Impact of Plastic Hinge Properties on Capacity Curve of...
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Research Article Impact of Plastic Hinge Properties on Capacity Curve of Reinforced Concrete Bridges Nasim Shatarat, 1 Mutasem Shehadeh, 2 and Mohammad Naser 3 1 Civil Engineering Department, e University of Jordan, Amman 11942, Jordan 2 Department of Mechanical Engineering, American University of Beirut, Beirut, Lebanon 3 e Hashemite University of Jordan, Zarqa, Jordan Correspondence should be addressed to Nasim Shatarat; [email protected] Received 15 February 2017; Revised 16 May 2017; Accepted 6 June 2017; Published 16 August 2017 Academic Editor: Jun Liu Copyright © 2017 Nasim Shatarat et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Pushover analysis is becoming recently the most practical tool for nonlinear analysis of regular and irregular highway bridges. e nonlinear behaviour of structural elements in this type of analysis can be modeled through automated-hinge or user-defined hinge models. e nonlinear properties of the user-defined hinge model for existing highway bridges can be determined in accordance with the recommendations of the Seismic Retrofit Manual by the Federal Highway Administration (FHWA-SRM). Finite element soſtware such as the soſtware SAP2000 offers a simpler and easier approach to determine the nonlinear hinge properties through the automated-hinge model which are determined automatically from the member material and cross section properties. However, the uncertainties in using the automated-hinge model in place of user-defined hinge model have never been addressed, especially for existing and widened bridges. In response to this need, pushover analysis was carried out for four old highway bridges, of which two were widened using the same superstructure but with more attention to seismic detailing requirements. e results of the analyses showed noticeable differences in the capacity curves obtained utilizing the user-defined and automated-hinge models. e study recommends that bridge design manuals clearly ask bridge designers to evaluate the deformation capacities of existing bridges and widened bridges using user-defined hinge model that is determined in accordance with the provisions of the FHWA-SRM. 1. Introduction Several methods are available to capture the seismic behaviour of buildings and highway bridges. ese methods range from simple equivalent static analysis to complex nonlinear dynamic analysis. Nonlinear time-history analysis constitutes the most reliable approach to estimate seismic behaviour because it can realistically predict the deformation demand on and capacity of structures, especially for irregular ones. However, complexities in the application of this method limit its use by practicing engineers [1]. e nonlinear static procedure oſten called “Pushover analysis” appears therefore as an interesting alternative approach due to its simplicity, yet ensuring reasonably accurate results [2]. Pushover analysis is not a recent development and its origin traces back to 1970s [3]. e validity and applicability of pushover analysis to seismic assessment of buildings and highway bridges have been extensively investigated in literature [4–13]. Currently, pushover analysis is a very com- mon method of analysis among the structural engineering profession and researchers and is recommended by most guidelines and codes, such as in FEMA 273 [14], ATC-40 [15], FEMA 356 [16], Eurocode 8 [17], FEMA-440 (ATC-55) [18], and ASCE/SEI 41-06 Standard [19]. In pushover analysis, the results depend on the approach used to define the plastic hinges, whether it is lumped or distributed plasticity model [2]. Concentrated plasticity is the most commonly used approach for estimating the deforma- tion capacity in the seismic codes, manuals, and structural analysis soſtware [2, 20]. However, a proper definition of the concentrated plastic hinge model depends on many factors such as mechanical properties of longitudinal and transverse reinforcement, reinforcement details, reinforcement ratio, concrete compressive strength, cross-sectional shape, axial Hindawi Advances in Materials Science and Engineering Volume 2017, Article ID 6310321, 13 pages https://doi.org/10.1155/2017/6310321
Transcript of Impact of Plastic Hinge Properties on Capacity Curve of...
Research ArticleImpact of Plastic Hinge Properties on Capacity Curve ofReinforced Concrete Bridges
Nasim Shatarat1 Mutasem Shehadeh2 andMohammad Naser3
1Civil Engineering Department The University of Jordan Amman 11942 Jordan2Department of Mechanical Engineering American University of Beirut Beirut Lebanon3The Hashemite University of Jordan Zarqa Jordan
Correspondence should be addressed to Nasim Shatarat nshataratjuedujo
Received 15 February 2017 Revised 16 May 2017 Accepted 6 June 2017 Published 16 August 2017
Academic Editor Jun Liu
Copyright copy 2017 Nasim Shatarat et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Pushover analysis is becoming recently the most practical tool for nonlinear analysis of regular and irregular highway bridges Thenonlinear behaviour of structural elements in this type of analysis can be modeled through automated-hinge or user-defined hingemodels The nonlinear properties of the user-defined hinge model for existing highway bridges can be determined in accordancewith the recommendations of the Seismic Retrofit Manual by the Federal Highway Administration (FHWA-SRM) Finite elementsoftware such as the software SAP2000 offers a simpler and easier approach to determine the nonlinear hinge properties through theautomated-hinge model which are determined automatically from the member material and cross section properties However theuncertainties in using the automated-hinge model in place of user-defined hinge model have never been addressed especially forexisting andwidened bridges In response to this need pushover analysis was carried out for four old highway bridges of which twowere widened using the same superstructure but with more attention to seismic detailing requirements The results of the analysesshowed noticeable differences in the capacity curves obtained utilizing the user-defined and automated-hinge models The studyrecommends that bridge design manuals clearly ask bridge designers to evaluate the deformation capacities of existing bridges andwidened bridges using user-defined hinge model that is determined in accordance with the provisions of the FHWA-SRM
1 Introduction
Several methods are available to capture the seismicbehaviour of buildings and highway bridges These methodsrange from simple equivalent static analysis to complexnonlinear dynamic analysis Nonlinear time-history analysisconstitutes the most reliable approach to estimate seismicbehaviour because it can realistically predict the deformationdemand on and capacity of structures especially for irregularones However complexities in the application of thismethodlimit its use by practicing engineers [1] The nonlinear staticprocedure often called ldquoPushover analysisrdquo appears thereforeas an interesting alternative approach due to its simplicityyet ensuring reasonably accurate results [2]
Pushover analysis is not a recent development and itsorigin traces back to 1970s [3] The validity and applicabilityof pushover analysis to seismic assessment of buildings
and highway bridges have been extensively investigated inliterature [4ndash13] Currently pushover analysis is a very com-mon method of analysis among the structural engineeringprofession and researchers and is recommended by mostguidelines and codes such as in FEMA 273 [14] ATC-40 [15]FEMA 356 [16] Eurocode 8 [17] FEMA-440 (ATC-55) [18]and ASCESEI 41-06 Standard [19]
In pushover analysis the results depend on the approachused to define the plastic hinges whether it is lumped ordistributed plasticitymodel [2] Concentrated plasticity is themost commonly used approach for estimating the deforma-tion capacity in the seismic codes manuals and structuralanalysis software [2 20] However a proper definition of theconcentrated plastic hinge model depends on many factorssuch as mechanical properties of longitudinal and transversereinforcement reinforcement details reinforcement ratioconcrete compressive strength cross-sectional shape axial
HindawiAdvances in Materials Science and EngineeringVolume 2017 Article ID 6310321 13 pageshttpsdoiorg10115520176310321
2 Advances in Materials Science and Engineering
force level level of confinement plastic hinge length andpossible local failure mechanisms within the plastic hingezone [21ndash23] Practically most often the nonlinear propertiesrecommended by FEMA-356 [16] ATC-40 [15] and Caltrans[24] documents are used to describe the deformation capacityof the plastic hinge without any consideration to possiblelocal failure mechanisms due to convenience and simplicity[20]
Many commercial software programs are available toperform pushover analysis A survey on engineering firmsshowed that the software SAP2000 [25] is the most usedsoftware by bridge engineers for nonlinear static analysis ofhighway bridges [2] In SAP2000 the nonlinear behaviourof structural elements for pushover analysis can be modeledthrough automated-hinge or user-defined hinge models Thenonlinear properties of the user-defined hinge model forexisting highway bridges can be determined in accordancewith the recommendations of the FHWA-SRM [26] whichprovides the most current state-of-practice for evaluating theseismic vulnerability of old and existing highway bridgesThe document demonstrates detailed procedures for cal-culating the curvature capacity of the structural elementsbased on potential local failure mechanisms within theplastic hinge On the other hand the nonlinear propertiesof the automated-hinge model may be based on FEMA-356Caltrans specifications or can be determined automaticallyfrom the member material and cross section properties
The literature review showed that very limited researchis available on the possible differences in the capacity curvewhen using user-defined versus automated-hinge modelsInel and Ozmen [20] investigated the influence of differentplastic hinge properties on the capacity curve of four- andseven-storey reinforced concrete buildings The results oftheir study showed that the improper use of default-hingemodel could lead to displacement capacities that might beunreasonable The authors concluded that the user-definedhinge model is better than the default-hinge model as itreflects nonlinear behaviour compatible with the elementproperties It is worth noting that this study was explicitlyoriented to reinforced concrete buildings and that default-hinge properties were defined based on FEMA-356 Fur-thermore user-defined hinge properties were obtained frommoment-curvature analysis based on extreme compressionfiber reaching the ultimate concrete compressive strain asdetermined by Priestley et al [1] or the longitudinal steelreaching a tensile strain of 50 of the ultimate strain capacity
Shatarat [27] studied the effect of plastic hinge propertieson the capacity curve of highway bridges A bridge thatwas built in the 1940s was considered for the purpose ofthe study The curvature capacity of the plastic hinge zonewas controlled by buckling of longitudinal rebars Pushoveranalysis was carried out for the bridge in one direction onlyusing user-defined and automated plastic hinge models Theresults of the study showed a difference in the capacity curvewhen using the two different models However the study waslimited to one bridgewith one type of local failuremechanismof the plastic hinge zone
Due to the growing use of pushover analysis in seismicassessment of old highway bridges there is a need to assess
the suitability of utilizing automated plastic hinge proper-ties which is based on material and section properties asan alternative to user-defined plastic hinge properties thatare determined based on FHWA-SRM for obtaining bridgecapacity curves utilizing the software SAP2000 This paperaddresses that need by examining the capacity curves of fourhighway bridges that were built in the 1960s of which twowere widened in 1980s using two alternatives in defining theproperties of the plastic hinge zone The four bridges wereselected to represent old bridges and widened bridges and tocover all types of possible local failuremechanismswithin theplastic hinge zone
2 Plastic Hinge Local Failure Mechanisms
According to the FHWA-SRM [26] the plastic curvaturecapacity of a reinforced concrete element should be based onthe controlling limit state of the potential plastic hinge zoneshear strength of the member and strength of the joint Shearstrength of themembers and the joints is not addressed in thisstudy A complete discussion of these limit states is covered inthe FHWA-SRM [26] However a summary of the equationscorresponding to each limit state is given in Table 1
3 Pushover Analysis
31 User-Defined Plastic Hinge Properties For user-definedhinge properties moment-curvature relationship and theaxial-moment interaction surface of the potential plastichinge are determined by the user and input into the softwareSAP2000 A minimum of five axial load levels are requiredto define the interaction surface An elastic perfectly plasticmoment-curvature relationship is established for each axialload level based on the controlling plastic curvature limit statethat is determined in accordance with the FHWA-SRM [26]For axial load levels other than the five values used to createthe interaction surface the software SAP2000 uses linearinterpolation to determine the plastic hinge curvature Plastichinge length and location are determined in accordance withthe FHWA-SRM [26] and are input by the user MathCADsheets [28] were developed to handle the large amount ofcalculations under this part
32 Automated Plastic Hinge Properties For this model themoment-curvature relationship and the axial-moment inter-action surface of the potential plastic hinge are determinedby the software SAP2000The parameters required for gener-ating moment-curvature relationship and interaction surfacecompromise the definition of the column cross section geom-etry longitudinal and transverse reinforcement details andunconfined concrete and steel stress-strain curve parametersUnconfined stress-strain parameters are set based on theexpected concrete strength and strain levels as requiredin the AASHTO guide specifications for LRFD SeismicBridge Design [29] Longitudinal and transverse stress-strainparameters are set based on the expected strengths followingthe models suggested by Caltrans specifications Mander etal [30] confined concrete stress-strain curve of the column
Advances in Materials Science and Engineering 3
Table 1 Curvature limit states
Failure criteria Plastic curvature (Cp)
Compression failure of unconfined concrete Cp =120585cu119888minus Cy
Compression failure of confined concrete Cp =120576cu(119888 minus 11988910158401015840)
minus Cy
Buckling of longitudinal bars Cp =2119891y
119864119904(119888 minus 1198891015840)minus Cy 6119889119887 lt 119904 lt 30119889119887
Fracture of the longitudinal reinforcement Cp =120576119904max(119889 minus 119888)minus Cy
Low cycle fatigue of longitudinal reinforcement Cp =2120576ap
1198631015840Failure in the lap-splice zone Cp = (120583lapC + 7)Cy
120585cu is the ultimate concrete compression strain for unconfined concrete and is limited to 0005 119888 is the distance from the extreme compression fiber to theneutral axisCy is the yield curvature given by the following equationCy = 2120576y1198631015840 120576y is equal to the expected yield strength of the longitudinal reinforcement119891ye divided by the modulus of elasticity 1198631015840 is the length between the center lines of the transverse reinforcement 11988910158401015840 is distance measured from centerlineof the perimeter stirrup to the extreme compression fiber of the cover concrete 120576cu is the ultimate strain of the confined concrete and is determined by120576cu = 0005+14120588s119891yh120576su1198911015840cc 120576su is strain corresponding to themaximum stress of the transverse rebars119891yh is yield stress of the transverse steel120588s is volumetricratio of transverse steel 1198911015840cc is confined concrete strength 1198891015840 is the distance from the extreme compression fiber to the centroid of the nearest compressionrebars 120576119904max is limited to a value of 010 or less and 119889 is the effective depth of the cross section 120576ap is plastic strain amplitude as given by 120576ap = 008(2119873119891)minus05119873119891 is given by119873119891 = 35(119879119899)minus13 provided that 2 le 119873119891 le 10119879119899 is natural period of vibration of the bridge 119897lap is the length of the lap-splice that is provided 119897119904is the lap-splice length 119897119904 = 04(119891yeradic1198911015840ce)119889119887 119871p is plastic hinge length 119871p = [008119871 + 4400120576y119889119887] and 119871p = 119897lap if 119897lap is smaller than 119897119904 1198911015840ce is the expectedstrength of concrete surrounding the lap-splice zone 119871 is the shear length of the member 120583lapC is the curvature ductility at the initial breakdown of bond inthe lap-splice zone
core is consequently generated based on the aforementionedparameters The software divides the cross section into fiberelements to generate the moment-curvature relationshipThe plastic hinge length and its relative location are takenidentical to user-defined hinge properties
4 Description of Selected Bridges
A preliminary evaluation of plastic hinge properties wasperformed on a group of old bridges that were built in early1960s with little attention to seismic forces and reinforcementdetails This step helped in selecting four candidates thatwould have different local failure mechanisms within thepotential plastic hinge zones Two of the selected bridges werewidened with same superstructure however the substructurereceived more attention to seismic detailing requirementsThe following is a description of the selected bridges
41 Bridge 1-WDescription Bridge 1-Wwas originally builtin 1961 and consists of four simply supported spans supportedon three intermediate piers The original superstructure con-sisted of precast concrete girders with span lengths of 60 ft98 ft 98 ft and 80 ft (328ft = 1m) The original roadwaywidth was 27 ft with a 6 ft wide sidewalk The intermediatepiers are supported on three 3-ft circular columns that areconnected through a beam of 45 ft height The intermediatepiers are constructed on isolated footings while the bridgeabutments are seat type abutments supported on concretepiles In 1983 the roadway was widened by 45 ft to an overallwidth of 72 ft and the sidewalk was expanded by 6 ft to anoverall width of 12 ft At each intermediate pier the newprecast concrete girders are supported on four columnseach having a diameter of 3 ft Unlike the original columns
longitudinal reinforcement lap splices were removed fromthe plastic hinge zone and the transverse reinforcement waschanged to spiral reinforcement with a larger bar size Table 2shows columnsrsquo geometric properties concrete strength andreinforcement details
42 Bridge 2-E Description Bridge 2-E consists of threesimply supported spans totaling 213 ft in length with a 22-ftroadway width The superstructure consists of precast con-crete girders supported by 45-degrees skewed intermediatepiers that are comprised of two circular 3-ft diameter columnsconstructed on footings with timber piles The bridge abut-ments are seat type abutments founded on precast concretepiles Poor seismic detailing of the column ends showed theexistence of a lap splice of the longitudinal reinforcementwithin the potential plastic hinge zone with a length of40 in Also the transverse reinforcement consisted of 3 hooprebars that are spaced at 120 in Table 3 shows columnsrsquogeometric properties concrete strength and reinforcementdetails
43 Bridge 3-E Description Bridge 3-E consists of a 45-ft deep multicell cast-in-situ reinforced concrete box girderwith spans of 47 73 73 and 47 feetThe bridge roadwaywidthis 49 ft with two 6-ft wide sidewalks The intermediate Piers2 and 4 are comprised of four square 25 ft columns whileintermediate Pier 3 is comprised of four rectangular 20 ft by25 ft columns The bridge abutments are spill-through typeabutments with four square 25 ft columns hinged at the topand bottom in the bridge longitudinal directionThe columnsof the abutments and the intermediate Piers are founded onsquare spread footings Column longitudinal reinforcementwas spliced in the potential plastic hinge zone with poor
4 Advances in Materials Science and Engineering
Table 2 Bridge 1-W columnsrsquo geometric properties and reinforcement detailslowast
Pier 2 Pier 3 Pier 4Old Widened Old Widened Old Widened
ColumnClear length (ft) 286 258 322 292 268 242Shape Circular Circular Circular Circular Circular CircularDimensions (in) 36 36 36 36 36 36Compressive strength (ksi) 40 40 40 40 40 40
Longitudinal reinforcementSize and number 129 129 129 129 129 129Yield strength (ksi) 40 60 40 60 40 60
Transverse reinforcementType Hoop Spiral Hoop Spiral Hoop SpiralSize and number 3 4 3 4 3 4Spacing (in) 120 33 120 33 120 33
Lap spliceWithin plastic hinge Yes No Yes No Yes NoLength (in) 500 mdash 500 mdash 500 mdash
lowast(1 in = 254mm 1 ksi = 689MPa)
Table 3 Bridge 2-E columnsrsquo geometric properties and reinforce-ment details
Pier 2 Pier 3Column
Clear length (ft) 2075 1950Shape Circular CircularDimensions (in) 36 36Compressive strength (ksi) 40 40
Longitudinal reinforcementSize and number 129 129Yield strength (ksi) 40 40
Transverse reinforcementType Hoop HoopSize and number 3 3Spacing (in) 120 120
Lap spliceWithin plastic hinge Yes YesLength (in) 400 400
transverse confinement that is comprised of a single 3 hoopspaced at 12 in on centre Table 4 shows columnsrsquo geometricproperties concrete strength and reinforcement details
44 Bridge 4-W Description Bridge 4-W consists of threesimply supported spans totaling 260 ft in length The road-way width was 44 ft before widening The superstructure iscomprised of precast concrete girders with span lengths of78 ft 93 ft and 89 ft Each intermediate pier is comprisedof five 3-ft diameter circular columns supported by singlefootings The bridge abutments are seat type abutments
founded on spread footings The roadway was widenedby 23 ft to an overall width of 67 ft This bridge wideningincluded the addition of precast concrete girders and two3-ft diameter columns founded on 45-ft diameter shaftsat each intermediate bent The original and new columnlongitudinal reinforcements were spliced within the potentialplastic hinge zone However column transverse confinementwas improved through the use of 4 spiral reinforcementspaced at 30 in on centre Table 5 shows columnsrsquo geometricproperties concrete strength and reinforcement details
5 Modeling of the Selected Bridges
A three-dimensional spine-type model was created for eachbridge as shown in Figure 1 for Bridge 2-E The superstruc-ture and pier elements are represented by frame elementsthat pass through their centroid The columns are split intothree frame elements as required by Section 543 of theAASHTO Guide Specifications for LRFD Seismic BridgeDesign Effective moments of inertia were used to reflectconcrete cracking and reinforcement yielding as provided inTable 7-1 of the FHWA-SRM [26] Gross section propertieswere used for the elements representing the super structurethe cross beam and the foundation as they are assumedto behave elastically Figure 2 shows a typical bridge pierthe frame elements and their associated stiffness Spreadfootings were represented by spring elements which weredetermined utilizing the method for spread footings outlinedin the FHWA-SRM [26] L-pile software [31] was used togenerate equivalent linear-elastic springs for the piles
A modal analysis was performed to identify fundamentalnatural periods andmode shapes Pushover analysis was thencarried out for each pier individually and independently in
Advances in Materials Science and Engineering 5
Table 4 Bridge 3-E columnsrsquo geometric properties and reinforcement details
Pier 2 Pier 3 Pier 4Column
Clear length (ft) 225 220 215Shape Square Rectangular Square
Dimensions (in) 30 Width = 30Depth = 24 30
Compressive strength (ksi) 40 40 40Longitudinal reinforcement
Size and number 810 89 810Yield strength (ksi) 40 40 40
Transverse reinforcementType Hoop Hoop HoopSize and number 13 13 13Spacing (in) 120 120 120
Lap spliceWithin plastic hinge Yes Yes YesLength (in) 500 440 500
Table 5 Bridge 4-W columnsrsquo geometric properties and reinforce-ment details
Pier 2 and Pier 3Old Widened
ColumnClear length (ft) 260 260Shape Circular CircularDimensions (in) 36 36Compressive strength (ksi) 40 40
Longitudinal reinforcementSize and number 129 1310Yield strength (ksi) 40 60
Transverse reinforcementType Hoop SpiralSize and number 3 4Spacing (in) 120 30
Lap spliceWithin plastic hinge Yes YesLength (in) 40 40
both the longitudinal and the transverse direction as per therequirements of the FHWA-SRM [26]
6 Approach for Studying the Effect ofPlastic Hinge Properties
Accurate determination of the nonlinear capacity curve ofa highway bridge depends on the properties of the plastichinge zone Typically design documents and seismic man-uals proposed plastic hinge properties based on mechanicalproperties of longitudinal and transverse reinforcement rein-forcement details reinforcement ratio concrete compressive
Abutment 4
Abutment 1
Pier 3
Pier 2
Cross beam-frame element
Deck-frameelement
Column-frameelement
Figure 1 Three-dimensional model of Bridge 2-E
strength cross-sectional shape axial force level and level ofconfinement The FHWA-SRM [26] is the only documentto include the effect of possible local failure mechanismsin the hinge zone on the properties of the hinge modelThe following summarizes the approach used in this studyto determine the capacity curve based on user-defined andautomated plastic hinge properties
(1) A three-dimensional model was created to determinethe natural periods of the selected bridges
(2) For user-defined plastic hinge properties the curva-ture capacity of each limit state for each pier columnat three axial load levels balanced point 119875119887 dead andseismic loads119875119904 and pure flexure119875119891 in the transverseand longitudinal directions is determined using thein-house developed MathCAD sheets
(3) The ordinates of the moment-curvature relationshipsat the associated axial load levels axial-momentinteraction surface and plastic hinge length were
6 Advances in Materials Science and Engineering
Table 6 Plastic curvature capacity of Pier 2 old columns Bridge 1-Wlowast
Axial loadlevel
Axial forcelowastlowast(kips)
DirectionCompression
failureUnconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020726 00011435119875119904 minus5840 T 00004549 00003543 00040599 00020726 00014724119875119904 minus3020 L 00006400 00006224 00037028 00020726 00017314119875119891 00 T amp L 00011457 00024662 00033434 00020726 00024387lowast1 kip = 445 kN 1 ksdotft = 000135 kNsdotm lowastlowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
Uncracked propertiesCracked propertiesPlastic hinge
Springs
Actualcolumn
Spreadfooting
Crossbeam
Lp2
Lp2
Figure 2 Bridge pier elements and associated stiffness
input into the software SAP2000 under user-definedplastic hinge properties
(4) The capacity curve using user-defined hinge proper-ties was obtained by pushing each pier individuallyand independently in both the longitudinal and thetransverse direction as per the requirements of theFHWA-SRM
(5) For automated plastic hinge properties the moment-curvature relationship and the axial-moment interac-tion surface of the potential plastic hinge are deter-mined by the software SAP2000 based on the columncross section geometry longitudinal and transversereinforcement details and unconfined concrete andsteel stress-strain curve parameters
(6) The capacity curve using automated plastic hingeproperties was obtained by pushing each pier individ-ually and independently in both the longitudinal andthe transverse direction
(7) Capacity curves using user-defined and automatedplastic hinge properties were then compared anddiscussed
7 Analysis Results and Discussions
For user-defined plastic hinge properties the value of thecontrolling limit state is shown in bold type font Plasticcurvature and plastic rotation for pure compression 119875119900 andpure Tension 119875119905 are not included because they are equal tozero The ordinates of the moment-curvature relationshipsat the associated axial load levels axial-moment interactionsurface and plastic hinge length to be input into the softwareSAP2000 are shown in Tables 6 7 8 and 9
71 Bridge 1-W Pier 2 Pier 3 andPier 4 columns showedsimilar behaviour in regard to curvature capacity limit statesTherefore for brevity results for Pier 2 are reported It isclear from Table 6 that buckling of longitudinal rebars is thecontrolling limit state of the columns of the old piers at 119875119887and Ps axial load levels in both directions This behaviouris attributed to the poor confinement details 3 hoops at120 in spacing As the axial load decreases and reaches zeroPf compression failure of the unconfined concrete becomesthe controlling limit state The unconfined concrete in hererefers to the cover concrete and the core concreteThe changein the type of the controlling limit state supports the effect ofthe axial load level on the deformation capacity of the plastic
Advances in Materials Science and Engineering 7
Table 7 User-defined plastic hinge properties of Pier 2 old columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
2118 996 00021100001173 000248
119875119904 minus5840 12901 00003543 000750119875119891 00 8702 00011457 002427
L119875119887 minus15430 15544
3491 996 00034800001173 000409
119875119904 minus3020 11118 00006224 002173119875119891 00 8702 00011457 004000
Table 8 Plastic curvature capacity of Pier 2 widened columns Bridge 1-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus17057 T amp L 00011781 NAlowastlowast 00055760 00020899 NA119875119904 minus5840 T 00025015 NA 00040056 00020899 NA119875119904 minus3020 L 00035630 NA 00037024 00020899 NA119875119891 00 T amp L 00068851 NA 00033970 00020899 NAlowast119875119900 = minus45853 kips and 119875119905 = 11740 kips lowastlowastNA = Not applicable
Table 9 User-defined plastic hinge properties of Pier 2 widened columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
Plasticrotation
radAxial(kips)
Moment(kipsdotft)
T119875119887 minus17057 195851
2357 1506 00035500011781 002776
119875119904 minus5840 166135 00020899 004925119875119891 00 127137 00020899 004925
L119875119887 minus17057 195851
3595 1506 00054100011781 004235
119875119904 minus3020 149315 00020899 007513119875119891 00 127137 00020899 007513
hinge Also the values of the controlling curvature capacitiesshown in Table 6 identify the effect of the axial force onthe deformation capacity of the plastic hinge For examplethe curvature capacity was equal to 00001173 radin at axialforce of 15430 kips and 00011457 radin at zero axial forcelevel Table 7 shows the moment-curvature ordinates and themoment-axial force interaction surface
The columns of the new piers had confined concretedetails where transverse reinforcement consisted of 4 spiralsat 33 in and column longitudinal reinforcement was notspliced within the plastic hinge zone Therefore bucklingof longitudinal rebars and failure in the lap splice zoneare not applicable as shown in Table 8 Accordingly lowcycle fatigue of longitudinal rebars was the controlling limitstate at Ps and Pf axial load levels while compressionfailure of the confined concrete controlled the curvaturecapacity at Pb axial load level Failure limit state pertaining
to unconfined concrete is not considered for the widenedcolumns because the core concrete has the capability towithstand higher plastic curvature demands after spallingoff the cover concrete Comparison of curvature capacitiesbetween the old and the new columns shows the effect of theconfinement on the deformation capacity of the plastic hingeFor example the plastic curvature capacity of the old columnwas 00011457 radin while the curvature capacity of the newcolumn was 00020899 radin at the zero axial load level
Tables 7 and 9 show that the plastic hinge length inthe transverse direction is less than the plastic hinge lengthin the longitudinal direction which is basically attributedto the difference in the shear span in both directionsSubsequently higher deformation capacities are expectedin the longitudinal direction It should be noted that theplastic hinge length was determined in accordance withthe equations in the FHWA-SRM which depends on the
8 Advances in Materials Science and Engineering
Table 10 Plastic curvature capacity of Pier 2 columns Bridge 2-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020010 00011435119875119904 minus4050 T 00005576 00004913 00038295 00020010 00016161119875119904 minus3020 L 00006404 00006231 00037024 00020010 00017319119875119891 00 T amp L 00011457 00024662 00033434 00020010 00024387lowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
shear span of the member and the yield strain and thediameter of the longitudinal bars However other researchers[21 23] identified that the plastic hinge length dependson the axial load level aspect ratio of the member typeof reinforcement longitudinal and transverse reinforcementratios and concrete strength
Figures 3 and 4 show the capacity curves of Bridge 1-W in the longitudinal and transverse directions respectivelyThe figures also show the capacity curves based on user-defined and automated plastic hinge properties It is clearfrom Figure 3 that the base shear capacity of Pier 2 Pier 3andPier 4 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 177 152 and 154 respectivelyOn the other hand the displacement capacity of Pier 2Pier 3 and Pier 4 in the longitudinal direction usingthe automated-hinge model is higher than the displacementcapacity using user-defined hinge model by 97 189 and97 respectively Similarly Figure 4 shows that base shearcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is less than baseshear capacity using user-defined hinge model by 159157 and 160 respectively However the displacementcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by109 202 and 150 respectively
The differences in the base shear and displacementcapacities of the bridge piers using the two hinge modelsare retained to the differences in the associated moment-curvature relationship At an axial load level of minus5840 kipsPs the ultimate curvature capacity is equal to 633 times10minus4 radin and the associated idealized moment capacityis equal to 11554 ksdotft using the automated-hinge model inSAP2000 The corresponding values using the user-definedmodel are equal to 354 times 10minus4 radin and 12901 ksdotft respec-tively
72 Bridge 2-E Analysis results showed that the behavioursof Pier 2 and Pier 3 are similar thus only the deformationcapacities for Pier 2 are discussed Table 10 shows thatbuckling of longitudinal rebars is the controlling limit stateof Pier 2 columns at Pb and Ps axial load levels in thelongitudinal and transverse directions This behaviour isattributed to the poor confinement details 3 hoops at 120 in
0
50
100
150
200
250
300
350
400
Base
shea
r (Ki
ps)
10
20
90
00
50
60
70
80
30
40
150
120
130
140
160
100
110
Longitudinal displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 3 Longitudinal pushover capacity curve of Bridge 1-W
0100200300400500600700800900
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Transverse displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 4 Transverse pushover capacity curve of Bridge 1-W
spacing As the axial load level decreases the value of theplastic curvature capacity increases until the axial load levelreaches zero Pf whereat compression of the unconfinedconcrete is the controlling limit state Table 11 shows themoment-curvature ordinates and the plastic hinge lengths ofPier 2 columns Similar to the findings for Bridge 1 the
Advances in Materials Science and Engineering 9
Table 11 User-defined plastic hinge properties of Pier 2 columns Bridge 2-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
1741 996 00017300001173 000204
119875119904 minus4050 11822 00004913 000856119875119891 00 8702 00011457 001995
L119875119887 minus15430 15544
2737 996 00027300001173 000321
119875119904 minus3020 11118 00006231 001706119875119891 00 8702 00011457 003136
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
25
50
75
100
125
150
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Longitudinal displacement (in)
Figure 5 Longitudinal pushover capacity curve of Bridge 2-E
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
50
100
150
200
250
300
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 4000Transverse displacement (in)
Figure 6 Transverse pushover capacity curve of Bridge 2-E andBridge 3-E
change in the type of the controlling limit state supports theeffect of the axial load level on the deformation capacity ofthe plastic hinge For example the plastic curvature capacitywas equal to 00001173 radin at axial force of 15430 kips and00011457 radin at zero axial force level
Figures 5 and 6 show the capacity curves of Bridge 2-E in the longitudinal and transverse directions respectively
Figure 5 shows that the base shear capacity of Pier 2 andPier 3 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 164 and 154 respectively Thisdifference is basically due to the fact that the idealizedflexural capacity in the FHWA-SRM is an overstrengthmoment which includes an overstrength factor in addition tothe factor associated with the expected material propertiesThe displacement capacity of Pier 2 and Pier 3 in thelongitudinal direction using the automated-hinge model ishigher than the displacement capacity using user-definedhinge model by 259 and 113 respectively SimilarlyFigure 6 shows that base shear capacity of Pier 2 and Pier3 in the transverse direction using the automated-hingemodel is less than base shear capacity using user-definedhinge model by 160 and 146 respectively However thedisplacement capacity of Pier 2 and Pier 3 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by392 and 220 respectively A close look at the capacitycurves shows higher differences in the displacement capacityin the transverse direction than in the longitudinal directionbetween the two different hingemodelsThis difference is dueto the fact that the expected seismic and gravity axial loadlevel in the transverse direction is higher than the axial loadlevel in the longitudinal direction which in turn shifts thecontrolling capacity limit state to buckling of the longitudinalbars The higher this shift is the higher the differencebetween the curvature values obtained from buckling oflongitudinal rebars limit state and the failure compression ofthe unconfined concrete limit state is The latter is one of thetwo controlling limit states for the automated-hinge model
73 Bridge 3-E The pier columns of this bridge are rect-angular columns with poor confinement details 3 hoops at120 in spacing Table 12 supports the notion that buckling oflongitudinal rebars is the controlling limit state at Pb axialload level as expected from the behaviour of the previousbridges Compression failure of the unconfined concretelimited the curvature capacity of the columns at Ps axial loadlevel while low cycle fatigue of longitudinal rebars was thecontrolling limit state at 119875119891 axial load level Table 13 showsthe user-defined hinge properties of Pier 2 columns whereinthe plastic hinge length has the same value in the longitudinal
10 Advances in Materials Science and Engineering
Table 12 Plastic curvature capacity of Pier 2 columns Bridge 3-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus13001 T amp L 00003102 00002003 00063260 00021910 00015229119875119904 minus4320 T 00008436 00011569 00044562 00021910 00023165119875119904 minus3030 L 00010593 00021517 00042670 00021910 00026375119875119891 00 T amp L 00023579 Tension 00038788 00021910 00045696lowast119875119900 = minus32629 kips and 119875119905 = 6624 kips
Table 13 User-defined plastic hinge properties of Pier 2 columns Bridge 3-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T amp L119875119887 minus13001 13092
1918 1250 0002400002003 000384
119875119904 minus4320 10530 00008436 001618119875119891 00 7347 00021910 004202
L 119875119904 minus3030 9713 1918 1250 00024 00010593 002032
and transverse directions This is because the shear span isidentical in both directions A comparison between the ulti-mate curvature capacities of the columns of this bridge andthe columns of Bridge 2 shows the effect of the column crosssection dimensions on the value of the curvature capacityFor the compression failure of the unconfined concrete limitstate at zero axial load level the plastic curvature capacitywas equal to 00001173 radin for Bridge 2 while the plasticcurvature capacity was 00023579 radin for Bridge 3 Thisfinding is related to the smaller depth of the column sectionin Bridge 3 which is equal to 30 in compared to 36 in forthe columns of Bridge 2 This difference in the section sizewill support the capability of the smaller column section toundergo higher curvature levels for the same level of concretestrain
Figures 7 and 8 show the capacity curves of the bridgein the transverse and longitudinal directions respectivelyThe capacity curve in the longitudinal direction was obtainedfor the whole bridge because the soil behind the bridgeabutments was part of the seismic load resisting systemAccording to Figure 7 the displacement capacity of Pier 2Pier 3 and Pier 4 determined using the automated-hingemodel is higher than the displacement capacity using theuser-defined model by 03 05 and 16 respectivelyHowever the corresponding base shear capacity was lowerby 192 234 and 206 respectively A similar trendwas experienced in the longitudinal direction for the wholebridge with 268 and 44 difference in the displacementand base shear capacities respectively The differences in thecapacity curves between the two hinge models are attributedto differences in the moment-curvature values At an axialload level of minus4320 kips the ultimate curvature capacityis equal to 109 times 10minus3 radin and the associated idealized
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
10 20 30 40 50 60 70 8000Transverse displacement (in)
050
100150200250300350400450500
Base
shea
r (Ki
ps)
Figure 7 Transverse pushover capacity curve of Bridge 3-E
moment capacity is equal to 9013 ksdotft using the automated-hinge model in SAP2000 The corresponding values usingthe user-defined model are equal to 084 times 10minus3 radin and10530 ksdotft respectively
74 Bridge 4-W For brevity the results of Pier 2 widenedcolumns will be discussed The columns in the widened partof Bridge 4-Wwere provided by 4 transverse reinforcementat 30 in on centre However the longitudinal rebars werespliced within the plastic hinge zone with a length of 400 inTable 14 demonstrates that failure of the confined concrete isthe controlling limit state atPb axial load level whereas failurein the lap splice zone is the controlling limit state at all otheraxial load levels
Advances in Materials Science and Engineering 11
Table 14 Plastic curvature capacity of new columns Pier 2 amp 3 of Bridge 4-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus18248 T amp L 00011169 NClowastlowast 00056628 00019116 00011484119875119904 minus2680 T amp L 00030921 NC 00037002 00019116 00012960119875119891 00 T amp L 00046158 NC 00034514 00019116 00013836lowast119875119900 = minus52647 kips and 119875119905 = 16152 kips lowastlowastNC = Not controlling
Table 15 User-defined plastic hinge properties of new columns Pier 2 Bridge 4-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
Yield rotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus18248 24185 2505
1464 00036700011169 002798
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
L119875119887 minus18248 24185 3753
1464 00054900011169 004191
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
Bridge - AutoBridge - User
0
1000
2000
3000
4000
5000
Base
shea
r (ki
ps)
10 20 30 40 50 60 7000Longitudinal displacement (in)
Figure 8 Longitudinal pushover capacity curve of Bridge 3-E
A comparison between the ultimate curvature capacitiesof the columns of this bridge and the columns of Bridge2 shows the effect of the confinement on the value of thecurvature capacity For the compression failure of the uncon-fined concrete limit state at zero axial load level the plasticcurvature capacity was equal to 00001173 radin for Bridge 2while the plastic curvature capacity was 00046158 radin forBridge 4This finding is related to the huge difference in thedetails of the transverse reinforcement of the column sectionin Bridge 2 which has 3 hoops at 12 in and the transversereinforcement of the column section in Bridge 4 which has4 spirals at 30 in This difference in the confinement detailswill allow the section to undergo higher plastic deformations
Table 15 includes the nonlinear properties of the user-defined hinge model It is for the first time that two different
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
050
100150200250300350400450
Base
shea
r (Ki
ps)
10 20 30 40 50 60 70 80 90 100 110 12000Longitudinal displacement (in)
Figure 9 Longitudinal pushover capacity curve of Bridge 4-W
plastic hinge lengths are reported for the column in the samedirection as shown in Table 15 This result is pertained tochange in the controlling deformation limit state from failureof the confined concrete at Pb axial load level to low cyclefatigue of the longitudinal bars at Ps and Pf axial load levelsBased on the FHWA-SRM when at the deformation capacityis controlled by low cycle fatigue of longitudinal bars theeffective plastic hinge length is reduced in length and theeffective plastic hinge is concentrated at the beginning of thelapThis finding brings attention to the limited capabilities ofthe lumped plasticity model in dealing with conditions wherethe plastic hinge length changes with the axial load level
Figures 9 and 10 show the capacity curves of the bridgein the longitudinal and transverse directions respectively
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
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Biomaterials
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NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Advances in
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2 Advances in Materials Science and Engineering
force level level of confinement plastic hinge length andpossible local failure mechanisms within the plastic hingezone [21ndash23] Practically most often the nonlinear propertiesrecommended by FEMA-356 [16] ATC-40 [15] and Caltrans[24] documents are used to describe the deformation capacityof the plastic hinge without any consideration to possiblelocal failure mechanisms due to convenience and simplicity[20]
Many commercial software programs are available toperform pushover analysis A survey on engineering firmsshowed that the software SAP2000 [25] is the most usedsoftware by bridge engineers for nonlinear static analysis ofhighway bridges [2] In SAP2000 the nonlinear behaviourof structural elements for pushover analysis can be modeledthrough automated-hinge or user-defined hinge models Thenonlinear properties of the user-defined hinge model forexisting highway bridges can be determined in accordancewith the recommendations of the FHWA-SRM [26] whichprovides the most current state-of-practice for evaluating theseismic vulnerability of old and existing highway bridgesThe document demonstrates detailed procedures for cal-culating the curvature capacity of the structural elementsbased on potential local failure mechanisms within theplastic hinge On the other hand the nonlinear propertiesof the automated-hinge model may be based on FEMA-356Caltrans specifications or can be determined automaticallyfrom the member material and cross section properties
The literature review showed that very limited researchis available on the possible differences in the capacity curvewhen using user-defined versus automated-hinge modelsInel and Ozmen [20] investigated the influence of differentplastic hinge properties on the capacity curve of four- andseven-storey reinforced concrete buildings The results oftheir study showed that the improper use of default-hingemodel could lead to displacement capacities that might beunreasonable The authors concluded that the user-definedhinge model is better than the default-hinge model as itreflects nonlinear behaviour compatible with the elementproperties It is worth noting that this study was explicitlyoriented to reinforced concrete buildings and that default-hinge properties were defined based on FEMA-356 Fur-thermore user-defined hinge properties were obtained frommoment-curvature analysis based on extreme compressionfiber reaching the ultimate concrete compressive strain asdetermined by Priestley et al [1] or the longitudinal steelreaching a tensile strain of 50 of the ultimate strain capacity
Shatarat [27] studied the effect of plastic hinge propertieson the capacity curve of highway bridges A bridge thatwas built in the 1940s was considered for the purpose ofthe study The curvature capacity of the plastic hinge zonewas controlled by buckling of longitudinal rebars Pushoveranalysis was carried out for the bridge in one direction onlyusing user-defined and automated plastic hinge models Theresults of the study showed a difference in the capacity curvewhen using the two different models However the study waslimited to one bridgewith one type of local failuremechanismof the plastic hinge zone
Due to the growing use of pushover analysis in seismicassessment of old highway bridges there is a need to assess
the suitability of utilizing automated plastic hinge proper-ties which is based on material and section properties asan alternative to user-defined plastic hinge properties thatare determined based on FHWA-SRM for obtaining bridgecapacity curves utilizing the software SAP2000 This paperaddresses that need by examining the capacity curves of fourhighway bridges that were built in the 1960s of which twowere widened in 1980s using two alternatives in defining theproperties of the plastic hinge zone The four bridges wereselected to represent old bridges and widened bridges and tocover all types of possible local failuremechanismswithin theplastic hinge zone
2 Plastic Hinge Local Failure Mechanisms
According to the FHWA-SRM [26] the plastic curvaturecapacity of a reinforced concrete element should be based onthe controlling limit state of the potential plastic hinge zoneshear strength of the member and strength of the joint Shearstrength of themembers and the joints is not addressed in thisstudy A complete discussion of these limit states is covered inthe FHWA-SRM [26] However a summary of the equationscorresponding to each limit state is given in Table 1
3 Pushover Analysis
31 User-Defined Plastic Hinge Properties For user-definedhinge properties moment-curvature relationship and theaxial-moment interaction surface of the potential plastichinge are determined by the user and input into the softwareSAP2000 A minimum of five axial load levels are requiredto define the interaction surface An elastic perfectly plasticmoment-curvature relationship is established for each axialload level based on the controlling plastic curvature limit statethat is determined in accordance with the FHWA-SRM [26]For axial load levels other than the five values used to createthe interaction surface the software SAP2000 uses linearinterpolation to determine the plastic hinge curvature Plastichinge length and location are determined in accordance withthe FHWA-SRM [26] and are input by the user MathCADsheets [28] were developed to handle the large amount ofcalculations under this part
32 Automated Plastic Hinge Properties For this model themoment-curvature relationship and the axial-moment inter-action surface of the potential plastic hinge are determinedby the software SAP2000The parameters required for gener-ating moment-curvature relationship and interaction surfacecompromise the definition of the column cross section geom-etry longitudinal and transverse reinforcement details andunconfined concrete and steel stress-strain curve parametersUnconfined stress-strain parameters are set based on theexpected concrete strength and strain levels as requiredin the AASHTO guide specifications for LRFD SeismicBridge Design [29] Longitudinal and transverse stress-strainparameters are set based on the expected strengths followingthe models suggested by Caltrans specifications Mander etal [30] confined concrete stress-strain curve of the column
Advances in Materials Science and Engineering 3
Table 1 Curvature limit states
Failure criteria Plastic curvature (Cp)
Compression failure of unconfined concrete Cp =120585cu119888minus Cy
Compression failure of confined concrete Cp =120576cu(119888 minus 11988910158401015840)
minus Cy
Buckling of longitudinal bars Cp =2119891y
119864119904(119888 minus 1198891015840)minus Cy 6119889119887 lt 119904 lt 30119889119887
Fracture of the longitudinal reinforcement Cp =120576119904max(119889 minus 119888)minus Cy
Low cycle fatigue of longitudinal reinforcement Cp =2120576ap
1198631015840Failure in the lap-splice zone Cp = (120583lapC + 7)Cy
120585cu is the ultimate concrete compression strain for unconfined concrete and is limited to 0005 119888 is the distance from the extreme compression fiber to theneutral axisCy is the yield curvature given by the following equationCy = 2120576y1198631015840 120576y is equal to the expected yield strength of the longitudinal reinforcement119891ye divided by the modulus of elasticity 1198631015840 is the length between the center lines of the transverse reinforcement 11988910158401015840 is distance measured from centerlineof the perimeter stirrup to the extreme compression fiber of the cover concrete 120576cu is the ultimate strain of the confined concrete and is determined by120576cu = 0005+14120588s119891yh120576su1198911015840cc 120576su is strain corresponding to themaximum stress of the transverse rebars119891yh is yield stress of the transverse steel120588s is volumetricratio of transverse steel 1198911015840cc is confined concrete strength 1198891015840 is the distance from the extreme compression fiber to the centroid of the nearest compressionrebars 120576119904max is limited to a value of 010 or less and 119889 is the effective depth of the cross section 120576ap is plastic strain amplitude as given by 120576ap = 008(2119873119891)minus05119873119891 is given by119873119891 = 35(119879119899)minus13 provided that 2 le 119873119891 le 10119879119899 is natural period of vibration of the bridge 119897lap is the length of the lap-splice that is provided 119897119904is the lap-splice length 119897119904 = 04(119891yeradic1198911015840ce)119889119887 119871p is plastic hinge length 119871p = [008119871 + 4400120576y119889119887] and 119871p = 119897lap if 119897lap is smaller than 119897119904 1198911015840ce is the expectedstrength of concrete surrounding the lap-splice zone 119871 is the shear length of the member 120583lapC is the curvature ductility at the initial breakdown of bond inthe lap-splice zone
core is consequently generated based on the aforementionedparameters The software divides the cross section into fiberelements to generate the moment-curvature relationshipThe plastic hinge length and its relative location are takenidentical to user-defined hinge properties
4 Description of Selected Bridges
A preliminary evaluation of plastic hinge properties wasperformed on a group of old bridges that were built in early1960s with little attention to seismic forces and reinforcementdetails This step helped in selecting four candidates thatwould have different local failure mechanisms within thepotential plastic hinge zones Two of the selected bridges werewidened with same superstructure however the substructurereceived more attention to seismic detailing requirementsThe following is a description of the selected bridges
41 Bridge 1-WDescription Bridge 1-Wwas originally builtin 1961 and consists of four simply supported spans supportedon three intermediate piers The original superstructure con-sisted of precast concrete girders with span lengths of 60 ft98 ft 98 ft and 80 ft (328ft = 1m) The original roadwaywidth was 27 ft with a 6 ft wide sidewalk The intermediatepiers are supported on three 3-ft circular columns that areconnected through a beam of 45 ft height The intermediatepiers are constructed on isolated footings while the bridgeabutments are seat type abutments supported on concretepiles In 1983 the roadway was widened by 45 ft to an overallwidth of 72 ft and the sidewalk was expanded by 6 ft to anoverall width of 12 ft At each intermediate pier the newprecast concrete girders are supported on four columnseach having a diameter of 3 ft Unlike the original columns
longitudinal reinforcement lap splices were removed fromthe plastic hinge zone and the transverse reinforcement waschanged to spiral reinforcement with a larger bar size Table 2shows columnsrsquo geometric properties concrete strength andreinforcement details
42 Bridge 2-E Description Bridge 2-E consists of threesimply supported spans totaling 213 ft in length with a 22-ftroadway width The superstructure consists of precast con-crete girders supported by 45-degrees skewed intermediatepiers that are comprised of two circular 3-ft diameter columnsconstructed on footings with timber piles The bridge abut-ments are seat type abutments founded on precast concretepiles Poor seismic detailing of the column ends showed theexistence of a lap splice of the longitudinal reinforcementwithin the potential plastic hinge zone with a length of40 in Also the transverse reinforcement consisted of 3 hooprebars that are spaced at 120 in Table 3 shows columnsrsquogeometric properties concrete strength and reinforcementdetails
43 Bridge 3-E Description Bridge 3-E consists of a 45-ft deep multicell cast-in-situ reinforced concrete box girderwith spans of 47 73 73 and 47 feetThe bridge roadwaywidthis 49 ft with two 6-ft wide sidewalks The intermediate Piers2 and 4 are comprised of four square 25 ft columns whileintermediate Pier 3 is comprised of four rectangular 20 ft by25 ft columns The bridge abutments are spill-through typeabutments with four square 25 ft columns hinged at the topand bottom in the bridge longitudinal directionThe columnsof the abutments and the intermediate Piers are founded onsquare spread footings Column longitudinal reinforcementwas spliced in the potential plastic hinge zone with poor
4 Advances in Materials Science and Engineering
Table 2 Bridge 1-W columnsrsquo geometric properties and reinforcement detailslowast
Pier 2 Pier 3 Pier 4Old Widened Old Widened Old Widened
ColumnClear length (ft) 286 258 322 292 268 242Shape Circular Circular Circular Circular Circular CircularDimensions (in) 36 36 36 36 36 36Compressive strength (ksi) 40 40 40 40 40 40
Longitudinal reinforcementSize and number 129 129 129 129 129 129Yield strength (ksi) 40 60 40 60 40 60
Transverse reinforcementType Hoop Spiral Hoop Spiral Hoop SpiralSize and number 3 4 3 4 3 4Spacing (in) 120 33 120 33 120 33
Lap spliceWithin plastic hinge Yes No Yes No Yes NoLength (in) 500 mdash 500 mdash 500 mdash
lowast(1 in = 254mm 1 ksi = 689MPa)
Table 3 Bridge 2-E columnsrsquo geometric properties and reinforce-ment details
Pier 2 Pier 3Column
Clear length (ft) 2075 1950Shape Circular CircularDimensions (in) 36 36Compressive strength (ksi) 40 40
Longitudinal reinforcementSize and number 129 129Yield strength (ksi) 40 40
Transverse reinforcementType Hoop HoopSize and number 3 3Spacing (in) 120 120
Lap spliceWithin plastic hinge Yes YesLength (in) 400 400
transverse confinement that is comprised of a single 3 hoopspaced at 12 in on centre Table 4 shows columnsrsquo geometricproperties concrete strength and reinforcement details
44 Bridge 4-W Description Bridge 4-W consists of threesimply supported spans totaling 260 ft in length The road-way width was 44 ft before widening The superstructure iscomprised of precast concrete girders with span lengths of78 ft 93 ft and 89 ft Each intermediate pier is comprisedof five 3-ft diameter circular columns supported by singlefootings The bridge abutments are seat type abutments
founded on spread footings The roadway was widenedby 23 ft to an overall width of 67 ft This bridge wideningincluded the addition of precast concrete girders and two3-ft diameter columns founded on 45-ft diameter shaftsat each intermediate bent The original and new columnlongitudinal reinforcements were spliced within the potentialplastic hinge zone However column transverse confinementwas improved through the use of 4 spiral reinforcementspaced at 30 in on centre Table 5 shows columnsrsquo geometricproperties concrete strength and reinforcement details
5 Modeling of the Selected Bridges
A three-dimensional spine-type model was created for eachbridge as shown in Figure 1 for Bridge 2-E The superstruc-ture and pier elements are represented by frame elementsthat pass through their centroid The columns are split intothree frame elements as required by Section 543 of theAASHTO Guide Specifications for LRFD Seismic BridgeDesign Effective moments of inertia were used to reflectconcrete cracking and reinforcement yielding as provided inTable 7-1 of the FHWA-SRM [26] Gross section propertieswere used for the elements representing the super structurethe cross beam and the foundation as they are assumedto behave elastically Figure 2 shows a typical bridge pierthe frame elements and their associated stiffness Spreadfootings were represented by spring elements which weredetermined utilizing the method for spread footings outlinedin the FHWA-SRM [26] L-pile software [31] was used togenerate equivalent linear-elastic springs for the piles
A modal analysis was performed to identify fundamentalnatural periods andmode shapes Pushover analysis was thencarried out for each pier individually and independently in
Advances in Materials Science and Engineering 5
Table 4 Bridge 3-E columnsrsquo geometric properties and reinforcement details
Pier 2 Pier 3 Pier 4Column
Clear length (ft) 225 220 215Shape Square Rectangular Square
Dimensions (in) 30 Width = 30Depth = 24 30
Compressive strength (ksi) 40 40 40Longitudinal reinforcement
Size and number 810 89 810Yield strength (ksi) 40 40 40
Transverse reinforcementType Hoop Hoop HoopSize and number 13 13 13Spacing (in) 120 120 120
Lap spliceWithin plastic hinge Yes Yes YesLength (in) 500 440 500
Table 5 Bridge 4-W columnsrsquo geometric properties and reinforce-ment details
Pier 2 and Pier 3Old Widened
ColumnClear length (ft) 260 260Shape Circular CircularDimensions (in) 36 36Compressive strength (ksi) 40 40
Longitudinal reinforcementSize and number 129 1310Yield strength (ksi) 40 60
Transverse reinforcementType Hoop SpiralSize and number 3 4Spacing (in) 120 30
Lap spliceWithin plastic hinge Yes YesLength (in) 40 40
both the longitudinal and the transverse direction as per therequirements of the FHWA-SRM [26]
6 Approach for Studying the Effect ofPlastic Hinge Properties
Accurate determination of the nonlinear capacity curve ofa highway bridge depends on the properties of the plastichinge zone Typically design documents and seismic man-uals proposed plastic hinge properties based on mechanicalproperties of longitudinal and transverse reinforcement rein-forcement details reinforcement ratio concrete compressive
Abutment 4
Abutment 1
Pier 3
Pier 2
Cross beam-frame element
Deck-frameelement
Column-frameelement
Figure 1 Three-dimensional model of Bridge 2-E
strength cross-sectional shape axial force level and level ofconfinement The FHWA-SRM [26] is the only documentto include the effect of possible local failure mechanismsin the hinge zone on the properties of the hinge modelThe following summarizes the approach used in this studyto determine the capacity curve based on user-defined andautomated plastic hinge properties
(1) A three-dimensional model was created to determinethe natural periods of the selected bridges
(2) For user-defined plastic hinge properties the curva-ture capacity of each limit state for each pier columnat three axial load levels balanced point 119875119887 dead andseismic loads119875119904 and pure flexure119875119891 in the transverseand longitudinal directions is determined using thein-house developed MathCAD sheets
(3) The ordinates of the moment-curvature relationshipsat the associated axial load levels axial-momentinteraction surface and plastic hinge length were
6 Advances in Materials Science and Engineering
Table 6 Plastic curvature capacity of Pier 2 old columns Bridge 1-Wlowast
Axial loadlevel
Axial forcelowastlowast(kips)
DirectionCompression
failureUnconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020726 00011435119875119904 minus5840 T 00004549 00003543 00040599 00020726 00014724119875119904 minus3020 L 00006400 00006224 00037028 00020726 00017314119875119891 00 T amp L 00011457 00024662 00033434 00020726 00024387lowast1 kip = 445 kN 1 ksdotft = 000135 kNsdotm lowastlowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
Uncracked propertiesCracked propertiesPlastic hinge
Springs
Actualcolumn
Spreadfooting
Crossbeam
Lp2
Lp2
Figure 2 Bridge pier elements and associated stiffness
input into the software SAP2000 under user-definedplastic hinge properties
(4) The capacity curve using user-defined hinge proper-ties was obtained by pushing each pier individuallyand independently in both the longitudinal and thetransverse direction as per the requirements of theFHWA-SRM
(5) For automated plastic hinge properties the moment-curvature relationship and the axial-moment interac-tion surface of the potential plastic hinge are deter-mined by the software SAP2000 based on the columncross section geometry longitudinal and transversereinforcement details and unconfined concrete andsteel stress-strain curve parameters
(6) The capacity curve using automated plastic hingeproperties was obtained by pushing each pier individ-ually and independently in both the longitudinal andthe transverse direction
(7) Capacity curves using user-defined and automatedplastic hinge properties were then compared anddiscussed
7 Analysis Results and Discussions
For user-defined plastic hinge properties the value of thecontrolling limit state is shown in bold type font Plasticcurvature and plastic rotation for pure compression 119875119900 andpure Tension 119875119905 are not included because they are equal tozero The ordinates of the moment-curvature relationshipsat the associated axial load levels axial-moment interactionsurface and plastic hinge length to be input into the softwareSAP2000 are shown in Tables 6 7 8 and 9
71 Bridge 1-W Pier 2 Pier 3 andPier 4 columns showedsimilar behaviour in regard to curvature capacity limit statesTherefore for brevity results for Pier 2 are reported It isclear from Table 6 that buckling of longitudinal rebars is thecontrolling limit state of the columns of the old piers at 119875119887and Ps axial load levels in both directions This behaviouris attributed to the poor confinement details 3 hoops at120 in spacing As the axial load decreases and reaches zeroPf compression failure of the unconfined concrete becomesthe controlling limit state The unconfined concrete in hererefers to the cover concrete and the core concreteThe changein the type of the controlling limit state supports the effect ofthe axial load level on the deformation capacity of the plastic
Advances in Materials Science and Engineering 7
Table 7 User-defined plastic hinge properties of Pier 2 old columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
2118 996 00021100001173 000248
119875119904 minus5840 12901 00003543 000750119875119891 00 8702 00011457 002427
L119875119887 minus15430 15544
3491 996 00034800001173 000409
119875119904 minus3020 11118 00006224 002173119875119891 00 8702 00011457 004000
Table 8 Plastic curvature capacity of Pier 2 widened columns Bridge 1-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus17057 T amp L 00011781 NAlowastlowast 00055760 00020899 NA119875119904 minus5840 T 00025015 NA 00040056 00020899 NA119875119904 minus3020 L 00035630 NA 00037024 00020899 NA119875119891 00 T amp L 00068851 NA 00033970 00020899 NAlowast119875119900 = minus45853 kips and 119875119905 = 11740 kips lowastlowastNA = Not applicable
Table 9 User-defined plastic hinge properties of Pier 2 widened columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
Plasticrotation
radAxial(kips)
Moment(kipsdotft)
T119875119887 minus17057 195851
2357 1506 00035500011781 002776
119875119904 minus5840 166135 00020899 004925119875119891 00 127137 00020899 004925
L119875119887 minus17057 195851
3595 1506 00054100011781 004235
119875119904 minus3020 149315 00020899 007513119875119891 00 127137 00020899 007513
hinge Also the values of the controlling curvature capacitiesshown in Table 6 identify the effect of the axial force onthe deformation capacity of the plastic hinge For examplethe curvature capacity was equal to 00001173 radin at axialforce of 15430 kips and 00011457 radin at zero axial forcelevel Table 7 shows the moment-curvature ordinates and themoment-axial force interaction surface
The columns of the new piers had confined concretedetails where transverse reinforcement consisted of 4 spiralsat 33 in and column longitudinal reinforcement was notspliced within the plastic hinge zone Therefore bucklingof longitudinal rebars and failure in the lap splice zoneare not applicable as shown in Table 8 Accordingly lowcycle fatigue of longitudinal rebars was the controlling limitstate at Ps and Pf axial load levels while compressionfailure of the confined concrete controlled the curvaturecapacity at Pb axial load level Failure limit state pertaining
to unconfined concrete is not considered for the widenedcolumns because the core concrete has the capability towithstand higher plastic curvature demands after spallingoff the cover concrete Comparison of curvature capacitiesbetween the old and the new columns shows the effect of theconfinement on the deformation capacity of the plastic hingeFor example the plastic curvature capacity of the old columnwas 00011457 radin while the curvature capacity of the newcolumn was 00020899 radin at the zero axial load level
Tables 7 and 9 show that the plastic hinge length inthe transverse direction is less than the plastic hinge lengthin the longitudinal direction which is basically attributedto the difference in the shear span in both directionsSubsequently higher deformation capacities are expectedin the longitudinal direction It should be noted that theplastic hinge length was determined in accordance withthe equations in the FHWA-SRM which depends on the
8 Advances in Materials Science and Engineering
Table 10 Plastic curvature capacity of Pier 2 columns Bridge 2-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020010 00011435119875119904 minus4050 T 00005576 00004913 00038295 00020010 00016161119875119904 minus3020 L 00006404 00006231 00037024 00020010 00017319119875119891 00 T amp L 00011457 00024662 00033434 00020010 00024387lowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
shear span of the member and the yield strain and thediameter of the longitudinal bars However other researchers[21 23] identified that the plastic hinge length dependson the axial load level aspect ratio of the member typeof reinforcement longitudinal and transverse reinforcementratios and concrete strength
Figures 3 and 4 show the capacity curves of Bridge 1-W in the longitudinal and transverse directions respectivelyThe figures also show the capacity curves based on user-defined and automated plastic hinge properties It is clearfrom Figure 3 that the base shear capacity of Pier 2 Pier 3andPier 4 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 177 152 and 154 respectivelyOn the other hand the displacement capacity of Pier 2Pier 3 and Pier 4 in the longitudinal direction usingthe automated-hinge model is higher than the displacementcapacity using user-defined hinge model by 97 189 and97 respectively Similarly Figure 4 shows that base shearcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is less than baseshear capacity using user-defined hinge model by 159157 and 160 respectively However the displacementcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by109 202 and 150 respectively
The differences in the base shear and displacementcapacities of the bridge piers using the two hinge modelsare retained to the differences in the associated moment-curvature relationship At an axial load level of minus5840 kipsPs the ultimate curvature capacity is equal to 633 times10minus4 radin and the associated idealized moment capacityis equal to 11554 ksdotft using the automated-hinge model inSAP2000 The corresponding values using the user-definedmodel are equal to 354 times 10minus4 radin and 12901 ksdotft respec-tively
72 Bridge 2-E Analysis results showed that the behavioursof Pier 2 and Pier 3 are similar thus only the deformationcapacities for Pier 2 are discussed Table 10 shows thatbuckling of longitudinal rebars is the controlling limit stateof Pier 2 columns at Pb and Ps axial load levels in thelongitudinal and transverse directions This behaviour isattributed to the poor confinement details 3 hoops at 120 in
0
50
100
150
200
250
300
350
400
Base
shea
r (Ki
ps)
10
20
90
00
50
60
70
80
30
40
150
120
130
140
160
100
110
Longitudinal displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 3 Longitudinal pushover capacity curve of Bridge 1-W
0100200300400500600700800900
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Transverse displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 4 Transverse pushover capacity curve of Bridge 1-W
spacing As the axial load level decreases the value of theplastic curvature capacity increases until the axial load levelreaches zero Pf whereat compression of the unconfinedconcrete is the controlling limit state Table 11 shows themoment-curvature ordinates and the plastic hinge lengths ofPier 2 columns Similar to the findings for Bridge 1 the
Advances in Materials Science and Engineering 9
Table 11 User-defined plastic hinge properties of Pier 2 columns Bridge 2-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
1741 996 00017300001173 000204
119875119904 minus4050 11822 00004913 000856119875119891 00 8702 00011457 001995
L119875119887 minus15430 15544
2737 996 00027300001173 000321
119875119904 minus3020 11118 00006231 001706119875119891 00 8702 00011457 003136
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
25
50
75
100
125
150
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Longitudinal displacement (in)
Figure 5 Longitudinal pushover capacity curve of Bridge 2-E
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
50
100
150
200
250
300
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 4000Transverse displacement (in)
Figure 6 Transverse pushover capacity curve of Bridge 2-E andBridge 3-E
change in the type of the controlling limit state supports theeffect of the axial load level on the deformation capacity ofthe plastic hinge For example the plastic curvature capacitywas equal to 00001173 radin at axial force of 15430 kips and00011457 radin at zero axial force level
Figures 5 and 6 show the capacity curves of Bridge 2-E in the longitudinal and transverse directions respectively
Figure 5 shows that the base shear capacity of Pier 2 andPier 3 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 164 and 154 respectively Thisdifference is basically due to the fact that the idealizedflexural capacity in the FHWA-SRM is an overstrengthmoment which includes an overstrength factor in addition tothe factor associated with the expected material propertiesThe displacement capacity of Pier 2 and Pier 3 in thelongitudinal direction using the automated-hinge model ishigher than the displacement capacity using user-definedhinge model by 259 and 113 respectively SimilarlyFigure 6 shows that base shear capacity of Pier 2 and Pier3 in the transverse direction using the automated-hingemodel is less than base shear capacity using user-definedhinge model by 160 and 146 respectively However thedisplacement capacity of Pier 2 and Pier 3 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by392 and 220 respectively A close look at the capacitycurves shows higher differences in the displacement capacityin the transverse direction than in the longitudinal directionbetween the two different hingemodelsThis difference is dueto the fact that the expected seismic and gravity axial loadlevel in the transverse direction is higher than the axial loadlevel in the longitudinal direction which in turn shifts thecontrolling capacity limit state to buckling of the longitudinalbars The higher this shift is the higher the differencebetween the curvature values obtained from buckling oflongitudinal rebars limit state and the failure compression ofthe unconfined concrete limit state is The latter is one of thetwo controlling limit states for the automated-hinge model
73 Bridge 3-E The pier columns of this bridge are rect-angular columns with poor confinement details 3 hoops at120 in spacing Table 12 supports the notion that buckling oflongitudinal rebars is the controlling limit state at Pb axialload level as expected from the behaviour of the previousbridges Compression failure of the unconfined concretelimited the curvature capacity of the columns at Ps axial loadlevel while low cycle fatigue of longitudinal rebars was thecontrolling limit state at 119875119891 axial load level Table 13 showsthe user-defined hinge properties of Pier 2 columns whereinthe plastic hinge length has the same value in the longitudinal
10 Advances in Materials Science and Engineering
Table 12 Plastic curvature capacity of Pier 2 columns Bridge 3-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus13001 T amp L 00003102 00002003 00063260 00021910 00015229119875119904 minus4320 T 00008436 00011569 00044562 00021910 00023165119875119904 minus3030 L 00010593 00021517 00042670 00021910 00026375119875119891 00 T amp L 00023579 Tension 00038788 00021910 00045696lowast119875119900 = minus32629 kips and 119875119905 = 6624 kips
Table 13 User-defined plastic hinge properties of Pier 2 columns Bridge 3-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T amp L119875119887 minus13001 13092
1918 1250 0002400002003 000384
119875119904 minus4320 10530 00008436 001618119875119891 00 7347 00021910 004202
L 119875119904 minus3030 9713 1918 1250 00024 00010593 002032
and transverse directions This is because the shear span isidentical in both directions A comparison between the ulti-mate curvature capacities of the columns of this bridge andthe columns of Bridge 2 shows the effect of the column crosssection dimensions on the value of the curvature capacityFor the compression failure of the unconfined concrete limitstate at zero axial load level the plastic curvature capacitywas equal to 00001173 radin for Bridge 2 while the plasticcurvature capacity was 00023579 radin for Bridge 3 Thisfinding is related to the smaller depth of the column sectionin Bridge 3 which is equal to 30 in compared to 36 in forthe columns of Bridge 2 This difference in the section sizewill support the capability of the smaller column section toundergo higher curvature levels for the same level of concretestrain
Figures 7 and 8 show the capacity curves of the bridgein the transverse and longitudinal directions respectivelyThe capacity curve in the longitudinal direction was obtainedfor the whole bridge because the soil behind the bridgeabutments was part of the seismic load resisting systemAccording to Figure 7 the displacement capacity of Pier 2Pier 3 and Pier 4 determined using the automated-hingemodel is higher than the displacement capacity using theuser-defined model by 03 05 and 16 respectivelyHowever the corresponding base shear capacity was lowerby 192 234 and 206 respectively A similar trendwas experienced in the longitudinal direction for the wholebridge with 268 and 44 difference in the displacementand base shear capacities respectively The differences in thecapacity curves between the two hinge models are attributedto differences in the moment-curvature values At an axialload level of minus4320 kips the ultimate curvature capacityis equal to 109 times 10minus3 radin and the associated idealized
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
10 20 30 40 50 60 70 8000Transverse displacement (in)
050
100150200250300350400450500
Base
shea
r (Ki
ps)
Figure 7 Transverse pushover capacity curve of Bridge 3-E
moment capacity is equal to 9013 ksdotft using the automated-hinge model in SAP2000 The corresponding values usingthe user-defined model are equal to 084 times 10minus3 radin and10530 ksdotft respectively
74 Bridge 4-W For brevity the results of Pier 2 widenedcolumns will be discussed The columns in the widened partof Bridge 4-Wwere provided by 4 transverse reinforcementat 30 in on centre However the longitudinal rebars werespliced within the plastic hinge zone with a length of 400 inTable 14 demonstrates that failure of the confined concrete isthe controlling limit state atPb axial load level whereas failurein the lap splice zone is the controlling limit state at all otheraxial load levels
Advances in Materials Science and Engineering 11
Table 14 Plastic curvature capacity of new columns Pier 2 amp 3 of Bridge 4-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus18248 T amp L 00011169 NClowastlowast 00056628 00019116 00011484119875119904 minus2680 T amp L 00030921 NC 00037002 00019116 00012960119875119891 00 T amp L 00046158 NC 00034514 00019116 00013836lowast119875119900 = minus52647 kips and 119875119905 = 16152 kips lowastlowastNC = Not controlling
Table 15 User-defined plastic hinge properties of new columns Pier 2 Bridge 4-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
Yield rotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus18248 24185 2505
1464 00036700011169 002798
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
L119875119887 minus18248 24185 3753
1464 00054900011169 004191
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
Bridge - AutoBridge - User
0
1000
2000
3000
4000
5000
Base
shea
r (ki
ps)
10 20 30 40 50 60 7000Longitudinal displacement (in)
Figure 8 Longitudinal pushover capacity curve of Bridge 3-E
A comparison between the ultimate curvature capacitiesof the columns of this bridge and the columns of Bridge2 shows the effect of the confinement on the value of thecurvature capacity For the compression failure of the uncon-fined concrete limit state at zero axial load level the plasticcurvature capacity was equal to 00001173 radin for Bridge 2while the plastic curvature capacity was 00046158 radin forBridge 4This finding is related to the huge difference in thedetails of the transverse reinforcement of the column sectionin Bridge 2 which has 3 hoops at 12 in and the transversereinforcement of the column section in Bridge 4 which has4 spirals at 30 in This difference in the confinement detailswill allow the section to undergo higher plastic deformations
Table 15 includes the nonlinear properties of the user-defined hinge model It is for the first time that two different
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
050
100150200250300350400450
Base
shea
r (Ki
ps)
10 20 30 40 50 60 70 80 90 100 110 12000Longitudinal displacement (in)
Figure 9 Longitudinal pushover capacity curve of Bridge 4-W
plastic hinge lengths are reported for the column in the samedirection as shown in Table 15 This result is pertained tochange in the controlling deformation limit state from failureof the confined concrete at Pb axial load level to low cyclefatigue of the longitudinal bars at Ps and Pf axial load levelsBased on the FHWA-SRM when at the deformation capacityis controlled by low cycle fatigue of longitudinal bars theeffective plastic hinge length is reduced in length and theeffective plastic hinge is concentrated at the beginning of thelapThis finding brings attention to the limited capabilities ofthe lumped plasticity model in dealing with conditions wherethe plastic hinge length changes with the axial load level
Figures 9 and 10 show the capacity curves of the bridgein the longitudinal and transverse directions respectively
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Materials Science and Engineering 3
Table 1 Curvature limit states
Failure criteria Plastic curvature (Cp)
Compression failure of unconfined concrete Cp =120585cu119888minus Cy
Compression failure of confined concrete Cp =120576cu(119888 minus 11988910158401015840)
minus Cy
Buckling of longitudinal bars Cp =2119891y
119864119904(119888 minus 1198891015840)minus Cy 6119889119887 lt 119904 lt 30119889119887
Fracture of the longitudinal reinforcement Cp =120576119904max(119889 minus 119888)minus Cy
Low cycle fatigue of longitudinal reinforcement Cp =2120576ap
1198631015840Failure in the lap-splice zone Cp = (120583lapC + 7)Cy
120585cu is the ultimate concrete compression strain for unconfined concrete and is limited to 0005 119888 is the distance from the extreme compression fiber to theneutral axisCy is the yield curvature given by the following equationCy = 2120576y1198631015840 120576y is equal to the expected yield strength of the longitudinal reinforcement119891ye divided by the modulus of elasticity 1198631015840 is the length between the center lines of the transverse reinforcement 11988910158401015840 is distance measured from centerlineof the perimeter stirrup to the extreme compression fiber of the cover concrete 120576cu is the ultimate strain of the confined concrete and is determined by120576cu = 0005+14120588s119891yh120576su1198911015840cc 120576su is strain corresponding to themaximum stress of the transverse rebars119891yh is yield stress of the transverse steel120588s is volumetricratio of transverse steel 1198911015840cc is confined concrete strength 1198891015840 is the distance from the extreme compression fiber to the centroid of the nearest compressionrebars 120576119904max is limited to a value of 010 or less and 119889 is the effective depth of the cross section 120576ap is plastic strain amplitude as given by 120576ap = 008(2119873119891)minus05119873119891 is given by119873119891 = 35(119879119899)minus13 provided that 2 le 119873119891 le 10119879119899 is natural period of vibration of the bridge 119897lap is the length of the lap-splice that is provided 119897119904is the lap-splice length 119897119904 = 04(119891yeradic1198911015840ce)119889119887 119871p is plastic hinge length 119871p = [008119871 + 4400120576y119889119887] and 119871p = 119897lap if 119897lap is smaller than 119897119904 1198911015840ce is the expectedstrength of concrete surrounding the lap-splice zone 119871 is the shear length of the member 120583lapC is the curvature ductility at the initial breakdown of bond inthe lap-splice zone
core is consequently generated based on the aforementionedparameters The software divides the cross section into fiberelements to generate the moment-curvature relationshipThe plastic hinge length and its relative location are takenidentical to user-defined hinge properties
4 Description of Selected Bridges
A preliminary evaluation of plastic hinge properties wasperformed on a group of old bridges that were built in early1960s with little attention to seismic forces and reinforcementdetails This step helped in selecting four candidates thatwould have different local failure mechanisms within thepotential plastic hinge zones Two of the selected bridges werewidened with same superstructure however the substructurereceived more attention to seismic detailing requirementsThe following is a description of the selected bridges
41 Bridge 1-WDescription Bridge 1-Wwas originally builtin 1961 and consists of four simply supported spans supportedon three intermediate piers The original superstructure con-sisted of precast concrete girders with span lengths of 60 ft98 ft 98 ft and 80 ft (328ft = 1m) The original roadwaywidth was 27 ft with a 6 ft wide sidewalk The intermediatepiers are supported on three 3-ft circular columns that areconnected through a beam of 45 ft height The intermediatepiers are constructed on isolated footings while the bridgeabutments are seat type abutments supported on concretepiles In 1983 the roadway was widened by 45 ft to an overallwidth of 72 ft and the sidewalk was expanded by 6 ft to anoverall width of 12 ft At each intermediate pier the newprecast concrete girders are supported on four columnseach having a diameter of 3 ft Unlike the original columns
longitudinal reinforcement lap splices were removed fromthe plastic hinge zone and the transverse reinforcement waschanged to spiral reinforcement with a larger bar size Table 2shows columnsrsquo geometric properties concrete strength andreinforcement details
42 Bridge 2-E Description Bridge 2-E consists of threesimply supported spans totaling 213 ft in length with a 22-ftroadway width The superstructure consists of precast con-crete girders supported by 45-degrees skewed intermediatepiers that are comprised of two circular 3-ft diameter columnsconstructed on footings with timber piles The bridge abut-ments are seat type abutments founded on precast concretepiles Poor seismic detailing of the column ends showed theexistence of a lap splice of the longitudinal reinforcementwithin the potential plastic hinge zone with a length of40 in Also the transverse reinforcement consisted of 3 hooprebars that are spaced at 120 in Table 3 shows columnsrsquogeometric properties concrete strength and reinforcementdetails
43 Bridge 3-E Description Bridge 3-E consists of a 45-ft deep multicell cast-in-situ reinforced concrete box girderwith spans of 47 73 73 and 47 feetThe bridge roadwaywidthis 49 ft with two 6-ft wide sidewalks The intermediate Piers2 and 4 are comprised of four square 25 ft columns whileintermediate Pier 3 is comprised of four rectangular 20 ft by25 ft columns The bridge abutments are spill-through typeabutments with four square 25 ft columns hinged at the topand bottom in the bridge longitudinal directionThe columnsof the abutments and the intermediate Piers are founded onsquare spread footings Column longitudinal reinforcementwas spliced in the potential plastic hinge zone with poor
4 Advances in Materials Science and Engineering
Table 2 Bridge 1-W columnsrsquo geometric properties and reinforcement detailslowast
Pier 2 Pier 3 Pier 4Old Widened Old Widened Old Widened
ColumnClear length (ft) 286 258 322 292 268 242Shape Circular Circular Circular Circular Circular CircularDimensions (in) 36 36 36 36 36 36Compressive strength (ksi) 40 40 40 40 40 40
Longitudinal reinforcementSize and number 129 129 129 129 129 129Yield strength (ksi) 40 60 40 60 40 60
Transverse reinforcementType Hoop Spiral Hoop Spiral Hoop SpiralSize and number 3 4 3 4 3 4Spacing (in) 120 33 120 33 120 33
Lap spliceWithin plastic hinge Yes No Yes No Yes NoLength (in) 500 mdash 500 mdash 500 mdash
lowast(1 in = 254mm 1 ksi = 689MPa)
Table 3 Bridge 2-E columnsrsquo geometric properties and reinforce-ment details
Pier 2 Pier 3Column
Clear length (ft) 2075 1950Shape Circular CircularDimensions (in) 36 36Compressive strength (ksi) 40 40
Longitudinal reinforcementSize and number 129 129Yield strength (ksi) 40 40
Transverse reinforcementType Hoop HoopSize and number 3 3Spacing (in) 120 120
Lap spliceWithin plastic hinge Yes YesLength (in) 400 400
transverse confinement that is comprised of a single 3 hoopspaced at 12 in on centre Table 4 shows columnsrsquo geometricproperties concrete strength and reinforcement details
44 Bridge 4-W Description Bridge 4-W consists of threesimply supported spans totaling 260 ft in length The road-way width was 44 ft before widening The superstructure iscomprised of precast concrete girders with span lengths of78 ft 93 ft and 89 ft Each intermediate pier is comprisedof five 3-ft diameter circular columns supported by singlefootings The bridge abutments are seat type abutments
founded on spread footings The roadway was widenedby 23 ft to an overall width of 67 ft This bridge wideningincluded the addition of precast concrete girders and two3-ft diameter columns founded on 45-ft diameter shaftsat each intermediate bent The original and new columnlongitudinal reinforcements were spliced within the potentialplastic hinge zone However column transverse confinementwas improved through the use of 4 spiral reinforcementspaced at 30 in on centre Table 5 shows columnsrsquo geometricproperties concrete strength and reinforcement details
5 Modeling of the Selected Bridges
A three-dimensional spine-type model was created for eachbridge as shown in Figure 1 for Bridge 2-E The superstruc-ture and pier elements are represented by frame elementsthat pass through their centroid The columns are split intothree frame elements as required by Section 543 of theAASHTO Guide Specifications for LRFD Seismic BridgeDesign Effective moments of inertia were used to reflectconcrete cracking and reinforcement yielding as provided inTable 7-1 of the FHWA-SRM [26] Gross section propertieswere used for the elements representing the super structurethe cross beam and the foundation as they are assumedto behave elastically Figure 2 shows a typical bridge pierthe frame elements and their associated stiffness Spreadfootings were represented by spring elements which weredetermined utilizing the method for spread footings outlinedin the FHWA-SRM [26] L-pile software [31] was used togenerate equivalent linear-elastic springs for the piles
A modal analysis was performed to identify fundamentalnatural periods andmode shapes Pushover analysis was thencarried out for each pier individually and independently in
Advances in Materials Science and Engineering 5
Table 4 Bridge 3-E columnsrsquo geometric properties and reinforcement details
Pier 2 Pier 3 Pier 4Column
Clear length (ft) 225 220 215Shape Square Rectangular Square
Dimensions (in) 30 Width = 30Depth = 24 30
Compressive strength (ksi) 40 40 40Longitudinal reinforcement
Size and number 810 89 810Yield strength (ksi) 40 40 40
Transverse reinforcementType Hoop Hoop HoopSize and number 13 13 13Spacing (in) 120 120 120
Lap spliceWithin plastic hinge Yes Yes YesLength (in) 500 440 500
Table 5 Bridge 4-W columnsrsquo geometric properties and reinforce-ment details
Pier 2 and Pier 3Old Widened
ColumnClear length (ft) 260 260Shape Circular CircularDimensions (in) 36 36Compressive strength (ksi) 40 40
Longitudinal reinforcementSize and number 129 1310Yield strength (ksi) 40 60
Transverse reinforcementType Hoop SpiralSize and number 3 4Spacing (in) 120 30
Lap spliceWithin plastic hinge Yes YesLength (in) 40 40
both the longitudinal and the transverse direction as per therequirements of the FHWA-SRM [26]
6 Approach for Studying the Effect ofPlastic Hinge Properties
Accurate determination of the nonlinear capacity curve ofa highway bridge depends on the properties of the plastichinge zone Typically design documents and seismic man-uals proposed plastic hinge properties based on mechanicalproperties of longitudinal and transverse reinforcement rein-forcement details reinforcement ratio concrete compressive
Abutment 4
Abutment 1
Pier 3
Pier 2
Cross beam-frame element
Deck-frameelement
Column-frameelement
Figure 1 Three-dimensional model of Bridge 2-E
strength cross-sectional shape axial force level and level ofconfinement The FHWA-SRM [26] is the only documentto include the effect of possible local failure mechanismsin the hinge zone on the properties of the hinge modelThe following summarizes the approach used in this studyto determine the capacity curve based on user-defined andautomated plastic hinge properties
(1) A three-dimensional model was created to determinethe natural periods of the selected bridges
(2) For user-defined plastic hinge properties the curva-ture capacity of each limit state for each pier columnat three axial load levels balanced point 119875119887 dead andseismic loads119875119904 and pure flexure119875119891 in the transverseand longitudinal directions is determined using thein-house developed MathCAD sheets
(3) The ordinates of the moment-curvature relationshipsat the associated axial load levels axial-momentinteraction surface and plastic hinge length were
6 Advances in Materials Science and Engineering
Table 6 Plastic curvature capacity of Pier 2 old columns Bridge 1-Wlowast
Axial loadlevel
Axial forcelowastlowast(kips)
DirectionCompression
failureUnconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020726 00011435119875119904 minus5840 T 00004549 00003543 00040599 00020726 00014724119875119904 minus3020 L 00006400 00006224 00037028 00020726 00017314119875119891 00 T amp L 00011457 00024662 00033434 00020726 00024387lowast1 kip = 445 kN 1 ksdotft = 000135 kNsdotm lowastlowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
Uncracked propertiesCracked propertiesPlastic hinge
Springs
Actualcolumn
Spreadfooting
Crossbeam
Lp2
Lp2
Figure 2 Bridge pier elements and associated stiffness
input into the software SAP2000 under user-definedplastic hinge properties
(4) The capacity curve using user-defined hinge proper-ties was obtained by pushing each pier individuallyand independently in both the longitudinal and thetransverse direction as per the requirements of theFHWA-SRM
(5) For automated plastic hinge properties the moment-curvature relationship and the axial-moment interac-tion surface of the potential plastic hinge are deter-mined by the software SAP2000 based on the columncross section geometry longitudinal and transversereinforcement details and unconfined concrete andsteel stress-strain curve parameters
(6) The capacity curve using automated plastic hingeproperties was obtained by pushing each pier individ-ually and independently in both the longitudinal andthe transverse direction
(7) Capacity curves using user-defined and automatedplastic hinge properties were then compared anddiscussed
7 Analysis Results and Discussions
For user-defined plastic hinge properties the value of thecontrolling limit state is shown in bold type font Plasticcurvature and plastic rotation for pure compression 119875119900 andpure Tension 119875119905 are not included because they are equal tozero The ordinates of the moment-curvature relationshipsat the associated axial load levels axial-moment interactionsurface and plastic hinge length to be input into the softwareSAP2000 are shown in Tables 6 7 8 and 9
71 Bridge 1-W Pier 2 Pier 3 andPier 4 columns showedsimilar behaviour in regard to curvature capacity limit statesTherefore for brevity results for Pier 2 are reported It isclear from Table 6 that buckling of longitudinal rebars is thecontrolling limit state of the columns of the old piers at 119875119887and Ps axial load levels in both directions This behaviouris attributed to the poor confinement details 3 hoops at120 in spacing As the axial load decreases and reaches zeroPf compression failure of the unconfined concrete becomesthe controlling limit state The unconfined concrete in hererefers to the cover concrete and the core concreteThe changein the type of the controlling limit state supports the effect ofthe axial load level on the deformation capacity of the plastic
Advances in Materials Science and Engineering 7
Table 7 User-defined plastic hinge properties of Pier 2 old columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
2118 996 00021100001173 000248
119875119904 minus5840 12901 00003543 000750119875119891 00 8702 00011457 002427
L119875119887 minus15430 15544
3491 996 00034800001173 000409
119875119904 minus3020 11118 00006224 002173119875119891 00 8702 00011457 004000
Table 8 Plastic curvature capacity of Pier 2 widened columns Bridge 1-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus17057 T amp L 00011781 NAlowastlowast 00055760 00020899 NA119875119904 minus5840 T 00025015 NA 00040056 00020899 NA119875119904 minus3020 L 00035630 NA 00037024 00020899 NA119875119891 00 T amp L 00068851 NA 00033970 00020899 NAlowast119875119900 = minus45853 kips and 119875119905 = 11740 kips lowastlowastNA = Not applicable
Table 9 User-defined plastic hinge properties of Pier 2 widened columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
Plasticrotation
radAxial(kips)
Moment(kipsdotft)
T119875119887 minus17057 195851
2357 1506 00035500011781 002776
119875119904 minus5840 166135 00020899 004925119875119891 00 127137 00020899 004925
L119875119887 minus17057 195851
3595 1506 00054100011781 004235
119875119904 minus3020 149315 00020899 007513119875119891 00 127137 00020899 007513
hinge Also the values of the controlling curvature capacitiesshown in Table 6 identify the effect of the axial force onthe deformation capacity of the plastic hinge For examplethe curvature capacity was equal to 00001173 radin at axialforce of 15430 kips and 00011457 radin at zero axial forcelevel Table 7 shows the moment-curvature ordinates and themoment-axial force interaction surface
The columns of the new piers had confined concretedetails where transverse reinforcement consisted of 4 spiralsat 33 in and column longitudinal reinforcement was notspliced within the plastic hinge zone Therefore bucklingof longitudinal rebars and failure in the lap splice zoneare not applicable as shown in Table 8 Accordingly lowcycle fatigue of longitudinal rebars was the controlling limitstate at Ps and Pf axial load levels while compressionfailure of the confined concrete controlled the curvaturecapacity at Pb axial load level Failure limit state pertaining
to unconfined concrete is not considered for the widenedcolumns because the core concrete has the capability towithstand higher plastic curvature demands after spallingoff the cover concrete Comparison of curvature capacitiesbetween the old and the new columns shows the effect of theconfinement on the deformation capacity of the plastic hingeFor example the plastic curvature capacity of the old columnwas 00011457 radin while the curvature capacity of the newcolumn was 00020899 radin at the zero axial load level
Tables 7 and 9 show that the plastic hinge length inthe transverse direction is less than the plastic hinge lengthin the longitudinal direction which is basically attributedto the difference in the shear span in both directionsSubsequently higher deformation capacities are expectedin the longitudinal direction It should be noted that theplastic hinge length was determined in accordance withthe equations in the FHWA-SRM which depends on the
8 Advances in Materials Science and Engineering
Table 10 Plastic curvature capacity of Pier 2 columns Bridge 2-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020010 00011435119875119904 minus4050 T 00005576 00004913 00038295 00020010 00016161119875119904 minus3020 L 00006404 00006231 00037024 00020010 00017319119875119891 00 T amp L 00011457 00024662 00033434 00020010 00024387lowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
shear span of the member and the yield strain and thediameter of the longitudinal bars However other researchers[21 23] identified that the plastic hinge length dependson the axial load level aspect ratio of the member typeof reinforcement longitudinal and transverse reinforcementratios and concrete strength
Figures 3 and 4 show the capacity curves of Bridge 1-W in the longitudinal and transverse directions respectivelyThe figures also show the capacity curves based on user-defined and automated plastic hinge properties It is clearfrom Figure 3 that the base shear capacity of Pier 2 Pier 3andPier 4 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 177 152 and 154 respectivelyOn the other hand the displacement capacity of Pier 2Pier 3 and Pier 4 in the longitudinal direction usingthe automated-hinge model is higher than the displacementcapacity using user-defined hinge model by 97 189 and97 respectively Similarly Figure 4 shows that base shearcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is less than baseshear capacity using user-defined hinge model by 159157 and 160 respectively However the displacementcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by109 202 and 150 respectively
The differences in the base shear and displacementcapacities of the bridge piers using the two hinge modelsare retained to the differences in the associated moment-curvature relationship At an axial load level of minus5840 kipsPs the ultimate curvature capacity is equal to 633 times10minus4 radin and the associated idealized moment capacityis equal to 11554 ksdotft using the automated-hinge model inSAP2000 The corresponding values using the user-definedmodel are equal to 354 times 10minus4 radin and 12901 ksdotft respec-tively
72 Bridge 2-E Analysis results showed that the behavioursof Pier 2 and Pier 3 are similar thus only the deformationcapacities for Pier 2 are discussed Table 10 shows thatbuckling of longitudinal rebars is the controlling limit stateof Pier 2 columns at Pb and Ps axial load levels in thelongitudinal and transverse directions This behaviour isattributed to the poor confinement details 3 hoops at 120 in
0
50
100
150
200
250
300
350
400
Base
shea
r (Ki
ps)
10
20
90
00
50
60
70
80
30
40
150
120
130
140
160
100
110
Longitudinal displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 3 Longitudinal pushover capacity curve of Bridge 1-W
0100200300400500600700800900
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Transverse displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 4 Transverse pushover capacity curve of Bridge 1-W
spacing As the axial load level decreases the value of theplastic curvature capacity increases until the axial load levelreaches zero Pf whereat compression of the unconfinedconcrete is the controlling limit state Table 11 shows themoment-curvature ordinates and the plastic hinge lengths ofPier 2 columns Similar to the findings for Bridge 1 the
Advances in Materials Science and Engineering 9
Table 11 User-defined plastic hinge properties of Pier 2 columns Bridge 2-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
1741 996 00017300001173 000204
119875119904 minus4050 11822 00004913 000856119875119891 00 8702 00011457 001995
L119875119887 minus15430 15544
2737 996 00027300001173 000321
119875119904 minus3020 11118 00006231 001706119875119891 00 8702 00011457 003136
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
25
50
75
100
125
150
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Longitudinal displacement (in)
Figure 5 Longitudinal pushover capacity curve of Bridge 2-E
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
50
100
150
200
250
300
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 4000Transverse displacement (in)
Figure 6 Transverse pushover capacity curve of Bridge 2-E andBridge 3-E
change in the type of the controlling limit state supports theeffect of the axial load level on the deformation capacity ofthe plastic hinge For example the plastic curvature capacitywas equal to 00001173 radin at axial force of 15430 kips and00011457 radin at zero axial force level
Figures 5 and 6 show the capacity curves of Bridge 2-E in the longitudinal and transverse directions respectively
Figure 5 shows that the base shear capacity of Pier 2 andPier 3 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 164 and 154 respectively Thisdifference is basically due to the fact that the idealizedflexural capacity in the FHWA-SRM is an overstrengthmoment which includes an overstrength factor in addition tothe factor associated with the expected material propertiesThe displacement capacity of Pier 2 and Pier 3 in thelongitudinal direction using the automated-hinge model ishigher than the displacement capacity using user-definedhinge model by 259 and 113 respectively SimilarlyFigure 6 shows that base shear capacity of Pier 2 and Pier3 in the transverse direction using the automated-hingemodel is less than base shear capacity using user-definedhinge model by 160 and 146 respectively However thedisplacement capacity of Pier 2 and Pier 3 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by392 and 220 respectively A close look at the capacitycurves shows higher differences in the displacement capacityin the transverse direction than in the longitudinal directionbetween the two different hingemodelsThis difference is dueto the fact that the expected seismic and gravity axial loadlevel in the transverse direction is higher than the axial loadlevel in the longitudinal direction which in turn shifts thecontrolling capacity limit state to buckling of the longitudinalbars The higher this shift is the higher the differencebetween the curvature values obtained from buckling oflongitudinal rebars limit state and the failure compression ofthe unconfined concrete limit state is The latter is one of thetwo controlling limit states for the automated-hinge model
73 Bridge 3-E The pier columns of this bridge are rect-angular columns with poor confinement details 3 hoops at120 in spacing Table 12 supports the notion that buckling oflongitudinal rebars is the controlling limit state at Pb axialload level as expected from the behaviour of the previousbridges Compression failure of the unconfined concretelimited the curvature capacity of the columns at Ps axial loadlevel while low cycle fatigue of longitudinal rebars was thecontrolling limit state at 119875119891 axial load level Table 13 showsthe user-defined hinge properties of Pier 2 columns whereinthe plastic hinge length has the same value in the longitudinal
10 Advances in Materials Science and Engineering
Table 12 Plastic curvature capacity of Pier 2 columns Bridge 3-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus13001 T amp L 00003102 00002003 00063260 00021910 00015229119875119904 minus4320 T 00008436 00011569 00044562 00021910 00023165119875119904 minus3030 L 00010593 00021517 00042670 00021910 00026375119875119891 00 T amp L 00023579 Tension 00038788 00021910 00045696lowast119875119900 = minus32629 kips and 119875119905 = 6624 kips
Table 13 User-defined plastic hinge properties of Pier 2 columns Bridge 3-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T amp L119875119887 minus13001 13092
1918 1250 0002400002003 000384
119875119904 minus4320 10530 00008436 001618119875119891 00 7347 00021910 004202
L 119875119904 minus3030 9713 1918 1250 00024 00010593 002032
and transverse directions This is because the shear span isidentical in both directions A comparison between the ulti-mate curvature capacities of the columns of this bridge andthe columns of Bridge 2 shows the effect of the column crosssection dimensions on the value of the curvature capacityFor the compression failure of the unconfined concrete limitstate at zero axial load level the plastic curvature capacitywas equal to 00001173 radin for Bridge 2 while the plasticcurvature capacity was 00023579 radin for Bridge 3 Thisfinding is related to the smaller depth of the column sectionin Bridge 3 which is equal to 30 in compared to 36 in forthe columns of Bridge 2 This difference in the section sizewill support the capability of the smaller column section toundergo higher curvature levels for the same level of concretestrain
Figures 7 and 8 show the capacity curves of the bridgein the transverse and longitudinal directions respectivelyThe capacity curve in the longitudinal direction was obtainedfor the whole bridge because the soil behind the bridgeabutments was part of the seismic load resisting systemAccording to Figure 7 the displacement capacity of Pier 2Pier 3 and Pier 4 determined using the automated-hingemodel is higher than the displacement capacity using theuser-defined model by 03 05 and 16 respectivelyHowever the corresponding base shear capacity was lowerby 192 234 and 206 respectively A similar trendwas experienced in the longitudinal direction for the wholebridge with 268 and 44 difference in the displacementand base shear capacities respectively The differences in thecapacity curves between the two hinge models are attributedto differences in the moment-curvature values At an axialload level of minus4320 kips the ultimate curvature capacityis equal to 109 times 10minus3 radin and the associated idealized
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
10 20 30 40 50 60 70 8000Transverse displacement (in)
050
100150200250300350400450500
Base
shea
r (Ki
ps)
Figure 7 Transverse pushover capacity curve of Bridge 3-E
moment capacity is equal to 9013 ksdotft using the automated-hinge model in SAP2000 The corresponding values usingthe user-defined model are equal to 084 times 10minus3 radin and10530 ksdotft respectively
74 Bridge 4-W For brevity the results of Pier 2 widenedcolumns will be discussed The columns in the widened partof Bridge 4-Wwere provided by 4 transverse reinforcementat 30 in on centre However the longitudinal rebars werespliced within the plastic hinge zone with a length of 400 inTable 14 demonstrates that failure of the confined concrete isthe controlling limit state atPb axial load level whereas failurein the lap splice zone is the controlling limit state at all otheraxial load levels
Advances in Materials Science and Engineering 11
Table 14 Plastic curvature capacity of new columns Pier 2 amp 3 of Bridge 4-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus18248 T amp L 00011169 NClowastlowast 00056628 00019116 00011484119875119904 minus2680 T amp L 00030921 NC 00037002 00019116 00012960119875119891 00 T amp L 00046158 NC 00034514 00019116 00013836lowast119875119900 = minus52647 kips and 119875119905 = 16152 kips lowastlowastNC = Not controlling
Table 15 User-defined plastic hinge properties of new columns Pier 2 Bridge 4-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
Yield rotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus18248 24185 2505
1464 00036700011169 002798
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
L119875119887 minus18248 24185 3753
1464 00054900011169 004191
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
Bridge - AutoBridge - User
0
1000
2000
3000
4000
5000
Base
shea
r (ki
ps)
10 20 30 40 50 60 7000Longitudinal displacement (in)
Figure 8 Longitudinal pushover capacity curve of Bridge 3-E
A comparison between the ultimate curvature capacitiesof the columns of this bridge and the columns of Bridge2 shows the effect of the confinement on the value of thecurvature capacity For the compression failure of the uncon-fined concrete limit state at zero axial load level the plasticcurvature capacity was equal to 00001173 radin for Bridge 2while the plastic curvature capacity was 00046158 radin forBridge 4This finding is related to the huge difference in thedetails of the transverse reinforcement of the column sectionin Bridge 2 which has 3 hoops at 12 in and the transversereinforcement of the column section in Bridge 4 which has4 spirals at 30 in This difference in the confinement detailswill allow the section to undergo higher plastic deformations
Table 15 includes the nonlinear properties of the user-defined hinge model It is for the first time that two different
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
050
100150200250300350400450
Base
shea
r (Ki
ps)
10 20 30 40 50 60 70 80 90 100 110 12000Longitudinal displacement (in)
Figure 9 Longitudinal pushover capacity curve of Bridge 4-W
plastic hinge lengths are reported for the column in the samedirection as shown in Table 15 This result is pertained tochange in the controlling deformation limit state from failureof the confined concrete at Pb axial load level to low cyclefatigue of the longitudinal bars at Ps and Pf axial load levelsBased on the FHWA-SRM when at the deformation capacityis controlled by low cycle fatigue of longitudinal bars theeffective plastic hinge length is reduced in length and theeffective plastic hinge is concentrated at the beginning of thelapThis finding brings attention to the limited capabilities ofthe lumped plasticity model in dealing with conditions wherethe plastic hinge length changes with the axial load level
Figures 9 and 10 show the capacity curves of the bridgein the longitudinal and transverse directions respectively
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
4 Advances in Materials Science and Engineering
Table 2 Bridge 1-W columnsrsquo geometric properties and reinforcement detailslowast
Pier 2 Pier 3 Pier 4Old Widened Old Widened Old Widened
ColumnClear length (ft) 286 258 322 292 268 242Shape Circular Circular Circular Circular Circular CircularDimensions (in) 36 36 36 36 36 36Compressive strength (ksi) 40 40 40 40 40 40
Longitudinal reinforcementSize and number 129 129 129 129 129 129Yield strength (ksi) 40 60 40 60 40 60
Transverse reinforcementType Hoop Spiral Hoop Spiral Hoop SpiralSize and number 3 4 3 4 3 4Spacing (in) 120 33 120 33 120 33
Lap spliceWithin plastic hinge Yes No Yes No Yes NoLength (in) 500 mdash 500 mdash 500 mdash
lowast(1 in = 254mm 1 ksi = 689MPa)
Table 3 Bridge 2-E columnsrsquo geometric properties and reinforce-ment details
Pier 2 Pier 3Column
Clear length (ft) 2075 1950Shape Circular CircularDimensions (in) 36 36Compressive strength (ksi) 40 40
Longitudinal reinforcementSize and number 129 129Yield strength (ksi) 40 40
Transverse reinforcementType Hoop HoopSize and number 3 3Spacing (in) 120 120
Lap spliceWithin plastic hinge Yes YesLength (in) 400 400
transverse confinement that is comprised of a single 3 hoopspaced at 12 in on centre Table 4 shows columnsrsquo geometricproperties concrete strength and reinforcement details
44 Bridge 4-W Description Bridge 4-W consists of threesimply supported spans totaling 260 ft in length The road-way width was 44 ft before widening The superstructure iscomprised of precast concrete girders with span lengths of78 ft 93 ft and 89 ft Each intermediate pier is comprisedof five 3-ft diameter circular columns supported by singlefootings The bridge abutments are seat type abutments
founded on spread footings The roadway was widenedby 23 ft to an overall width of 67 ft This bridge wideningincluded the addition of precast concrete girders and two3-ft diameter columns founded on 45-ft diameter shaftsat each intermediate bent The original and new columnlongitudinal reinforcements were spliced within the potentialplastic hinge zone However column transverse confinementwas improved through the use of 4 spiral reinforcementspaced at 30 in on centre Table 5 shows columnsrsquo geometricproperties concrete strength and reinforcement details
5 Modeling of the Selected Bridges
A three-dimensional spine-type model was created for eachbridge as shown in Figure 1 for Bridge 2-E The superstruc-ture and pier elements are represented by frame elementsthat pass through their centroid The columns are split intothree frame elements as required by Section 543 of theAASHTO Guide Specifications for LRFD Seismic BridgeDesign Effective moments of inertia were used to reflectconcrete cracking and reinforcement yielding as provided inTable 7-1 of the FHWA-SRM [26] Gross section propertieswere used for the elements representing the super structurethe cross beam and the foundation as they are assumedto behave elastically Figure 2 shows a typical bridge pierthe frame elements and their associated stiffness Spreadfootings were represented by spring elements which weredetermined utilizing the method for spread footings outlinedin the FHWA-SRM [26] L-pile software [31] was used togenerate equivalent linear-elastic springs for the piles
A modal analysis was performed to identify fundamentalnatural periods andmode shapes Pushover analysis was thencarried out for each pier individually and independently in
Advances in Materials Science and Engineering 5
Table 4 Bridge 3-E columnsrsquo geometric properties and reinforcement details
Pier 2 Pier 3 Pier 4Column
Clear length (ft) 225 220 215Shape Square Rectangular Square
Dimensions (in) 30 Width = 30Depth = 24 30
Compressive strength (ksi) 40 40 40Longitudinal reinforcement
Size and number 810 89 810Yield strength (ksi) 40 40 40
Transverse reinforcementType Hoop Hoop HoopSize and number 13 13 13Spacing (in) 120 120 120
Lap spliceWithin plastic hinge Yes Yes YesLength (in) 500 440 500
Table 5 Bridge 4-W columnsrsquo geometric properties and reinforce-ment details
Pier 2 and Pier 3Old Widened
ColumnClear length (ft) 260 260Shape Circular CircularDimensions (in) 36 36Compressive strength (ksi) 40 40
Longitudinal reinforcementSize and number 129 1310Yield strength (ksi) 40 60
Transverse reinforcementType Hoop SpiralSize and number 3 4Spacing (in) 120 30
Lap spliceWithin plastic hinge Yes YesLength (in) 40 40
both the longitudinal and the transverse direction as per therequirements of the FHWA-SRM [26]
6 Approach for Studying the Effect ofPlastic Hinge Properties
Accurate determination of the nonlinear capacity curve ofa highway bridge depends on the properties of the plastichinge zone Typically design documents and seismic man-uals proposed plastic hinge properties based on mechanicalproperties of longitudinal and transverse reinforcement rein-forcement details reinforcement ratio concrete compressive
Abutment 4
Abutment 1
Pier 3
Pier 2
Cross beam-frame element
Deck-frameelement
Column-frameelement
Figure 1 Three-dimensional model of Bridge 2-E
strength cross-sectional shape axial force level and level ofconfinement The FHWA-SRM [26] is the only documentto include the effect of possible local failure mechanismsin the hinge zone on the properties of the hinge modelThe following summarizes the approach used in this studyto determine the capacity curve based on user-defined andautomated plastic hinge properties
(1) A three-dimensional model was created to determinethe natural periods of the selected bridges
(2) For user-defined plastic hinge properties the curva-ture capacity of each limit state for each pier columnat three axial load levels balanced point 119875119887 dead andseismic loads119875119904 and pure flexure119875119891 in the transverseand longitudinal directions is determined using thein-house developed MathCAD sheets
(3) The ordinates of the moment-curvature relationshipsat the associated axial load levels axial-momentinteraction surface and plastic hinge length were
6 Advances in Materials Science and Engineering
Table 6 Plastic curvature capacity of Pier 2 old columns Bridge 1-Wlowast
Axial loadlevel
Axial forcelowastlowast(kips)
DirectionCompression
failureUnconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020726 00011435119875119904 minus5840 T 00004549 00003543 00040599 00020726 00014724119875119904 minus3020 L 00006400 00006224 00037028 00020726 00017314119875119891 00 T amp L 00011457 00024662 00033434 00020726 00024387lowast1 kip = 445 kN 1 ksdotft = 000135 kNsdotm lowastlowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
Uncracked propertiesCracked propertiesPlastic hinge
Springs
Actualcolumn
Spreadfooting
Crossbeam
Lp2
Lp2
Figure 2 Bridge pier elements and associated stiffness
input into the software SAP2000 under user-definedplastic hinge properties
(4) The capacity curve using user-defined hinge proper-ties was obtained by pushing each pier individuallyand independently in both the longitudinal and thetransverse direction as per the requirements of theFHWA-SRM
(5) For automated plastic hinge properties the moment-curvature relationship and the axial-moment interac-tion surface of the potential plastic hinge are deter-mined by the software SAP2000 based on the columncross section geometry longitudinal and transversereinforcement details and unconfined concrete andsteel stress-strain curve parameters
(6) The capacity curve using automated plastic hingeproperties was obtained by pushing each pier individ-ually and independently in both the longitudinal andthe transverse direction
(7) Capacity curves using user-defined and automatedplastic hinge properties were then compared anddiscussed
7 Analysis Results and Discussions
For user-defined plastic hinge properties the value of thecontrolling limit state is shown in bold type font Plasticcurvature and plastic rotation for pure compression 119875119900 andpure Tension 119875119905 are not included because they are equal tozero The ordinates of the moment-curvature relationshipsat the associated axial load levels axial-moment interactionsurface and plastic hinge length to be input into the softwareSAP2000 are shown in Tables 6 7 8 and 9
71 Bridge 1-W Pier 2 Pier 3 andPier 4 columns showedsimilar behaviour in regard to curvature capacity limit statesTherefore for brevity results for Pier 2 are reported It isclear from Table 6 that buckling of longitudinal rebars is thecontrolling limit state of the columns of the old piers at 119875119887and Ps axial load levels in both directions This behaviouris attributed to the poor confinement details 3 hoops at120 in spacing As the axial load decreases and reaches zeroPf compression failure of the unconfined concrete becomesthe controlling limit state The unconfined concrete in hererefers to the cover concrete and the core concreteThe changein the type of the controlling limit state supports the effect ofthe axial load level on the deformation capacity of the plastic
Advances in Materials Science and Engineering 7
Table 7 User-defined plastic hinge properties of Pier 2 old columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
2118 996 00021100001173 000248
119875119904 minus5840 12901 00003543 000750119875119891 00 8702 00011457 002427
L119875119887 minus15430 15544
3491 996 00034800001173 000409
119875119904 minus3020 11118 00006224 002173119875119891 00 8702 00011457 004000
Table 8 Plastic curvature capacity of Pier 2 widened columns Bridge 1-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus17057 T amp L 00011781 NAlowastlowast 00055760 00020899 NA119875119904 minus5840 T 00025015 NA 00040056 00020899 NA119875119904 minus3020 L 00035630 NA 00037024 00020899 NA119875119891 00 T amp L 00068851 NA 00033970 00020899 NAlowast119875119900 = minus45853 kips and 119875119905 = 11740 kips lowastlowastNA = Not applicable
Table 9 User-defined plastic hinge properties of Pier 2 widened columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
Plasticrotation
radAxial(kips)
Moment(kipsdotft)
T119875119887 minus17057 195851
2357 1506 00035500011781 002776
119875119904 minus5840 166135 00020899 004925119875119891 00 127137 00020899 004925
L119875119887 minus17057 195851
3595 1506 00054100011781 004235
119875119904 minus3020 149315 00020899 007513119875119891 00 127137 00020899 007513
hinge Also the values of the controlling curvature capacitiesshown in Table 6 identify the effect of the axial force onthe deformation capacity of the plastic hinge For examplethe curvature capacity was equal to 00001173 radin at axialforce of 15430 kips and 00011457 radin at zero axial forcelevel Table 7 shows the moment-curvature ordinates and themoment-axial force interaction surface
The columns of the new piers had confined concretedetails where transverse reinforcement consisted of 4 spiralsat 33 in and column longitudinal reinforcement was notspliced within the plastic hinge zone Therefore bucklingof longitudinal rebars and failure in the lap splice zoneare not applicable as shown in Table 8 Accordingly lowcycle fatigue of longitudinal rebars was the controlling limitstate at Ps and Pf axial load levels while compressionfailure of the confined concrete controlled the curvaturecapacity at Pb axial load level Failure limit state pertaining
to unconfined concrete is not considered for the widenedcolumns because the core concrete has the capability towithstand higher plastic curvature demands after spallingoff the cover concrete Comparison of curvature capacitiesbetween the old and the new columns shows the effect of theconfinement on the deformation capacity of the plastic hingeFor example the plastic curvature capacity of the old columnwas 00011457 radin while the curvature capacity of the newcolumn was 00020899 radin at the zero axial load level
Tables 7 and 9 show that the plastic hinge length inthe transverse direction is less than the plastic hinge lengthin the longitudinal direction which is basically attributedto the difference in the shear span in both directionsSubsequently higher deformation capacities are expectedin the longitudinal direction It should be noted that theplastic hinge length was determined in accordance withthe equations in the FHWA-SRM which depends on the
8 Advances in Materials Science and Engineering
Table 10 Plastic curvature capacity of Pier 2 columns Bridge 2-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020010 00011435119875119904 minus4050 T 00005576 00004913 00038295 00020010 00016161119875119904 minus3020 L 00006404 00006231 00037024 00020010 00017319119875119891 00 T amp L 00011457 00024662 00033434 00020010 00024387lowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
shear span of the member and the yield strain and thediameter of the longitudinal bars However other researchers[21 23] identified that the plastic hinge length dependson the axial load level aspect ratio of the member typeof reinforcement longitudinal and transverse reinforcementratios and concrete strength
Figures 3 and 4 show the capacity curves of Bridge 1-W in the longitudinal and transverse directions respectivelyThe figures also show the capacity curves based on user-defined and automated plastic hinge properties It is clearfrom Figure 3 that the base shear capacity of Pier 2 Pier 3andPier 4 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 177 152 and 154 respectivelyOn the other hand the displacement capacity of Pier 2Pier 3 and Pier 4 in the longitudinal direction usingthe automated-hinge model is higher than the displacementcapacity using user-defined hinge model by 97 189 and97 respectively Similarly Figure 4 shows that base shearcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is less than baseshear capacity using user-defined hinge model by 159157 and 160 respectively However the displacementcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by109 202 and 150 respectively
The differences in the base shear and displacementcapacities of the bridge piers using the two hinge modelsare retained to the differences in the associated moment-curvature relationship At an axial load level of minus5840 kipsPs the ultimate curvature capacity is equal to 633 times10minus4 radin and the associated idealized moment capacityis equal to 11554 ksdotft using the automated-hinge model inSAP2000 The corresponding values using the user-definedmodel are equal to 354 times 10minus4 radin and 12901 ksdotft respec-tively
72 Bridge 2-E Analysis results showed that the behavioursof Pier 2 and Pier 3 are similar thus only the deformationcapacities for Pier 2 are discussed Table 10 shows thatbuckling of longitudinal rebars is the controlling limit stateof Pier 2 columns at Pb and Ps axial load levels in thelongitudinal and transverse directions This behaviour isattributed to the poor confinement details 3 hoops at 120 in
0
50
100
150
200
250
300
350
400
Base
shea
r (Ki
ps)
10
20
90
00
50
60
70
80
30
40
150
120
130
140
160
100
110
Longitudinal displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 3 Longitudinal pushover capacity curve of Bridge 1-W
0100200300400500600700800900
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Transverse displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 4 Transverse pushover capacity curve of Bridge 1-W
spacing As the axial load level decreases the value of theplastic curvature capacity increases until the axial load levelreaches zero Pf whereat compression of the unconfinedconcrete is the controlling limit state Table 11 shows themoment-curvature ordinates and the plastic hinge lengths ofPier 2 columns Similar to the findings for Bridge 1 the
Advances in Materials Science and Engineering 9
Table 11 User-defined plastic hinge properties of Pier 2 columns Bridge 2-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
1741 996 00017300001173 000204
119875119904 minus4050 11822 00004913 000856119875119891 00 8702 00011457 001995
L119875119887 minus15430 15544
2737 996 00027300001173 000321
119875119904 minus3020 11118 00006231 001706119875119891 00 8702 00011457 003136
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
25
50
75
100
125
150
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Longitudinal displacement (in)
Figure 5 Longitudinal pushover capacity curve of Bridge 2-E
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
50
100
150
200
250
300
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 4000Transverse displacement (in)
Figure 6 Transverse pushover capacity curve of Bridge 2-E andBridge 3-E
change in the type of the controlling limit state supports theeffect of the axial load level on the deformation capacity ofthe plastic hinge For example the plastic curvature capacitywas equal to 00001173 radin at axial force of 15430 kips and00011457 radin at zero axial force level
Figures 5 and 6 show the capacity curves of Bridge 2-E in the longitudinal and transverse directions respectively
Figure 5 shows that the base shear capacity of Pier 2 andPier 3 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 164 and 154 respectively Thisdifference is basically due to the fact that the idealizedflexural capacity in the FHWA-SRM is an overstrengthmoment which includes an overstrength factor in addition tothe factor associated with the expected material propertiesThe displacement capacity of Pier 2 and Pier 3 in thelongitudinal direction using the automated-hinge model ishigher than the displacement capacity using user-definedhinge model by 259 and 113 respectively SimilarlyFigure 6 shows that base shear capacity of Pier 2 and Pier3 in the transverse direction using the automated-hingemodel is less than base shear capacity using user-definedhinge model by 160 and 146 respectively However thedisplacement capacity of Pier 2 and Pier 3 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by392 and 220 respectively A close look at the capacitycurves shows higher differences in the displacement capacityin the transverse direction than in the longitudinal directionbetween the two different hingemodelsThis difference is dueto the fact that the expected seismic and gravity axial loadlevel in the transverse direction is higher than the axial loadlevel in the longitudinal direction which in turn shifts thecontrolling capacity limit state to buckling of the longitudinalbars The higher this shift is the higher the differencebetween the curvature values obtained from buckling oflongitudinal rebars limit state and the failure compression ofthe unconfined concrete limit state is The latter is one of thetwo controlling limit states for the automated-hinge model
73 Bridge 3-E The pier columns of this bridge are rect-angular columns with poor confinement details 3 hoops at120 in spacing Table 12 supports the notion that buckling oflongitudinal rebars is the controlling limit state at Pb axialload level as expected from the behaviour of the previousbridges Compression failure of the unconfined concretelimited the curvature capacity of the columns at Ps axial loadlevel while low cycle fatigue of longitudinal rebars was thecontrolling limit state at 119875119891 axial load level Table 13 showsthe user-defined hinge properties of Pier 2 columns whereinthe plastic hinge length has the same value in the longitudinal
10 Advances in Materials Science and Engineering
Table 12 Plastic curvature capacity of Pier 2 columns Bridge 3-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus13001 T amp L 00003102 00002003 00063260 00021910 00015229119875119904 minus4320 T 00008436 00011569 00044562 00021910 00023165119875119904 minus3030 L 00010593 00021517 00042670 00021910 00026375119875119891 00 T amp L 00023579 Tension 00038788 00021910 00045696lowast119875119900 = minus32629 kips and 119875119905 = 6624 kips
Table 13 User-defined plastic hinge properties of Pier 2 columns Bridge 3-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T amp L119875119887 minus13001 13092
1918 1250 0002400002003 000384
119875119904 minus4320 10530 00008436 001618119875119891 00 7347 00021910 004202
L 119875119904 minus3030 9713 1918 1250 00024 00010593 002032
and transverse directions This is because the shear span isidentical in both directions A comparison between the ulti-mate curvature capacities of the columns of this bridge andthe columns of Bridge 2 shows the effect of the column crosssection dimensions on the value of the curvature capacityFor the compression failure of the unconfined concrete limitstate at zero axial load level the plastic curvature capacitywas equal to 00001173 radin for Bridge 2 while the plasticcurvature capacity was 00023579 radin for Bridge 3 Thisfinding is related to the smaller depth of the column sectionin Bridge 3 which is equal to 30 in compared to 36 in forthe columns of Bridge 2 This difference in the section sizewill support the capability of the smaller column section toundergo higher curvature levels for the same level of concretestrain
Figures 7 and 8 show the capacity curves of the bridgein the transverse and longitudinal directions respectivelyThe capacity curve in the longitudinal direction was obtainedfor the whole bridge because the soil behind the bridgeabutments was part of the seismic load resisting systemAccording to Figure 7 the displacement capacity of Pier 2Pier 3 and Pier 4 determined using the automated-hingemodel is higher than the displacement capacity using theuser-defined model by 03 05 and 16 respectivelyHowever the corresponding base shear capacity was lowerby 192 234 and 206 respectively A similar trendwas experienced in the longitudinal direction for the wholebridge with 268 and 44 difference in the displacementand base shear capacities respectively The differences in thecapacity curves between the two hinge models are attributedto differences in the moment-curvature values At an axialload level of minus4320 kips the ultimate curvature capacityis equal to 109 times 10minus3 radin and the associated idealized
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
10 20 30 40 50 60 70 8000Transverse displacement (in)
050
100150200250300350400450500
Base
shea
r (Ki
ps)
Figure 7 Transverse pushover capacity curve of Bridge 3-E
moment capacity is equal to 9013 ksdotft using the automated-hinge model in SAP2000 The corresponding values usingthe user-defined model are equal to 084 times 10minus3 radin and10530 ksdotft respectively
74 Bridge 4-W For brevity the results of Pier 2 widenedcolumns will be discussed The columns in the widened partof Bridge 4-Wwere provided by 4 transverse reinforcementat 30 in on centre However the longitudinal rebars werespliced within the plastic hinge zone with a length of 400 inTable 14 demonstrates that failure of the confined concrete isthe controlling limit state atPb axial load level whereas failurein the lap splice zone is the controlling limit state at all otheraxial load levels
Advances in Materials Science and Engineering 11
Table 14 Plastic curvature capacity of new columns Pier 2 amp 3 of Bridge 4-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus18248 T amp L 00011169 NClowastlowast 00056628 00019116 00011484119875119904 minus2680 T amp L 00030921 NC 00037002 00019116 00012960119875119891 00 T amp L 00046158 NC 00034514 00019116 00013836lowast119875119900 = minus52647 kips and 119875119905 = 16152 kips lowastlowastNC = Not controlling
Table 15 User-defined plastic hinge properties of new columns Pier 2 Bridge 4-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
Yield rotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus18248 24185 2505
1464 00036700011169 002798
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
L119875119887 minus18248 24185 3753
1464 00054900011169 004191
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
Bridge - AutoBridge - User
0
1000
2000
3000
4000
5000
Base
shea
r (ki
ps)
10 20 30 40 50 60 7000Longitudinal displacement (in)
Figure 8 Longitudinal pushover capacity curve of Bridge 3-E
A comparison between the ultimate curvature capacitiesof the columns of this bridge and the columns of Bridge2 shows the effect of the confinement on the value of thecurvature capacity For the compression failure of the uncon-fined concrete limit state at zero axial load level the plasticcurvature capacity was equal to 00001173 radin for Bridge 2while the plastic curvature capacity was 00046158 radin forBridge 4This finding is related to the huge difference in thedetails of the transverse reinforcement of the column sectionin Bridge 2 which has 3 hoops at 12 in and the transversereinforcement of the column section in Bridge 4 which has4 spirals at 30 in This difference in the confinement detailswill allow the section to undergo higher plastic deformations
Table 15 includes the nonlinear properties of the user-defined hinge model It is for the first time that two different
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
050
100150200250300350400450
Base
shea
r (Ki
ps)
10 20 30 40 50 60 70 80 90 100 110 12000Longitudinal displacement (in)
Figure 9 Longitudinal pushover capacity curve of Bridge 4-W
plastic hinge lengths are reported for the column in the samedirection as shown in Table 15 This result is pertained tochange in the controlling deformation limit state from failureof the confined concrete at Pb axial load level to low cyclefatigue of the longitudinal bars at Ps and Pf axial load levelsBased on the FHWA-SRM when at the deformation capacityis controlled by low cycle fatigue of longitudinal bars theeffective plastic hinge length is reduced in length and theeffective plastic hinge is concentrated at the beginning of thelapThis finding brings attention to the limited capabilities ofthe lumped plasticity model in dealing with conditions wherethe plastic hinge length changes with the axial load level
Figures 9 and 10 show the capacity curves of the bridgein the longitudinal and transverse directions respectively
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
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International Journal of
Biomaterials
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TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Advances in
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MaterialsJournal of
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Advances in Materials Science and Engineering 5
Table 4 Bridge 3-E columnsrsquo geometric properties and reinforcement details
Pier 2 Pier 3 Pier 4Column
Clear length (ft) 225 220 215Shape Square Rectangular Square
Dimensions (in) 30 Width = 30Depth = 24 30
Compressive strength (ksi) 40 40 40Longitudinal reinforcement
Size and number 810 89 810Yield strength (ksi) 40 40 40
Transverse reinforcementType Hoop Hoop HoopSize and number 13 13 13Spacing (in) 120 120 120
Lap spliceWithin plastic hinge Yes Yes YesLength (in) 500 440 500
Table 5 Bridge 4-W columnsrsquo geometric properties and reinforce-ment details
Pier 2 and Pier 3Old Widened
ColumnClear length (ft) 260 260Shape Circular CircularDimensions (in) 36 36Compressive strength (ksi) 40 40
Longitudinal reinforcementSize and number 129 1310Yield strength (ksi) 40 60
Transverse reinforcementType Hoop SpiralSize and number 3 4Spacing (in) 120 30
Lap spliceWithin plastic hinge Yes YesLength (in) 40 40
both the longitudinal and the transverse direction as per therequirements of the FHWA-SRM [26]
6 Approach for Studying the Effect ofPlastic Hinge Properties
Accurate determination of the nonlinear capacity curve ofa highway bridge depends on the properties of the plastichinge zone Typically design documents and seismic man-uals proposed plastic hinge properties based on mechanicalproperties of longitudinal and transverse reinforcement rein-forcement details reinforcement ratio concrete compressive
Abutment 4
Abutment 1
Pier 3
Pier 2
Cross beam-frame element
Deck-frameelement
Column-frameelement
Figure 1 Three-dimensional model of Bridge 2-E
strength cross-sectional shape axial force level and level ofconfinement The FHWA-SRM [26] is the only documentto include the effect of possible local failure mechanismsin the hinge zone on the properties of the hinge modelThe following summarizes the approach used in this studyto determine the capacity curve based on user-defined andautomated plastic hinge properties
(1) A three-dimensional model was created to determinethe natural periods of the selected bridges
(2) For user-defined plastic hinge properties the curva-ture capacity of each limit state for each pier columnat three axial load levels balanced point 119875119887 dead andseismic loads119875119904 and pure flexure119875119891 in the transverseand longitudinal directions is determined using thein-house developed MathCAD sheets
(3) The ordinates of the moment-curvature relationshipsat the associated axial load levels axial-momentinteraction surface and plastic hinge length were
6 Advances in Materials Science and Engineering
Table 6 Plastic curvature capacity of Pier 2 old columns Bridge 1-Wlowast
Axial loadlevel
Axial forcelowastlowast(kips)
DirectionCompression
failureUnconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020726 00011435119875119904 minus5840 T 00004549 00003543 00040599 00020726 00014724119875119904 minus3020 L 00006400 00006224 00037028 00020726 00017314119875119891 00 T amp L 00011457 00024662 00033434 00020726 00024387lowast1 kip = 445 kN 1 ksdotft = 000135 kNsdotm lowastlowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
Uncracked propertiesCracked propertiesPlastic hinge
Springs
Actualcolumn
Spreadfooting
Crossbeam
Lp2
Lp2
Figure 2 Bridge pier elements and associated stiffness
input into the software SAP2000 under user-definedplastic hinge properties
(4) The capacity curve using user-defined hinge proper-ties was obtained by pushing each pier individuallyand independently in both the longitudinal and thetransverse direction as per the requirements of theFHWA-SRM
(5) For automated plastic hinge properties the moment-curvature relationship and the axial-moment interac-tion surface of the potential plastic hinge are deter-mined by the software SAP2000 based on the columncross section geometry longitudinal and transversereinforcement details and unconfined concrete andsteel stress-strain curve parameters
(6) The capacity curve using automated plastic hingeproperties was obtained by pushing each pier individ-ually and independently in both the longitudinal andthe transverse direction
(7) Capacity curves using user-defined and automatedplastic hinge properties were then compared anddiscussed
7 Analysis Results and Discussions
For user-defined plastic hinge properties the value of thecontrolling limit state is shown in bold type font Plasticcurvature and plastic rotation for pure compression 119875119900 andpure Tension 119875119905 are not included because they are equal tozero The ordinates of the moment-curvature relationshipsat the associated axial load levels axial-moment interactionsurface and plastic hinge length to be input into the softwareSAP2000 are shown in Tables 6 7 8 and 9
71 Bridge 1-W Pier 2 Pier 3 andPier 4 columns showedsimilar behaviour in regard to curvature capacity limit statesTherefore for brevity results for Pier 2 are reported It isclear from Table 6 that buckling of longitudinal rebars is thecontrolling limit state of the columns of the old piers at 119875119887and Ps axial load levels in both directions This behaviouris attributed to the poor confinement details 3 hoops at120 in spacing As the axial load decreases and reaches zeroPf compression failure of the unconfined concrete becomesthe controlling limit state The unconfined concrete in hererefers to the cover concrete and the core concreteThe changein the type of the controlling limit state supports the effect ofthe axial load level on the deformation capacity of the plastic
Advances in Materials Science and Engineering 7
Table 7 User-defined plastic hinge properties of Pier 2 old columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
2118 996 00021100001173 000248
119875119904 minus5840 12901 00003543 000750119875119891 00 8702 00011457 002427
L119875119887 minus15430 15544
3491 996 00034800001173 000409
119875119904 minus3020 11118 00006224 002173119875119891 00 8702 00011457 004000
Table 8 Plastic curvature capacity of Pier 2 widened columns Bridge 1-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus17057 T amp L 00011781 NAlowastlowast 00055760 00020899 NA119875119904 minus5840 T 00025015 NA 00040056 00020899 NA119875119904 minus3020 L 00035630 NA 00037024 00020899 NA119875119891 00 T amp L 00068851 NA 00033970 00020899 NAlowast119875119900 = minus45853 kips and 119875119905 = 11740 kips lowastlowastNA = Not applicable
Table 9 User-defined plastic hinge properties of Pier 2 widened columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
Plasticrotation
radAxial(kips)
Moment(kipsdotft)
T119875119887 minus17057 195851
2357 1506 00035500011781 002776
119875119904 minus5840 166135 00020899 004925119875119891 00 127137 00020899 004925
L119875119887 minus17057 195851
3595 1506 00054100011781 004235
119875119904 minus3020 149315 00020899 007513119875119891 00 127137 00020899 007513
hinge Also the values of the controlling curvature capacitiesshown in Table 6 identify the effect of the axial force onthe deformation capacity of the plastic hinge For examplethe curvature capacity was equal to 00001173 radin at axialforce of 15430 kips and 00011457 radin at zero axial forcelevel Table 7 shows the moment-curvature ordinates and themoment-axial force interaction surface
The columns of the new piers had confined concretedetails where transverse reinforcement consisted of 4 spiralsat 33 in and column longitudinal reinforcement was notspliced within the plastic hinge zone Therefore bucklingof longitudinal rebars and failure in the lap splice zoneare not applicable as shown in Table 8 Accordingly lowcycle fatigue of longitudinal rebars was the controlling limitstate at Ps and Pf axial load levels while compressionfailure of the confined concrete controlled the curvaturecapacity at Pb axial load level Failure limit state pertaining
to unconfined concrete is not considered for the widenedcolumns because the core concrete has the capability towithstand higher plastic curvature demands after spallingoff the cover concrete Comparison of curvature capacitiesbetween the old and the new columns shows the effect of theconfinement on the deformation capacity of the plastic hingeFor example the plastic curvature capacity of the old columnwas 00011457 radin while the curvature capacity of the newcolumn was 00020899 radin at the zero axial load level
Tables 7 and 9 show that the plastic hinge length inthe transverse direction is less than the plastic hinge lengthin the longitudinal direction which is basically attributedto the difference in the shear span in both directionsSubsequently higher deformation capacities are expectedin the longitudinal direction It should be noted that theplastic hinge length was determined in accordance withthe equations in the FHWA-SRM which depends on the
8 Advances in Materials Science and Engineering
Table 10 Plastic curvature capacity of Pier 2 columns Bridge 2-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020010 00011435119875119904 minus4050 T 00005576 00004913 00038295 00020010 00016161119875119904 minus3020 L 00006404 00006231 00037024 00020010 00017319119875119891 00 T amp L 00011457 00024662 00033434 00020010 00024387lowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
shear span of the member and the yield strain and thediameter of the longitudinal bars However other researchers[21 23] identified that the plastic hinge length dependson the axial load level aspect ratio of the member typeof reinforcement longitudinal and transverse reinforcementratios and concrete strength
Figures 3 and 4 show the capacity curves of Bridge 1-W in the longitudinal and transverse directions respectivelyThe figures also show the capacity curves based on user-defined and automated plastic hinge properties It is clearfrom Figure 3 that the base shear capacity of Pier 2 Pier 3andPier 4 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 177 152 and 154 respectivelyOn the other hand the displacement capacity of Pier 2Pier 3 and Pier 4 in the longitudinal direction usingthe automated-hinge model is higher than the displacementcapacity using user-defined hinge model by 97 189 and97 respectively Similarly Figure 4 shows that base shearcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is less than baseshear capacity using user-defined hinge model by 159157 and 160 respectively However the displacementcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by109 202 and 150 respectively
The differences in the base shear and displacementcapacities of the bridge piers using the two hinge modelsare retained to the differences in the associated moment-curvature relationship At an axial load level of minus5840 kipsPs the ultimate curvature capacity is equal to 633 times10minus4 radin and the associated idealized moment capacityis equal to 11554 ksdotft using the automated-hinge model inSAP2000 The corresponding values using the user-definedmodel are equal to 354 times 10minus4 radin and 12901 ksdotft respec-tively
72 Bridge 2-E Analysis results showed that the behavioursof Pier 2 and Pier 3 are similar thus only the deformationcapacities for Pier 2 are discussed Table 10 shows thatbuckling of longitudinal rebars is the controlling limit stateof Pier 2 columns at Pb and Ps axial load levels in thelongitudinal and transverse directions This behaviour isattributed to the poor confinement details 3 hoops at 120 in
0
50
100
150
200
250
300
350
400
Base
shea
r (Ki
ps)
10
20
90
00
50
60
70
80
30
40
150
120
130
140
160
100
110
Longitudinal displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 3 Longitudinal pushover capacity curve of Bridge 1-W
0100200300400500600700800900
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Transverse displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 4 Transverse pushover capacity curve of Bridge 1-W
spacing As the axial load level decreases the value of theplastic curvature capacity increases until the axial load levelreaches zero Pf whereat compression of the unconfinedconcrete is the controlling limit state Table 11 shows themoment-curvature ordinates and the plastic hinge lengths ofPier 2 columns Similar to the findings for Bridge 1 the
Advances in Materials Science and Engineering 9
Table 11 User-defined plastic hinge properties of Pier 2 columns Bridge 2-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
1741 996 00017300001173 000204
119875119904 minus4050 11822 00004913 000856119875119891 00 8702 00011457 001995
L119875119887 minus15430 15544
2737 996 00027300001173 000321
119875119904 minus3020 11118 00006231 001706119875119891 00 8702 00011457 003136
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
25
50
75
100
125
150
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Longitudinal displacement (in)
Figure 5 Longitudinal pushover capacity curve of Bridge 2-E
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
50
100
150
200
250
300
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 4000Transverse displacement (in)
Figure 6 Transverse pushover capacity curve of Bridge 2-E andBridge 3-E
change in the type of the controlling limit state supports theeffect of the axial load level on the deformation capacity ofthe plastic hinge For example the plastic curvature capacitywas equal to 00001173 radin at axial force of 15430 kips and00011457 radin at zero axial force level
Figures 5 and 6 show the capacity curves of Bridge 2-E in the longitudinal and transverse directions respectively
Figure 5 shows that the base shear capacity of Pier 2 andPier 3 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 164 and 154 respectively Thisdifference is basically due to the fact that the idealizedflexural capacity in the FHWA-SRM is an overstrengthmoment which includes an overstrength factor in addition tothe factor associated with the expected material propertiesThe displacement capacity of Pier 2 and Pier 3 in thelongitudinal direction using the automated-hinge model ishigher than the displacement capacity using user-definedhinge model by 259 and 113 respectively SimilarlyFigure 6 shows that base shear capacity of Pier 2 and Pier3 in the transverse direction using the automated-hingemodel is less than base shear capacity using user-definedhinge model by 160 and 146 respectively However thedisplacement capacity of Pier 2 and Pier 3 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by392 and 220 respectively A close look at the capacitycurves shows higher differences in the displacement capacityin the transverse direction than in the longitudinal directionbetween the two different hingemodelsThis difference is dueto the fact that the expected seismic and gravity axial loadlevel in the transverse direction is higher than the axial loadlevel in the longitudinal direction which in turn shifts thecontrolling capacity limit state to buckling of the longitudinalbars The higher this shift is the higher the differencebetween the curvature values obtained from buckling oflongitudinal rebars limit state and the failure compression ofthe unconfined concrete limit state is The latter is one of thetwo controlling limit states for the automated-hinge model
73 Bridge 3-E The pier columns of this bridge are rect-angular columns with poor confinement details 3 hoops at120 in spacing Table 12 supports the notion that buckling oflongitudinal rebars is the controlling limit state at Pb axialload level as expected from the behaviour of the previousbridges Compression failure of the unconfined concretelimited the curvature capacity of the columns at Ps axial loadlevel while low cycle fatigue of longitudinal rebars was thecontrolling limit state at 119875119891 axial load level Table 13 showsthe user-defined hinge properties of Pier 2 columns whereinthe plastic hinge length has the same value in the longitudinal
10 Advances in Materials Science and Engineering
Table 12 Plastic curvature capacity of Pier 2 columns Bridge 3-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus13001 T amp L 00003102 00002003 00063260 00021910 00015229119875119904 minus4320 T 00008436 00011569 00044562 00021910 00023165119875119904 minus3030 L 00010593 00021517 00042670 00021910 00026375119875119891 00 T amp L 00023579 Tension 00038788 00021910 00045696lowast119875119900 = minus32629 kips and 119875119905 = 6624 kips
Table 13 User-defined plastic hinge properties of Pier 2 columns Bridge 3-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T amp L119875119887 minus13001 13092
1918 1250 0002400002003 000384
119875119904 minus4320 10530 00008436 001618119875119891 00 7347 00021910 004202
L 119875119904 minus3030 9713 1918 1250 00024 00010593 002032
and transverse directions This is because the shear span isidentical in both directions A comparison between the ulti-mate curvature capacities of the columns of this bridge andthe columns of Bridge 2 shows the effect of the column crosssection dimensions on the value of the curvature capacityFor the compression failure of the unconfined concrete limitstate at zero axial load level the plastic curvature capacitywas equal to 00001173 radin for Bridge 2 while the plasticcurvature capacity was 00023579 radin for Bridge 3 Thisfinding is related to the smaller depth of the column sectionin Bridge 3 which is equal to 30 in compared to 36 in forthe columns of Bridge 2 This difference in the section sizewill support the capability of the smaller column section toundergo higher curvature levels for the same level of concretestrain
Figures 7 and 8 show the capacity curves of the bridgein the transverse and longitudinal directions respectivelyThe capacity curve in the longitudinal direction was obtainedfor the whole bridge because the soil behind the bridgeabutments was part of the seismic load resisting systemAccording to Figure 7 the displacement capacity of Pier 2Pier 3 and Pier 4 determined using the automated-hingemodel is higher than the displacement capacity using theuser-defined model by 03 05 and 16 respectivelyHowever the corresponding base shear capacity was lowerby 192 234 and 206 respectively A similar trendwas experienced in the longitudinal direction for the wholebridge with 268 and 44 difference in the displacementand base shear capacities respectively The differences in thecapacity curves between the two hinge models are attributedto differences in the moment-curvature values At an axialload level of minus4320 kips the ultimate curvature capacityis equal to 109 times 10minus3 radin and the associated idealized
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
10 20 30 40 50 60 70 8000Transverse displacement (in)
050
100150200250300350400450500
Base
shea
r (Ki
ps)
Figure 7 Transverse pushover capacity curve of Bridge 3-E
moment capacity is equal to 9013 ksdotft using the automated-hinge model in SAP2000 The corresponding values usingthe user-defined model are equal to 084 times 10minus3 radin and10530 ksdotft respectively
74 Bridge 4-W For brevity the results of Pier 2 widenedcolumns will be discussed The columns in the widened partof Bridge 4-Wwere provided by 4 transverse reinforcementat 30 in on centre However the longitudinal rebars werespliced within the plastic hinge zone with a length of 400 inTable 14 demonstrates that failure of the confined concrete isthe controlling limit state atPb axial load level whereas failurein the lap splice zone is the controlling limit state at all otheraxial load levels
Advances in Materials Science and Engineering 11
Table 14 Plastic curvature capacity of new columns Pier 2 amp 3 of Bridge 4-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus18248 T amp L 00011169 NClowastlowast 00056628 00019116 00011484119875119904 minus2680 T amp L 00030921 NC 00037002 00019116 00012960119875119891 00 T amp L 00046158 NC 00034514 00019116 00013836lowast119875119900 = minus52647 kips and 119875119905 = 16152 kips lowastlowastNC = Not controlling
Table 15 User-defined plastic hinge properties of new columns Pier 2 Bridge 4-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
Yield rotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus18248 24185 2505
1464 00036700011169 002798
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
L119875119887 minus18248 24185 3753
1464 00054900011169 004191
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
Bridge - AutoBridge - User
0
1000
2000
3000
4000
5000
Base
shea
r (ki
ps)
10 20 30 40 50 60 7000Longitudinal displacement (in)
Figure 8 Longitudinal pushover capacity curve of Bridge 3-E
A comparison between the ultimate curvature capacitiesof the columns of this bridge and the columns of Bridge2 shows the effect of the confinement on the value of thecurvature capacity For the compression failure of the uncon-fined concrete limit state at zero axial load level the plasticcurvature capacity was equal to 00001173 radin for Bridge 2while the plastic curvature capacity was 00046158 radin forBridge 4This finding is related to the huge difference in thedetails of the transverse reinforcement of the column sectionin Bridge 2 which has 3 hoops at 12 in and the transversereinforcement of the column section in Bridge 4 which has4 spirals at 30 in This difference in the confinement detailswill allow the section to undergo higher plastic deformations
Table 15 includes the nonlinear properties of the user-defined hinge model It is for the first time that two different
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
050
100150200250300350400450
Base
shea
r (Ki
ps)
10 20 30 40 50 60 70 80 90 100 110 12000Longitudinal displacement (in)
Figure 9 Longitudinal pushover capacity curve of Bridge 4-W
plastic hinge lengths are reported for the column in the samedirection as shown in Table 15 This result is pertained tochange in the controlling deformation limit state from failureof the confined concrete at Pb axial load level to low cyclefatigue of the longitudinal bars at Ps and Pf axial load levelsBased on the FHWA-SRM when at the deformation capacityis controlled by low cycle fatigue of longitudinal bars theeffective plastic hinge length is reduced in length and theeffective plastic hinge is concentrated at the beginning of thelapThis finding brings attention to the limited capabilities ofthe lumped plasticity model in dealing with conditions wherethe plastic hinge length changes with the axial load level
Figures 9 and 10 show the capacity curves of the bridgein the longitudinal and transverse directions respectively
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
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NanoparticlesJournal of
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International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
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BioMed Research International
MaterialsJournal of
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6 Advances in Materials Science and Engineering
Table 6 Plastic curvature capacity of Pier 2 old columns Bridge 1-Wlowast
Axial loadlevel
Axial forcelowastlowast(kips)
DirectionCompression
failureUnconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020726 00011435119875119904 minus5840 T 00004549 00003543 00040599 00020726 00014724119875119904 minus3020 L 00006400 00006224 00037028 00020726 00017314119875119891 00 T amp L 00011457 00024662 00033434 00020726 00024387lowast1 kip = 445 kN 1 ksdotft = 000135 kNsdotm lowastlowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
Uncracked propertiesCracked propertiesPlastic hinge
Springs
Actualcolumn
Spreadfooting
Crossbeam
Lp2
Lp2
Figure 2 Bridge pier elements and associated stiffness
input into the software SAP2000 under user-definedplastic hinge properties
(4) The capacity curve using user-defined hinge proper-ties was obtained by pushing each pier individuallyand independently in both the longitudinal and thetransverse direction as per the requirements of theFHWA-SRM
(5) For automated plastic hinge properties the moment-curvature relationship and the axial-moment interac-tion surface of the potential plastic hinge are deter-mined by the software SAP2000 based on the columncross section geometry longitudinal and transversereinforcement details and unconfined concrete andsteel stress-strain curve parameters
(6) The capacity curve using automated plastic hingeproperties was obtained by pushing each pier individ-ually and independently in both the longitudinal andthe transverse direction
(7) Capacity curves using user-defined and automatedplastic hinge properties were then compared anddiscussed
7 Analysis Results and Discussions
For user-defined plastic hinge properties the value of thecontrolling limit state is shown in bold type font Plasticcurvature and plastic rotation for pure compression 119875119900 andpure Tension 119875119905 are not included because they are equal tozero The ordinates of the moment-curvature relationshipsat the associated axial load levels axial-moment interactionsurface and plastic hinge length to be input into the softwareSAP2000 are shown in Tables 6 7 8 and 9
71 Bridge 1-W Pier 2 Pier 3 andPier 4 columns showedsimilar behaviour in regard to curvature capacity limit statesTherefore for brevity results for Pier 2 are reported It isclear from Table 6 that buckling of longitudinal rebars is thecontrolling limit state of the columns of the old piers at 119875119887and Ps axial load levels in both directions This behaviouris attributed to the poor confinement details 3 hoops at120 in spacing As the axial load decreases and reaches zeroPf compression failure of the unconfined concrete becomesthe controlling limit state The unconfined concrete in hererefers to the cover concrete and the core concreteThe changein the type of the controlling limit state supports the effect ofthe axial load level on the deformation capacity of the plastic
Advances in Materials Science and Engineering 7
Table 7 User-defined plastic hinge properties of Pier 2 old columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
2118 996 00021100001173 000248
119875119904 minus5840 12901 00003543 000750119875119891 00 8702 00011457 002427
L119875119887 minus15430 15544
3491 996 00034800001173 000409
119875119904 minus3020 11118 00006224 002173119875119891 00 8702 00011457 004000
Table 8 Plastic curvature capacity of Pier 2 widened columns Bridge 1-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus17057 T amp L 00011781 NAlowastlowast 00055760 00020899 NA119875119904 minus5840 T 00025015 NA 00040056 00020899 NA119875119904 minus3020 L 00035630 NA 00037024 00020899 NA119875119891 00 T amp L 00068851 NA 00033970 00020899 NAlowast119875119900 = minus45853 kips and 119875119905 = 11740 kips lowastlowastNA = Not applicable
Table 9 User-defined plastic hinge properties of Pier 2 widened columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
Plasticrotation
radAxial(kips)
Moment(kipsdotft)
T119875119887 minus17057 195851
2357 1506 00035500011781 002776
119875119904 minus5840 166135 00020899 004925119875119891 00 127137 00020899 004925
L119875119887 minus17057 195851
3595 1506 00054100011781 004235
119875119904 minus3020 149315 00020899 007513119875119891 00 127137 00020899 007513
hinge Also the values of the controlling curvature capacitiesshown in Table 6 identify the effect of the axial force onthe deformation capacity of the plastic hinge For examplethe curvature capacity was equal to 00001173 radin at axialforce of 15430 kips and 00011457 radin at zero axial forcelevel Table 7 shows the moment-curvature ordinates and themoment-axial force interaction surface
The columns of the new piers had confined concretedetails where transverse reinforcement consisted of 4 spiralsat 33 in and column longitudinal reinforcement was notspliced within the plastic hinge zone Therefore bucklingof longitudinal rebars and failure in the lap splice zoneare not applicable as shown in Table 8 Accordingly lowcycle fatigue of longitudinal rebars was the controlling limitstate at Ps and Pf axial load levels while compressionfailure of the confined concrete controlled the curvaturecapacity at Pb axial load level Failure limit state pertaining
to unconfined concrete is not considered for the widenedcolumns because the core concrete has the capability towithstand higher plastic curvature demands after spallingoff the cover concrete Comparison of curvature capacitiesbetween the old and the new columns shows the effect of theconfinement on the deformation capacity of the plastic hingeFor example the plastic curvature capacity of the old columnwas 00011457 radin while the curvature capacity of the newcolumn was 00020899 radin at the zero axial load level
Tables 7 and 9 show that the plastic hinge length inthe transverse direction is less than the plastic hinge lengthin the longitudinal direction which is basically attributedto the difference in the shear span in both directionsSubsequently higher deformation capacities are expectedin the longitudinal direction It should be noted that theplastic hinge length was determined in accordance withthe equations in the FHWA-SRM which depends on the
8 Advances in Materials Science and Engineering
Table 10 Plastic curvature capacity of Pier 2 columns Bridge 2-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020010 00011435119875119904 minus4050 T 00005576 00004913 00038295 00020010 00016161119875119904 minus3020 L 00006404 00006231 00037024 00020010 00017319119875119891 00 T amp L 00011457 00024662 00033434 00020010 00024387lowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
shear span of the member and the yield strain and thediameter of the longitudinal bars However other researchers[21 23] identified that the plastic hinge length dependson the axial load level aspect ratio of the member typeof reinforcement longitudinal and transverse reinforcementratios and concrete strength
Figures 3 and 4 show the capacity curves of Bridge 1-W in the longitudinal and transverse directions respectivelyThe figures also show the capacity curves based on user-defined and automated plastic hinge properties It is clearfrom Figure 3 that the base shear capacity of Pier 2 Pier 3andPier 4 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 177 152 and 154 respectivelyOn the other hand the displacement capacity of Pier 2Pier 3 and Pier 4 in the longitudinal direction usingthe automated-hinge model is higher than the displacementcapacity using user-defined hinge model by 97 189 and97 respectively Similarly Figure 4 shows that base shearcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is less than baseshear capacity using user-defined hinge model by 159157 and 160 respectively However the displacementcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by109 202 and 150 respectively
The differences in the base shear and displacementcapacities of the bridge piers using the two hinge modelsare retained to the differences in the associated moment-curvature relationship At an axial load level of minus5840 kipsPs the ultimate curvature capacity is equal to 633 times10minus4 radin and the associated idealized moment capacityis equal to 11554 ksdotft using the automated-hinge model inSAP2000 The corresponding values using the user-definedmodel are equal to 354 times 10minus4 radin and 12901 ksdotft respec-tively
72 Bridge 2-E Analysis results showed that the behavioursof Pier 2 and Pier 3 are similar thus only the deformationcapacities for Pier 2 are discussed Table 10 shows thatbuckling of longitudinal rebars is the controlling limit stateof Pier 2 columns at Pb and Ps axial load levels in thelongitudinal and transverse directions This behaviour isattributed to the poor confinement details 3 hoops at 120 in
0
50
100
150
200
250
300
350
400
Base
shea
r (Ki
ps)
10
20
90
00
50
60
70
80
30
40
150
120
130
140
160
100
110
Longitudinal displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 3 Longitudinal pushover capacity curve of Bridge 1-W
0100200300400500600700800900
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Transverse displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 4 Transverse pushover capacity curve of Bridge 1-W
spacing As the axial load level decreases the value of theplastic curvature capacity increases until the axial load levelreaches zero Pf whereat compression of the unconfinedconcrete is the controlling limit state Table 11 shows themoment-curvature ordinates and the plastic hinge lengths ofPier 2 columns Similar to the findings for Bridge 1 the
Advances in Materials Science and Engineering 9
Table 11 User-defined plastic hinge properties of Pier 2 columns Bridge 2-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
1741 996 00017300001173 000204
119875119904 minus4050 11822 00004913 000856119875119891 00 8702 00011457 001995
L119875119887 minus15430 15544
2737 996 00027300001173 000321
119875119904 minus3020 11118 00006231 001706119875119891 00 8702 00011457 003136
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
25
50
75
100
125
150
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Longitudinal displacement (in)
Figure 5 Longitudinal pushover capacity curve of Bridge 2-E
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
50
100
150
200
250
300
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 4000Transverse displacement (in)
Figure 6 Transverse pushover capacity curve of Bridge 2-E andBridge 3-E
change in the type of the controlling limit state supports theeffect of the axial load level on the deformation capacity ofthe plastic hinge For example the plastic curvature capacitywas equal to 00001173 radin at axial force of 15430 kips and00011457 radin at zero axial force level
Figures 5 and 6 show the capacity curves of Bridge 2-E in the longitudinal and transverse directions respectively
Figure 5 shows that the base shear capacity of Pier 2 andPier 3 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 164 and 154 respectively Thisdifference is basically due to the fact that the idealizedflexural capacity in the FHWA-SRM is an overstrengthmoment which includes an overstrength factor in addition tothe factor associated with the expected material propertiesThe displacement capacity of Pier 2 and Pier 3 in thelongitudinal direction using the automated-hinge model ishigher than the displacement capacity using user-definedhinge model by 259 and 113 respectively SimilarlyFigure 6 shows that base shear capacity of Pier 2 and Pier3 in the transverse direction using the automated-hingemodel is less than base shear capacity using user-definedhinge model by 160 and 146 respectively However thedisplacement capacity of Pier 2 and Pier 3 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by392 and 220 respectively A close look at the capacitycurves shows higher differences in the displacement capacityin the transverse direction than in the longitudinal directionbetween the two different hingemodelsThis difference is dueto the fact that the expected seismic and gravity axial loadlevel in the transverse direction is higher than the axial loadlevel in the longitudinal direction which in turn shifts thecontrolling capacity limit state to buckling of the longitudinalbars The higher this shift is the higher the differencebetween the curvature values obtained from buckling oflongitudinal rebars limit state and the failure compression ofthe unconfined concrete limit state is The latter is one of thetwo controlling limit states for the automated-hinge model
73 Bridge 3-E The pier columns of this bridge are rect-angular columns with poor confinement details 3 hoops at120 in spacing Table 12 supports the notion that buckling oflongitudinal rebars is the controlling limit state at Pb axialload level as expected from the behaviour of the previousbridges Compression failure of the unconfined concretelimited the curvature capacity of the columns at Ps axial loadlevel while low cycle fatigue of longitudinal rebars was thecontrolling limit state at 119875119891 axial load level Table 13 showsthe user-defined hinge properties of Pier 2 columns whereinthe plastic hinge length has the same value in the longitudinal
10 Advances in Materials Science and Engineering
Table 12 Plastic curvature capacity of Pier 2 columns Bridge 3-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus13001 T amp L 00003102 00002003 00063260 00021910 00015229119875119904 minus4320 T 00008436 00011569 00044562 00021910 00023165119875119904 minus3030 L 00010593 00021517 00042670 00021910 00026375119875119891 00 T amp L 00023579 Tension 00038788 00021910 00045696lowast119875119900 = minus32629 kips and 119875119905 = 6624 kips
Table 13 User-defined plastic hinge properties of Pier 2 columns Bridge 3-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T amp L119875119887 minus13001 13092
1918 1250 0002400002003 000384
119875119904 minus4320 10530 00008436 001618119875119891 00 7347 00021910 004202
L 119875119904 minus3030 9713 1918 1250 00024 00010593 002032
and transverse directions This is because the shear span isidentical in both directions A comparison between the ulti-mate curvature capacities of the columns of this bridge andthe columns of Bridge 2 shows the effect of the column crosssection dimensions on the value of the curvature capacityFor the compression failure of the unconfined concrete limitstate at zero axial load level the plastic curvature capacitywas equal to 00001173 radin for Bridge 2 while the plasticcurvature capacity was 00023579 radin for Bridge 3 Thisfinding is related to the smaller depth of the column sectionin Bridge 3 which is equal to 30 in compared to 36 in forthe columns of Bridge 2 This difference in the section sizewill support the capability of the smaller column section toundergo higher curvature levels for the same level of concretestrain
Figures 7 and 8 show the capacity curves of the bridgein the transverse and longitudinal directions respectivelyThe capacity curve in the longitudinal direction was obtainedfor the whole bridge because the soil behind the bridgeabutments was part of the seismic load resisting systemAccording to Figure 7 the displacement capacity of Pier 2Pier 3 and Pier 4 determined using the automated-hingemodel is higher than the displacement capacity using theuser-defined model by 03 05 and 16 respectivelyHowever the corresponding base shear capacity was lowerby 192 234 and 206 respectively A similar trendwas experienced in the longitudinal direction for the wholebridge with 268 and 44 difference in the displacementand base shear capacities respectively The differences in thecapacity curves between the two hinge models are attributedto differences in the moment-curvature values At an axialload level of minus4320 kips the ultimate curvature capacityis equal to 109 times 10minus3 radin and the associated idealized
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
10 20 30 40 50 60 70 8000Transverse displacement (in)
050
100150200250300350400450500
Base
shea
r (Ki
ps)
Figure 7 Transverse pushover capacity curve of Bridge 3-E
moment capacity is equal to 9013 ksdotft using the automated-hinge model in SAP2000 The corresponding values usingthe user-defined model are equal to 084 times 10minus3 radin and10530 ksdotft respectively
74 Bridge 4-W For brevity the results of Pier 2 widenedcolumns will be discussed The columns in the widened partof Bridge 4-Wwere provided by 4 transverse reinforcementat 30 in on centre However the longitudinal rebars werespliced within the plastic hinge zone with a length of 400 inTable 14 demonstrates that failure of the confined concrete isthe controlling limit state atPb axial load level whereas failurein the lap splice zone is the controlling limit state at all otheraxial load levels
Advances in Materials Science and Engineering 11
Table 14 Plastic curvature capacity of new columns Pier 2 amp 3 of Bridge 4-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus18248 T amp L 00011169 NClowastlowast 00056628 00019116 00011484119875119904 minus2680 T amp L 00030921 NC 00037002 00019116 00012960119875119891 00 T amp L 00046158 NC 00034514 00019116 00013836lowast119875119900 = minus52647 kips and 119875119905 = 16152 kips lowastlowastNC = Not controlling
Table 15 User-defined plastic hinge properties of new columns Pier 2 Bridge 4-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
Yield rotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus18248 24185 2505
1464 00036700011169 002798
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
L119875119887 minus18248 24185 3753
1464 00054900011169 004191
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
Bridge - AutoBridge - User
0
1000
2000
3000
4000
5000
Base
shea
r (ki
ps)
10 20 30 40 50 60 7000Longitudinal displacement (in)
Figure 8 Longitudinal pushover capacity curve of Bridge 3-E
A comparison between the ultimate curvature capacitiesof the columns of this bridge and the columns of Bridge2 shows the effect of the confinement on the value of thecurvature capacity For the compression failure of the uncon-fined concrete limit state at zero axial load level the plasticcurvature capacity was equal to 00001173 radin for Bridge 2while the plastic curvature capacity was 00046158 radin forBridge 4This finding is related to the huge difference in thedetails of the transverse reinforcement of the column sectionin Bridge 2 which has 3 hoops at 12 in and the transversereinforcement of the column section in Bridge 4 which has4 spirals at 30 in This difference in the confinement detailswill allow the section to undergo higher plastic deformations
Table 15 includes the nonlinear properties of the user-defined hinge model It is for the first time that two different
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
050
100150200250300350400450
Base
shea
r (Ki
ps)
10 20 30 40 50 60 70 80 90 100 110 12000Longitudinal displacement (in)
Figure 9 Longitudinal pushover capacity curve of Bridge 4-W
plastic hinge lengths are reported for the column in the samedirection as shown in Table 15 This result is pertained tochange in the controlling deformation limit state from failureof the confined concrete at Pb axial load level to low cyclefatigue of the longitudinal bars at Ps and Pf axial load levelsBased on the FHWA-SRM when at the deformation capacityis controlled by low cycle fatigue of longitudinal bars theeffective plastic hinge length is reduced in length and theeffective plastic hinge is concentrated at the beginning of thelapThis finding brings attention to the limited capabilities ofthe lumped plasticity model in dealing with conditions wherethe plastic hinge length changes with the axial load level
Figures 9 and 10 show the capacity curves of the bridgein the longitudinal and transverse directions respectively
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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CeramicsJournal of
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NanoparticlesJournal of
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International Journal of
Biomaterials
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TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
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Advances in
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MetallurgyJournal of
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BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Materials Science and Engineering 7
Table 7 User-defined plastic hinge properties of Pier 2 old columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
2118 996 00021100001173 000248
119875119904 minus5840 12901 00003543 000750119875119891 00 8702 00011457 002427
L119875119887 minus15430 15544
3491 996 00034800001173 000409
119875119904 minus3020 11118 00006224 002173119875119891 00 8702 00011457 004000
Table 8 Plastic curvature capacity of Pier 2 widened columns Bridge 1-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus17057 T amp L 00011781 NAlowastlowast 00055760 00020899 NA119875119904 minus5840 T 00025015 NA 00040056 00020899 NA119875119904 minus3020 L 00035630 NA 00037024 00020899 NA119875119891 00 T amp L 00068851 NA 00033970 00020899 NAlowast119875119900 = minus45853 kips and 119875119905 = 11740 kips lowastlowastNA = Not applicable
Table 9 User-defined plastic hinge properties of Pier 2 widened columns Bridge 1-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
Plasticrotation
radAxial(kips)
Moment(kipsdotft)
T119875119887 minus17057 195851
2357 1506 00035500011781 002776
119875119904 minus5840 166135 00020899 004925119875119891 00 127137 00020899 004925
L119875119887 minus17057 195851
3595 1506 00054100011781 004235
119875119904 minus3020 149315 00020899 007513119875119891 00 127137 00020899 007513
hinge Also the values of the controlling curvature capacitiesshown in Table 6 identify the effect of the axial force onthe deformation capacity of the plastic hinge For examplethe curvature capacity was equal to 00001173 radin at axialforce of 15430 kips and 00011457 radin at zero axial forcelevel Table 7 shows the moment-curvature ordinates and themoment-axial force interaction surface
The columns of the new piers had confined concretedetails where transverse reinforcement consisted of 4 spiralsat 33 in and column longitudinal reinforcement was notspliced within the plastic hinge zone Therefore bucklingof longitudinal rebars and failure in the lap splice zoneare not applicable as shown in Table 8 Accordingly lowcycle fatigue of longitudinal rebars was the controlling limitstate at Ps and Pf axial load levels while compressionfailure of the confined concrete controlled the curvaturecapacity at Pb axial load level Failure limit state pertaining
to unconfined concrete is not considered for the widenedcolumns because the core concrete has the capability towithstand higher plastic curvature demands after spallingoff the cover concrete Comparison of curvature capacitiesbetween the old and the new columns shows the effect of theconfinement on the deformation capacity of the plastic hingeFor example the plastic curvature capacity of the old columnwas 00011457 radin while the curvature capacity of the newcolumn was 00020899 radin at the zero axial load level
Tables 7 and 9 show that the plastic hinge length inthe transverse direction is less than the plastic hinge lengthin the longitudinal direction which is basically attributedto the difference in the shear span in both directionsSubsequently higher deformation capacities are expectedin the longitudinal direction It should be noted that theplastic hinge length was determined in accordance withthe equations in the FHWA-SRM which depends on the
8 Advances in Materials Science and Engineering
Table 10 Plastic curvature capacity of Pier 2 columns Bridge 2-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020010 00011435119875119904 minus4050 T 00005576 00004913 00038295 00020010 00016161119875119904 minus3020 L 00006404 00006231 00037024 00020010 00017319119875119891 00 T amp L 00011457 00024662 00033434 00020010 00024387lowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
shear span of the member and the yield strain and thediameter of the longitudinal bars However other researchers[21 23] identified that the plastic hinge length dependson the axial load level aspect ratio of the member typeof reinforcement longitudinal and transverse reinforcementratios and concrete strength
Figures 3 and 4 show the capacity curves of Bridge 1-W in the longitudinal and transverse directions respectivelyThe figures also show the capacity curves based on user-defined and automated plastic hinge properties It is clearfrom Figure 3 that the base shear capacity of Pier 2 Pier 3andPier 4 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 177 152 and 154 respectivelyOn the other hand the displacement capacity of Pier 2Pier 3 and Pier 4 in the longitudinal direction usingthe automated-hinge model is higher than the displacementcapacity using user-defined hinge model by 97 189 and97 respectively Similarly Figure 4 shows that base shearcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is less than baseshear capacity using user-defined hinge model by 159157 and 160 respectively However the displacementcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by109 202 and 150 respectively
The differences in the base shear and displacementcapacities of the bridge piers using the two hinge modelsare retained to the differences in the associated moment-curvature relationship At an axial load level of minus5840 kipsPs the ultimate curvature capacity is equal to 633 times10minus4 radin and the associated idealized moment capacityis equal to 11554 ksdotft using the automated-hinge model inSAP2000 The corresponding values using the user-definedmodel are equal to 354 times 10minus4 radin and 12901 ksdotft respec-tively
72 Bridge 2-E Analysis results showed that the behavioursof Pier 2 and Pier 3 are similar thus only the deformationcapacities for Pier 2 are discussed Table 10 shows thatbuckling of longitudinal rebars is the controlling limit stateof Pier 2 columns at Pb and Ps axial load levels in thelongitudinal and transverse directions This behaviour isattributed to the poor confinement details 3 hoops at 120 in
0
50
100
150
200
250
300
350
400
Base
shea
r (Ki
ps)
10
20
90
00
50
60
70
80
30
40
150
120
130
140
160
100
110
Longitudinal displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 3 Longitudinal pushover capacity curve of Bridge 1-W
0100200300400500600700800900
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Transverse displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 4 Transverse pushover capacity curve of Bridge 1-W
spacing As the axial load level decreases the value of theplastic curvature capacity increases until the axial load levelreaches zero Pf whereat compression of the unconfinedconcrete is the controlling limit state Table 11 shows themoment-curvature ordinates and the plastic hinge lengths ofPier 2 columns Similar to the findings for Bridge 1 the
Advances in Materials Science and Engineering 9
Table 11 User-defined plastic hinge properties of Pier 2 columns Bridge 2-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
1741 996 00017300001173 000204
119875119904 minus4050 11822 00004913 000856119875119891 00 8702 00011457 001995
L119875119887 minus15430 15544
2737 996 00027300001173 000321
119875119904 minus3020 11118 00006231 001706119875119891 00 8702 00011457 003136
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
25
50
75
100
125
150
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Longitudinal displacement (in)
Figure 5 Longitudinal pushover capacity curve of Bridge 2-E
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
50
100
150
200
250
300
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 4000Transverse displacement (in)
Figure 6 Transverse pushover capacity curve of Bridge 2-E andBridge 3-E
change in the type of the controlling limit state supports theeffect of the axial load level on the deformation capacity ofthe plastic hinge For example the plastic curvature capacitywas equal to 00001173 radin at axial force of 15430 kips and00011457 radin at zero axial force level
Figures 5 and 6 show the capacity curves of Bridge 2-E in the longitudinal and transverse directions respectively
Figure 5 shows that the base shear capacity of Pier 2 andPier 3 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 164 and 154 respectively Thisdifference is basically due to the fact that the idealizedflexural capacity in the FHWA-SRM is an overstrengthmoment which includes an overstrength factor in addition tothe factor associated with the expected material propertiesThe displacement capacity of Pier 2 and Pier 3 in thelongitudinal direction using the automated-hinge model ishigher than the displacement capacity using user-definedhinge model by 259 and 113 respectively SimilarlyFigure 6 shows that base shear capacity of Pier 2 and Pier3 in the transverse direction using the automated-hingemodel is less than base shear capacity using user-definedhinge model by 160 and 146 respectively However thedisplacement capacity of Pier 2 and Pier 3 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by392 and 220 respectively A close look at the capacitycurves shows higher differences in the displacement capacityin the transverse direction than in the longitudinal directionbetween the two different hingemodelsThis difference is dueto the fact that the expected seismic and gravity axial loadlevel in the transverse direction is higher than the axial loadlevel in the longitudinal direction which in turn shifts thecontrolling capacity limit state to buckling of the longitudinalbars The higher this shift is the higher the differencebetween the curvature values obtained from buckling oflongitudinal rebars limit state and the failure compression ofthe unconfined concrete limit state is The latter is one of thetwo controlling limit states for the automated-hinge model
73 Bridge 3-E The pier columns of this bridge are rect-angular columns with poor confinement details 3 hoops at120 in spacing Table 12 supports the notion that buckling oflongitudinal rebars is the controlling limit state at Pb axialload level as expected from the behaviour of the previousbridges Compression failure of the unconfined concretelimited the curvature capacity of the columns at Ps axial loadlevel while low cycle fatigue of longitudinal rebars was thecontrolling limit state at 119875119891 axial load level Table 13 showsthe user-defined hinge properties of Pier 2 columns whereinthe plastic hinge length has the same value in the longitudinal
10 Advances in Materials Science and Engineering
Table 12 Plastic curvature capacity of Pier 2 columns Bridge 3-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus13001 T amp L 00003102 00002003 00063260 00021910 00015229119875119904 minus4320 T 00008436 00011569 00044562 00021910 00023165119875119904 minus3030 L 00010593 00021517 00042670 00021910 00026375119875119891 00 T amp L 00023579 Tension 00038788 00021910 00045696lowast119875119900 = minus32629 kips and 119875119905 = 6624 kips
Table 13 User-defined plastic hinge properties of Pier 2 columns Bridge 3-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T amp L119875119887 minus13001 13092
1918 1250 0002400002003 000384
119875119904 minus4320 10530 00008436 001618119875119891 00 7347 00021910 004202
L 119875119904 minus3030 9713 1918 1250 00024 00010593 002032
and transverse directions This is because the shear span isidentical in both directions A comparison between the ulti-mate curvature capacities of the columns of this bridge andthe columns of Bridge 2 shows the effect of the column crosssection dimensions on the value of the curvature capacityFor the compression failure of the unconfined concrete limitstate at zero axial load level the plastic curvature capacitywas equal to 00001173 radin for Bridge 2 while the plasticcurvature capacity was 00023579 radin for Bridge 3 Thisfinding is related to the smaller depth of the column sectionin Bridge 3 which is equal to 30 in compared to 36 in forthe columns of Bridge 2 This difference in the section sizewill support the capability of the smaller column section toundergo higher curvature levels for the same level of concretestrain
Figures 7 and 8 show the capacity curves of the bridgein the transverse and longitudinal directions respectivelyThe capacity curve in the longitudinal direction was obtainedfor the whole bridge because the soil behind the bridgeabutments was part of the seismic load resisting systemAccording to Figure 7 the displacement capacity of Pier 2Pier 3 and Pier 4 determined using the automated-hingemodel is higher than the displacement capacity using theuser-defined model by 03 05 and 16 respectivelyHowever the corresponding base shear capacity was lowerby 192 234 and 206 respectively A similar trendwas experienced in the longitudinal direction for the wholebridge with 268 and 44 difference in the displacementand base shear capacities respectively The differences in thecapacity curves between the two hinge models are attributedto differences in the moment-curvature values At an axialload level of minus4320 kips the ultimate curvature capacityis equal to 109 times 10minus3 radin and the associated idealized
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
10 20 30 40 50 60 70 8000Transverse displacement (in)
050
100150200250300350400450500
Base
shea
r (Ki
ps)
Figure 7 Transverse pushover capacity curve of Bridge 3-E
moment capacity is equal to 9013 ksdotft using the automated-hinge model in SAP2000 The corresponding values usingthe user-defined model are equal to 084 times 10minus3 radin and10530 ksdotft respectively
74 Bridge 4-W For brevity the results of Pier 2 widenedcolumns will be discussed The columns in the widened partof Bridge 4-Wwere provided by 4 transverse reinforcementat 30 in on centre However the longitudinal rebars werespliced within the plastic hinge zone with a length of 400 inTable 14 demonstrates that failure of the confined concrete isthe controlling limit state atPb axial load level whereas failurein the lap splice zone is the controlling limit state at all otheraxial load levels
Advances in Materials Science and Engineering 11
Table 14 Plastic curvature capacity of new columns Pier 2 amp 3 of Bridge 4-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus18248 T amp L 00011169 NClowastlowast 00056628 00019116 00011484119875119904 minus2680 T amp L 00030921 NC 00037002 00019116 00012960119875119891 00 T amp L 00046158 NC 00034514 00019116 00013836lowast119875119900 = minus52647 kips and 119875119905 = 16152 kips lowastlowastNC = Not controlling
Table 15 User-defined plastic hinge properties of new columns Pier 2 Bridge 4-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
Yield rotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus18248 24185 2505
1464 00036700011169 002798
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
L119875119887 minus18248 24185 3753
1464 00054900011169 004191
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
Bridge - AutoBridge - User
0
1000
2000
3000
4000
5000
Base
shea
r (ki
ps)
10 20 30 40 50 60 7000Longitudinal displacement (in)
Figure 8 Longitudinal pushover capacity curve of Bridge 3-E
A comparison between the ultimate curvature capacitiesof the columns of this bridge and the columns of Bridge2 shows the effect of the confinement on the value of thecurvature capacity For the compression failure of the uncon-fined concrete limit state at zero axial load level the plasticcurvature capacity was equal to 00001173 radin for Bridge 2while the plastic curvature capacity was 00046158 radin forBridge 4This finding is related to the huge difference in thedetails of the transverse reinforcement of the column sectionin Bridge 2 which has 3 hoops at 12 in and the transversereinforcement of the column section in Bridge 4 which has4 spirals at 30 in This difference in the confinement detailswill allow the section to undergo higher plastic deformations
Table 15 includes the nonlinear properties of the user-defined hinge model It is for the first time that two different
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
050
100150200250300350400450
Base
shea
r (Ki
ps)
10 20 30 40 50 60 70 80 90 100 110 12000Longitudinal displacement (in)
Figure 9 Longitudinal pushover capacity curve of Bridge 4-W
plastic hinge lengths are reported for the column in the samedirection as shown in Table 15 This result is pertained tochange in the controlling deformation limit state from failureof the confined concrete at Pb axial load level to low cyclefatigue of the longitudinal bars at Ps and Pf axial load levelsBased on the FHWA-SRM when at the deformation capacityis controlled by low cycle fatigue of longitudinal bars theeffective plastic hinge length is reduced in length and theeffective plastic hinge is concentrated at the beginning of thelapThis finding brings attention to the limited capabilities ofthe lumped plasticity model in dealing with conditions wherethe plastic hinge length changes with the axial load level
Figures 9 and 10 show the capacity curves of the bridgein the longitudinal and transverse directions respectively
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
8 Advances in Materials Science and Engineering
Table 10 Plastic curvature capacity of Pier 2 columns Bridge 2-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
radin119875119887 minus15430 T amp L 00002197 00001173 00056480 00020010 00011435119875119904 minus4050 T 00005576 00004913 00038295 00020010 00016161119875119904 minus3020 L 00006404 00006231 00037024 00020010 00017319119875119891 00 T amp L 00011457 00024662 00033434 00020010 00024387lowast119875119900 = minus38686 kips and 119875119905 = 7826 kips
shear span of the member and the yield strain and thediameter of the longitudinal bars However other researchers[21 23] identified that the plastic hinge length dependson the axial load level aspect ratio of the member typeof reinforcement longitudinal and transverse reinforcementratios and concrete strength
Figures 3 and 4 show the capacity curves of Bridge 1-W in the longitudinal and transverse directions respectivelyThe figures also show the capacity curves based on user-defined and automated plastic hinge properties It is clearfrom Figure 3 that the base shear capacity of Pier 2 Pier 3andPier 4 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 177 152 and 154 respectivelyOn the other hand the displacement capacity of Pier 2Pier 3 and Pier 4 in the longitudinal direction usingthe automated-hinge model is higher than the displacementcapacity using user-defined hinge model by 97 189 and97 respectively Similarly Figure 4 shows that base shearcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is less than baseshear capacity using user-defined hinge model by 159157 and 160 respectively However the displacementcapacity of Pier 2 Pier 3 and Pier 4 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by109 202 and 150 respectively
The differences in the base shear and displacementcapacities of the bridge piers using the two hinge modelsare retained to the differences in the associated moment-curvature relationship At an axial load level of minus5840 kipsPs the ultimate curvature capacity is equal to 633 times10minus4 radin and the associated idealized moment capacityis equal to 11554 ksdotft using the automated-hinge model inSAP2000 The corresponding values using the user-definedmodel are equal to 354 times 10minus4 radin and 12901 ksdotft respec-tively
72 Bridge 2-E Analysis results showed that the behavioursof Pier 2 and Pier 3 are similar thus only the deformationcapacities for Pier 2 are discussed Table 10 shows thatbuckling of longitudinal rebars is the controlling limit stateof Pier 2 columns at Pb and Ps axial load levels in thelongitudinal and transverse directions This behaviour isattributed to the poor confinement details 3 hoops at 120 in
0
50
100
150
200
250
300
350
400
Base
shea
r (Ki
ps)
10
20
90
00
50
60
70
80
30
40
150
120
130
140
160
100
110
Longitudinal displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 3 Longitudinal pushover capacity curve of Bridge 1-W
0100200300400500600700800900
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Transverse displacement (in)
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
Figure 4 Transverse pushover capacity curve of Bridge 1-W
spacing As the axial load level decreases the value of theplastic curvature capacity increases until the axial load levelreaches zero Pf whereat compression of the unconfinedconcrete is the controlling limit state Table 11 shows themoment-curvature ordinates and the plastic hinge lengths ofPier 2 columns Similar to the findings for Bridge 1 the
Advances in Materials Science and Engineering 9
Table 11 User-defined plastic hinge properties of Pier 2 columns Bridge 2-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
1741 996 00017300001173 000204
119875119904 minus4050 11822 00004913 000856119875119891 00 8702 00011457 001995
L119875119887 minus15430 15544
2737 996 00027300001173 000321
119875119904 minus3020 11118 00006231 001706119875119891 00 8702 00011457 003136
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
25
50
75
100
125
150
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Longitudinal displacement (in)
Figure 5 Longitudinal pushover capacity curve of Bridge 2-E
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
50
100
150
200
250
300
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 4000Transverse displacement (in)
Figure 6 Transverse pushover capacity curve of Bridge 2-E andBridge 3-E
change in the type of the controlling limit state supports theeffect of the axial load level on the deformation capacity ofthe plastic hinge For example the plastic curvature capacitywas equal to 00001173 radin at axial force of 15430 kips and00011457 radin at zero axial force level
Figures 5 and 6 show the capacity curves of Bridge 2-E in the longitudinal and transverse directions respectively
Figure 5 shows that the base shear capacity of Pier 2 andPier 3 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 164 and 154 respectively Thisdifference is basically due to the fact that the idealizedflexural capacity in the FHWA-SRM is an overstrengthmoment which includes an overstrength factor in addition tothe factor associated with the expected material propertiesThe displacement capacity of Pier 2 and Pier 3 in thelongitudinal direction using the automated-hinge model ishigher than the displacement capacity using user-definedhinge model by 259 and 113 respectively SimilarlyFigure 6 shows that base shear capacity of Pier 2 and Pier3 in the transverse direction using the automated-hingemodel is less than base shear capacity using user-definedhinge model by 160 and 146 respectively However thedisplacement capacity of Pier 2 and Pier 3 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by392 and 220 respectively A close look at the capacitycurves shows higher differences in the displacement capacityin the transverse direction than in the longitudinal directionbetween the two different hingemodelsThis difference is dueto the fact that the expected seismic and gravity axial loadlevel in the transverse direction is higher than the axial loadlevel in the longitudinal direction which in turn shifts thecontrolling capacity limit state to buckling of the longitudinalbars The higher this shift is the higher the differencebetween the curvature values obtained from buckling oflongitudinal rebars limit state and the failure compression ofthe unconfined concrete limit state is The latter is one of thetwo controlling limit states for the automated-hinge model
73 Bridge 3-E The pier columns of this bridge are rect-angular columns with poor confinement details 3 hoops at120 in spacing Table 12 supports the notion that buckling oflongitudinal rebars is the controlling limit state at Pb axialload level as expected from the behaviour of the previousbridges Compression failure of the unconfined concretelimited the curvature capacity of the columns at Ps axial loadlevel while low cycle fatigue of longitudinal rebars was thecontrolling limit state at 119875119891 axial load level Table 13 showsthe user-defined hinge properties of Pier 2 columns whereinthe plastic hinge length has the same value in the longitudinal
10 Advances in Materials Science and Engineering
Table 12 Plastic curvature capacity of Pier 2 columns Bridge 3-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus13001 T amp L 00003102 00002003 00063260 00021910 00015229119875119904 minus4320 T 00008436 00011569 00044562 00021910 00023165119875119904 minus3030 L 00010593 00021517 00042670 00021910 00026375119875119891 00 T amp L 00023579 Tension 00038788 00021910 00045696lowast119875119900 = minus32629 kips and 119875119905 = 6624 kips
Table 13 User-defined plastic hinge properties of Pier 2 columns Bridge 3-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T amp L119875119887 minus13001 13092
1918 1250 0002400002003 000384
119875119904 minus4320 10530 00008436 001618119875119891 00 7347 00021910 004202
L 119875119904 minus3030 9713 1918 1250 00024 00010593 002032
and transverse directions This is because the shear span isidentical in both directions A comparison between the ulti-mate curvature capacities of the columns of this bridge andthe columns of Bridge 2 shows the effect of the column crosssection dimensions on the value of the curvature capacityFor the compression failure of the unconfined concrete limitstate at zero axial load level the plastic curvature capacitywas equal to 00001173 radin for Bridge 2 while the plasticcurvature capacity was 00023579 radin for Bridge 3 Thisfinding is related to the smaller depth of the column sectionin Bridge 3 which is equal to 30 in compared to 36 in forthe columns of Bridge 2 This difference in the section sizewill support the capability of the smaller column section toundergo higher curvature levels for the same level of concretestrain
Figures 7 and 8 show the capacity curves of the bridgein the transverse and longitudinal directions respectivelyThe capacity curve in the longitudinal direction was obtainedfor the whole bridge because the soil behind the bridgeabutments was part of the seismic load resisting systemAccording to Figure 7 the displacement capacity of Pier 2Pier 3 and Pier 4 determined using the automated-hingemodel is higher than the displacement capacity using theuser-defined model by 03 05 and 16 respectivelyHowever the corresponding base shear capacity was lowerby 192 234 and 206 respectively A similar trendwas experienced in the longitudinal direction for the wholebridge with 268 and 44 difference in the displacementand base shear capacities respectively The differences in thecapacity curves between the two hinge models are attributedto differences in the moment-curvature values At an axialload level of minus4320 kips the ultimate curvature capacityis equal to 109 times 10minus3 radin and the associated idealized
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
10 20 30 40 50 60 70 8000Transverse displacement (in)
050
100150200250300350400450500
Base
shea
r (Ki
ps)
Figure 7 Transverse pushover capacity curve of Bridge 3-E
moment capacity is equal to 9013 ksdotft using the automated-hinge model in SAP2000 The corresponding values usingthe user-defined model are equal to 084 times 10minus3 radin and10530 ksdotft respectively
74 Bridge 4-W For brevity the results of Pier 2 widenedcolumns will be discussed The columns in the widened partof Bridge 4-Wwere provided by 4 transverse reinforcementat 30 in on centre However the longitudinal rebars werespliced within the plastic hinge zone with a length of 400 inTable 14 demonstrates that failure of the confined concrete isthe controlling limit state atPb axial load level whereas failurein the lap splice zone is the controlling limit state at all otheraxial load levels
Advances in Materials Science and Engineering 11
Table 14 Plastic curvature capacity of new columns Pier 2 amp 3 of Bridge 4-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus18248 T amp L 00011169 NClowastlowast 00056628 00019116 00011484119875119904 minus2680 T amp L 00030921 NC 00037002 00019116 00012960119875119891 00 T amp L 00046158 NC 00034514 00019116 00013836lowast119875119900 = minus52647 kips and 119875119905 = 16152 kips lowastlowastNC = Not controlling
Table 15 User-defined plastic hinge properties of new columns Pier 2 Bridge 4-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
Yield rotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus18248 24185 2505
1464 00036700011169 002798
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
L119875119887 minus18248 24185 3753
1464 00054900011169 004191
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
Bridge - AutoBridge - User
0
1000
2000
3000
4000
5000
Base
shea
r (ki
ps)
10 20 30 40 50 60 7000Longitudinal displacement (in)
Figure 8 Longitudinal pushover capacity curve of Bridge 3-E
A comparison between the ultimate curvature capacitiesof the columns of this bridge and the columns of Bridge2 shows the effect of the confinement on the value of thecurvature capacity For the compression failure of the uncon-fined concrete limit state at zero axial load level the plasticcurvature capacity was equal to 00001173 radin for Bridge 2while the plastic curvature capacity was 00046158 radin forBridge 4This finding is related to the huge difference in thedetails of the transverse reinforcement of the column sectionin Bridge 2 which has 3 hoops at 12 in and the transversereinforcement of the column section in Bridge 4 which has4 spirals at 30 in This difference in the confinement detailswill allow the section to undergo higher plastic deformations
Table 15 includes the nonlinear properties of the user-defined hinge model It is for the first time that two different
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
050
100150200250300350400450
Base
shea
r (Ki
ps)
10 20 30 40 50 60 70 80 90 100 110 12000Longitudinal displacement (in)
Figure 9 Longitudinal pushover capacity curve of Bridge 4-W
plastic hinge lengths are reported for the column in the samedirection as shown in Table 15 This result is pertained tochange in the controlling deformation limit state from failureof the confined concrete at Pb axial load level to low cyclefatigue of the longitudinal bars at Ps and Pf axial load levelsBased on the FHWA-SRM when at the deformation capacityis controlled by low cycle fatigue of longitudinal bars theeffective plastic hinge length is reduced in length and theeffective plastic hinge is concentrated at the beginning of thelapThis finding brings attention to the limited capabilities ofthe lumped plasticity model in dealing with conditions wherethe plastic hinge length changes with the axial load level
Figures 9 and 10 show the capacity curves of the bridgein the longitudinal and transverse directions respectively
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Materials Science and Engineering 9
Table 11 User-defined plastic hinge properties of Pier 2 columns Bridge 2-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus15430 15544
1741 996 00017300001173 000204
119875119904 minus4050 11822 00004913 000856119875119891 00 8702 00011457 001995
L119875119887 minus15430 15544
2737 996 00027300001173 000321
119875119904 minus3020 11118 00006231 001706119875119891 00 8702 00011457 003136
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
25
50
75
100
125
150
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 8000Longitudinal displacement (in)
Figure 5 Longitudinal pushover capacity curve of Bridge 2-E
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
0
50
100
150
200
250
300
Base
shea
r (Ki
ps)
05 10 15 20 25 30 35 4000Transverse displacement (in)
Figure 6 Transverse pushover capacity curve of Bridge 2-E andBridge 3-E
change in the type of the controlling limit state supports theeffect of the axial load level on the deformation capacity ofthe plastic hinge For example the plastic curvature capacitywas equal to 00001173 radin at axial force of 15430 kips and00011457 radin at zero axial force level
Figures 5 and 6 show the capacity curves of Bridge 2-E in the longitudinal and transverse directions respectively
Figure 5 shows that the base shear capacity of Pier 2 andPier 3 in the longitudinal direction using the automated-hinge model is less than base shear capacity using user-defined hinge model by 164 and 154 respectively Thisdifference is basically due to the fact that the idealizedflexural capacity in the FHWA-SRM is an overstrengthmoment which includes an overstrength factor in addition tothe factor associated with the expected material propertiesThe displacement capacity of Pier 2 and Pier 3 in thelongitudinal direction using the automated-hinge model ishigher than the displacement capacity using user-definedhinge model by 259 and 113 respectively SimilarlyFigure 6 shows that base shear capacity of Pier 2 and Pier3 in the transverse direction using the automated-hingemodel is less than base shear capacity using user-definedhinge model by 160 and 146 respectively However thedisplacement capacity of Pier 2 and Pier 3 in the transversedirection using the automated-hinge model is higher thanthe displacement capacity using user-defined hinge model by392 and 220 respectively A close look at the capacitycurves shows higher differences in the displacement capacityin the transverse direction than in the longitudinal directionbetween the two different hingemodelsThis difference is dueto the fact that the expected seismic and gravity axial loadlevel in the transverse direction is higher than the axial loadlevel in the longitudinal direction which in turn shifts thecontrolling capacity limit state to buckling of the longitudinalbars The higher this shift is the higher the differencebetween the curvature values obtained from buckling oflongitudinal rebars limit state and the failure compression ofthe unconfined concrete limit state is The latter is one of thetwo controlling limit states for the automated-hinge model
73 Bridge 3-E The pier columns of this bridge are rect-angular columns with poor confinement details 3 hoops at120 in spacing Table 12 supports the notion that buckling oflongitudinal rebars is the controlling limit state at Pb axialload level as expected from the behaviour of the previousbridges Compression failure of the unconfined concretelimited the curvature capacity of the columns at Ps axial loadlevel while low cycle fatigue of longitudinal rebars was thecontrolling limit state at 119875119891 axial load level Table 13 showsthe user-defined hinge properties of Pier 2 columns whereinthe plastic hinge length has the same value in the longitudinal
10 Advances in Materials Science and Engineering
Table 12 Plastic curvature capacity of Pier 2 columns Bridge 3-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus13001 T amp L 00003102 00002003 00063260 00021910 00015229119875119904 minus4320 T 00008436 00011569 00044562 00021910 00023165119875119904 minus3030 L 00010593 00021517 00042670 00021910 00026375119875119891 00 T amp L 00023579 Tension 00038788 00021910 00045696lowast119875119900 = minus32629 kips and 119875119905 = 6624 kips
Table 13 User-defined plastic hinge properties of Pier 2 columns Bridge 3-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T amp L119875119887 minus13001 13092
1918 1250 0002400002003 000384
119875119904 minus4320 10530 00008436 001618119875119891 00 7347 00021910 004202
L 119875119904 minus3030 9713 1918 1250 00024 00010593 002032
and transverse directions This is because the shear span isidentical in both directions A comparison between the ulti-mate curvature capacities of the columns of this bridge andthe columns of Bridge 2 shows the effect of the column crosssection dimensions on the value of the curvature capacityFor the compression failure of the unconfined concrete limitstate at zero axial load level the plastic curvature capacitywas equal to 00001173 radin for Bridge 2 while the plasticcurvature capacity was 00023579 radin for Bridge 3 Thisfinding is related to the smaller depth of the column sectionin Bridge 3 which is equal to 30 in compared to 36 in forthe columns of Bridge 2 This difference in the section sizewill support the capability of the smaller column section toundergo higher curvature levels for the same level of concretestrain
Figures 7 and 8 show the capacity curves of the bridgein the transverse and longitudinal directions respectivelyThe capacity curve in the longitudinal direction was obtainedfor the whole bridge because the soil behind the bridgeabutments was part of the seismic load resisting systemAccording to Figure 7 the displacement capacity of Pier 2Pier 3 and Pier 4 determined using the automated-hingemodel is higher than the displacement capacity using theuser-defined model by 03 05 and 16 respectivelyHowever the corresponding base shear capacity was lowerby 192 234 and 206 respectively A similar trendwas experienced in the longitudinal direction for the wholebridge with 268 and 44 difference in the displacementand base shear capacities respectively The differences in thecapacity curves between the two hinge models are attributedto differences in the moment-curvature values At an axialload level of minus4320 kips the ultimate curvature capacityis equal to 109 times 10minus3 radin and the associated idealized
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
10 20 30 40 50 60 70 8000Transverse displacement (in)
050
100150200250300350400450500
Base
shea
r (Ki
ps)
Figure 7 Transverse pushover capacity curve of Bridge 3-E
moment capacity is equal to 9013 ksdotft using the automated-hinge model in SAP2000 The corresponding values usingthe user-defined model are equal to 084 times 10minus3 radin and10530 ksdotft respectively
74 Bridge 4-W For brevity the results of Pier 2 widenedcolumns will be discussed The columns in the widened partof Bridge 4-Wwere provided by 4 transverse reinforcementat 30 in on centre However the longitudinal rebars werespliced within the plastic hinge zone with a length of 400 inTable 14 demonstrates that failure of the confined concrete isthe controlling limit state atPb axial load level whereas failurein the lap splice zone is the controlling limit state at all otheraxial load levels
Advances in Materials Science and Engineering 11
Table 14 Plastic curvature capacity of new columns Pier 2 amp 3 of Bridge 4-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus18248 T amp L 00011169 NClowastlowast 00056628 00019116 00011484119875119904 minus2680 T amp L 00030921 NC 00037002 00019116 00012960119875119891 00 T amp L 00046158 NC 00034514 00019116 00013836lowast119875119900 = minus52647 kips and 119875119905 = 16152 kips lowastlowastNC = Not controlling
Table 15 User-defined plastic hinge properties of new columns Pier 2 Bridge 4-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
Yield rotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus18248 24185 2505
1464 00036700011169 002798
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
L119875119887 minus18248 24185 3753
1464 00054900011169 004191
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
Bridge - AutoBridge - User
0
1000
2000
3000
4000
5000
Base
shea
r (ki
ps)
10 20 30 40 50 60 7000Longitudinal displacement (in)
Figure 8 Longitudinal pushover capacity curve of Bridge 3-E
A comparison between the ultimate curvature capacitiesof the columns of this bridge and the columns of Bridge2 shows the effect of the confinement on the value of thecurvature capacity For the compression failure of the uncon-fined concrete limit state at zero axial load level the plasticcurvature capacity was equal to 00001173 radin for Bridge 2while the plastic curvature capacity was 00046158 radin forBridge 4This finding is related to the huge difference in thedetails of the transverse reinforcement of the column sectionin Bridge 2 which has 3 hoops at 12 in and the transversereinforcement of the column section in Bridge 4 which has4 spirals at 30 in This difference in the confinement detailswill allow the section to undergo higher plastic deformations
Table 15 includes the nonlinear properties of the user-defined hinge model It is for the first time that two different
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
050
100150200250300350400450
Base
shea
r (Ki
ps)
10 20 30 40 50 60 70 80 90 100 110 12000Longitudinal displacement (in)
Figure 9 Longitudinal pushover capacity curve of Bridge 4-W
plastic hinge lengths are reported for the column in the samedirection as shown in Table 15 This result is pertained tochange in the controlling deformation limit state from failureof the confined concrete at Pb axial load level to low cyclefatigue of the longitudinal bars at Ps and Pf axial load levelsBased on the FHWA-SRM when at the deformation capacityis controlled by low cycle fatigue of longitudinal bars theeffective plastic hinge length is reduced in length and theeffective plastic hinge is concentrated at the beginning of thelapThis finding brings attention to the limited capabilities ofthe lumped plasticity model in dealing with conditions wherethe plastic hinge length changes with the axial load level
Figures 9 and 10 show the capacity curves of the bridgein the longitudinal and transverse directions respectively
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
10 Advances in Materials Science and Engineering
Table 12 Plastic curvature capacity of Pier 2 columns Bridge 3-E
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureunconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus13001 T amp L 00003102 00002003 00063260 00021910 00015229119875119904 minus4320 T 00008436 00011569 00044562 00021910 00023165119875119904 minus3030 L 00010593 00021517 00042670 00021910 00026375119875119891 00 T amp L 00023579 Tension 00038788 00021910 00045696lowast119875119900 = minus32629 kips and 119875119905 = 6624 kips
Table 13 User-defined plastic hinge properties of Pier 2 columns Bridge 3-E
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
YieldrotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T amp L119875119887 minus13001 13092
1918 1250 0002400002003 000384
119875119904 minus4320 10530 00008436 001618119875119891 00 7347 00021910 004202
L 119875119904 minus3030 9713 1918 1250 00024 00010593 002032
and transverse directions This is because the shear span isidentical in both directions A comparison between the ulti-mate curvature capacities of the columns of this bridge andthe columns of Bridge 2 shows the effect of the column crosssection dimensions on the value of the curvature capacityFor the compression failure of the unconfined concrete limitstate at zero axial load level the plastic curvature capacitywas equal to 00001173 radin for Bridge 2 while the plasticcurvature capacity was 00023579 radin for Bridge 3 Thisfinding is related to the smaller depth of the column sectionin Bridge 3 which is equal to 30 in compared to 36 in forthe columns of Bridge 2 This difference in the section sizewill support the capability of the smaller column section toundergo higher curvature levels for the same level of concretestrain
Figures 7 and 8 show the capacity curves of the bridgein the transverse and longitudinal directions respectivelyThe capacity curve in the longitudinal direction was obtainedfor the whole bridge because the soil behind the bridgeabutments was part of the seismic load resisting systemAccording to Figure 7 the displacement capacity of Pier 2Pier 3 and Pier 4 determined using the automated-hingemodel is higher than the displacement capacity using theuser-defined model by 03 05 and 16 respectivelyHowever the corresponding base shear capacity was lowerby 192 234 and 206 respectively A similar trendwas experienced in the longitudinal direction for the wholebridge with 268 and 44 difference in the displacementand base shear capacities respectively The differences in thecapacity curves between the two hinge models are attributedto differences in the moment-curvature values At an axialload level of minus4320 kips the ultimate curvature capacityis equal to 109 times 10minus3 radin and the associated idealized
Pier 2 - AutoPier 3 - AutoPier 4 - Auto
Pier 2 - UserPier 3 - UserPier 4 - User
10 20 30 40 50 60 70 8000Transverse displacement (in)
050
100150200250300350400450500
Base
shea
r (Ki
ps)
Figure 7 Transverse pushover capacity curve of Bridge 3-E
moment capacity is equal to 9013 ksdotft using the automated-hinge model in SAP2000 The corresponding values usingthe user-defined model are equal to 084 times 10minus3 radin and10530 ksdotft respectively
74 Bridge 4-W For brevity the results of Pier 2 widenedcolumns will be discussed The columns in the widened partof Bridge 4-Wwere provided by 4 transverse reinforcementat 30 in on centre However the longitudinal rebars werespliced within the plastic hinge zone with a length of 400 inTable 14 demonstrates that failure of the confined concrete isthe controlling limit state atPb axial load level whereas failurein the lap splice zone is the controlling limit state at all otheraxial load levels
Advances in Materials Science and Engineering 11
Table 14 Plastic curvature capacity of new columns Pier 2 amp 3 of Bridge 4-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus18248 T amp L 00011169 NClowastlowast 00056628 00019116 00011484119875119904 minus2680 T amp L 00030921 NC 00037002 00019116 00012960119875119891 00 T amp L 00046158 NC 00034514 00019116 00013836lowast119875119900 = minus52647 kips and 119875119905 = 16152 kips lowastlowastNC = Not controlling
Table 15 User-defined plastic hinge properties of new columns Pier 2 Bridge 4-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
Yield rotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus18248 24185 2505
1464 00036700011169 002798
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
L119875119887 minus18248 24185 3753
1464 00054900011169 004191
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
Bridge - AutoBridge - User
0
1000
2000
3000
4000
5000
Base
shea
r (ki
ps)
10 20 30 40 50 60 7000Longitudinal displacement (in)
Figure 8 Longitudinal pushover capacity curve of Bridge 3-E
A comparison between the ultimate curvature capacitiesof the columns of this bridge and the columns of Bridge2 shows the effect of the confinement on the value of thecurvature capacity For the compression failure of the uncon-fined concrete limit state at zero axial load level the plasticcurvature capacity was equal to 00001173 radin for Bridge 2while the plastic curvature capacity was 00046158 radin forBridge 4This finding is related to the huge difference in thedetails of the transverse reinforcement of the column sectionin Bridge 2 which has 3 hoops at 12 in and the transversereinforcement of the column section in Bridge 4 which has4 spirals at 30 in This difference in the confinement detailswill allow the section to undergo higher plastic deformations
Table 15 includes the nonlinear properties of the user-defined hinge model It is for the first time that two different
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
050
100150200250300350400450
Base
shea
r (Ki
ps)
10 20 30 40 50 60 70 80 90 100 110 12000Longitudinal displacement (in)
Figure 9 Longitudinal pushover capacity curve of Bridge 4-W
plastic hinge lengths are reported for the column in the samedirection as shown in Table 15 This result is pertained tochange in the controlling deformation limit state from failureof the confined concrete at Pb axial load level to low cyclefatigue of the longitudinal bars at Ps and Pf axial load levelsBased on the FHWA-SRM when at the deformation capacityis controlled by low cycle fatigue of longitudinal bars theeffective plastic hinge length is reduced in length and theeffective plastic hinge is concentrated at the beginning of thelapThis finding brings attention to the limited capabilities ofthe lumped plasticity model in dealing with conditions wherethe plastic hinge length changes with the axial load level
Figures 9 and 10 show the capacity curves of the bridgein the longitudinal and transverse directions respectively
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Materials Science and Engineering 11
Table 14 Plastic curvature capacity of new columns Pier 2 amp 3 of Bridge 4-W
Axial loadlevel
Axial Forcelowast(kips)
DirectionCompression
failureconfined
Buckling oflong rebars
Fracture oflong rebars
Low-cyclefatigue oflong rebars
Failure in thelap-splicezone
Radin119875119887 minus18248 T amp L 00011169 NClowastlowast 00056628 00019116 00011484119875119904 minus2680 T amp L 00030921 NC 00037002 00019116 00012960119875119891 00 T amp L 00046158 NC 00034514 00019116 00013836lowast119875119900 = minus52647 kips and 119875119905 = 16152 kips lowastlowastNC = Not controlling
Table 15 User-defined plastic hinge properties of new columns Pier 2 Bridge 4-W
Direction Axial loadlevel
Overstrength Plastic hingelength (119871p)
(in)
Yieldcurvatureradinlowast10minus6
Yield rotationRad
Plasticcurvatureradinlowast10minus6
PlasticrotationRad
Axial(kips)
Moment(kipsdotft)
T119875119887 minus18248 24185 2505
1464 00036700011169 002798
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
L119875119887 minus18248 24185 3753
1464 00054900011169 004191
119875119904 minus2680 19231 2312 00012960 002997119875119891 00 17379 00013836 003199
Bridge - AutoBridge - User
0
1000
2000
3000
4000
5000
Base
shea
r (ki
ps)
10 20 30 40 50 60 7000Longitudinal displacement (in)
Figure 8 Longitudinal pushover capacity curve of Bridge 3-E
A comparison between the ultimate curvature capacitiesof the columns of this bridge and the columns of Bridge2 shows the effect of the confinement on the value of thecurvature capacity For the compression failure of the uncon-fined concrete limit state at zero axial load level the plasticcurvature capacity was equal to 00001173 radin for Bridge 2while the plastic curvature capacity was 00046158 radin forBridge 4This finding is related to the huge difference in thedetails of the transverse reinforcement of the column sectionin Bridge 2 which has 3 hoops at 12 in and the transversereinforcement of the column section in Bridge 4 which has4 spirals at 30 in This difference in the confinement detailswill allow the section to undergo higher plastic deformations
Table 15 includes the nonlinear properties of the user-defined hinge model It is for the first time that two different
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
050
100150200250300350400450
Base
shea
r (Ki
ps)
10 20 30 40 50 60 70 80 90 100 110 12000Longitudinal displacement (in)
Figure 9 Longitudinal pushover capacity curve of Bridge 4-W
plastic hinge lengths are reported for the column in the samedirection as shown in Table 15 This result is pertained tochange in the controlling deformation limit state from failureof the confined concrete at Pb axial load level to low cyclefatigue of the longitudinal bars at Ps and Pf axial load levelsBased on the FHWA-SRM when at the deformation capacityis controlled by low cycle fatigue of longitudinal bars theeffective plastic hinge length is reduced in length and theeffective plastic hinge is concentrated at the beginning of thelapThis finding brings attention to the limited capabilities ofthe lumped plasticity model in dealing with conditions wherethe plastic hinge length changes with the axial load level
Figures 9 and 10 show the capacity curves of the bridgein the longitudinal and transverse directions respectively
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
12 Advances in Materials Science and Engineering
Pier 2 - AutoPier 3 - Auto
Pier 2 - UserPier 3 - User
05 10 15 20 25 30 35 40 45 50 55 60 65 7000Transverse displacement (in)
0100200300400500600700800900
Base
shea
r (Ki
ps)
Figure 10 Transverse pushover capacity curve of Bridge 4-W
According to Figure 9 the displacement capacity of Pier 2and Pier 3 determined using the automated-hinge modelis higher than the displacement capacity using the user-defined model by 35 and 30 respectively However thecorresponding base shear capacity was lower by 172 and167 respectively A similar trend was experienced in thetransverse direction with 25 and 32 difference in thedisplacement capacity and 167 and 166 difference in thebase shear capacity for Pier 2 and Pier 3 respectively
8 Conclusions
The conclusions of the study may be summarized as follows
(1) The results of the analyses clearly showed that thecapacity curve depends on the plastic hinge proper-ties The base shear capacity of models with auto-mated hinges is less than the shear capacity of modelswith user-defined hinge properties Also the dis-placement capacity of models with automated hingesis higher than the shear capacity of models with user-defined hinges
(2) User-defined hinge model determined using the pro-visions of the FHWA-SRM is more reliable than theautomated-hinge model since it deals with the effectof possible local failuremechanismswithin the plastichinge zone
(3) Capacity curves of existing and widened highwaybridges are impacted approximately in the samemanner when using different hinge models
(4) It is recommended that bridge design manuals clearlyask bridge designers to evaluate the deformationcapacities of existing bridges and widened bridgeswhich have members that do not meet current seis-mic detailing standards using the provisions of theFHWA-SRM
(5) It is recommended that the software industry like thesoftware SAP2000 includes in its future versions the
capability to model plastic hinges that do not meetcurrent seismic detailing standards
The scope of the present study was limited to flexuredominated conventionally reinforced concrete bridge pierswith the plastic hinge length defined in accordance with theFHWA-SRM Further research needs to be carried out con-sidering shear dominant piers other types of reinforcementsuch as shape memory alloys and other models for plastichinge lengths
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
References
[1] M J N Priestley F Seible and G M Calvi Seismic Design andRetrofit of Bridges John Wiley Sons New York NY USA 1996
[2] N K Shattarat M D Symans D I McLean and W F CoferldquoEvaluation of nonlinear static analysis methods and softwaretools for seismic analysis of highway bridgesrdquo EngineeringStructures vol 30 no 5 pp 1335ndash1345 2008
[3] N Panandikar Hede and K S B Narayan ldquoSensitivity ofpushover curve to material and geometric modellingmdashan ana-lytical investigationrdquo Structures vol 2 pp 91ndash97 2015
[4] R Pinho C Casarotti and S Antoniou ldquoA comparison ofsingle-run pushover analysis techniques for seismic assessmentof bridgesrdquo Earthquake Engineering and Structural Dynamicsvol 36 no 10 pp 1347ndash1362 2007
[5] R Pinho R Monteiro C Casarotti and R Delgado ldquoAssess-ment of continuous span bridges through nonlinear staticproceduresrdquoEarthquake Spectra vol 25 no 1 pp 143ndash159 2009
[6] T Isakovic M P Nino Lazaro andM Fischinger ldquoApplicabilityof pushover methods for the seismic analysis of single-columnbent viaductsrdquo Earthquake Engineering and Structural Dynam-ics vol 37 no 8 pp 1185ndash1202 2008
[7] T S Paraskeva A J Kappos and A G Sextos ldquoExtensionof modal pushover analysis to seismic assessment of bridgesrdquoEarthquake Engineering and Structural Dynamics vol 35 no10 pp 1269ndash1293 2006
[8] S Antoniou and R Pinho ldquoAdvantages and limitations ofadaptive and non-adaptive force-based pushover proceduresrdquoJournal of Earthquake Engineering vol 8 no 4 pp 497ndash5222004
[9] A S Elnashai ldquoAdvanced inelastic static (pushover) analysis forearthquake applicationsrdquo Structural Engineering andMechanicsvol 12 no 1 pp 51ndash69 2001
[10] F Naeim Ten Commandments on Pushover Analysis John AMartin and Associates Los Angeles Calif USA 1999
[11] A K Chopra and R K Goel A Modal Pushover AnalysisProcedure to estimate Seismic Demands for Buildings Theoryand Preliminary Evaluation Pacific Earthquake EngineeringResearch Center College of Engineering University of BerkeleyBerkeley Calif USA 2001
[12] J Mao C Zhai and L Xie ldquoAn improvedmodal pushover anal-ysis procedure for estimating seismic demands of structuresrdquoEarthquake Engineering and Engineering Vibration vol 7 no 1pp 25ndash31 2008
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Materials Science and Engineering 13
[13] H Krawinkler and G D P K Seneviratna ldquoPros and consof a pushover analysis of seismic performance evaluationrdquoEngineering Structures vol 20 no 4-6 pp 452ndash464 1998
[14] FEMA ldquoNEHRP guidelines for the seismic rehabilitation ofbuildingsrdquo Report FEMA-273 (Guidelines) and Report FEMA-274 (Commentary) Washington DC USA 1997
[15] ATC ldquoSeismic evaluation and retrofit of concrete buildingsrdquoTech Rep ATC-40 Applied Technology Council RedwoodCalif USA 1997
[16] FEMA ldquoPrestandard and commentary for the seismic rehabil-itation of buildingsrdquo Tech Rep FEMA 356 American Societyof Civil Engineers for the Federal Emergency ManagementAgency Washington DC USA 2000
[17] CEN ldquoEurocode 8 Design of structures for earthquake resis-tance Part 1 general rules seismic actions and rules forbuildingsrdquo Tech Rep EN1998-1 European Committee forStandardization 2004
[18] FEMA ldquoImprovement of nonlinear static seismic analysis pro-ceduresrdquo Applied Technology Council (ATC-55 Project) FEMA440 Federal Emergency Management Agency WashingtonDC USA 2005
[19] ASCE ldquoSeismic rehabilitation of existing buildingsrdquo Tech RepASCESEI 7- 05 American Society of Civil Engineers 2005
[20] M Inel and H B Ozmen ldquoEffects of plastic hinge properties innonlinear analysis of reinforced concrete buildingsrdquo Engineer-ing Structures vol 28 no 11 pp 1494ndash1502 2006
[21] A H M M Billah and M Shahria Alam ldquoPlastic hinge lengthof shape memory alloy (SMA) reinforced concrete bridge pierrdquoEngineering Structures vol 117 pp 321ndash331 2016
[22] K C Shrestha M S Saiidi and C A Cruz ldquoAdvancedmaterials for control of post-earthquake damage in bridgesrdquoSmartMaterials and Structures vol 24 no 2 Article ID 0250352015
[23] A H M Muntasir Billah and M Shahria Alam ldquoPerformance-based seismic design of shape memory alloy-reinforced con-crete bridge piers I development of performance-based dam-age statesrdquo Journal of Structural Engineering vol 142 no 12Article ID 4016140 2016
[24] CALTRANS ldquoCaltrans seismic design criteriardquo Tech RepVersion 16 California Department of Transportation 2010
[25] CSI ldquoSAP2000 integrated software for structural analysis anddesignrdquo Tech Rep Version 182 Computers and Structures2016
[26] FHWA ldquoSeismic retrofitting manual for highway structurespart 1-bridgesrdquo Publication No FHWA-HRT-06-032 FederalHighway Administration US Department of TransportationWashington DC USA 2006
[27] N Shatarat ldquoEffect of plastic hinge properties in nonlinearanalysis of highway bridgesrdquo Jordan Journal of Civil Engineeringvol 6 no 4 pp 501ndash510 2012
[28] PTC MathCAD ldquoEngineering math softwarerdquo Tech Rep Ver-sion 15 PTC Needham Mass USA 2010
[29] AASHTO Guide Specifications for LRFD Seismic Bridge DesignAmerican Association of State Highway and TransportationOfficials (AASHTO) Washington DC USA 2nd edition 2011with 2012 2014 and 2015 Interim Revisions
[30] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988
[31] LpileAProgram for theAnalysis of Piles andDrilled Shafts underLater Load Version 2014 Ensoft Austin Tex USA 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Submit your manuscripts athttpswwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
