comparisonofnonlinearstaticproceduresandmodeling ... pezeshk, huff... · goel (1999) developed the...

Comparison of Nonlinear Static Procedures and ModelingAssumptions for the Seismic Design of Ordinary Bridges

Ali Hajihashemi1; Shahram Pezeshk, F.ASCE2; and Tim Huff3

Abstract: The three most common nonlinear displacement-based methods were applied in the seismic design of two bridges in westernTennessee, and their results in terms ofmaximum seismic displacement demand and displacement ductility were compared. In addition, two differ-ent support-modeling configurations were evaluated. The results indicate that use of the simplified LRFD procedure results in a displacementdemand higher than that of the other procedures. The support configuration with simplified seat-type abutments with rigid bent foundations pro-vides results not significantly different than those achieved from themore detailed configuration with stub-wall abutment with flexible bent founda-tions, but it required fewer modeling efforts.DOI: 10.1061/(ASCE)SC.1943-5576.0000309.© 2016 American Society of Civil Engineers.

Introduction

The focus of this paper was to evaluate two available nonlinearstatic displacement-based procedures for the design of ordinarybridges in highly seismic regions. The common practice for seismicbridge design is to follow the AASHTO Guide Specifications forLRFD Seismic Bridge Design (AASHTO 2009), herein referred toas AASHTO specifications (Hajihashemi et al. 2013a). In thispaper, two displacement-based methods, which represent two dif-ferent concepts for estimating the inelastic seismic response ofstructural systems, are investigated. Also, two different assump-tions are assessed for modeling the support configuration of bridgestructures. Maximum seismic displacement demand on the struc-tural system and the displacement ductility of the system areselected as the seismic responses. Results from various computerprograms are presented to illustrate the range of responses that canbe obtained from each seismic designmethod.

Nonlinear time history analysis is the ideal approach to evalu-ating structural behavior when subjected to earthquake loadings.However, the process of ground-motion selection and matching/scaling, and the additional computational efforts involved, makethe nonlinear static procedure (NSP), commonly referred to aspushover analysis, more attractive when designing regular bridgestructures. Pushover analysis provides a compromise between thesimplification of linear static analysis and the accuracy of nonlin-ear dynamic analysis (Gencturk and Elnashai 2008). In the cur-rent AASHTO-specifications method, seismic demand on abridge structure is determined through a linear elastic responsespectrum analysis. For bridges in Seismic Design Category(SDC) B or C, the AASHTO specifications provide implicit

formulas for displacement capacity, DC. For SDC D bridges, thepushover analysis must be used to determine the reliable displace-ment capacity, DC, of a bridge structure or bent frame as it reachesits limit of structural stability. The procedure is similar to that pre-sented in the Caltrans seismic design criteria (Caltrans 2010) fordetermining the seismic demand and displacement capacity forordinary bridges.

Conventional pushover analysis requires the application of anincreasing but invariant lateral load pattern on the structural system.Several multimodal pushover procedures have been proposed [e.g.,Chopra and Goel (2002)] to take the effects of all significant modesinto account. More recently, many so-called adaptive pushovermethods have been introduced [e.g., Kunnath (2004)] to considerthe progressive stiffness degradation of the structure through updat-ing the lateral forces vector at each step of analysis (Hajihashemi etal. 2013a). One of the most popular uses of pushover analysis is incapacity spectrummethods (CSMs), in which the pushover curve inthe force-displacement format is converted into a capacity diagramof the system in acceleration-displacement-response-spectrum(ADRS) format. The original CSMs estimated the earthquakeresponse of an inelastic system by replacing it with an equivalentlinear system, the accuracy of which depends mostly on adoptingthe equivalent viscous damping model. Combining the advantageof visual representation in ADRS format and the superior physicalbases of constant-ductility inelastic demand spectra, Chopra andGoel (1999) developed the capacity-demand-diagram method.They suggested obtaining inelastic acceleration-demand diagramsfrom their elastic counterparts by using reduction factors, Rm. Thecapacity-demand-diagram method produces results that are up to50%more accurate than those obtained from equivalent elastic pro-cedures (Chopra and Goel 1999, 2000). FEMA conducted theATC-55 Project, released as FEMA-440 (FEMA 2005), to evaluatethe accuracy of available CSMs. FEMA-440 (FEMA 2005) pro-posed three modified equivalent linearization procedures; amongthem, Procedure C is practically more attractive. This noniterativeprocedure determines the maximum seismic displacement as theintersection point of the capacity curve and the loci of possible per-formance points on different demand diagrams obtained frommodi-fied equivalent viscous damping relationships.

A variety of computer programs are available for performing practi-cal seismic analysis of structures. A survey of bridge engineering con-sulting firms and state departments of transportation (DOTs) found thatSAP200015.1andADINA8.6.4are themostpopular softwareprograms

1Graduate Research Assistant, Univ. of Memphis, 100 EngineeringAdministration Building, Memphis, TN 38152.

2Chair and Professor, Univ. of Memphis, 104B Engineering ScienceBuilding, Memphis, TN 38152 (corresponding author). ORCID: http://orcid.org/0000-0002-4367-1184. E-mail: [email protected]

3Civil Engineering Manager 2, Tennessee Dept. of TransportationStructures, 505 Deaderick St., Suite 1100, J. K. Polk Building, Nashville,TN 37243.

Note. This manuscript was submitted on June 22, 2016; approved onSeptember 11, 2016; published online on November 2, 2016. Discussionperiod open until April 2, 2017; separate discussions must be submittedfor individual papers. This paper is part of the Practice Periodical onStructural Design and Construction, © ASCE, ISSN 1084-0680.

© ASCE 04016022-1 Pract. Period. Struct. Des. Constr.

Pract. Period. Struct. Des. Constr., 2017, 22(2): 04016022

Dow

nloa

ded

from

asc

elib

rary

.org

by

Mem

phis

, Uni

vers

ity o

f on

10/

13/1

7. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

http://dx.doi.org/10.1061/(ASCE)SC.1943-5576.0000309

http://orcid.org/0000-0002-4367-1184

http://orcid.org/0000-0002-4367-1184

mailto:[email protected]

for performing nonlinear analysis (Shattarat et al. 2008). In recentyears, OpenSees 2.3.2, as an open-source finite-element platformfor earthquake-engineering simulations, has increasingly beendrawing attention for both research and practice purposes [e.g.,Kalkan and Kwong (2011)]. These three computer programs wereselected to perform the nonlinear static analysis in this study.

Case Study: Bridges andModeling Properties

Two case-study bridges were investigated in this study: the StateRoute 21 over Interstate 69 bridge (herein referred to as the SR21-I69 bridge), a two-span continuous bridge with prestressed bulb Tgirders and a four-column bent frame, and the Forrester Road overInterstate 69 bridge (herein referred to as the Forrester Rd-I69bridge), a two-span continuous bridge with steel plate girders and atwo-column bent frame. Figs. 1 and 2 show the elevation and a typi-cal cross section of the bent frame of each bridge, respectively(Hajihashemi and Pezeshk 2012; Hajihashemi et al. 2012, 2013a, b).

Both bridges were designed originally by Tennessee Departmentof Transportation (TDOT) engineers following the AASHTO-specifications procedure. To create the finite-element model of thebridges, the superstructure was represented by a single line ofmultiple three-dimensional frame elements passing through thecross-sectional centroid of the superstructure. The columns and

the cap beam were represented by single three-dimensional frameelements that passed through the geometric center and middepth,respectively. A constraint was used to tie the superstructure centerjoint to the midpoint of the cap beam. Detailed descriptions of thematerial, member, loading, and modeling properties were pre-sented by Hajihashemi (2013).

Blow count data and inferred shear wave-velocity data indicatedAASHTO Class D conditions for both sites. Fig. 3 shows a sampleshear wave-velocity profile for each site location, constructed onthe basis of available bore logs. The seismic behavior of the bridgeswas evaluated in the transverse direction only. Because the SD1value for each bridge was higher than 0.5g, both were assigned tothe SDCD (AASHTO 2009).

A configuration with seat-type abutments with rigid bent founda-tions (referred to herein as basic support) was used in the TDOT designprocess in which the column footings were fixed against both transla-tion and rotation in all directions, and the abutments were assumed toprovide fixed support for rotation in all directions and vertical transla-tion. The longitudinal and transverse translational degrees of freedomat the abutments were modeled by linear springs, the stiffness of whichwas calculated following Caltrans Bridge Design Specifications(Caltrans 2004). In addition to the basic-support configuration, a morerealistic configuration with stub-wall abutment with flexible bent foun-dations (herein referred to as nonlinear-springs support) was studied.In a joint research project between the University of Memphis and the

Fig. 1. Elevation view of the (a) SR21-I69 and (b) Forrester Rd-I69 bridges

Fig. 2. Typical cross section of the (a) SR21-I69 and (b) Forrester Rd-I69 bridges



Dow

nloa

ded

from

asc

elib

rary

.org

by

Mem

phis

, Uni

vers

ity o

f on

10/

13/1

7. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

University of Tennessee Knoxville (Vasheghani-Farahani et al. 2010),detailed models of abutments and column footings were createdusing appropriate spring/damper series at different depths of pileelements to account for soil–structure interaction effects. Asrequested by the Tennessee DOT Structures division and to makethe findings of the joint study comparable with those of the currentbasic-support configuration, a pushover analysis was performedfor each foundation model, and force-displacement relationshipsof inelastic springs in horizontal directions were constructed(Figs. 4 and 5). These inelastic springs can easily replace the elas-tic springs used in the basic-support configuration while more pre-cisely representing foundation behavior.

Selected Computer Software Programs

When using SAP2000, the nonlinearity of the system was modeledby assigning concentrated plastic hinges at the ends of each columnelement. The computer program CONSEC 1.4 was used to perform

moment-curvature analysis for various axial load values, the resultsof which were used to model the SAP2000 user-defined hinge prop-erties. The computer program ADINA 8.6.4 can perform pushoveranalysis, but unlike SAP2000, there is no specific utility available inADINA to aid the user. Tomodel nonlinearity inADINA, the columnelements were defined as beam elements in which the stiffness wasdefined by a moment-curvature rigidity model. This model accu-rately captures the dependency of moment-curvature data on theaxial force. In the case of using OpenSees, the nonlinearity of thesystem was taken into account when defining the columns’ section.The column section was modeled as a fiber section. A step-by-stepmodeling and analyzing process using each of the computer pro-grams was presented by Hajihashemi (2013).

Modal Analysis

Before the seismic analysis, the SAP2000 computer program wasused to perform an eigenvalue analysis. The dominant mode(s) in

-80000

-60000

-40000

-20000

0

20000

40000

60000

-0.2 -0.1 0 0.1

F (k

N)

D (m)

(a)

-15000

-10000

-5000

0

5000

10000

15000

-0.15 -0.1 -0.05 0 0.05 0.1 0.15

F (k

N)

D (m)

(b)

-10000

-5000

0

5000

10000

-0.1 -0.05 0 0.05 0.1

F (k

N)

D (m)

(c)East Abutment West Abutment Interior Footings Exterior Footings

Fig. 4. Force-displacement curve for nonlinear springs at the SR21-I69 bridge: (a) abutments in the longitudinal direction; (b) abutments in the trans-verse direction; (c) footings in both directions

0

10

20

30

40

50

100 300 500

Dep

th (m

)

Shear Wave Velocity (m/sec)

The SR21-I69 BridgeSite Location

The Forrester Rd-I69Bridge Site Location

Fig. 3. Shear wave-velocity profiles



Dow

nloa

ded

from

asc

elib

rary

.org

by

Mem

phis

, Uni

vers

ity o

f on

10/

13/1

7. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

transverse direction that captures at least 90% of the total modalmass participating ratio in that direction was determined (Table 1).In each case, an assumed 5% modal damping for each mode ofvibration was used. For the nonlinear-spring-support cases, the ini-tial stiffness of each nonlinear spring was used as the effectivesupport-spring stiffness.

Nonlinear Static (Pushover) Analysis

In this study, the pushover curves were obtained by pushing thebridge structure in the transverse direction after analyzing thebridge under the effect of gravity loads. The monitoring variablewas defined as the transverse displacement at the control node,located at the intersection of the cap beam and the superstructure.The analysis was to stop when the monitored displacement reached0.23 m. The gradually increasing lateral forces were defined using aforce distribution s = mu, wherem is the structural mass matrix andu is the fundamental transverse mode shape. To perform the push-over analysis, the lateral load pattern was applied to the superstruc-ture joints only.

Pushover Curves

SAP2000 was used first to construct the pushover curve for thebasic-support and nonlinear-springs-support models. For theSR21-I69 bridge with the nonlinear-springs-support configurationonly, because its higher transverse modes are significant (Fig. 5),multimodal pushover analysis (MPA) was performed followingthe MPA procedure (Chopra and Goel 2002). Fig. 6 shows the

pushover analysis results for both of the studied bridges using theSAP2000 program.

With the ADINA computer program, constant and linear timefunctions were defined to apply the gravity loads and pushover anal-ysis lateral load, respectively, for the basic-support models only.Last, OpenSees was used to develop the pushover curves for thebasic-support models only. The model was first subjected to gravityloads. Then, the gravity load effects of the system were saved byusing the loadConst command, and the pushover lateral load wasapplied to the structure in an incremental fashion. The pushovercurves obtained for the basic-support models using each of theselected software programs are shown in Fig. 7.

Capacity Diagrams

The pushover curves in the base shear (Vb) versus control node dis-placement (uN) format were converted to capacity diagrams in thespectral acceleration (Sa) versus the spectral displacement (Sd) for-mat using the conversion factors, as presented in Eqs. (1) and (2).

Sa ¼ Vb

M�1

(1)

Sd ¼ uNC1f N1

(2)

whereM�1 = effective modal mass of the fundamental mode; wN1 =

modal amplitude of the control node in the fundamental mode; andC1 = modal participation factor of the fundamental mode. The mid-dle node of the superstructure was taken to be the control node. The

-10000

-8000

-6000

-4000

-2000

0

2000

4000

-0.2 -0.1 0 0.1 0.2

F (k

N)

D (m)

(a) (b)

-3000

-2000

-1000

0

1000

2000

3000

-0.1 -0.05 0 0.05 0.1

F (k

N)

D (m)

Transverse Direction Longitudinal Direction Footings

Fig. 5. Force-displacement curve for nonlinear springs at the Forrester Rd-I69 bridge: (a) abutments; (b) footings in both directions

Table 1.Modal Analysis Results Using SAP2000

Case-study bridge Support configuration Number of dominant transverse modes Period [T (s)] Modal participating mass ratio (%)

SR21-I69 Basic 2 0.84 99.7Nonlinear springs 1 0.71 78.9

6 0.3 12.6Forrester Rd-I69 Basic 1 0.75 99.8

Nonlinear springs 1 0.61 96.1



Dow

nloa

ded

from

asc

elib

rary

.org

by

Mem

phis

, Uni

vers

ity o

f on

10/

13/1

7. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

conversion factors were obtained and are summarized in Table 2,where mj = lumped mass at the jth node, w j1 = jth node modal am-plitude in the fundamental mode, and N = number of modes, asdefined as

M�1 ¼

PNj¼1

mjf j1

!2

PNj¼1

mjf2j1

(3)

and

C1 ¼

PNj¼1

mjf j1

PNj¼1

mjf2j1

(4)

In every displacement-based method, it is necessary to determinethe ductility of the structure at different points along the capacitycurve. This property can be achieved by replacing the actual capacitycurve with its bilinear representation, on which the yielding spectraldisplacement, (Sd)y, is clearly determined. Fig. 8 displays all bilinearcapacity diagrams for the SR21-I69 and Forrester Rd-I69 bridges.

0

5000

10000

15000

20000

25000

0.00 0.05 0.10 0.15 0.20 0.25

Bas

e Sh

ear (

kN)

Control Node Displacement (m)

0

2000

4000

6000

8000

10000

12000

14000

0.00 0.05 0.10 0.15 0.20 0.25

Bas

e Sh

ear (

kN)


Basic Support Model

Nonlinear Springs Support Model (Single Mode Pushover)Nonlinear Springs Support Model (Multi-Modal Pushover)

(a) (b)

Fig. 6. Pushover curves for different support configurations using the SAP2000 computer program: (a) SR21-I69 bridge; (b) Forrester Rd-I69 bridge

0

5000

10000

15000

20000

25000

0.00 0.05 0.10 0.15 0.20 0.25

Bas

e Sh

ear (

kN)


0

2000

4000

6000

8000

10000

12000

14000

0.00 0.05 0.10 0.15 0.20 0.25

Bas

e Sh

ear (

kN)


SAP 2000 ADINA OpenSees

(a) (b)

Fig. 7. Pushover curves for the basic-support models obtained from different computer programs: (a) SR21-I69 bridge; (b) Forrester Rd-I69 bridge



Dow

nloa

ded

from

asc

elib

rary

.org

by

Mem

phis

, Uni

vers

ity o

f on

10/

13/1

7. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

Displacement-Based Analysis Procedures

AASHTO-Specifications Procedure

On the basis of the TDOT design documents, the finite-element modelof the bridge supported by the basic-support configuration had beensubjected to the design response spectrum, and themaximum transversedisplacement of the bent frame was calculated through the completequadratic combination (CQC) modal combination. The seismic dis-placement demands,DD, in the transverse direction were determined tobe 0.114 and 0.102 m for the SR21-I69 and Forrester Rd-I69 bridges,respectively. The displacement capacity of the bent frame was thendetermined using TDOT-developed pushover-analysis spreadsheets.The idealized yield displacements, Dy, corresponding to the idealizedyield curvatures, w yi, were determined to be 0.027 and 0.034m for theSR21-I69 and Forrester Rd-I69 bridges, respectively. Last, the seismicdisplacement capacities, DC, of the bent frame had been calculated as0.118 m for the SR21-I69 bridge and 0.146 m for the Forrester Rd-I69bridge. In terms of displacement ductility demands, mD =Dmax/Dy, thevalues of 4.202 and 2.997 had been calculated for the SR21-I69 andForrester Rd-I69 bridges, respectively.

FEMA-440 (FEMA 2005) Procedure C

Similarly, the next two displacement-based procedures use the inter-section of the capacity (pushover) curve and the demand diagram toestimate the maximum seismic displacement, which is called theperformance point. They differ in reducing the elastic (m = 1)response spectrum to an inelastic (m i) demand diagram. FEMA-440

Procedure C (FEMA 2005) uses the modified acceleration-responsespectrum for multiple assumed solutions (Sapi, Sdpi) and the corre-sponding ductilities to generate the loci of possible performancepoints. The actual performance point is located at the intersection ofthis locus and the capacity curve (FEMA 2005). Procedure C, simi-lar to the other procedures in FEMA-440 (FEMA 2005), is an equiv-alent linearization procedure that adjusts the initial response spec-trum to the appropriate level of effective damping, b eff, using Eq.(5) (Hajihashemi et al. 2013b).

Sað Þm i ¼ Mi �Sað Þm¼1

45:6�ln b effð Þi

(5)

where, m i = assumed ductility; and Mi = acceleration-modificationfactor, as defined in the FEMA-440 document (FEMA 2005). Byconstructing a family of demand curves for selected m values (2.0,2.5, 3.0, and 3.5), the spectral displacement of the performancepoint was determined for each of the SAP2000 basic-support andnonlinear-springs-support models. Fig. 9 illustrates the procedureapplied for the basic-support model of the Forrester Rd-I69 bridgeas a typical example.

Capacity-Demand-DiagramMethod

The third displacement-based seismic design procedure is thecapacity-demand-diagram method (Chopra and Goel 1999). Thisprocedure determines the demand by analyzing the inelastic systeminstead of equivalent linear systems in the CSMs of ATC-40(Applied Technology Council 1996). A family of constant-ductilitydemand spectra is constructed by reducing the elastic design spec-trum by appropriate ductility-dependent factors (Hajihashemi et al.2013b), Ry [Eq. (6)]

ðSaÞm i ¼ ðSaÞm¼1=ðRyÞm i (6)

Various Ry-m -T equations were presented by Chopra (2007). Inthis study, the Newmark-Hall equations were used. The demandcurves were plotted on the same chart as the bilinear capacity

0

0.05

0.1

0.15

0.2

0 0.05 0.1 0.15 0.2 0.25

Spec

tral A

ccel

erat

ion

(m/s

2 )

Spectral Displacement (m)

0

0.05

0.1

0.15

0.2

0.25

0 0.05 0.1 0.15 0.2 0.25

Spec

tral A

ccel

erat

ion

(m/s

2 )


SAP 2000 ADINA OpenSees

Single-Mode Pushover Multi-Mode Pushover

Basic Support Model:

Nonlinear Spring Support Model:

(a) (b)

Fig. 8. Bilinear capacity diagrams: (a) SR21-I69 bridge; (b) Forrester Rd-I69 bridge

Table 2. Capacity-Curve Conversion Factors

Case-study bridge Support configuration M�1 (kN·s

2/m) C1 (m/m)

SR21-I69 Basic 131,561 0.9928Nonlinear springs 104,172 1.2138

Forrester Rd-I69 Basic 48,862 0.9885Nonlinear springs 47,044 0.9836



Dow

nloa

ded

from

asc

elib

rary

.org

by

Mem

phis

, Uni

vers

ity o

f on

10/

13/1

7. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

spectrum for each combination of support configuration and utilizedcomputer software for selected values of m (1.5, 1.75, 2.0, and 2.25).At one relevant intersection point, the ductility factor calculated fromthe ratio of the displacement of the point to the yielding displacementmatches the ductility value associated with the intersecting demandcurve, which determines the performance point of the structure.Fig. 10 shows the capacity-demand-diagram procedure for theForrester Rd-I69 bridge with the basic-support configuration(Hajihashemi and Pezeshk 2012; Hajihashemi et al. 2012, 2013a, b).

Conclusions and Discussion

The results of this study indicate that the current AASHTO-specifications method predicts higher response values than thoseof the other two evaluated methods proposed by Chopra andGoel (1999) and FEMA-440 (FEMA 2005) in terms of the seis-mic displacement demand (maximum displacement) on thebridge systems and the displacement ductility demand of thesystem. Fig. 11 displays a comparison of the seismic response

0

0.1

0.2

0.3

0 0.05 0.1 0.15 0.2

Spec

tral A

ccel

erat

ion

(m/s

2 )


Bilinear Capacity Diagram Family of Demand Curves

Performance Point Possible Performance Points

Fig. 10. Seismic analysis of the basic-support model of the Forrester-I69 bridge using the capacity-demand-diagrammethod

0

0.1

0.2

0.3

0 0.05 0.1 0.15 0.2

Spec

tral A

ccel

erat

ion

(m/s

2 )


Radial Secant Period Lines Bilinear Capacity Diagram Family of Demand Curves

Performance Point Locus of Possible Performance Points

Fig. 9. Seismic analysis of the basic-support model of the Forrester Rd-I69 bridge using FEMA-440 Procedure C



Dow

nloa

ded

from

asc

elib

rary

.org

by

Mem

phis

, Uni

vers

ity o

f on

10/

13/1

7. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

of both case-study bridges with the basic-support configurationobtained from different displacement-based analysis methods.

As shown in Figs. 12 and 13, in the case of using thecapacity-demand-diagram method, using the basic-support config-uration results in almost the same values for the seismic responseof both bridges when compared to the same variables obtainedfrom the nonlinear-springs-support models (Hajihashemi andPezeshk 2012; Hajihashemi et al. 2012, 2013a, and 2013b).When using FEMA-440 Procedure C (FEMA 2005), although thebasic-support configuration provides higher values than does thenonlinear-springs-support configuration, the difference is still not

significant (especially for the SR21-I69 bridge) (Fig. 13).Therefore, the configuration with simplified seat-type abutmentswith rigid bent foundations (basic) support can be considered arelatively more efficient way to model the bridge than the moredetailed configuration with stub-wall abutment with flexible bentfoundations (nonlinear-springs) support, because it requires muchless computational effort. In addition, using the multimodal push-over procedure makes slight changes in the seismic design resultsfor the SR21-I69 bridge with the nonlinear-springs-support con-figuration when compared with the results of the single-modepushover procedure (Fig. 13).

0 0.02 0.04 0.06 0.08 0.1

FEMA-440 Procedure C

Capacity-demand-diagram Method

Seismic Displacement Demand, ΔD, (m)

0 0.5 1 1.5 2 2.5



Displacement Ductility, μD

Basic Support Configuration

Nonlinear Springs Support Configuration (Single-Mode Pushover)

Fig. 12. Seismic response of the Forrester Rd-I69 bridge using various analysis methods

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

SR21-I69 Bridge Forrester Rd-I69Bridge

Dis

plac

emen

t Duc

tility

, μD

0

0.04

0.08

0.12

SR21-I69Bridge

Forrester Rd-I69 Bridge

Seis

mic

Dis

plac

emen

t Dem

and,

ΔD, (

m)

AASHTO Specifications Procedure

FEMA-440Procedure C

Capacity-Demand-DiagramMethod

(a) (b)

Fig. 11. Seismic response of the bridges with the basic-support configuration using different displacement-based methods



Dow

nloa

ded

from

asc

elib

rary

.org

by

Mem

phis

, Uni

vers

ity o

f on

10/

13/1

7. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

Fig. 14 shows the seismic displacement demand and the dis-placement ductility that resulted from the seismic analysis of bothcase-study bridges by using the capacity-demand-diagram method;different computer software packages were used to perform the

pushover analysis. Theoretically, the ability to model the distributednonlinearity in ADINA andOpenSeeswould provide results that aremore accurate than those of SAP2000. The results of this study(Fig. 14) indicate that SAP2000 computed the seismic response

0

0.5

1

1.5

2

2.5


Dis

plac

emen

t Duc

tility

, μD

0

0.02

0.04

0.06

0.08


Seis

mic

Dis

plac

emen

t Dem

and,

ΔD, (

m)

SAP2000

ADINA

OpenSees

Fig. 14. Seismic response of the bridges with the basic-support configuration using different computer programs

0 0.02 0.04 0.06 0.08 0.1



Seismic Displacement Demand, ΔD, (m)

0 0.5 1 1.5 2 2.5 3



Displacement Ductility, μD

Basic Support Configuration

Nonlinear Springs Support Configuration (Single-Mode Pushover)

Nonlinear Springs Support Configuration (Multi-Modal Pushover)

Fig. 13. Seismic response of the SR21-I69 bridge using various analysis methods



Dow

nloa

ded

from

asc

elib

rary

.org

by

Mem

phis

, Uni

vers

ity o

f on

10/

13/1

7. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

quantities of both case-study bridges in acceptable agreement withthe same results obtained from the other more powerful computersoftware programs. In contrast, SAP2000 is well suited for perform-ing pushover analysis and is largely graphical in nature, which ena-bles straightforward data input and interpretation of results.

Acknowledgments

This project was funded by the TDOT. The authors thank Mr. Ed.Wasserman, Mr. Wayne Seger, Mr. Houston Walker, and Ms.Kathleen McLaughlin.

References

ADINA 8.6.4 [Computer software]. ADINAR&D, Inc., Watertown,MA.AASHTO. (2009). AASHTO guide specifications for LRFD seismic bridge

design, Washington, DC.Applied Technology Council. (1996). “Seismic evaluation and retrofit of

concrete buildings.” Rep. ATC-40, Redwood City, CA.Caltrans (California Dept. of Transportation). (2004). Caltrans bridge

design specifications, Sacramento, CA.Caltrans (California Dept. of Transportation). (2010). Seismic design

criteria: Version 1.6, Sacramento, CA. hhttp://www.dot.ca.gov/hq/esc/earthquake_engineering/sdc/documents/2010-11-17_SDC_1.6_Full_Version_OEE_Release.pdfi (Oct. 22, 2016).

Chopra, A. K. (2007). Dynamics of structures: Theory and applications toearthquake engineering, 3rd Ed., Prentice-Hall, Englewood Cliffs, NJ.

Chopra, A. K., and Goel, R. K. (1999). “Capacity-demand-diagram meth-ods based on inelastic design.” Earthquake Spectra, 15(4), 637–656.

Chopra, A. K., and Goel, R. K. (2000). “Evaluation of NSP to estimate seis-mic deformation: SDF systems.” J. Struct. Eng., 10.1061/(ASCE)0733-9445(2000)126:4(482), 482–490.

Chopra, A. K., and Goel, R. K. (2002). “A modal pushover analysis proce-dure for estimating seismic demands for buildings.” Earthquake Eng.Struct. Dyn., 31(3), 561–582.

CONSEC 1.4 [Computer software]. R.Matthews, Orange, CA.FEMA. (2005). “Improvement of nonlinear static seismic analysis proce-

dures.” FEMA-440, Washington, DC.

Gencturk, B., and Elnashai, A. S. (2008). “Development and application ofan advanced capacity spectrum method.” Eng. Struct., 30(11),3345–3354.

Hajihashemi, A. (2013). “Comparison and evaluation of displacement-based methods and modeling assumptions for design of ordinary bridgesin high seismic regions using various computer software.” Doctoral dis-sertation, Univ. ofMemphis, Memphis, TN.

Hajihashemi, A., and Pezeshk, S. (2012). “Applying displacement-basedmethods in seismic design of the SRE21-I69 bridge.” Proc., EERI 2013Annual Meeting, Earthquake Engineering Research Institute, Oakland,CA.

Hajihashemi, A., Pezeshk, S., and Burdette, E. G. (2012). “Applying differ-ent support modeling assumptions in seismic analysis of the SR21-I69bridge.” Proc., 7th National Seismic Conf. on Bridges and Highways(7NSC), Federal Highway Administration,Washington, DC.

Hajihashemi, A., Pezeshk, S., and Burdette, E. (2013a). “Effects of differentsupport modeling assumptions on the seismic response of ordinarybridges.” Structures Congress, 531–540.

Hajihashemi, A., Pezeshk, S., and Burdette, E. G. (2013b). “Investigatingthe efficiency and accuracy of available displacement-based methodsand modeling assumptions in seismic design of bridges.” Proc., EERI2013 Annual Meeting, ASCE, Reston, VA.

Kalkan, E., and Kwong, N. S. (2011). “Documentation for assessment ofmodal pushover-based scaling procedure for nonlinear response historyanalysis of ‘ordinary standard’ bridges.” U.S. Geological Survey Open-File Rep. 2010–1328, U.S. Geological Survey, Reston, VA. hhttp://pubs.usgs.gov/of/2010/1328/i (Oct. 22, 2016).

Kunnath, S. K. (2004). “Identification of modal combination for nonlinearstatic analysis of building structures.” Comput.-Aided Civ. Infrastruct.Eng., 19(4), 246–259.

OpenSees 2.3.2 [Computer software]. Pacific Earthquake EngineeringCenter, Univ. of California, Berkeley, CA.

SAP2000 15.1 [Computer software]. Computers and Structures, Inc.,Berkeley, CA.

Shattarat, N. K., Syman, M. D., McLean, D. I., and Cofer, W. F. (2008).“Evaluation of nonlinear static analysis methods and software tools forseismic analysis of highway bridges.” Eng. Struct., 30(5), 1335–1345.

Vasheghani-Farahani, R., Zhao, Q., and Burdette, E. G. (2010). “Seismicanalysis of integral abutment bridge in Tennessee, including soil-structure interaction.” Transportation Research Record, 2201(2),70–79.



Dow

nloa

ded

from

asc

elib

rary

.org

by

Mem

phis

, Uni

vers

ity o

f on

10/

13/1

7. C

opyr

ight

ASC

E. F

or p

erso

nal u

se o

nly;

all

righ

ts r

eser

ved.

http://www.dot.ca.gov/hq/esc/earthquake_engineering/sdc/documents/2010-11-17_SDC_1.6_Full_Version_OEE_Release.pdf



http://dx.doi.org/10.1193/1.1586065

http://dx.doi.org/10.1061/(ASCE)0733-9445(2000)126:4(482)

http://dx.doi.org/10.1061/(ASCE)0733-9445(2000)126:4(482)

http://dx.doi.org/10.1002/eqe.144

http://dx.doi.org/10.1002/eqe.144

http://dx.doi.org/10.1016/j.engstruct.2008.05.008


http://dx.doi.org/10.1061/9780784412848.047

http://pubs.usgs.gov/of/2010/1328

http://pubs.usgs.gov/of/2010/1328

http://dx.doi.org/10.1111/j.1467-8667.2004.00352.x

http://dx.doi.org/10.1111/j.1467-8667.2004.00352.x


http://dx.doi.org/10.3141/2201-09

http://dx.doi.org/10.3141/2201-09

comparisonofnonlinearstaticproceduresandmodeling ... pezeshk, huff... · goel (1999) developed the...

Documents