearcapacity according to the triangular load pattern, in cases both lumped and spread hinge models.Although, for two load patterns, the lumped hinge model yields higher initial stiffness accordingto the fiber hinge model, the base shear capacity is to be same approximately in case two hingemodels. From the point of view of interstory drifts, the uniform load pattern yields higherinterstory drifts at lower stories while this load shape gives less interstory drifts at upper storiesaccording to the triangular load pattern, in cases both lumped and spread hinge models. Also, thefiber hinge model yields higher interstory drifts at lower stories for triangular load pattern.However, this situation is not clear for the uniform load shape.AcknowledgementThe authors gratefully thank Seismosoft for providing a free license for the SeismoStructsoftware.REFERENCES[1] İnel, M. and Özmen, H. B. (2006) Effects of plastic hinge properties in nonlinear analysis ofreinforced concrete buildings. Engineering Structures 28 1494–1502.[2] İnel, M., Özmen, H. B. and Bilgin, (2008) H. Re-evaluation of building damage during recentearthquakes in Turkey. Engineering Structures 30, 412–427.[3] Chan, C.M. and Zou, X.K. (2004) Elastic and inelastic drift performance optimization forreinforced concrete buildings under earthquake loads. Earthquake Engineering andStructural Dynamics 33,929–950.[4] Eslami, A. and Ronagh, H. R. Effect of elaborate plastic hinge definition on the pushoveranalysis of reinforced concrete buildings. The Structural Design of Tall Special BuildingsDOI: 10.1002/tal.1035.

2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania.[5] Bazant, S., Bhat, P. (1977) Prediction of hysteresis in reinforced concrete members. Journalof Structural Engineering (ASCE)103, 151–167.[6] Kaba, S. and Mahin, S.A. (1984) Refined modeling of reinforced concrete columns forseismic analysis. EERC Report 84-03, Earthquake Engineering Research Center, Universityof California, Berkeley.[7] Spacone, E. Filippou, F.C. Taucer, F.F. (1996) Fibre beam–column model for non-linearanalysis of RC frames: Part I: Formulation. Earthquake Engineering and StructuralDynamics 25, 711–725.[8] Spacone, E. and Filippou, F.C. Taucer, F.F. (1996) Fibre beam–column model for non-linearanalysis of RC frames: Part II: Applications. Earthquake Engineering and StructuralDynamics 25,727–742.[9] Mwafy, A.M. and Elnashai, A.S. (2001) Static pushover versus dynamic collapse analysis ofRC buildings. Engineering Structures 23, 407–424.[10] Dides, M.A. and Llera, J.C. (2005) A comparative study of concentrated plasticity modelsin dynamic analysis of building structures. Earthquake Engineering and StructuralDynamics 34, 1005–1026.[11] Mwafy, A. (2011) Assessment of seismic design response factors of concrete wall buildings.Earthquake Engineering & Engineering Vibration 10, 115-127.[12] Kenneth, S.K. and Kalkan, E. (2004) Evaluation of seismic deformation demands usingnon-linear procedures in multistory steel and concrete moment frames. ISET Journal ofEarthquake Technology 41,159-181.[13] Duan H, Hueste, M.B. D. (2012) Seismic performance of a reinforced concrete framebuilding in China. Engineering Structures 41, 77–89.[14] Kwon, O.S. and Kim, E. (2010) Case study: Analytical investigation on the failure of a twostory RC building damaged during the 2007 Pisco-Chincha earthquake. EngineeringStructures 32, 1876-1887.[15] Hancock, J. and Bommer, J.J. (2007) Using spectral matched records to explore theinfluence of strong-motion duration on inelastic structural response. Soil Dynamics andEarthquake Engineering 27, 291–299.[16] Kadid, A., Yahiaoui, D. and Chebili, R. (2010) Behaviour of reinforced concrete buildingsunder simultaneous horizontal and vertical ground motions. Asian Journal of CivilEngineering (Building and Housing) 11, 463-476.[17] Thomos, G.C. and Trezos, G.C. (2006) Examination of the probabilistic response ofreinforced concrete structures under static non-linear analysis. Engineering Structures 28,120–133.

2nd International Balkans Conference on Challenges of Civil Engineering, BCCCE, 23-25 May 2013, Epoka University, Tirana, Albania.[18] Sarno, L. D. and Manfredi, G. (2010) Seismic retrofitting with buckling restrained braces:Application to an existing non-ductile RC framed building. Soil Dynamics and EarthquakeEngineering 30, 1279–1297.[19] SAP 2000 14.1.0 Computers and Structures Inc. 2009. Berkeley, CA[20] SeismoStruct Version 6 avaliable on www.seismosoft.com/en/SeismoStruct.aspx[21] (TS500) Requirements for Design and Construction of Reinforced Concrete Structures2000, Ankara[22] Turkish Seismic Code 2007, Ankara[23] Mander, J.B., Priestley, M.J.N. and Park, R. (1988) Theoretical stress-strain model forconfined concrete. Journal of Structural Engineering 1804–1826.

Static pushover analysis which shows nonlinear static behavior of buildings subjected to lateral loads has been used in structural engineering due to simplicity. This analysis method is a practice procedure for estimating the structural capacity of buildings in the post-elastic range. Capacity curve of a building shows the relationship between the base shear force and the roof displacement .

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