Research ArticleComparative Study of Nonlinear Static and Time-HistoryAnalyses of Typical Korean STS Container Cranes

Quang Huy Tran 1 Jungwon Huh 1 Van Bac Nguyen1 Achintya Haldar2

Choonghyun Kang1 and Kyeong Min Hwang3

1Department of Civil and Environmental Engineering Chonnam National University Yeosu 59626 Republic of Korea2Department of Civil Engineering and Engineering Mechanics University of Arizona Tucson AZ 85721 USA3Korea Electric Power Corporation Research Institute Yuseong-Gu Republic of Korea

Correspondence should be addressed to Jungwon Huh jwonhuhchonnamackr

Received 28 March 2018 Accepted 18 July 2018 Published 16 August 2018

Academic Editor Tadeh Zirakian

Copyright copy 2018 Quang Huy Tran et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Ship-to-shore (STS) container gantry cranes used at terminals for loading and unloading containers from a ship are an importantpart of harbor structures e size and weight of modern STS container cranes are increasing to satisfy the demand for biggerships is is expected to result in more lateral load when excited by seismic motions e existing Korean STS container cranesdid not behave properly during several recent moderate earthquakes in South Korea Typical Korean STS container cranes must bechecked for the earthquake-resistant capacity In this research two nonlinear static analyses procedures also known as pushoveranalyses commonly used for seismic design of buildings namely capacity spectrummethod and equivalent linearizationmethodare comprehensively studied to check their suitability for studying seismic behavior of STS cranes Results obtained by these twononlinear static analysis methods are then compared with the results obtained by nonlinear time-history analyses of the STScranes by exciting them with nine recorded earthquake time histories around worldwidee behaviors of the cranes are analyzedin terms of the total base shear drift and base uplift e comparisons indicate that the nonlinear static methods can beappropriate for estimating the total base shear and drift of the portal frame of a container crane e pushover analyses alsoprovide information on performance levels as defined in ASCESEI 41-13 of a typical Korean STS container crane Furthermore itis observed that the uplift response of the crane is strongly influenced by the duration of an earthquake

1 Introduction

Nonlinear static analysis (NSA) also known as pushoveranalysis (PA) is an effective tool for performance assessmentof a structure under a seismic event It requires less cal-culation than nonlinear dynamic analysis and avoids usinga set of ground motion time histories [1] As expected NSAtakes a shorter time but is less accurate than the time-historyanalysis (THA)method since it uses static analysis to capturedynamic effects e overall steps of the NSA method in-clude the selection of load patterns nonlinear analysis of thestructure to obtain the capacity curve calculation of dis-placement demand using a response spectrum and theassessment of the performance of the structure [1]ere areseveral NSA methods with the same basic overall schemes

but the detailed steps required to implement them aredifferent Some of the concepts officially incorporated indesign guidelines include capacity spectrum method (CSM)and displacement coefficient method (DCM) as adopted inATC-40 [2] and ASCE-41 [3] N2 method as proposed inEurocode 8 [4] and equivalent linearization method (ELM)and displacement modification method (DMM) as pre-sented in FEMA 440 [5] In addition several researchersproposed other procedures ey include the adaptive ca-pacity spectrum method (ACSM) by Casarotti and Pinho[6] the improved capacity spectrum method (ICSM) byFajfar [7] Lin and Chang [8] and Mingkui et al [9] modalpushover analysis (MPA) by Chopra and Goel [10] Freeman[11] Sucuoglu and Gunay [12] adaptive modal combinations(AMC) by Kalkan and Kunnath [13] and the iterative

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 2176894 13 pageshttpsdoiorg10115520182176894

displacement coefficient method (IDCM) by Cosic and Brcic[14] ese methods generally give different results e def-inition of the performance pointdisplacement target and theselection of lateral load patterns used in these methods are thetwo major reasons for the different results [15] It is importantto note that most of these studies were developed for buildings

For a special steel structure such as a ship-to-shore (STS)container crane very different from buildings as shown inFigure 1 the use of NSA for seismic analyses are expected tobe different with their unique support conditions In thisstudy two NSAmethods conventional CSM of ATC-40 andthe ELM of FEMA 440 are selected for further consider-ation ey are selected because they provide a graphicalrelationship between the capacity of a structure and theseismic demand and it is relatively easy for engineers toestimate the maximum displacement by using them Inaddition these methods are recommended in many designguidelines and standards worldwide

e seismic behavior assessment of a typical STS con-tainer crane used in South Korea is specifically addressed inthis paper A three-dimensional (3D) finite element (FE)model generated by SAP2000 is analyzed first by CSM andELM e results of these NSA methods are then verified byexciting the crane by nine scaled recorded ground motiontime histories e results obtained by CSM and ELM werethen compared with the more comprehensive and accuratenonlinear THA e primary objective of this study is toinvestigate whether commonly used NSA methods de-veloped for the seismic design of buildings can also be usedfor a STS container crane For a comprehensive comparisonthe uplift response base shear and drift are specificallyaddressed and compared in this study

2 Nonlinear Static and Dynamic Analyses

21 Capacity Spectrum Method (CSM) Procedure CSM wasfirst proposed by Freeman et al in 1975 [16] and later in-troduced in ATC-40 in 1996 [2] and FEMA 274 in 1997 [17] Itis a graphical procedure is method provides a specialtreatment for reduction of the seismic demand to intersect thecapacity curve in spectral coordinates to find a performancepoint [2] An interesting study related to CSM was theAutoCSM method proposed by Guyader and Iwan [18]AutoCSM is an automated Excel sheet in which the improvedeffective linear periods are used to replace the secant periodused in the conventional CSM Essentially the seismic demandis reshaped by a modification factor In addition to improvethe accuracy of CSMChopra andGoel [19] proposed the use ofthe constant-ductility inelastic design spectra instead of theelastic damped spectra of the conventional CSM commonlydenoted as ICSM e procedure is controlled by the ductilityfactor Lin and Chang [8] improved ICSM by using the realabsolute acceleration response spectrum instead of the pseu-doacceleration response spectrum especially for them systemwith equivalent viscous damping ratio βeq gt 10 and periodTgt 015 s Later Mingkui et al in 2006 [9] proposed twoimprovements for the conventional CSM ey consideredinelastic demand spectra by using yield strength factor as an

elastoplastic index ey also defined and formulated the de-sign acceleration response spectra from the China designbuilding code Based on the energy equivalent criterion theequivalent single degree of freedom (SDOF) system was esti-mated instead of bilinear modeling of pushover curves underthe assumption of area equivalence In 2007 Casarotti andPinho [6] proposed another procedure especially for bridgeapplications known as ACSMey constructed an equivalentsingle-mode capacity curve by combining multimodal push-over response curves It can be used to study multiple degree offreedom (MDOF) continuous span bridges considering bothflexible and rigid superstructures Gencturk and Elnashai in2008 [20] proposed a method for seismic evaluation of wood-frame structurese results showed a significant improvementin the accuracy of CSM as updating the bilinear idealization ofthe structural system based on the selected trial performancepoint on the capacity diagram Recent studies also comparedand verified methods proposed by Causevic and Mitrovic [21]and Ferraioli et al [22] As discussed previously the use of NSAfor the design of STS crane is very limited e question re-mains whether the conventional CSM as suggested in ATC-40for the design of buildings can also be used for the design ofSTS containers

e conventional CSM procedure consists of the fol-lowing steps as illustrated in Figure 2 [10]

(1) Construct the pushover curve which represents therelationship between the base shear Vb and the roofdisplacement Δroof

(2) Convert the pushover curve to a capacity diagram bytransforming Vb to the spectral acceleration Sa andΔroof to the spectral displacement Sd by using thefollowing equations

Sai 1

α1W1113888 1113889Vbi

Sdi 1Γ1ϕroof1

1113888 1113889Δroof

(1)

where W is the total dead load of the structure andapplicable portions of other loads (ie service liveloads) ϕroof1 is the amplitude of mode 1 at the rooflevel and Γ1 and α1 are the modal participationfactor and the modal mass coefficient for the firstnatural mode respectively ey can be calculated asfollows

Γ1 1113936

Ni1 wiϕi1( 1113857g

1113936Ni1 wiϕ

2i1( 1113857g

α1 1113936

Ni1 wiϕi1( 1113857g1113872 1113873

2

1113936Ni1wig1113872 1113873 1113936

Ni1 wiϕ

2i1( 1113857g1113872 1113873

(2)

(3) Convert the elastic response spectrum (Sa versus T

diagram) to the accelerationmdashdeformation responsespectrum format (Sa versus Sd format or ldquoADRSrdquo)using the following equation

2 Advances in Civil Engineering

Sdi T2

4π2Saig (3)

where T is the natural period of the system vibratingwithin linearly elastic range (ule uy)

(4) Plot the demand and capacity diagrams on the top ofeach other Instead of dynamic analyses a sequenceof equivalent linear systems with successivelyupdated values of the natural period of the structureTeq and total equivalent viscous damping 1113954βeqprovide a basis for estimating the deformation of theinelastic system [10] e total viscous damping 1113954βeqof the equivalent linear system is defined as follows

1113954βeq β0 + κβeq (4)

where β0 is the viscous damping ratio of a bilinearsystem for vibrations in linear range (ule uy) κ is theadjustment factor depending on structural behaviorand βeq is the equivalent viscous damping ratio asdefined in (5) It can also be expressed in detail in (6)for bilinear systems based on Figure 3

βeq 14π

ED

ES (5)

βeq 2π

(μminus 1)(1minus α)

μ(1 + αμminus α) (6)

175

m

Backreach Rail gage

200m 305m630m

Outreach

778

m

Container

400

m

Boom

Trolley

Apex

Node 20

Node 10

Node 40

Node 30

Figure 1 3D numerical FE model of Korea STS container crane

Displacement Δroof

Forc

e V b

Spectral displacement Sd

Spectral displacement Sd

Spec

tral

acce

lerat

ion

Sa

Spec

tral

acce

lerat

ion

Sa

Spec

tral

acce

lerat

ion

Sa

Capacity diagram

Period T

Elastic response spectrum

Spec

tral

acce

lerat

ion

Sa

Demand diagram

Pushover curveStep 1 Step 2

Step 3

Spectral displacement Sd

SandashSd diagram or ADRS

Performance point

Capacity diagram

Demand diagram

5 elastic demand diagram

Step 4

Displacement Δroof

Forc

e V b

Step 5

Figure 2 Conventional CSM procedure

Advances in Civil Engineering 3

where ED and ES are the energy dissipated in thenonlinear system (area of enclosed by hysteresisloop) and linear system (area of triangle) re-spectively μ umuy is the ductility factor α is thepost-yield stiffness ratio and ksec is the secantstiffness e natural vibration period of theequivalent linear system can be calculated as follows

Teq T

μ1 + αμminus α

1113970

(7)

(5) Convert Sd from step 4 to Δroof or an individualcomponent deformation and then compare themwith the limiting values for the specified perfor-mance goals [10 19]

Δroof Sdiϕroof1Γ1 (8)

Vb α1SaW (9)

where all the parameters in (8) and (9) are alreadyexplained in (1) and (2)

22 Equivalent Linearization Method (ELM) ProcedureSimilar to CSM ELM requires a response spectrum familyand uses estimates of ductility to obtain effective period andeffective damping In both procedures the global de-formation demand (including elastic and inelastic) on thestructure is computed from the response of an equivalentSDOF system e difference is in the technique used toobtain the maximum displacement demand [5] In con-ventional CSM the equivalent stiffness of inelastic system isassumed to be the secant stiffness and the equivalentdamping is related to the area under the capacity curve asillustrated in Figure 3 In ELM however the equivalentstiffness is estimated from effective period Teff and effectivedamping βeff derived from statistical analyses expressed asfunctions of ductility μ [5] Teff and βeff optimized for ap-plication to any capacity curve can be estimated as follows

For 10lt μlt 40

βeff 49(μminus 1)2 minus 11(μminus 1)

3+ β0

Teff 02(μminus 1)2 minus 0038(μminus 1)

3+ 11113960 1113961T

(10)

For 40le μle 65

βeff 14 + 032(μminus 1) + β0

Teff [028 + 013(μminus 1) + 1]T(11)

For μgt 65

βeff 19064(μminus 1)minus 1[064(μminus 1)]2

1113890 1113891Teff

T1113874 1113875

2+ β0

Teff 089

μminus 1

1 + 005(μminus 2)

1113971

minus 1⎛⎝ ⎞⎠ + 1⎡⎢⎢⎣ ⎤⎥⎥⎦T

(12)

e above expressions are limited for the initial period ofvibration T from 02 to 20 s [5] e effective accelerationaeff must lie on the capacity curve and coincide with themaximum displacement dmax us the modification factorM defined by (13) is used to adjust the demand spectrume modified ADRS (MADRS) procedure is described anddepicted in Figure 4 [5]

M amax

aeff (13)

23 Nonlinear Modal Time-History Analysis To verify theNSA methods nonlinear modal THA is used in this study Itis also known as fast nonlinear analysis (FNA) in SAP2000e fundamental equilibrium equation of FNA can beexpressed as [23 24]

Meurou(t) + C _u(t) + Ku(t) + RNL(t) R(t) (14)

where M C and K are the mass proportional viscousdamping and stiffness matrices respectively the RNL(t) isthe nonlinear object force vector from the sum of the forcesin the nonlinear elements and R(t) is the applied load Ateach point of time the uncoupled modal equations aresolved exactly within the elastic structural system whereasforces within the predefined nonlinear DOF (indexed withinRNL(t)) are solved through an iterative process whichconverges to satisfy equilibrium In (14) the nonlinear forcesare treated as external loads and a set of load-dependent ritz(LDR) vectors Φ is generated to accurately capture theeffects of those forces

e input earthquake time histories used in this studyconsist of nine horizontal ground motions with magnituderanging from 653 to 76 All the data were obtained fromPacific Earthquake Engineering Research Center (PEER)[25] Table 1 shows seven near-fault ground motions (simplyassumed with a rupture distance lt15 km) and 2 far-faultground motions

3 A Case Study of Numerical Modeling fora Typical Korean STS Container Crane

31 Numerical Simulations e STS container crane con-sidered in this study is located at a seaport in South KoreaMost of the structural components were made of stiffenedhollow box sections except for diagonal braces which weretubes and forestays and backstays which were wide-flange

Displacement

Forc

e

umuy

fy(1 + αμ ndash α)fy

k ksecESED

1

αk

Figure 3 SDOF nonlinear system and equivalent viscous dampingdue to hysteretic energy dissipation

4 Advances in Civil Engineering

shapese properties of materials comply with the Japaneseindustrial standards (JIS) JIS-SM490Y and JIS-STK490 egeneral dimensions of the crane that is outreach cranegagespan backreach and height are illustrated in Figure 1A 3D FE model of the container was developed by theSAP2000 software package as discussed earlier In the FErepresentation the total number of elements is 9916 9912frame elements and 4 gap elementse forestays backstaysand diagonal braces were assigned end releases hence theseelements worked as truss elements All nonstructural loadsthat is stairs drive trucks stowed pins machinery house12 festoon snag device and boom hoist rope were appliedas concentrated or distributed loads e modal shapesnatural periods and frequencies of the first and third modeanalyzed by the Ritz vectors method are shown in Figure 5

32 Selection of Seismic Demand Several boreholes weredriven in the area of the seaport to consider the site soilconditions e soil investigation report showed that theshear wave velocity for the top 30m of ground for the fiveboreholes of the S-PS logging test were from 247ms to447ms as shown in Table 2 As a result the soil profile typesranged from SC to SD according to Korean Building Code[26] as shown in Table 3 In this study the soil type SD wasselected For the cranersquos site seismic zone I was consideredto be appropriate and a seismic zone factor S 022 g wasassigned for the maximum considered earthquake (MCE)with a return period of 2400 years e design accelerationresponse spectrum of soil type SD was then developed

corresponding to site coefficients Fa (for short period) and Fv(for 1 s period) of 136 and 196 respectively From the 5damping elastic response spectrum of soil type SD as shownin Figure 6 (the red curve) the Sa at the fundamental period(mode 3 with T135 s) is 021 g To verify the results ofnonlinear static analyses the response spectra of ninerecorded ground motions as shown in Table 1 were thenscaled to a spectral acceleration Sa of 021 g at the funda-mental period e scaled response spectra of the recordedground motions and design response spectrum according toKBC 2016 are shown in Figure 6

33 Nonlinear Static Analysis and Damage Criteria eplastic hinges were assigned to the portal frame as illustratedin Figure 7 assuming that they develop at the end of theframes using concentrated plasticity model [23 27] eproperties of plastic hinges are suggested in ASCESEI 41-13[3] For portal beams the moment-curvature (M-ϕ) re-lationship is sufficient to model the hinges assuming no axialforce is acting in them Although interaction relationship ofthe axial force (P) and the moments (M) in both axes isrequired for portal columns of a 3Dmodel a pinned supportis used for the pushover analysis to generate large portaldeformations during autoincrement static pushinge limitstate obtained by pushover analyses can be applied to THAfor a FE model using gap elements because the structuralcapacity is independent of the loading [28] According to thestructural performance levels and damage defined inASCESEI 41-13 for buildings the expected performance

Sd

Sa

dmax = μ dydy

amax

Tsec

Teff (μ)

ADRS (β0)

ADRS (βeff (μ))

MADRS (βeff (μ) M)

aeff

Capacity spectrum

M = amaxaeff

Spectral displacement Sd

Spec

tral

acce

lera

tion

Sa

Figure 4 Modified acceleration-displacement response spectrum (MADRS)

Table 1 Unscaled ground motions recorded during several earthquakes

Number (GM) Earthquake name Year Station Mag Mechanism RRUP (km) PGA (g)1 Imperial Valley-02 1940 El Centro array 09 695 Strike slip 61 0282 Imperial Valley-06 1979 El Centro array 06 653 Strike slip 14 0453 Landers 1992 Barstow 728 Strike slip 35 0134 Landers 1992 Yermo Fire station 728 Strike slip 24 0245 Loma Prieta 1989 Gilroy-Gavilan Coll 693 Rev oblique 10 0366 Northridge-01 1994 Newhall-Fire Sta 669 Reverse 59 0587 Northridge-01 1994 Sylmar-Converter Sta 669 Reverse 54 0628 Kobe Japan 1995 KJMA 690 Strike slip 10 0839 Chi-Chi Taiwan 1999 TCU065 762 Rev oblique 06 079Note RRUP is the closest distance to the rupture plane (rupture distance)

Advances in Civil Engineering 5

levels for steel container cranes (considering as steel momentframe SMF) are shown in Table 4 In previous studiesderailment defined as the reduction of the axial reaction ofat least one leg base to be zero due to sufficient lateral loadswas considered as a damage state [28] However it is re-ported that a crane was repaired by repositioning it on therails by jacking systems and mobile crane when it wasderailed without any damage to the upper structure that isthe repair of a Krupp crane at the Port of Oakland in the pastin this way [29] Hence derailment is assumed to be the onlyform of the cranersquos movement without damage of thestructure and the portal frame is still considered to beelastic Consideration of slight derailment is not consideredas a damage state in this study e damage state consideredin this study focuses only on the structural behavior of theportal frame Several other damage criteria for STS containercranes were suggested in previous studies [28 30] as brieflysummarized in Tables 5 and 6 based on observations ofdamages of container cranes subjected to past earthquakestesting of scaled models on shaking table and analyses of FEmodels

For the NSA procedures a concentrated force was ap-plied at the boom level as illustrated in Figure 7 underdisplacement-controlled analyses e results of pushoveranalyses indicate that both columns reach the limit states atthe same portal drift level even when the concentrated forceis applied in the seaward or landward direction In additionsince the cross sections of the waterside and landside legs areslightly different they are expected to have similar stiffnessand strength As a result Figure 7 indicates that both col-umns reach the immediate occupancy (IO) life safety (LS)and collapse prevention (CP) levels at a portal drift of ap-proximately 16 18 and 22 respectively In this study

the complex stiffened box sections of the portal columns havebeen converted into unstiffened box section for simplicitye section of the top of the portal columns is illustrated inFigure 8 e x-axis and y-axis are the trolley-travel directionand gantry-travel direction (along the rails) respectively It isnoted that the hollow box sections at the top of the portalcolumns of the Korean crane are smaller than those of craneJ100 as mentioned in Table 6 Even the overall height of theKorean crane is greater than that of the J100 Past recordsindicate that there were few moderate to large earthquakes inKorea us an optimization of the general stiffness of thewhole structure of a crane with less emphasis on the seismiceffect can reduce the initial cost for the owner

e ADRS diagrams consisting of both capacity andseismic demand are shown in Figure 9 e CSM and ELMwere performed under the seismic demand of KBC 2016with a selected damping ratio of 15 as suggested byKosbab for a jumbo container crane [28 31] e resultsfrom both pushover methods are similar e performancepoint of CSM indicates that the total base shear and max-imum horizontal displacement at the top of the portal frameare 169182 kN and 106 cm respectively e total baseshear and maximum displacement obtained from ELM are169186 kN and 106 cm respectively with a ductility ratioμ 10 and the modification factor M 1

34 Dynamic Analyses For the input ground motions theeffect of vertical excitation is high when the spectral accel-eration Sa of the crane (with a natural period of 03 s) is greaterthan 05 g as observed in the experimental study by KosbabFor lower Sa the effect of vertical excitation on the portal driftis around 01 [28] In this study the vertical groundmotionsare neglected with the assumption that their amplitudes areattenuated by the effect of quay wall and local site

e nonlinear modal THAwas considered incorporatingthe P-Δ effect e Rayleigh damping β which relates to themass and stiffness matrix was calculated by (15) and (16)considering mode 1 (boom torsion) and mode 3 (portalsway) as shown in Figure 5

β a01

2ωn

+ a1ωn

2 (15)

Mode 1 T = 382 s f = 026 Hz

(a)

Mode 3 T = 135 s f = 074 Hz

(b)

Figure 5 Numerical fundamental periods and modal shapes (a) boom torsion and (b) portal sway

Table 2 Soil investigation at a seaport in South Korea

Boreholes Shear wave velocity GL minus30m vs (ms) Soil typesBH-1 406 SCBH-2 252 SDBH-3 447 SCBH-4 247 SDBH-5 337 SD

6 Advances in Civil Engineering

Assuming that the frequencies of the two modes are ωi

and ωj having an equal damping ratio of 15 the co-efficients a0 and a1 can be obtained as follows

a0 β2ωiωj

ωi + ωj

a1 β2

ωi + ωj

(16)

During the operation the crane is not fixed to rails orquay wall For nonlinear THA therefore a gap link elementis used to simulate the contact between trucks and rails egap element is activated when structures come closer anddeactivated when they go far away [23] e axial force willbe set to zero when the portal leg is upliftede gap elementdoes not disengage in the horizontal direction duringuplifting It is also the limit of this support boundary asdiscussed in detail by Kosbab [28] However a gap element(or a similar type called no tension element) was proven tobe suitable to assess the uplift response as proposed byChaudhuri et al [32] e results of the THA together withthe NSA methods are discussed in detail in Section 4

4 Results and Discussions

41 Drift Response In contrast to the global drift analysis ofa building at the roof level most of the plastic hinges were

observed to be developed in the portal frame of the craneduring past earthquakes Furthermore the portal frame isthe main structure to support the whole upper structuresus the horizontal displacement or drift at the top of theportal frame is commonly considered [33 34] as shown inFigure 10e drift at the top of the portal frame (denoted asportal drift) of a container crane provides information onhow much of the horizontal deformation occurs at thefundamental mode in the trolley travel direction Besidesmeasuring the portal drift the drift at the top of upper legsand apex is monitored along with the corresponding heightas shown in Figure 10 e average drift of the portal frametop of upper leg and apex are estimated to be 061 026and 018 corresponding to heights of 166m 471m and766m respectively in the trolley travel direction from THAunder nine ground motions with scaled PGA ranging from010 g to 032 g e results of both pushover analyses usingCSM and ELM shown in Figure 9 are in good agreementwith that of THA In particular the average portal drift of064 is 003 larger than that of THA On the other handby using the deformation of the fundamental mode thedisplacements of the apex obtained from pushover analysesare significantly larger compared to the time-history ana-lyses with an error of over 16 e portal drifts obtainedfrom time-history and pushover analyses indicate that thecrane behaviors are in the elastic state under seismic exci-tations based on the performance levels in Figure 7According to other performance levels and damage criteria

Table 3 Site classification of KBC 2016

Soil types Soil profile nameAverage properties on the upper 30m of the site profile

Shear wavevelocity vs (ms)

Standard penetrationresistance N (blows30 cm)

Soil undrained shearstrength su (times10minus3MPa)

SA Hard rock gt1500 mdash mdashSB Rock 760 to 1500 mdash mdashSC Very dense soil and soft rock 360 to 760 gt50 gt100SD Stiff soil 180 to 360 15 to 50 50 to 100SE Soft soil lt180 lt15 lt50

00

02

04

06

08

10

12

00 05 10 15 20 25

Spec

tral

acce

lera

tion

Sa (

g)

Period T (s)

Design RS (KBC2016)Individual GMMean of GMs

Fundamental period

Figure 6 Scaled response spectra at the fundamental period

000

005

010

015

020

025

030

035

040

00 05 10 15 20 25 30

V bm

g

Portal dri ()Waterside legLandside leg

Imm

edia

te o

ccup

ancy

(IO

)

Life

safe

ty (L

S)

Colla

pse p

reve

ntio

n (C

P)

Hinge assignments

Figure 7 Pushover curve and limit states for typical Koreancontainer crane

Advances in Civil Engineering 7

as summarized in Tables 5 and 6 the cranemight work in thedamage degree I as defined by PIANC and between DR andIU levels according to Kosbabrsquos proposal

42 Total Base Shear e total base shears obtained fromCSM and ELM analyses are plotted in Figure 11 e totalbase shear is observed to be almost unrelated to the scaled

Table 4 Structural performance levels and damage based on ASCESEI 41-13 [3]

Elements Immediate occupancy (IO) Life safety (LS) Collapse prevention (CP)

For vertical elements of SMFs (ie portal columns of the crane)

Minor local yielding at a fewplaces No fractures Minorbuckling or observablepermanent distortion of

members

Hinges form Local buckling ofsome beam elements Severejoint distortion but shear

connections remain intact A fewelements may experience partial

fracture

Extensive distortion of beamsand column panels Many

fractures at momentconnections but shear

connections remain intact

Overall damage Light Moderate Severe

Table 5 Damage criteria for cranes according to PIANC [30]

Level of damage Degree I Degree II Degree III Degree IV

Displacement Withoutderailment With derailment Without overturning Overturning

Peak response stressesstrains(i) Upperstructures Elastic Elastic Plastic (ltμεmax for upper

structure)Plastic (geμεmax for upper

structure)

(ii) Portal frame Elastic Plastic (ltμεmax for portalframe) Without collapse Collapse

(iii) Toe Elastic Damage to toe (including pull-out of vehicle fracture of anchorbrakes)Note μ and εmax are the ductility factor and strain limit for the structure respectively

Table 6 Performance levels and limit states proposed by Kosbab [28]

Level ofdamageelements Derailment (DR) Immediate use (IU) Structural damage (SD) Complete collapse (CC)

Whole structures Derailed without anydamage to the structure

Minor structural damage(not significantly impacts its

operational capacity)Derailment may or may not

have occurred

Extensive damage and will notbe suitable for use without

major repairs but not collapse

Local buckling near theportal joints can quickly

lead to global instability andeventual collapse

Portal frame Elastic

Lower limit elastic Highlimit some minor bucklingof hollow sections (withinthe portal frame or not)

A portaldeformationlt deformation atmax load capacity up to thepoint of ultimate ductility

Portal deformationsurpasses the estimatedpoint of max ductility

Overall damage Derailed Minor damage Major damage CollapseLimit state in terms of portal drift (for reference)(i) Crane J100 13 20 30 45(ii) Crane LD100 mdash 15 20 30(iii) Crane LD50 15 19 25 35

182c

m

190cm 190cm

182c

m

Waterside leg tf = 20cmLandside leg tf = 16cm

Waterside leg tw = 16cm Landside leg tw = 12cm Flange

Web

(a) (b)

x

y

Figure 8 Hollow box elements (a) original stiffened section and (b) simplified unstiffened section

8 Advances in Civil Engineering

PGA magnitude and rupture distance For an example themaximum total base shear is obtained from a minimumPGA ground motion which is the Landers earthquake atYermo Fire station in 1992 (GM-4) with a PGA of 01 g orthe earthquake with a relatively high PGA value of around024 g (GM-2) at a short rupture distance (14 km) generatesa lower structural response of 141573 kN compared withthe average value of 167493 kN for the nine ground motionexcitations e total base shears obtained from pushovermethods show higher values than the average obtained fromTHA In particular the results for CSM and ELM are169182 kN and 169186 kN respectively as mentioned inthe previous section From this observation it can beconcluded that the pushover methods are suitable forseismic analysis of a STS container crane

43Uplift Behavior e uplifting of a crane will result in theredistribution of the load and will change the horizontal

displacement of the whole structure e uplift is defined bytwo conditions (1) the vertical displacement of the upliftedleg should be a positive value or zero (a negative value meansthe gap element is still ldquocloserdquo) and (2) the vertical reactionof the uplifted leg is zero In this study four portal legs twolandside legs (node 10 and 20) and two waterside legs (node30 and 40) as shown in Figure 1 are considered to studyuplift responses Figure 12 shows the potential uplift (interms of vertical responsedisplacement) and the time ofoccurrence of the landside leg (node 20) and waterside leg(node 30) It is noted that the term ldquopotential upliftrdquo is usedbecause the full uplift was not occurred under the earth-quake demand as discussed in Section 32 just a slight upliftmight happen in this study e full uplift of a crane leg isconsidered when a leg totally wins against the initial gravityload which meets both conditions as mentioned above Itcan be observed that the potential uplift of landside leg willoccur sooner than that of the waterside leg except for GM-3GM-8 and GM-9e reason could be that the center of total

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20

Hei

ght o

f cra

ne H

(m)

Horizontal displacement (cm)

Individual GMAverage of GMsPushover

Apex (3)

Top of upper leg (2)

Top of portalleg (1)

(3)

(1)

(2)

δ

(a)

0

10

20

30

40

50

60

70

80

90

0 02 04 06 08

Hei

ght o

f cra

ne H

(m)

Dri ()

Apex (3)

Top of upper leg (2)

Individual GMAverage of GMsPushover

Top of portalleg (1)

(b)

Figure 10 Height of crane versus (a) horizontal displacement and (b) drift

0

02

04

06

08

T=

05s

T = 10s

T = 15s

T = 20s

1

0 10 20 30 40

Spec

tral

acce

lera

tion

Sa (

g)

Spectral displacement Sd (cm)

15 dampingdemand spectrum

Capacity spectrum

(a)

T=

05s

T = 10s

T = 15s

T = 20s

Spec

tral

acce

lera

tion

Sa (

g)

0 10 20 30 40Spectral displacement Sd (cm)

Capacity spectrum

0

02

04

06

08

1

15 dampingdemand spectrum

(b)

Figure 9 Pushover analyses (a) CSM of ATC-40 and (b) ELM of FEMA 440

Advances in Civil Engineering 9

mass is not at the center of the two portal legs e total massconcentrates closer to the waterside legs than the landsidelegsus the first uplift will occur at the landside legs Whena leg is uplifted the axial force of the opposite leg will increasesignificantly In particular in this study it is observed that themaximum axial compressive force increases up to 120496 kNon the landside leg (node 10) due to the upward verticalresponsedisplacement of the waterside leg when excited bythe Landers earthquake (GM-4) at Yermo Fire station It isinteresting to note that the increase of the axial force of node10 is approximately 495 compared with the initial gravityforce of that node of around 243486 kN

On the other hand the vertical response of crane leg isobserved to be strongly influenced by the ground motionsrsquocharacteristics Figure 13 indicates that the amplitude of

vertical responsedisplacement decays significantly withtime after reaching the peak value when subjected to short-duration earthquakes such as GM-2 GM-5 GM-6 and GM-8 However the vertical response maintains large amplitudefor a long time when excited by long-duration earthquakeseven when the acceleration amplitude is not as high as inGM-4 GM-7 and GM-9 It can be stated that a long-duration earthquake may generate uplift and for a longperiod of time even when the input ground motion is of lowamplitude Assessment of the uplift behavior is an importantissue that should be considered in the seismic design ofa container crane to predict the overloading on the portallegs It is noted that a positive value of the vertical responseshown in Figure 13 means that the cranersquos leg moves upwardwhereas a negative value indicates a compression (downward

1300

1400

1500

1600

1700

1800

1900

2000

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tota

l bas

e she

ar V

b (k

N)

Earthquakes

Total base shear of each GMAverage of total base shear

Pushover-CSMPushover-ELM

Scaled PGA (g)Magnitude

02569561

02465314

025728350

010728240

032693100

01866959

01666954

01969010

02176206Rup distance (km)

Figure 11 Total base shear versus earthquakes

0

10

20

30

40

50

60

0

001

002

003

004

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tim

e of o

ccur

renc

e (s)

Upw

ard

vert

ical

resp

onse

(cm

)

Earthquakes

Time of occurrence (node 20)Time of occurrence (node 30)

Landside leg (node 20)Waterside leg (node 30)

Figure 12 Upward vertical responsesdisplacements of the landside and waterside legs versus time of occurrence due to dynamic analysis(gravity analysis not included)

10 Advances in Civil Engineering

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(a)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(b)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(c)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(d)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(e)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(f )

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(g)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(h)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(i)

Figure 13 Time-history vertical response of the landside leg (node 20) (a) Imperial Valley-02 (GM-1) (b) Imperial Valley-06 (GM-2) (c)Landers Barstow (GM-3) (d) Landers Yermo Fire Station (GM-4) (e) Loma Prieta (GM-5) (f ) Northridge-01 Newhall (GM-6) (g)Northridge-01 Sylmar (GM-7) (h) Kobe Japan (GM-8) (i) Chi-Chi Taiwan (GM-9)

Advances in Civil Engineering 11

movement) comparing with the state after analyzing gravityload When taking into account both static analysis (gravityload analysis) and dynamic analysis the value of verticaldisplacement is still negative in all cases indicating no fulluplift occurrence For example under subjected by theearthquake GM-4 (Landers at Yermo fire station) thelandside leg (node 20) results in a positive value of 0034 cmfor dynamic analysis and a negative value of minus0058 cm forgravity load analysis thus the value considering both cases ofanalysis is approximately minus0024 cm by summation ismeans that the crane might be slightly uplifted and will befully uplifted if the value of displacement reaches zero and thevertical reaction of the crane leg is zero as well

5 Conclusions

is study represents a preliminary investigation for theseismic behavior of a typical Korean STS container cranee complex seismic response of the crane is estimated byrepresenting it by a 3D FE model Nonlinear time-historyanalysis and both CSM and ELM pushover analyses methodsare used to analyze the crane and compare the resultsSeveral key observations can be made based on the resultsobtained from this study ey are as follows

e conventional CSM and ELM are found to be suf-ficient to analyze a STS container crane In particular therelative errors of the portal drift and total base shearobtained from pushover methods are 46 and 10 re-spectively comparing with those using the nonlinear time-history analyses However the horizontal displacements ofthe apex of the crane obtained from CSM and ELM appear tobe overestimated because these methods consider only thefundamental mode whereas the nonlinear time-historyanalysis uses the superposition principle of multiple modes

Assessment of uplift response is an important issue thatshould be considered in the seismic analysis of a containercrane It is clearly seen in this study that the axial force of thelandside legs increases nearly 50 of the initial gravity forceas the waterside legs are slightly uplifted us a gap ele-ment which is integrated into most of the commercialsoftware is appropriate for modeling base support to studythe uplift behavior On the other hand the uplift response isstrongly influenced by the characteristics of the groundmotions e potential uplift can have large amplitude fora long time when excited by long-duration earthquakes evenwhen the acceleration amplitude may not be high

e portal drifts of the typical Korean STS containercrane corresponding to performance levels of IO LS andCP as defined in ASCESEI 41-13 are 16 18 and 22respectively ese values can be used as damage limits forthe fragility analysis

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflict of interest

Acknowledgments

is research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education(2017R1D1A3B03032854) and by Ministry of public Ad-ministration and Security as Disaster Prevention SafetyHuman resource development Project and was also a part ofthe project titled ldquoDevelopment of performance-basedseismic design technologies for advancement in design codesfor port structuresrdquo funded by the Ministry of Oceans andFisheries Korea

References

[1] G H Powell Static Pushover Methods-Explanation Com-parison and Implementation 2013 httpswikicsiamericacomdisplayperformStatic+pushover+methods+-+explanation2C+comparison+and+implementation

[2] ATC 40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood CA USA 1996

[3] ASCESEI 41 Seismic Evaluation and Retrofit of ExistingBuildings American Society of Civil Engineers Reston VAUSA 2013

[4] Eurocode 8 Design of Structures for Earthquake ResistancePart 1 General Rules Seismic Actions and Rules for BuildingsEN 1998 European Committee for Standardization (CEN)Brussels Belgium 2004

[5] FEMA 440 Improvement of Nonlinear Static Seismic AnalysisProcedures Applied Technology Council (ATC-55 Project)Federal Emergency Management Agency Washington DCUSA 2006

[6] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 4pp 377ndash390 2007

[7] P Fajfar ldquoCapacity spectrum method based on inelasticdemand spectrardquo Earthquake Engineering and StructuralDynamics vol 28 no 9 pp 979ndash993 1999

[8] Y-Y Lin and K Chang ldquoAn improved capacity spectrummethod for ATC 40rdquo Earthquake Engineering and StructuralDynamics vol 32 no 13 pp 2013ndash2025 2003

[9] X Mingkui D Yinfeng L Gang and C Guangjun ldquoAnimproved capacity spectrum method based on inelastic de-mand spectrardquo in Proceedings of 4th International Conferenceon Earthquake Engineering Taipei Taiwan October 2006

[10] A Chopra and R Goel ldquoEvaluation of NSP to estimateseismic deformation SDF systemsrdquo Journal of StructuralEngineering vol 126 no 4 pp 482ndash490 2000

[11] S Freeman ldquoDevelopment and use of capacity spectrummethodrdquo in Proceedings of 6th US NCEE Conference onEarthquake Engineering pp 1ndash12 SeattleWA USA June 1998

[12] H Sucuoglu and M S Gunay ldquoGeneralized force vectors formulti-mode pushover analysisrdquo Earthquake Engineering andStructural Dynamics vol 40 no 1 pp 55ndash74 2011

[13] E Kalkan and S K Kunnath ldquoAdaptive modal combinationprocedure for nonlinear static analysis of building structuresrdquoJournal of Structural Engineering vol 132 no 11 pp 1721ndash1731 2006

[14] M Cosic and S Brcic ldquoIterative displacement coefficientmethod mathematical formulation and numerical analysesrdquoGraCevinar vol 65 no 3 pp 199ndash211 2013

12 Advances in Civil Engineering

Sdi T2

4π2Saig (3)

where T is the natural period of the system vibratingwithin linearly elastic range (ule uy)

(4) Plot the demand and capacity diagrams on the top ofeach other Instead of dynamic analyses a sequenceof equivalent linear systems with successivelyupdated values of the natural period of the structureTeq and total equivalent viscous damping 1113954βeqprovide a basis for estimating the deformation of theinelastic system [10] e total viscous damping 1113954βeqof the equivalent linear system is defined as follows

1113954βeq β0 + κβeq (4)

where β0 is the viscous damping ratio of a bilinearsystem for vibrations in linear range (ule uy) κ is theadjustment factor depending on structural behaviorand βeq is the equivalent viscous damping ratio asdefined in (5) It can also be expressed in detail in (6)for bilinear systems based on Figure 3

βeq 14π

ED

ES (5)

βeq 2π

(μminus 1)(1minus α)

μ(1 + αμminus α) (6)

175

m

Backreach Rail gage

200m 305m630m

Outreach

778

m

Container

400

m

Boom

Trolley

Apex

Node 20

Node 10

Node 40

Node 30

Figure 1 3D numerical FE model of Korea STS container crane

Displacement Δroof

Forc

e V b

Spectral displacement Sd

Spectral displacement Sd

Spec

tral

acce

lerat

ion

Sa

Spec

tral

acce

lerat

ion

Sa

Spec

tral

acce

lerat

ion

Sa

Capacity diagram

Period T

Elastic response spectrum

Spec

tral

acce

lerat

ion

Sa

Demand diagram

Pushover curveStep 1 Step 2

Step 3

Spectral displacement Sd

SandashSd diagram or ADRS

Performance point

Capacity diagram

Demand diagram

5 elastic demand diagram

Step 4

Displacement Δroof

Forc

e V b

Step 5

Figure 2 Conventional CSM procedure

Advances in Civil Engineering 3

where ED and ES are the energy dissipated in thenonlinear system (area of enclosed by hysteresisloop) and linear system (area of triangle) re-spectively μ umuy is the ductility factor α is thepost-yield stiffness ratio and ksec is the secantstiffness e natural vibration period of theequivalent linear system can be calculated as follows

Teq T

μ1 + αμminus α

1113970

(7)

(5) Convert Sd from step 4 to Δroof or an individualcomponent deformation and then compare themwith the limiting values for the specified perfor-mance goals [10 19]

Δroof Sdiϕroof1Γ1 (8)

Vb α1SaW (9)

where all the parameters in (8) and (9) are alreadyexplained in (1) and (2)

22 Equivalent Linearization Method (ELM) ProcedureSimilar to CSM ELM requires a response spectrum familyand uses estimates of ductility to obtain effective period andeffective damping In both procedures the global de-formation demand (including elastic and inelastic) on thestructure is computed from the response of an equivalentSDOF system e difference is in the technique used toobtain the maximum displacement demand [5] In con-ventional CSM the equivalent stiffness of inelastic system isassumed to be the secant stiffness and the equivalentdamping is related to the area under the capacity curve asillustrated in Figure 3 In ELM however the equivalentstiffness is estimated from effective period Teff and effectivedamping βeff derived from statistical analyses expressed asfunctions of ductility μ [5] Teff and βeff optimized for ap-plication to any capacity curve can be estimated as follows

For 10lt μlt 40

βeff 49(μminus 1)2 minus 11(μminus 1)

3+ β0

Teff 02(μminus 1)2 minus 0038(μminus 1)

3+ 11113960 1113961T

(10)

For 40le μle 65

βeff 14 + 032(μminus 1) + β0

Teff [028 + 013(μminus 1) + 1]T(11)

For μgt 65

βeff 19064(μminus 1)minus 1[064(μminus 1)]2

1113890 1113891Teff

T1113874 1113875

2+ β0

Teff 089

μminus 1

1 + 005(μminus 2)

1113971

minus 1⎛⎝ ⎞⎠ + 1⎡⎢⎢⎣ ⎤⎥⎥⎦T

(12)

e above expressions are limited for the initial period ofvibration T from 02 to 20 s [5] e effective accelerationaeff must lie on the capacity curve and coincide with themaximum displacement dmax us the modification factorM defined by (13) is used to adjust the demand spectrume modified ADRS (MADRS) procedure is described anddepicted in Figure 4 [5]

M amax

aeff (13)

23 Nonlinear Modal Time-History Analysis To verify theNSA methods nonlinear modal THA is used in this study Itis also known as fast nonlinear analysis (FNA) in SAP2000e fundamental equilibrium equation of FNA can beexpressed as [23 24]

Meurou(t) + C _u(t) + Ku(t) + RNL(t) R(t) (14)

where M C and K are the mass proportional viscousdamping and stiffness matrices respectively the RNL(t) isthe nonlinear object force vector from the sum of the forcesin the nonlinear elements and R(t) is the applied load Ateach point of time the uncoupled modal equations aresolved exactly within the elastic structural system whereasforces within the predefined nonlinear DOF (indexed withinRNL(t)) are solved through an iterative process whichconverges to satisfy equilibrium In (14) the nonlinear forcesare treated as external loads and a set of load-dependent ritz(LDR) vectors Φ is generated to accurately capture theeffects of those forces

e input earthquake time histories used in this studyconsist of nine horizontal ground motions with magnituderanging from 653 to 76 All the data were obtained fromPacific Earthquake Engineering Research Center (PEER)[25] Table 1 shows seven near-fault ground motions (simplyassumed with a rupture distance lt15 km) and 2 far-faultground motions

3 A Case Study of Numerical Modeling fora Typical Korean STS Container Crane

31 Numerical Simulations e STS container crane con-sidered in this study is located at a seaport in South KoreaMost of the structural components were made of stiffenedhollow box sections except for diagonal braces which weretubes and forestays and backstays which were wide-flange

Displacement

Forc

e

umuy

fy(1 + αμ ndash α)fy

k ksecESED

1

αk

Figure 3 SDOF nonlinear system and equivalent viscous dampingdue to hysteretic energy dissipation

4 Advances in Civil Engineering

shapese properties of materials comply with the Japaneseindustrial standards (JIS) JIS-SM490Y and JIS-STK490 egeneral dimensions of the crane that is outreach cranegagespan backreach and height are illustrated in Figure 1A 3D FE model of the container was developed by theSAP2000 software package as discussed earlier In the FErepresentation the total number of elements is 9916 9912frame elements and 4 gap elementse forestays backstaysand diagonal braces were assigned end releases hence theseelements worked as truss elements All nonstructural loadsthat is stairs drive trucks stowed pins machinery house12 festoon snag device and boom hoist rope were appliedas concentrated or distributed loads e modal shapesnatural periods and frequencies of the first and third modeanalyzed by the Ritz vectors method are shown in Figure 5

32 Selection of Seismic Demand Several boreholes weredriven in the area of the seaport to consider the site soilconditions e soil investigation report showed that theshear wave velocity for the top 30m of ground for the fiveboreholes of the S-PS logging test were from 247ms to447ms as shown in Table 2 As a result the soil profile typesranged from SC to SD according to Korean Building Code[26] as shown in Table 3 In this study the soil type SD wasselected For the cranersquos site seismic zone I was consideredto be appropriate and a seismic zone factor S 022 g wasassigned for the maximum considered earthquake (MCE)with a return period of 2400 years e design accelerationresponse spectrum of soil type SD was then developed

corresponding to site coefficients Fa (for short period) and Fv(for 1 s period) of 136 and 196 respectively From the 5damping elastic response spectrum of soil type SD as shownin Figure 6 (the red curve) the Sa at the fundamental period(mode 3 with T135 s) is 021 g To verify the results ofnonlinear static analyses the response spectra of ninerecorded ground motions as shown in Table 1 were thenscaled to a spectral acceleration Sa of 021 g at the funda-mental period e scaled response spectra of the recordedground motions and design response spectrum according toKBC 2016 are shown in Figure 6

33 Nonlinear Static Analysis and Damage Criteria eplastic hinges were assigned to the portal frame as illustratedin Figure 7 assuming that they develop at the end of theframes using concentrated plasticity model [23 27] eproperties of plastic hinges are suggested in ASCESEI 41-13[3] For portal beams the moment-curvature (M-ϕ) re-lationship is sufficient to model the hinges assuming no axialforce is acting in them Although interaction relationship ofthe axial force (P) and the moments (M) in both axes isrequired for portal columns of a 3Dmodel a pinned supportis used for the pushover analysis to generate large portaldeformations during autoincrement static pushinge limitstate obtained by pushover analyses can be applied to THAfor a FE model using gap elements because the structuralcapacity is independent of the loading [28] According to thestructural performance levels and damage defined inASCESEI 41-13 for buildings the expected performance

Sd

Sa

dmax = μ dydy

amax

Tsec

Teff (μ)

ADRS (β0)

ADRS (βeff (μ))

MADRS (βeff (μ) M)

aeff

Capacity spectrum

M = amaxaeff

Spectral displacement Sd

Spec

tral

acce

lera

tion

Sa

Figure 4 Modified acceleration-displacement response spectrum (MADRS)

Table 1 Unscaled ground motions recorded during several earthquakes

Number (GM) Earthquake name Year Station Mag Mechanism RRUP (km) PGA (g)1 Imperial Valley-02 1940 El Centro array 09 695 Strike slip 61 0282 Imperial Valley-06 1979 El Centro array 06 653 Strike slip 14 0453 Landers 1992 Barstow 728 Strike slip 35 0134 Landers 1992 Yermo Fire station 728 Strike slip 24 0245 Loma Prieta 1989 Gilroy-Gavilan Coll 693 Rev oblique 10 0366 Northridge-01 1994 Newhall-Fire Sta 669 Reverse 59 0587 Northridge-01 1994 Sylmar-Converter Sta 669 Reverse 54 0628 Kobe Japan 1995 KJMA 690 Strike slip 10 0839 Chi-Chi Taiwan 1999 TCU065 762 Rev oblique 06 079Note RRUP is the closest distance to the rupture plane (rupture distance)

Advances in Civil Engineering 5

levels for steel container cranes (considering as steel momentframe SMF) are shown in Table 4 In previous studiesderailment defined as the reduction of the axial reaction ofat least one leg base to be zero due to sufficient lateral loadswas considered as a damage state [28] However it is re-ported that a crane was repaired by repositioning it on therails by jacking systems and mobile crane when it wasderailed without any damage to the upper structure that isthe repair of a Krupp crane at the Port of Oakland in the pastin this way [29] Hence derailment is assumed to be the onlyform of the cranersquos movement without damage of thestructure and the portal frame is still considered to beelastic Consideration of slight derailment is not consideredas a damage state in this study e damage state consideredin this study focuses only on the structural behavior of theportal frame Several other damage criteria for STS containercranes were suggested in previous studies [28 30] as brieflysummarized in Tables 5 and 6 based on observations ofdamages of container cranes subjected to past earthquakestesting of scaled models on shaking table and analyses of FEmodels

For the NSA procedures a concentrated force was ap-plied at the boom level as illustrated in Figure 7 underdisplacement-controlled analyses e results of pushoveranalyses indicate that both columns reach the limit states atthe same portal drift level even when the concentrated forceis applied in the seaward or landward direction In additionsince the cross sections of the waterside and landside legs areslightly different they are expected to have similar stiffnessand strength As a result Figure 7 indicates that both col-umns reach the immediate occupancy (IO) life safety (LS)and collapse prevention (CP) levels at a portal drift of ap-proximately 16 18 and 22 respectively In this study

the complex stiffened box sections of the portal columns havebeen converted into unstiffened box section for simplicitye section of the top of the portal columns is illustrated inFigure 8 e x-axis and y-axis are the trolley-travel directionand gantry-travel direction (along the rails) respectively It isnoted that the hollow box sections at the top of the portalcolumns of the Korean crane are smaller than those of craneJ100 as mentioned in Table 6 Even the overall height of theKorean crane is greater than that of the J100 Past recordsindicate that there were few moderate to large earthquakes inKorea us an optimization of the general stiffness of thewhole structure of a crane with less emphasis on the seismiceffect can reduce the initial cost for the owner

e ADRS diagrams consisting of both capacity andseismic demand are shown in Figure 9 e CSM and ELMwere performed under the seismic demand of KBC 2016with a selected damping ratio of 15 as suggested byKosbab for a jumbo container crane [28 31] e resultsfrom both pushover methods are similar e performancepoint of CSM indicates that the total base shear and max-imum horizontal displacement at the top of the portal frameare 169182 kN and 106 cm respectively e total baseshear and maximum displacement obtained from ELM are169186 kN and 106 cm respectively with a ductility ratioμ 10 and the modification factor M 1

34 Dynamic Analyses For the input ground motions theeffect of vertical excitation is high when the spectral accel-eration Sa of the crane (with a natural period of 03 s) is greaterthan 05 g as observed in the experimental study by KosbabFor lower Sa the effect of vertical excitation on the portal driftis around 01 [28] In this study the vertical groundmotionsare neglected with the assumption that their amplitudes areattenuated by the effect of quay wall and local site

e nonlinear modal THAwas considered incorporatingthe P-Δ effect e Rayleigh damping β which relates to themass and stiffness matrix was calculated by (15) and (16)considering mode 1 (boom torsion) and mode 3 (portalsway) as shown in Figure 5

β a01

2ωn

+ a1ωn

2 (15)

Mode 1 T = 382 s f = 026 Hz

(a)

Mode 3 T = 135 s f = 074 Hz

(b)

Figure 5 Numerical fundamental periods and modal shapes (a) boom torsion and (b) portal sway

Table 2 Soil investigation at a seaport in South Korea

Boreholes Shear wave velocity GL minus30m vs (ms) Soil typesBH-1 406 SCBH-2 252 SDBH-3 447 SCBH-4 247 SDBH-5 337 SD

6 Advances in Civil Engineering

Assuming that the frequencies of the two modes are ωi

and ωj having an equal damping ratio of 15 the co-efficients a0 and a1 can be obtained as follows

a0 β2ωiωj

ωi + ωj

a1 β2

ωi + ωj

(16)

During the operation the crane is not fixed to rails orquay wall For nonlinear THA therefore a gap link elementis used to simulate the contact between trucks and rails egap element is activated when structures come closer anddeactivated when they go far away [23] e axial force willbe set to zero when the portal leg is upliftede gap elementdoes not disengage in the horizontal direction duringuplifting It is also the limit of this support boundary asdiscussed in detail by Kosbab [28] However a gap element(or a similar type called no tension element) was proven tobe suitable to assess the uplift response as proposed byChaudhuri et al [32] e results of the THA together withthe NSA methods are discussed in detail in Section 4

4 Results and Discussions

41 Drift Response In contrast to the global drift analysis ofa building at the roof level most of the plastic hinges were

observed to be developed in the portal frame of the craneduring past earthquakes Furthermore the portal frame isthe main structure to support the whole upper structuresus the horizontal displacement or drift at the top of theportal frame is commonly considered [33 34] as shown inFigure 10e drift at the top of the portal frame (denoted asportal drift) of a container crane provides information onhow much of the horizontal deformation occurs at thefundamental mode in the trolley travel direction Besidesmeasuring the portal drift the drift at the top of upper legsand apex is monitored along with the corresponding heightas shown in Figure 10 e average drift of the portal frametop of upper leg and apex are estimated to be 061 026and 018 corresponding to heights of 166m 471m and766m respectively in the trolley travel direction from THAunder nine ground motions with scaled PGA ranging from010 g to 032 g e results of both pushover analyses usingCSM and ELM shown in Figure 9 are in good agreementwith that of THA In particular the average portal drift of064 is 003 larger than that of THA On the other handby using the deformation of the fundamental mode thedisplacements of the apex obtained from pushover analysesare significantly larger compared to the time-history ana-lyses with an error of over 16 e portal drifts obtainedfrom time-history and pushover analyses indicate that thecrane behaviors are in the elastic state under seismic exci-tations based on the performance levels in Figure 7According to other performance levels and damage criteria

Table 3 Site classification of KBC 2016

Soil types Soil profile nameAverage properties on the upper 30m of the site profile

Shear wavevelocity vs (ms)

Standard penetrationresistance N (blows30 cm)

Soil undrained shearstrength su (times10minus3MPa)

SA Hard rock gt1500 mdash mdashSB Rock 760 to 1500 mdash mdashSC Very dense soil and soft rock 360 to 760 gt50 gt100SD Stiff soil 180 to 360 15 to 50 50 to 100SE Soft soil lt180 lt15 lt50

00

02

04

06

08

10

12

00 05 10 15 20 25

Spec

tral

acce

lera

tion

Sa (

g)

Period T (s)

Design RS (KBC2016)Individual GMMean of GMs

Fundamental period

Figure 6 Scaled response spectra at the fundamental period

000

005

010

015

020

025

030

035

040

00 05 10 15 20 25 30

V bm

g

Portal dri ()Waterside legLandside leg

Imm

edia

te o

ccup

ancy

(IO

)

Life

safe

ty (L

S)

Colla

pse p

reve

ntio

n (C

P)

Hinge assignments

Figure 7 Pushover curve and limit states for typical Koreancontainer crane

Advances in Civil Engineering 7

as summarized in Tables 5 and 6 the cranemight work in thedamage degree I as defined by PIANC and between DR andIU levels according to Kosbabrsquos proposal

42 Total Base Shear e total base shears obtained fromCSM and ELM analyses are plotted in Figure 11 e totalbase shear is observed to be almost unrelated to the scaled

Table 4 Structural performance levels and damage based on ASCESEI 41-13 [3]

Elements Immediate occupancy (IO) Life safety (LS) Collapse prevention (CP)

For vertical elements of SMFs (ie portal columns of the crane)

Minor local yielding at a fewplaces No fractures Minorbuckling or observablepermanent distortion of

members

Hinges form Local buckling ofsome beam elements Severejoint distortion but shear

connections remain intact A fewelements may experience partial

fracture

Extensive distortion of beamsand column panels Many

fractures at momentconnections but shear

connections remain intact

Overall damage Light Moderate Severe

Table 5 Damage criteria for cranes according to PIANC [30]

Level of damage Degree I Degree II Degree III Degree IV

Displacement Withoutderailment With derailment Without overturning Overturning

Peak response stressesstrains(i) Upperstructures Elastic Elastic Plastic (ltμεmax for upper

structure)Plastic (geμεmax for upper

structure)

(ii) Portal frame Elastic Plastic (ltμεmax for portalframe) Without collapse Collapse

(iii) Toe Elastic Damage to toe (including pull-out of vehicle fracture of anchorbrakes)Note μ and εmax are the ductility factor and strain limit for the structure respectively

Table 6 Performance levels and limit states proposed by Kosbab [28]

Level ofdamageelements Derailment (DR) Immediate use (IU) Structural damage (SD) Complete collapse (CC)

Whole structures Derailed without anydamage to the structure

Minor structural damage(not significantly impacts its

operational capacity)Derailment may or may not

have occurred

Extensive damage and will notbe suitable for use without

major repairs but not collapse

Local buckling near theportal joints can quickly

lead to global instability andeventual collapse

Portal frame Elastic

Lower limit elastic Highlimit some minor bucklingof hollow sections (withinthe portal frame or not)

A portaldeformationlt deformation atmax load capacity up to thepoint of ultimate ductility

Portal deformationsurpasses the estimatedpoint of max ductility

Overall damage Derailed Minor damage Major damage CollapseLimit state in terms of portal drift (for reference)(i) Crane J100 13 20 30 45(ii) Crane LD100 mdash 15 20 30(iii) Crane LD50 15 19 25 35

182c

m

190cm 190cm

182c

m

Waterside leg tf = 20cmLandside leg tf = 16cm

Waterside leg tw = 16cm Landside leg tw = 12cm Flange

Web

(a) (b)

x

y

Figure 8 Hollow box elements (a) original stiffened section and (b) simplified unstiffened section

8 Advances in Civil Engineering

PGA magnitude and rupture distance For an example themaximum total base shear is obtained from a minimumPGA ground motion which is the Landers earthquake atYermo Fire station in 1992 (GM-4) with a PGA of 01 g orthe earthquake with a relatively high PGA value of around024 g (GM-2) at a short rupture distance (14 km) generatesa lower structural response of 141573 kN compared withthe average value of 167493 kN for the nine ground motionexcitations e total base shears obtained from pushovermethods show higher values than the average obtained fromTHA In particular the results for CSM and ELM are169182 kN and 169186 kN respectively as mentioned inthe previous section From this observation it can beconcluded that the pushover methods are suitable forseismic analysis of a STS container crane

43Uplift Behavior e uplifting of a crane will result in theredistribution of the load and will change the horizontal

displacement of the whole structure e uplift is defined bytwo conditions (1) the vertical displacement of the upliftedleg should be a positive value or zero (a negative value meansthe gap element is still ldquocloserdquo) and (2) the vertical reactionof the uplifted leg is zero In this study four portal legs twolandside legs (node 10 and 20) and two waterside legs (node30 and 40) as shown in Figure 1 are considered to studyuplift responses Figure 12 shows the potential uplift (interms of vertical responsedisplacement) and the time ofoccurrence of the landside leg (node 20) and waterside leg(node 30) It is noted that the term ldquopotential upliftrdquo is usedbecause the full uplift was not occurred under the earth-quake demand as discussed in Section 32 just a slight upliftmight happen in this study e full uplift of a crane leg isconsidered when a leg totally wins against the initial gravityload which meets both conditions as mentioned above Itcan be observed that the potential uplift of landside leg willoccur sooner than that of the waterside leg except for GM-3GM-8 and GM-9e reason could be that the center of total

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20

Hei

ght o

f cra

ne H

(m)

Horizontal displacement (cm)

Individual GMAverage of GMsPushover

Apex (3)

Top of upper leg (2)

Top of portalleg (1)

(3)

(1)

(2)

δ

(a)

0

10

20

30

40

50

60

70

80

90

0 02 04 06 08

Hei

ght o

f cra

ne H

(m)

Dri ()

Apex (3)

Top of upper leg (2)

Individual GMAverage of GMsPushover

Top of portalleg (1)

(b)

Figure 10 Height of crane versus (a) horizontal displacement and (b) drift

0

02

04

06

08

T=

05s

T = 10s

T = 15s

T = 20s

1

0 10 20 30 40

Spec

tral

acce

lera

tion

Sa (

g)

Spectral displacement Sd (cm)

15 dampingdemand spectrum

Capacity spectrum

(a)

T=

05s

T = 10s

T = 15s

T = 20s

Spec

tral

acce

lera

tion

Sa (

g)

0 10 20 30 40Spectral displacement Sd (cm)

Capacity spectrum

0

02

04

06

08

1

15 dampingdemand spectrum

(b)

Figure 9 Pushover analyses (a) CSM of ATC-40 and (b) ELM of FEMA 440

Advances in Civil Engineering 9

mass is not at the center of the two portal legs e total massconcentrates closer to the waterside legs than the landsidelegsus the first uplift will occur at the landside legs Whena leg is uplifted the axial force of the opposite leg will increasesignificantly In particular in this study it is observed that themaximum axial compressive force increases up to 120496 kNon the landside leg (node 10) due to the upward verticalresponsedisplacement of the waterside leg when excited bythe Landers earthquake (GM-4) at Yermo Fire station It isinteresting to note that the increase of the axial force of node10 is approximately 495 compared with the initial gravityforce of that node of around 243486 kN

On the other hand the vertical response of crane leg isobserved to be strongly influenced by the ground motionsrsquocharacteristics Figure 13 indicates that the amplitude of

vertical responsedisplacement decays significantly withtime after reaching the peak value when subjected to short-duration earthquakes such as GM-2 GM-5 GM-6 and GM-8 However the vertical response maintains large amplitudefor a long time when excited by long-duration earthquakeseven when the acceleration amplitude is not as high as inGM-4 GM-7 and GM-9 It can be stated that a long-duration earthquake may generate uplift and for a longperiod of time even when the input ground motion is of lowamplitude Assessment of the uplift behavior is an importantissue that should be considered in the seismic design ofa container crane to predict the overloading on the portallegs It is noted that a positive value of the vertical responseshown in Figure 13 means that the cranersquos leg moves upwardwhereas a negative value indicates a compression (downward

1300

1400

1500

1600

1700

1800

1900

2000

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tota

l bas

e she

ar V

b (k

N)

Earthquakes

Total base shear of each GMAverage of total base shear

Pushover-CSMPushover-ELM

Scaled PGA (g)Magnitude

02569561

02465314

025728350

010728240

032693100

01866959

01666954

01969010

02176206Rup distance (km)

Figure 11 Total base shear versus earthquakes

0

10

20

30

40

50

60

0

001

002

003

004

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tim

e of o

ccur

renc

e (s)

Upw

ard

vert

ical

resp

onse

(cm

)

Earthquakes

Time of occurrence (node 20)Time of occurrence (node 30)

Landside leg (node 20)Waterside leg (node 30)

Figure 12 Upward vertical responsesdisplacements of the landside and waterside legs versus time of occurrence due to dynamic analysis(gravity analysis not included)

10 Advances in Civil Engineering

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(a)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(b)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(c)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(d)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(e)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(f )

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(g)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(h)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(i)

Figure 13 Time-history vertical response of the landside leg (node 20) (a) Imperial Valley-02 (GM-1) (b) Imperial Valley-06 (GM-2) (c)Landers Barstow (GM-3) (d) Landers Yermo Fire Station (GM-4) (e) Loma Prieta (GM-5) (f ) Northridge-01 Newhall (GM-6) (g)Northridge-01 Sylmar (GM-7) (h) Kobe Japan (GM-8) (i) Chi-Chi Taiwan (GM-9)

Advances in Civil Engineering 11

movement) comparing with the state after analyzing gravityload When taking into account both static analysis (gravityload analysis) and dynamic analysis the value of verticaldisplacement is still negative in all cases indicating no fulluplift occurrence For example under subjected by theearthquake GM-4 (Landers at Yermo fire station) thelandside leg (node 20) results in a positive value of 0034 cmfor dynamic analysis and a negative value of minus0058 cm forgravity load analysis thus the value considering both cases ofanalysis is approximately minus0024 cm by summation ismeans that the crane might be slightly uplifted and will befully uplifted if the value of displacement reaches zero and thevertical reaction of the crane leg is zero as well

5 Conclusions

is study represents a preliminary investigation for theseismic behavior of a typical Korean STS container cranee complex seismic response of the crane is estimated byrepresenting it by a 3D FE model Nonlinear time-historyanalysis and both CSM and ELM pushover analyses methodsare used to analyze the crane and compare the resultsSeveral key observations can be made based on the resultsobtained from this study ey are as follows

e conventional CSM and ELM are found to be suf-ficient to analyze a STS container crane In particular therelative errors of the portal drift and total base shearobtained from pushover methods are 46 and 10 re-spectively comparing with those using the nonlinear time-history analyses However the horizontal displacements ofthe apex of the crane obtained from CSM and ELM appear tobe overestimated because these methods consider only thefundamental mode whereas the nonlinear time-historyanalysis uses the superposition principle of multiple modes

Assessment of uplift response is an important issue thatshould be considered in the seismic analysis of a containercrane It is clearly seen in this study that the axial force of thelandside legs increases nearly 50 of the initial gravity forceas the waterside legs are slightly uplifted us a gap ele-ment which is integrated into most of the commercialsoftware is appropriate for modeling base support to studythe uplift behavior On the other hand the uplift response isstrongly influenced by the characteristics of the groundmotions e potential uplift can have large amplitude fora long time when excited by long-duration earthquakes evenwhen the acceleration amplitude may not be high

e portal drifts of the typical Korean STS containercrane corresponding to performance levels of IO LS andCP as defined in ASCESEI 41-13 are 16 18 and 22respectively ese values can be used as damage limits forthe fragility analysis

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflict of interest

Acknowledgments

is research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education(2017R1D1A3B03032854) and by Ministry of public Ad-ministration and Security as Disaster Prevention SafetyHuman resource development Project and was also a part ofthe project titled ldquoDevelopment of performance-basedseismic design technologies for advancement in design codesfor port structuresrdquo funded by the Ministry of Oceans andFisheries Korea

References

[1] G H Powell Static Pushover Methods-Explanation Com-parison and Implementation 2013 httpswikicsiamericacomdisplayperformStatic+pushover+methods+-+explanation2C+comparison+and+implementation

[2] ATC 40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood CA USA 1996

[3] ASCESEI 41 Seismic Evaluation and Retrofit of ExistingBuildings American Society of Civil Engineers Reston VAUSA 2013

[4] Eurocode 8 Design of Structures for Earthquake ResistancePart 1 General Rules Seismic Actions and Rules for BuildingsEN 1998 European Committee for Standardization (CEN)Brussels Belgium 2004

[5] FEMA 440 Improvement of Nonlinear Static Seismic AnalysisProcedures Applied Technology Council (ATC-55 Project)Federal Emergency Management Agency Washington DCUSA 2006

[6] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 4pp 377ndash390 2007

[7] P Fajfar ldquoCapacity spectrum method based on inelasticdemand spectrardquo Earthquake Engineering and StructuralDynamics vol 28 no 9 pp 979ndash993 1999

[8] Y-Y Lin and K Chang ldquoAn improved capacity spectrummethod for ATC 40rdquo Earthquake Engineering and StructuralDynamics vol 32 no 13 pp 2013ndash2025 2003

[9] X Mingkui D Yinfeng L Gang and C Guangjun ldquoAnimproved capacity spectrum method based on inelastic de-mand spectrardquo in Proceedings of 4th International Conferenceon Earthquake Engineering Taipei Taiwan October 2006

[10] A Chopra and R Goel ldquoEvaluation of NSP to estimateseismic deformation SDF systemsrdquo Journal of StructuralEngineering vol 126 no 4 pp 482ndash490 2000

[11] S Freeman ldquoDevelopment and use of capacity spectrummethodrdquo in Proceedings of 6th US NCEE Conference onEarthquake Engineering pp 1ndash12 SeattleWA USA June 1998

[12] H Sucuoglu and M S Gunay ldquoGeneralized force vectors formulti-mode pushover analysisrdquo Earthquake Engineering andStructural Dynamics vol 40 no 1 pp 55ndash74 2011

[13] E Kalkan and S K Kunnath ldquoAdaptive modal combinationprocedure for nonlinear static analysis of building structuresrdquoJournal of Structural Engineering vol 132 no 11 pp 1721ndash1731 2006

[14] M Cosic and S Brcic ldquoIterative displacement coefficientmethod mathematical formulation and numerical analysesrdquoGraCevinar vol 65 no 3 pp 199ndash211 2013

12 Advances in Civil Engineering

where ED and ES are the energy dissipated in thenonlinear system (area of enclosed by hysteresisloop) and linear system (area of triangle) re-spectively μ umuy is the ductility factor α is thepost-yield stiffness ratio and ksec is the secantstiffness e natural vibration period of theequivalent linear system can be calculated as follows

Teq T

μ1 + αμminus α

1113970

(7)

(5) Convert Sd from step 4 to Δroof or an individualcomponent deformation and then compare themwith the limiting values for the specified perfor-mance goals [10 19]

Δroof Sdiϕroof1Γ1 (8)

Vb α1SaW (9)

where all the parameters in (8) and (9) are alreadyexplained in (1) and (2)

22 Equivalent Linearization Method (ELM) ProcedureSimilar to CSM ELM requires a response spectrum familyand uses estimates of ductility to obtain effective period andeffective damping In both procedures the global de-formation demand (including elastic and inelastic) on thestructure is computed from the response of an equivalentSDOF system e difference is in the technique used toobtain the maximum displacement demand [5] In con-ventional CSM the equivalent stiffness of inelastic system isassumed to be the secant stiffness and the equivalentdamping is related to the area under the capacity curve asillustrated in Figure 3 In ELM however the equivalentstiffness is estimated from effective period Teff and effectivedamping βeff derived from statistical analyses expressed asfunctions of ductility μ [5] Teff and βeff optimized for ap-plication to any capacity curve can be estimated as follows

For 10lt μlt 40

βeff 49(μminus 1)2 minus 11(μminus 1)

3+ β0

Teff 02(μminus 1)2 minus 0038(μminus 1)

3+ 11113960 1113961T

(10)

For 40le μle 65

βeff 14 + 032(μminus 1) + β0

Teff [028 + 013(μminus 1) + 1]T(11)

For μgt 65

βeff 19064(μminus 1)minus 1[064(μminus 1)]2

1113890 1113891Teff

T1113874 1113875

2+ β0

Teff 089

μminus 1

1 + 005(μminus 2)

1113971

minus 1⎛⎝ ⎞⎠ + 1⎡⎢⎢⎣ ⎤⎥⎥⎦T

(12)

e above expressions are limited for the initial period ofvibration T from 02 to 20 s [5] e effective accelerationaeff must lie on the capacity curve and coincide with themaximum displacement dmax us the modification factorM defined by (13) is used to adjust the demand spectrume modified ADRS (MADRS) procedure is described anddepicted in Figure 4 [5]

M amax

aeff (13)

23 Nonlinear Modal Time-History Analysis To verify theNSA methods nonlinear modal THA is used in this study Itis also known as fast nonlinear analysis (FNA) in SAP2000e fundamental equilibrium equation of FNA can beexpressed as [23 24]

Meurou(t) + C _u(t) + Ku(t) + RNL(t) R(t) (14)

where M C and K are the mass proportional viscousdamping and stiffness matrices respectively the RNL(t) isthe nonlinear object force vector from the sum of the forcesin the nonlinear elements and R(t) is the applied load Ateach point of time the uncoupled modal equations aresolved exactly within the elastic structural system whereasforces within the predefined nonlinear DOF (indexed withinRNL(t)) are solved through an iterative process whichconverges to satisfy equilibrium In (14) the nonlinear forcesare treated as external loads and a set of load-dependent ritz(LDR) vectors Φ is generated to accurately capture theeffects of those forces

e input earthquake time histories used in this studyconsist of nine horizontal ground motions with magnituderanging from 653 to 76 All the data were obtained fromPacific Earthquake Engineering Research Center (PEER)[25] Table 1 shows seven near-fault ground motions (simplyassumed with a rupture distance lt15 km) and 2 far-faultground motions

3 A Case Study of Numerical Modeling fora Typical Korean STS Container Crane

31 Numerical Simulations e STS container crane con-sidered in this study is located at a seaport in South KoreaMost of the structural components were made of stiffenedhollow box sections except for diagonal braces which weretubes and forestays and backstays which were wide-flange

Displacement

Forc

e

umuy

fy(1 + αμ ndash α)fy

k ksecESED

1

αk

Figure 3 SDOF nonlinear system and equivalent viscous dampingdue to hysteretic energy dissipation

4 Advances in Civil Engineering

shapese properties of materials comply with the Japaneseindustrial standards (JIS) JIS-SM490Y and JIS-STK490 egeneral dimensions of the crane that is outreach cranegagespan backreach and height are illustrated in Figure 1A 3D FE model of the container was developed by theSAP2000 software package as discussed earlier In the FErepresentation the total number of elements is 9916 9912frame elements and 4 gap elementse forestays backstaysand diagonal braces were assigned end releases hence theseelements worked as truss elements All nonstructural loadsthat is stairs drive trucks stowed pins machinery house12 festoon snag device and boom hoist rope were appliedas concentrated or distributed loads e modal shapesnatural periods and frequencies of the first and third modeanalyzed by the Ritz vectors method are shown in Figure 5

32 Selection of Seismic Demand Several boreholes weredriven in the area of the seaport to consider the site soilconditions e soil investigation report showed that theshear wave velocity for the top 30m of ground for the fiveboreholes of the S-PS logging test were from 247ms to447ms as shown in Table 2 As a result the soil profile typesranged from SC to SD according to Korean Building Code[26] as shown in Table 3 In this study the soil type SD wasselected For the cranersquos site seismic zone I was consideredto be appropriate and a seismic zone factor S 022 g wasassigned for the maximum considered earthquake (MCE)with a return period of 2400 years e design accelerationresponse spectrum of soil type SD was then developed

corresponding to site coefficients Fa (for short period) and Fv(for 1 s period) of 136 and 196 respectively From the 5damping elastic response spectrum of soil type SD as shownin Figure 6 (the red curve) the Sa at the fundamental period(mode 3 with T135 s) is 021 g To verify the results ofnonlinear static analyses the response spectra of ninerecorded ground motions as shown in Table 1 were thenscaled to a spectral acceleration Sa of 021 g at the funda-mental period e scaled response spectra of the recordedground motions and design response spectrum according toKBC 2016 are shown in Figure 6

33 Nonlinear Static Analysis and Damage Criteria eplastic hinges were assigned to the portal frame as illustratedin Figure 7 assuming that they develop at the end of theframes using concentrated plasticity model [23 27] eproperties of plastic hinges are suggested in ASCESEI 41-13[3] For portal beams the moment-curvature (M-ϕ) re-lationship is sufficient to model the hinges assuming no axialforce is acting in them Although interaction relationship ofthe axial force (P) and the moments (M) in both axes isrequired for portal columns of a 3Dmodel a pinned supportis used for the pushover analysis to generate large portaldeformations during autoincrement static pushinge limitstate obtained by pushover analyses can be applied to THAfor a FE model using gap elements because the structuralcapacity is independent of the loading [28] According to thestructural performance levels and damage defined inASCESEI 41-13 for buildings the expected performance

Sd

Sa

dmax = μ dydy

amax

Tsec

Teff (μ)

ADRS (β0)

ADRS (βeff (μ))

MADRS (βeff (μ) M)

aeff

Capacity spectrum

M = amaxaeff

Spectral displacement Sd

Spec

tral

acce

lera

tion

Sa

Figure 4 Modified acceleration-displacement response spectrum (MADRS)

Table 1 Unscaled ground motions recorded during several earthquakes

Number (GM) Earthquake name Year Station Mag Mechanism RRUP (km) PGA (g)1 Imperial Valley-02 1940 El Centro array 09 695 Strike slip 61 0282 Imperial Valley-06 1979 El Centro array 06 653 Strike slip 14 0453 Landers 1992 Barstow 728 Strike slip 35 0134 Landers 1992 Yermo Fire station 728 Strike slip 24 0245 Loma Prieta 1989 Gilroy-Gavilan Coll 693 Rev oblique 10 0366 Northridge-01 1994 Newhall-Fire Sta 669 Reverse 59 0587 Northridge-01 1994 Sylmar-Converter Sta 669 Reverse 54 0628 Kobe Japan 1995 KJMA 690 Strike slip 10 0839 Chi-Chi Taiwan 1999 TCU065 762 Rev oblique 06 079Note RRUP is the closest distance to the rupture plane (rupture distance)

Advances in Civil Engineering 5

levels for steel container cranes (considering as steel momentframe SMF) are shown in Table 4 In previous studiesderailment defined as the reduction of the axial reaction ofat least one leg base to be zero due to sufficient lateral loadswas considered as a damage state [28] However it is re-ported that a crane was repaired by repositioning it on therails by jacking systems and mobile crane when it wasderailed without any damage to the upper structure that isthe repair of a Krupp crane at the Port of Oakland in the pastin this way [29] Hence derailment is assumed to be the onlyform of the cranersquos movement without damage of thestructure and the portal frame is still considered to beelastic Consideration of slight derailment is not consideredas a damage state in this study e damage state consideredin this study focuses only on the structural behavior of theportal frame Several other damage criteria for STS containercranes were suggested in previous studies [28 30] as brieflysummarized in Tables 5 and 6 based on observations ofdamages of container cranes subjected to past earthquakestesting of scaled models on shaking table and analyses of FEmodels

For the NSA procedures a concentrated force was ap-plied at the boom level as illustrated in Figure 7 underdisplacement-controlled analyses e results of pushoveranalyses indicate that both columns reach the limit states atthe same portal drift level even when the concentrated forceis applied in the seaward or landward direction In additionsince the cross sections of the waterside and landside legs areslightly different they are expected to have similar stiffnessand strength As a result Figure 7 indicates that both col-umns reach the immediate occupancy (IO) life safety (LS)and collapse prevention (CP) levels at a portal drift of ap-proximately 16 18 and 22 respectively In this study

the complex stiffened box sections of the portal columns havebeen converted into unstiffened box section for simplicitye section of the top of the portal columns is illustrated inFigure 8 e x-axis and y-axis are the trolley-travel directionand gantry-travel direction (along the rails) respectively It isnoted that the hollow box sections at the top of the portalcolumns of the Korean crane are smaller than those of craneJ100 as mentioned in Table 6 Even the overall height of theKorean crane is greater than that of the J100 Past recordsindicate that there were few moderate to large earthquakes inKorea us an optimization of the general stiffness of thewhole structure of a crane with less emphasis on the seismiceffect can reduce the initial cost for the owner

e ADRS diagrams consisting of both capacity andseismic demand are shown in Figure 9 e CSM and ELMwere performed under the seismic demand of KBC 2016with a selected damping ratio of 15 as suggested byKosbab for a jumbo container crane [28 31] e resultsfrom both pushover methods are similar e performancepoint of CSM indicates that the total base shear and max-imum horizontal displacement at the top of the portal frameare 169182 kN and 106 cm respectively e total baseshear and maximum displacement obtained from ELM are169186 kN and 106 cm respectively with a ductility ratioμ 10 and the modification factor M 1

34 Dynamic Analyses For the input ground motions theeffect of vertical excitation is high when the spectral accel-eration Sa of the crane (with a natural period of 03 s) is greaterthan 05 g as observed in the experimental study by KosbabFor lower Sa the effect of vertical excitation on the portal driftis around 01 [28] In this study the vertical groundmotionsare neglected with the assumption that their amplitudes areattenuated by the effect of quay wall and local site

e nonlinear modal THAwas considered incorporatingthe P-Δ effect e Rayleigh damping β which relates to themass and stiffness matrix was calculated by (15) and (16)considering mode 1 (boom torsion) and mode 3 (portalsway) as shown in Figure 5

β a01

2ωn

+ a1ωn

2 (15)

Mode 1 T = 382 s f = 026 Hz

(a)

Mode 3 T = 135 s f = 074 Hz

(b)

Figure 5 Numerical fundamental periods and modal shapes (a) boom torsion and (b) portal sway

Table 2 Soil investigation at a seaport in South Korea

Boreholes Shear wave velocity GL minus30m vs (ms) Soil typesBH-1 406 SCBH-2 252 SDBH-3 447 SCBH-4 247 SDBH-5 337 SD

6 Advances in Civil Engineering

Assuming that the frequencies of the two modes are ωi

and ωj having an equal damping ratio of 15 the co-efficients a0 and a1 can be obtained as follows

a0 β2ωiωj

ωi + ωj

a1 β2

ωi + ωj

(16)

During the operation the crane is not fixed to rails orquay wall For nonlinear THA therefore a gap link elementis used to simulate the contact between trucks and rails egap element is activated when structures come closer anddeactivated when they go far away [23] e axial force willbe set to zero when the portal leg is upliftede gap elementdoes not disengage in the horizontal direction duringuplifting It is also the limit of this support boundary asdiscussed in detail by Kosbab [28] However a gap element(or a similar type called no tension element) was proven tobe suitable to assess the uplift response as proposed byChaudhuri et al [32] e results of the THA together withthe NSA methods are discussed in detail in Section 4

4 Results and Discussions

41 Drift Response In contrast to the global drift analysis ofa building at the roof level most of the plastic hinges were

observed to be developed in the portal frame of the craneduring past earthquakes Furthermore the portal frame isthe main structure to support the whole upper structuresus the horizontal displacement or drift at the top of theportal frame is commonly considered [33 34] as shown inFigure 10e drift at the top of the portal frame (denoted asportal drift) of a container crane provides information onhow much of the horizontal deformation occurs at thefundamental mode in the trolley travel direction Besidesmeasuring the portal drift the drift at the top of upper legsand apex is monitored along with the corresponding heightas shown in Figure 10 e average drift of the portal frametop of upper leg and apex are estimated to be 061 026and 018 corresponding to heights of 166m 471m and766m respectively in the trolley travel direction from THAunder nine ground motions with scaled PGA ranging from010 g to 032 g e results of both pushover analyses usingCSM and ELM shown in Figure 9 are in good agreementwith that of THA In particular the average portal drift of064 is 003 larger than that of THA On the other handby using the deformation of the fundamental mode thedisplacements of the apex obtained from pushover analysesare significantly larger compared to the time-history ana-lyses with an error of over 16 e portal drifts obtainedfrom time-history and pushover analyses indicate that thecrane behaviors are in the elastic state under seismic exci-tations based on the performance levels in Figure 7According to other performance levels and damage criteria

Table 3 Site classification of KBC 2016

Soil types Soil profile nameAverage properties on the upper 30m of the site profile

Shear wavevelocity vs (ms)

Standard penetrationresistance N (blows30 cm)

Soil undrained shearstrength su (times10minus3MPa)

SA Hard rock gt1500 mdash mdashSB Rock 760 to 1500 mdash mdashSC Very dense soil and soft rock 360 to 760 gt50 gt100SD Stiff soil 180 to 360 15 to 50 50 to 100SE Soft soil lt180 lt15 lt50

00

02

04

06

08

10

12

00 05 10 15 20 25

Spec

tral

acce

lera

tion

Sa (

g)

Period T (s)

Design RS (KBC2016)Individual GMMean of GMs

Fundamental period

Figure 6 Scaled response spectra at the fundamental period

000

005

010

015

020

025

030

035

040

00 05 10 15 20 25 30

V bm

g

Portal dri ()Waterside legLandside leg

Imm

edia

te o

ccup

ancy

(IO

)

Life

safe

ty (L

S)

Colla

pse p

reve

ntio

n (C

P)

Hinge assignments

Figure 7 Pushover curve and limit states for typical Koreancontainer crane

Advances in Civil Engineering 7

as summarized in Tables 5 and 6 the cranemight work in thedamage degree I as defined by PIANC and between DR andIU levels according to Kosbabrsquos proposal

42 Total Base Shear e total base shears obtained fromCSM and ELM analyses are plotted in Figure 11 e totalbase shear is observed to be almost unrelated to the scaled

Table 4 Structural performance levels and damage based on ASCESEI 41-13 [3]

Elements Immediate occupancy (IO) Life safety (LS) Collapse prevention (CP)

For vertical elements of SMFs (ie portal columns of the crane)

Minor local yielding at a fewplaces No fractures Minorbuckling or observablepermanent distortion of

members

Hinges form Local buckling ofsome beam elements Severejoint distortion but shear

connections remain intact A fewelements may experience partial

fracture

Extensive distortion of beamsand column panels Many

fractures at momentconnections but shear

connections remain intact

Overall damage Light Moderate Severe

Table 5 Damage criteria for cranes according to PIANC [30]

Level of damage Degree I Degree II Degree III Degree IV

Displacement Withoutderailment With derailment Without overturning Overturning

Peak response stressesstrains(i) Upperstructures Elastic Elastic Plastic (ltμεmax for upper

structure)Plastic (geμεmax for upper

structure)

(ii) Portal frame Elastic Plastic (ltμεmax for portalframe) Without collapse Collapse

(iii) Toe Elastic Damage to toe (including pull-out of vehicle fracture of anchorbrakes)Note μ and εmax are the ductility factor and strain limit for the structure respectively

Table 6 Performance levels and limit states proposed by Kosbab [28]

Level ofdamageelements Derailment (DR) Immediate use (IU) Structural damage (SD) Complete collapse (CC)

Whole structures Derailed without anydamage to the structure

Minor structural damage(not significantly impacts its

operational capacity)Derailment may or may not

have occurred

Extensive damage and will notbe suitable for use without

major repairs but not collapse

Local buckling near theportal joints can quickly

lead to global instability andeventual collapse

Portal frame Elastic

Lower limit elastic Highlimit some minor bucklingof hollow sections (withinthe portal frame or not)

A portaldeformationlt deformation atmax load capacity up to thepoint of ultimate ductility

Portal deformationsurpasses the estimatedpoint of max ductility

Overall damage Derailed Minor damage Major damage CollapseLimit state in terms of portal drift (for reference)(i) Crane J100 13 20 30 45(ii) Crane LD100 mdash 15 20 30(iii) Crane LD50 15 19 25 35

182c

m

190cm 190cm

182c

m

Waterside leg tf = 20cmLandside leg tf = 16cm

Waterside leg tw = 16cm Landside leg tw = 12cm Flange

Web

(a) (b)

x

y

Figure 8 Hollow box elements (a) original stiffened section and (b) simplified unstiffened section

8 Advances in Civil Engineering

PGA magnitude and rupture distance For an example themaximum total base shear is obtained from a minimumPGA ground motion which is the Landers earthquake atYermo Fire station in 1992 (GM-4) with a PGA of 01 g orthe earthquake with a relatively high PGA value of around024 g (GM-2) at a short rupture distance (14 km) generatesa lower structural response of 141573 kN compared withthe average value of 167493 kN for the nine ground motionexcitations e total base shears obtained from pushovermethods show higher values than the average obtained fromTHA In particular the results for CSM and ELM are169182 kN and 169186 kN respectively as mentioned inthe previous section From this observation it can beconcluded that the pushover methods are suitable forseismic analysis of a STS container crane

43Uplift Behavior e uplifting of a crane will result in theredistribution of the load and will change the horizontal

displacement of the whole structure e uplift is defined bytwo conditions (1) the vertical displacement of the upliftedleg should be a positive value or zero (a negative value meansthe gap element is still ldquocloserdquo) and (2) the vertical reactionof the uplifted leg is zero In this study four portal legs twolandside legs (node 10 and 20) and two waterside legs (node30 and 40) as shown in Figure 1 are considered to studyuplift responses Figure 12 shows the potential uplift (interms of vertical responsedisplacement) and the time ofoccurrence of the landside leg (node 20) and waterside leg(node 30) It is noted that the term ldquopotential upliftrdquo is usedbecause the full uplift was not occurred under the earth-quake demand as discussed in Section 32 just a slight upliftmight happen in this study e full uplift of a crane leg isconsidered when a leg totally wins against the initial gravityload which meets both conditions as mentioned above Itcan be observed that the potential uplift of landside leg willoccur sooner than that of the waterside leg except for GM-3GM-8 and GM-9e reason could be that the center of total

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20

Hei

ght o

f cra

ne H

(m)

Horizontal displacement (cm)

Individual GMAverage of GMsPushover

Apex (3)

Top of upper leg (2)

Top of portalleg (1)

(3)

(1)

(2)

δ

(a)

0

10

20

30

40

50

60

70

80

90

0 02 04 06 08

Hei

ght o

f cra

ne H

(m)

Dri ()

Apex (3)

Top of upper leg (2)

Individual GMAverage of GMsPushover

Top of portalleg (1)

(b)

Figure 10 Height of crane versus (a) horizontal displacement and (b) drift

0

02

04

06

08

T=

05s

T = 10s

T = 15s

T = 20s

1

0 10 20 30 40

Spec

tral

acce

lera

tion

Sa (

g)

Spectral displacement Sd (cm)

15 dampingdemand spectrum

Capacity spectrum

(a)

T=

05s

T = 10s

T = 15s

T = 20s

Spec

tral

acce

lera

tion

Sa (

g)

0 10 20 30 40Spectral displacement Sd (cm)

Capacity spectrum

0

02

04

06

08

1

15 dampingdemand spectrum

(b)

Figure 9 Pushover analyses (a) CSM of ATC-40 and (b) ELM of FEMA 440

Advances in Civil Engineering 9

mass is not at the center of the two portal legs e total massconcentrates closer to the waterside legs than the landsidelegsus the first uplift will occur at the landside legs Whena leg is uplifted the axial force of the opposite leg will increasesignificantly In particular in this study it is observed that themaximum axial compressive force increases up to 120496 kNon the landside leg (node 10) due to the upward verticalresponsedisplacement of the waterside leg when excited bythe Landers earthquake (GM-4) at Yermo Fire station It isinteresting to note that the increase of the axial force of node10 is approximately 495 compared with the initial gravityforce of that node of around 243486 kN

On the other hand the vertical response of crane leg isobserved to be strongly influenced by the ground motionsrsquocharacteristics Figure 13 indicates that the amplitude of

vertical responsedisplacement decays significantly withtime after reaching the peak value when subjected to short-duration earthquakes such as GM-2 GM-5 GM-6 and GM-8 However the vertical response maintains large amplitudefor a long time when excited by long-duration earthquakeseven when the acceleration amplitude is not as high as inGM-4 GM-7 and GM-9 It can be stated that a long-duration earthquake may generate uplift and for a longperiod of time even when the input ground motion is of lowamplitude Assessment of the uplift behavior is an importantissue that should be considered in the seismic design ofa container crane to predict the overloading on the portallegs It is noted that a positive value of the vertical responseshown in Figure 13 means that the cranersquos leg moves upwardwhereas a negative value indicates a compression (downward

1300

1400

1500

1600

1700

1800

1900

2000

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tota

l bas

e she

ar V

b (k

N)

Earthquakes

Total base shear of each GMAverage of total base shear

Pushover-CSMPushover-ELM

Scaled PGA (g)Magnitude

02569561

02465314

025728350

010728240

032693100

01866959

01666954

01969010

02176206Rup distance (km)

Figure 11 Total base shear versus earthquakes

0

10

20

30

40

50

60

0

001

002

003

004

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tim

e of o

ccur

renc

e (s)

Upw

ard

vert

ical

resp

onse

(cm

)

Earthquakes

Time of occurrence (node 20)Time of occurrence (node 30)

Landside leg (node 20)Waterside leg (node 30)

Figure 12 Upward vertical responsesdisplacements of the landside and waterside legs versus time of occurrence due to dynamic analysis(gravity analysis not included)

10 Advances in Civil Engineering

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(a)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(b)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(c)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(d)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(e)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(f )

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(g)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(h)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(i)

Figure 13 Time-history vertical response of the landside leg (node 20) (a) Imperial Valley-02 (GM-1) (b) Imperial Valley-06 (GM-2) (c)Landers Barstow (GM-3) (d) Landers Yermo Fire Station (GM-4) (e) Loma Prieta (GM-5) (f ) Northridge-01 Newhall (GM-6) (g)Northridge-01 Sylmar (GM-7) (h) Kobe Japan (GM-8) (i) Chi-Chi Taiwan (GM-9)

Advances in Civil Engineering 11

movement) comparing with the state after analyzing gravityload When taking into account both static analysis (gravityload analysis) and dynamic analysis the value of verticaldisplacement is still negative in all cases indicating no fulluplift occurrence For example under subjected by theearthquake GM-4 (Landers at Yermo fire station) thelandside leg (node 20) results in a positive value of 0034 cmfor dynamic analysis and a negative value of minus0058 cm forgravity load analysis thus the value considering both cases ofanalysis is approximately minus0024 cm by summation ismeans that the crane might be slightly uplifted and will befully uplifted if the value of displacement reaches zero and thevertical reaction of the crane leg is zero as well

5 Conclusions

is study represents a preliminary investigation for theseismic behavior of a typical Korean STS container cranee complex seismic response of the crane is estimated byrepresenting it by a 3D FE model Nonlinear time-historyanalysis and both CSM and ELM pushover analyses methodsare used to analyze the crane and compare the resultsSeveral key observations can be made based on the resultsobtained from this study ey are as follows

e conventional CSM and ELM are found to be suf-ficient to analyze a STS container crane In particular therelative errors of the portal drift and total base shearobtained from pushover methods are 46 and 10 re-spectively comparing with those using the nonlinear time-history analyses However the horizontal displacements ofthe apex of the crane obtained from CSM and ELM appear tobe overestimated because these methods consider only thefundamental mode whereas the nonlinear time-historyanalysis uses the superposition principle of multiple modes

Assessment of uplift response is an important issue thatshould be considered in the seismic analysis of a containercrane It is clearly seen in this study that the axial force of thelandside legs increases nearly 50 of the initial gravity forceas the waterside legs are slightly uplifted us a gap ele-ment which is integrated into most of the commercialsoftware is appropriate for modeling base support to studythe uplift behavior On the other hand the uplift response isstrongly influenced by the characteristics of the groundmotions e potential uplift can have large amplitude fora long time when excited by long-duration earthquakes evenwhen the acceleration amplitude may not be high

e portal drifts of the typical Korean STS containercrane corresponding to performance levels of IO LS andCP as defined in ASCESEI 41-13 are 16 18 and 22respectively ese values can be used as damage limits forthe fragility analysis

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflict of interest

Acknowledgments

is research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education(2017R1D1A3B03032854) and by Ministry of public Ad-ministration and Security as Disaster Prevention SafetyHuman resource development Project and was also a part ofthe project titled ldquoDevelopment of performance-basedseismic design technologies for advancement in design codesfor port structuresrdquo funded by the Ministry of Oceans andFisheries Korea

References

[1] G H Powell Static Pushover Methods-Explanation Com-parison and Implementation 2013 httpswikicsiamericacomdisplayperformStatic+pushover+methods+-+explanation2C+comparison+and+implementation

[2] ATC 40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood CA USA 1996

[3] ASCESEI 41 Seismic Evaluation and Retrofit of ExistingBuildings American Society of Civil Engineers Reston VAUSA 2013

[4] Eurocode 8 Design of Structures for Earthquake ResistancePart 1 General Rules Seismic Actions and Rules for BuildingsEN 1998 European Committee for Standardization (CEN)Brussels Belgium 2004

[5] FEMA 440 Improvement of Nonlinear Static Seismic AnalysisProcedures Applied Technology Council (ATC-55 Project)Federal Emergency Management Agency Washington DCUSA 2006

[6] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 4pp 377ndash390 2007

[7] P Fajfar ldquoCapacity spectrum method based on inelasticdemand spectrardquo Earthquake Engineering and StructuralDynamics vol 28 no 9 pp 979ndash993 1999

[8] Y-Y Lin and K Chang ldquoAn improved capacity spectrummethod for ATC 40rdquo Earthquake Engineering and StructuralDynamics vol 32 no 13 pp 2013ndash2025 2003

[9] X Mingkui D Yinfeng L Gang and C Guangjun ldquoAnimproved capacity spectrum method based on inelastic de-mand spectrardquo in Proceedings of 4th International Conferenceon Earthquake Engineering Taipei Taiwan October 2006

[10] A Chopra and R Goel ldquoEvaluation of NSP to estimateseismic deformation SDF systemsrdquo Journal of StructuralEngineering vol 126 no 4 pp 482ndash490 2000

[11] S Freeman ldquoDevelopment and use of capacity spectrummethodrdquo in Proceedings of 6th US NCEE Conference onEarthquake Engineering pp 1ndash12 SeattleWA USA June 1998

[12] H Sucuoglu and M S Gunay ldquoGeneralized force vectors formulti-mode pushover analysisrdquo Earthquake Engineering andStructural Dynamics vol 40 no 1 pp 55ndash74 2011

[13] E Kalkan and S K Kunnath ldquoAdaptive modal combinationprocedure for nonlinear static analysis of building structuresrdquoJournal of Structural Engineering vol 132 no 11 pp 1721ndash1731 2006

[14] M Cosic and S Brcic ldquoIterative displacement coefficientmethod mathematical formulation and numerical analysesrdquoGraCevinar vol 65 no 3 pp 199ndash211 2013

12 Advances in Civil Engineering

shapese properties of materials comply with the Japaneseindustrial standards (JIS) JIS-SM490Y and JIS-STK490 egeneral dimensions of the crane that is outreach cranegagespan backreach and height are illustrated in Figure 1A 3D FE model of the container was developed by theSAP2000 software package as discussed earlier In the FErepresentation the total number of elements is 9916 9912frame elements and 4 gap elementse forestays backstaysand diagonal braces were assigned end releases hence theseelements worked as truss elements All nonstructural loadsthat is stairs drive trucks stowed pins machinery house12 festoon snag device and boom hoist rope were appliedas concentrated or distributed loads e modal shapesnatural periods and frequencies of the first and third modeanalyzed by the Ritz vectors method are shown in Figure 5

32 Selection of Seismic Demand Several boreholes weredriven in the area of the seaport to consider the site soilconditions e soil investigation report showed that theshear wave velocity for the top 30m of ground for the fiveboreholes of the S-PS logging test were from 247ms to447ms as shown in Table 2 As a result the soil profile typesranged from SC to SD according to Korean Building Code[26] as shown in Table 3 In this study the soil type SD wasselected For the cranersquos site seismic zone I was consideredto be appropriate and a seismic zone factor S 022 g wasassigned for the maximum considered earthquake (MCE)with a return period of 2400 years e design accelerationresponse spectrum of soil type SD was then developed

corresponding to site coefficients Fa (for short period) and Fv(for 1 s period) of 136 and 196 respectively From the 5damping elastic response spectrum of soil type SD as shownin Figure 6 (the red curve) the Sa at the fundamental period(mode 3 with T135 s) is 021 g To verify the results ofnonlinear static analyses the response spectra of ninerecorded ground motions as shown in Table 1 were thenscaled to a spectral acceleration Sa of 021 g at the funda-mental period e scaled response spectra of the recordedground motions and design response spectrum according toKBC 2016 are shown in Figure 6

33 Nonlinear Static Analysis and Damage Criteria eplastic hinges were assigned to the portal frame as illustratedin Figure 7 assuming that they develop at the end of theframes using concentrated plasticity model [23 27] eproperties of plastic hinges are suggested in ASCESEI 41-13[3] For portal beams the moment-curvature (M-ϕ) re-lationship is sufficient to model the hinges assuming no axialforce is acting in them Although interaction relationship ofthe axial force (P) and the moments (M) in both axes isrequired for portal columns of a 3Dmodel a pinned supportis used for the pushover analysis to generate large portaldeformations during autoincrement static pushinge limitstate obtained by pushover analyses can be applied to THAfor a FE model using gap elements because the structuralcapacity is independent of the loading [28] According to thestructural performance levels and damage defined inASCESEI 41-13 for buildings the expected performance

Sd

Sa

dmax = μ dydy

amax

Tsec

Teff (μ)

ADRS (β0)

ADRS (βeff (μ))

MADRS (βeff (μ) M)

aeff

Capacity spectrum

M = amaxaeff

Spectral displacement Sd

Spec

tral

acce

lera

tion

Sa

Figure 4 Modified acceleration-displacement response spectrum (MADRS)

Table 1 Unscaled ground motions recorded during several earthquakes

Number (GM) Earthquake name Year Station Mag Mechanism RRUP (km) PGA (g)1 Imperial Valley-02 1940 El Centro array 09 695 Strike slip 61 0282 Imperial Valley-06 1979 El Centro array 06 653 Strike slip 14 0453 Landers 1992 Barstow 728 Strike slip 35 0134 Landers 1992 Yermo Fire station 728 Strike slip 24 0245 Loma Prieta 1989 Gilroy-Gavilan Coll 693 Rev oblique 10 0366 Northridge-01 1994 Newhall-Fire Sta 669 Reverse 59 0587 Northridge-01 1994 Sylmar-Converter Sta 669 Reverse 54 0628 Kobe Japan 1995 KJMA 690 Strike slip 10 0839 Chi-Chi Taiwan 1999 TCU065 762 Rev oblique 06 079Note RRUP is the closest distance to the rupture plane (rupture distance)

Advances in Civil Engineering 5

levels for steel container cranes (considering as steel momentframe SMF) are shown in Table 4 In previous studiesderailment defined as the reduction of the axial reaction ofat least one leg base to be zero due to sufficient lateral loadswas considered as a damage state [28] However it is re-ported that a crane was repaired by repositioning it on therails by jacking systems and mobile crane when it wasderailed without any damage to the upper structure that isthe repair of a Krupp crane at the Port of Oakland in the pastin this way [29] Hence derailment is assumed to be the onlyform of the cranersquos movement without damage of thestructure and the portal frame is still considered to beelastic Consideration of slight derailment is not consideredas a damage state in this study e damage state consideredin this study focuses only on the structural behavior of theportal frame Several other damage criteria for STS containercranes were suggested in previous studies [28 30] as brieflysummarized in Tables 5 and 6 based on observations ofdamages of container cranes subjected to past earthquakestesting of scaled models on shaking table and analyses of FEmodels

For the NSA procedures a concentrated force was ap-plied at the boom level as illustrated in Figure 7 underdisplacement-controlled analyses e results of pushoveranalyses indicate that both columns reach the limit states atthe same portal drift level even when the concentrated forceis applied in the seaward or landward direction In additionsince the cross sections of the waterside and landside legs areslightly different they are expected to have similar stiffnessand strength As a result Figure 7 indicates that both col-umns reach the immediate occupancy (IO) life safety (LS)and collapse prevention (CP) levels at a portal drift of ap-proximately 16 18 and 22 respectively In this study

the complex stiffened box sections of the portal columns havebeen converted into unstiffened box section for simplicitye section of the top of the portal columns is illustrated inFigure 8 e x-axis and y-axis are the trolley-travel directionand gantry-travel direction (along the rails) respectively It isnoted that the hollow box sections at the top of the portalcolumns of the Korean crane are smaller than those of craneJ100 as mentioned in Table 6 Even the overall height of theKorean crane is greater than that of the J100 Past recordsindicate that there were few moderate to large earthquakes inKorea us an optimization of the general stiffness of thewhole structure of a crane with less emphasis on the seismiceffect can reduce the initial cost for the owner

e ADRS diagrams consisting of both capacity andseismic demand are shown in Figure 9 e CSM and ELMwere performed under the seismic demand of KBC 2016with a selected damping ratio of 15 as suggested byKosbab for a jumbo container crane [28 31] e resultsfrom both pushover methods are similar e performancepoint of CSM indicates that the total base shear and max-imum horizontal displacement at the top of the portal frameare 169182 kN and 106 cm respectively e total baseshear and maximum displacement obtained from ELM are169186 kN and 106 cm respectively with a ductility ratioμ 10 and the modification factor M 1

34 Dynamic Analyses For the input ground motions theeffect of vertical excitation is high when the spectral accel-eration Sa of the crane (with a natural period of 03 s) is greaterthan 05 g as observed in the experimental study by KosbabFor lower Sa the effect of vertical excitation on the portal driftis around 01 [28] In this study the vertical groundmotionsare neglected with the assumption that their amplitudes areattenuated by the effect of quay wall and local site

e nonlinear modal THAwas considered incorporatingthe P-Δ effect e Rayleigh damping β which relates to themass and stiffness matrix was calculated by (15) and (16)considering mode 1 (boom torsion) and mode 3 (portalsway) as shown in Figure 5

β a01

2ωn

+ a1ωn

2 (15)

Mode 1 T = 382 s f = 026 Hz

(a)

Mode 3 T = 135 s f = 074 Hz

(b)

Figure 5 Numerical fundamental periods and modal shapes (a) boom torsion and (b) portal sway

Table 2 Soil investigation at a seaport in South Korea

Boreholes Shear wave velocity GL minus30m vs (ms) Soil typesBH-1 406 SCBH-2 252 SDBH-3 447 SCBH-4 247 SDBH-5 337 SD

6 Advances in Civil Engineering

Assuming that the frequencies of the two modes are ωi

and ωj having an equal damping ratio of 15 the co-efficients a0 and a1 can be obtained as follows

a0 β2ωiωj

ωi + ωj

a1 β2

ωi + ωj

(16)

During the operation the crane is not fixed to rails orquay wall For nonlinear THA therefore a gap link elementis used to simulate the contact between trucks and rails egap element is activated when structures come closer anddeactivated when they go far away [23] e axial force willbe set to zero when the portal leg is upliftede gap elementdoes not disengage in the horizontal direction duringuplifting It is also the limit of this support boundary asdiscussed in detail by Kosbab [28] However a gap element(or a similar type called no tension element) was proven tobe suitable to assess the uplift response as proposed byChaudhuri et al [32] e results of the THA together withthe NSA methods are discussed in detail in Section 4

4 Results and Discussions

41 Drift Response In contrast to the global drift analysis ofa building at the roof level most of the plastic hinges were

observed to be developed in the portal frame of the craneduring past earthquakes Furthermore the portal frame isthe main structure to support the whole upper structuresus the horizontal displacement or drift at the top of theportal frame is commonly considered [33 34] as shown inFigure 10e drift at the top of the portal frame (denoted asportal drift) of a container crane provides information onhow much of the horizontal deformation occurs at thefundamental mode in the trolley travel direction Besidesmeasuring the portal drift the drift at the top of upper legsand apex is monitored along with the corresponding heightas shown in Figure 10 e average drift of the portal frametop of upper leg and apex are estimated to be 061 026and 018 corresponding to heights of 166m 471m and766m respectively in the trolley travel direction from THAunder nine ground motions with scaled PGA ranging from010 g to 032 g e results of both pushover analyses usingCSM and ELM shown in Figure 9 are in good agreementwith that of THA In particular the average portal drift of064 is 003 larger than that of THA On the other handby using the deformation of the fundamental mode thedisplacements of the apex obtained from pushover analysesare significantly larger compared to the time-history ana-lyses with an error of over 16 e portal drifts obtainedfrom time-history and pushover analyses indicate that thecrane behaviors are in the elastic state under seismic exci-tations based on the performance levels in Figure 7According to other performance levels and damage criteria

Table 3 Site classification of KBC 2016

Soil types Soil profile nameAverage properties on the upper 30m of the site profile

Shear wavevelocity vs (ms)

Standard penetrationresistance N (blows30 cm)

Soil undrained shearstrength su (times10minus3MPa)

SA Hard rock gt1500 mdash mdashSB Rock 760 to 1500 mdash mdashSC Very dense soil and soft rock 360 to 760 gt50 gt100SD Stiff soil 180 to 360 15 to 50 50 to 100SE Soft soil lt180 lt15 lt50

00

02

04

06

08

10

12

00 05 10 15 20 25

Spec

tral

acce

lera

tion

Sa (

g)

Period T (s)

Design RS (KBC2016)Individual GMMean of GMs

Fundamental period

Figure 6 Scaled response spectra at the fundamental period

000

005

010

015

020

025

030

035

040

00 05 10 15 20 25 30

V bm

g

Portal dri ()Waterside legLandside leg

Imm

edia

te o

ccup

ancy

(IO

)

Life

safe

ty (L

S)

Colla

pse p

reve

ntio

n (C

P)

Hinge assignments

Figure 7 Pushover curve and limit states for typical Koreancontainer crane

Advances in Civil Engineering 7

as summarized in Tables 5 and 6 the cranemight work in thedamage degree I as defined by PIANC and between DR andIU levels according to Kosbabrsquos proposal

42 Total Base Shear e total base shears obtained fromCSM and ELM analyses are plotted in Figure 11 e totalbase shear is observed to be almost unrelated to the scaled

Table 4 Structural performance levels and damage based on ASCESEI 41-13 [3]

Elements Immediate occupancy (IO) Life safety (LS) Collapse prevention (CP)

For vertical elements of SMFs (ie portal columns of the crane)

Minor local yielding at a fewplaces No fractures Minorbuckling or observablepermanent distortion of

members

Hinges form Local buckling ofsome beam elements Severejoint distortion but shear

connections remain intact A fewelements may experience partial

fracture

Extensive distortion of beamsand column panels Many

fractures at momentconnections but shear

connections remain intact

Overall damage Light Moderate Severe

Table 5 Damage criteria for cranes according to PIANC [30]

Level of damage Degree I Degree II Degree III Degree IV

Displacement Withoutderailment With derailment Without overturning Overturning

Peak response stressesstrains(i) Upperstructures Elastic Elastic Plastic (ltμεmax for upper

structure)Plastic (geμεmax for upper

structure)

(ii) Portal frame Elastic Plastic (ltμεmax for portalframe) Without collapse Collapse

(iii) Toe Elastic Damage to toe (including pull-out of vehicle fracture of anchorbrakes)Note μ and εmax are the ductility factor and strain limit for the structure respectively

Table 6 Performance levels and limit states proposed by Kosbab [28]

Level ofdamageelements Derailment (DR) Immediate use (IU) Structural damage (SD) Complete collapse (CC)

Whole structures Derailed without anydamage to the structure

Minor structural damage(not significantly impacts its

operational capacity)Derailment may or may not

have occurred

Extensive damage and will notbe suitable for use without

major repairs but not collapse

Local buckling near theportal joints can quickly

lead to global instability andeventual collapse

Portal frame Elastic

Lower limit elastic Highlimit some minor bucklingof hollow sections (withinthe portal frame or not)

A portaldeformationlt deformation atmax load capacity up to thepoint of ultimate ductility

Portal deformationsurpasses the estimatedpoint of max ductility

Overall damage Derailed Minor damage Major damage CollapseLimit state in terms of portal drift (for reference)(i) Crane J100 13 20 30 45(ii) Crane LD100 mdash 15 20 30(iii) Crane LD50 15 19 25 35

182c

m

190cm 190cm

182c

m

Waterside leg tf = 20cmLandside leg tf = 16cm

Waterside leg tw = 16cm Landside leg tw = 12cm Flange

Web

(a) (b)

x

y

Figure 8 Hollow box elements (a) original stiffened section and (b) simplified unstiffened section

8 Advances in Civil Engineering

PGA magnitude and rupture distance For an example themaximum total base shear is obtained from a minimumPGA ground motion which is the Landers earthquake atYermo Fire station in 1992 (GM-4) with a PGA of 01 g orthe earthquake with a relatively high PGA value of around024 g (GM-2) at a short rupture distance (14 km) generatesa lower structural response of 141573 kN compared withthe average value of 167493 kN for the nine ground motionexcitations e total base shears obtained from pushovermethods show higher values than the average obtained fromTHA In particular the results for CSM and ELM are169182 kN and 169186 kN respectively as mentioned inthe previous section From this observation it can beconcluded that the pushover methods are suitable forseismic analysis of a STS container crane

43Uplift Behavior e uplifting of a crane will result in theredistribution of the load and will change the horizontal

displacement of the whole structure e uplift is defined bytwo conditions (1) the vertical displacement of the upliftedleg should be a positive value or zero (a negative value meansthe gap element is still ldquocloserdquo) and (2) the vertical reactionof the uplifted leg is zero In this study four portal legs twolandside legs (node 10 and 20) and two waterside legs (node30 and 40) as shown in Figure 1 are considered to studyuplift responses Figure 12 shows the potential uplift (interms of vertical responsedisplacement) and the time ofoccurrence of the landside leg (node 20) and waterside leg(node 30) It is noted that the term ldquopotential upliftrdquo is usedbecause the full uplift was not occurred under the earth-quake demand as discussed in Section 32 just a slight upliftmight happen in this study e full uplift of a crane leg isconsidered when a leg totally wins against the initial gravityload which meets both conditions as mentioned above Itcan be observed that the potential uplift of landside leg willoccur sooner than that of the waterside leg except for GM-3GM-8 and GM-9e reason could be that the center of total

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20

Hei

ght o

f cra

ne H

(m)

Horizontal displacement (cm)

Individual GMAverage of GMsPushover

Apex (3)

Top of upper leg (2)

Top of portalleg (1)

(3)

(1)

(2)

δ

(a)

0

10

20

30

40

50

60

70

80

90

0 02 04 06 08

Hei

ght o

f cra

ne H

(m)

Dri ()

Apex (3)

Top of upper leg (2)

Individual GMAverage of GMsPushover

Top of portalleg (1)

(b)

Figure 10 Height of crane versus (a) horizontal displacement and (b) drift

0

02

04

06

08

T=

05s

T = 10s

T = 15s

T = 20s

1

0 10 20 30 40

Spec

tral

acce

lera

tion

Sa (

g)

Spectral displacement Sd (cm)

15 dampingdemand spectrum

Capacity spectrum

(a)

T=

05s

T = 10s

T = 15s

T = 20s

Spec

tral

acce

lera

tion

Sa (

g)

0 10 20 30 40Spectral displacement Sd (cm)

Capacity spectrum

0

02

04

06

08

1

15 dampingdemand spectrum

(b)

Figure 9 Pushover analyses (a) CSM of ATC-40 and (b) ELM of FEMA 440

Advances in Civil Engineering 9

mass is not at the center of the two portal legs e total massconcentrates closer to the waterside legs than the landsidelegsus the first uplift will occur at the landside legs Whena leg is uplifted the axial force of the opposite leg will increasesignificantly In particular in this study it is observed that themaximum axial compressive force increases up to 120496 kNon the landside leg (node 10) due to the upward verticalresponsedisplacement of the waterside leg when excited bythe Landers earthquake (GM-4) at Yermo Fire station It isinteresting to note that the increase of the axial force of node10 is approximately 495 compared with the initial gravityforce of that node of around 243486 kN

On the other hand the vertical response of crane leg isobserved to be strongly influenced by the ground motionsrsquocharacteristics Figure 13 indicates that the amplitude of

vertical responsedisplacement decays significantly withtime after reaching the peak value when subjected to short-duration earthquakes such as GM-2 GM-5 GM-6 and GM-8 However the vertical response maintains large amplitudefor a long time when excited by long-duration earthquakeseven when the acceleration amplitude is not as high as inGM-4 GM-7 and GM-9 It can be stated that a long-duration earthquake may generate uplift and for a longperiod of time even when the input ground motion is of lowamplitude Assessment of the uplift behavior is an importantissue that should be considered in the seismic design ofa container crane to predict the overloading on the portallegs It is noted that a positive value of the vertical responseshown in Figure 13 means that the cranersquos leg moves upwardwhereas a negative value indicates a compression (downward

1300

1400

1500

1600

1700

1800

1900

2000

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tota

l bas

e she

ar V

b (k

N)

Earthquakes

Total base shear of each GMAverage of total base shear

Pushover-CSMPushover-ELM

Scaled PGA (g)Magnitude

02569561

02465314

025728350

010728240

032693100

01866959

01666954

01969010

02176206Rup distance (km)

Figure 11 Total base shear versus earthquakes

0

10

20

30

40

50

60

0

001

002

003

004

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tim

e of o

ccur

renc

e (s)

Upw

ard

vert

ical

resp

onse

(cm

)

Earthquakes

Time of occurrence (node 20)Time of occurrence (node 30)

Landside leg (node 20)Waterside leg (node 30)

Figure 12 Upward vertical responsesdisplacements of the landside and waterside legs versus time of occurrence due to dynamic analysis(gravity analysis not included)

10 Advances in Civil Engineering

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(a)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(b)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(c)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(d)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(e)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(f )

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(g)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(h)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(i)

Figure 13 Time-history vertical response of the landside leg (node 20) (a) Imperial Valley-02 (GM-1) (b) Imperial Valley-06 (GM-2) (c)Landers Barstow (GM-3) (d) Landers Yermo Fire Station (GM-4) (e) Loma Prieta (GM-5) (f ) Northridge-01 Newhall (GM-6) (g)Northridge-01 Sylmar (GM-7) (h) Kobe Japan (GM-8) (i) Chi-Chi Taiwan (GM-9)

Advances in Civil Engineering 11

movement) comparing with the state after analyzing gravityload When taking into account both static analysis (gravityload analysis) and dynamic analysis the value of verticaldisplacement is still negative in all cases indicating no fulluplift occurrence For example under subjected by theearthquake GM-4 (Landers at Yermo fire station) thelandside leg (node 20) results in a positive value of 0034 cmfor dynamic analysis and a negative value of minus0058 cm forgravity load analysis thus the value considering both cases ofanalysis is approximately minus0024 cm by summation ismeans that the crane might be slightly uplifted and will befully uplifted if the value of displacement reaches zero and thevertical reaction of the crane leg is zero as well

5 Conclusions

is study represents a preliminary investigation for theseismic behavior of a typical Korean STS container cranee complex seismic response of the crane is estimated byrepresenting it by a 3D FE model Nonlinear time-historyanalysis and both CSM and ELM pushover analyses methodsare used to analyze the crane and compare the resultsSeveral key observations can be made based on the resultsobtained from this study ey are as follows

e conventional CSM and ELM are found to be suf-ficient to analyze a STS container crane In particular therelative errors of the portal drift and total base shearobtained from pushover methods are 46 and 10 re-spectively comparing with those using the nonlinear time-history analyses However the horizontal displacements ofthe apex of the crane obtained from CSM and ELM appear tobe overestimated because these methods consider only thefundamental mode whereas the nonlinear time-historyanalysis uses the superposition principle of multiple modes

Assessment of uplift response is an important issue thatshould be considered in the seismic analysis of a containercrane It is clearly seen in this study that the axial force of thelandside legs increases nearly 50 of the initial gravity forceas the waterside legs are slightly uplifted us a gap ele-ment which is integrated into most of the commercialsoftware is appropriate for modeling base support to studythe uplift behavior On the other hand the uplift response isstrongly influenced by the characteristics of the groundmotions e potential uplift can have large amplitude fora long time when excited by long-duration earthquakes evenwhen the acceleration amplitude may not be high

e portal drifts of the typical Korean STS containercrane corresponding to performance levels of IO LS andCP as defined in ASCESEI 41-13 are 16 18 and 22respectively ese values can be used as damage limits forthe fragility analysis

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflict of interest

Acknowledgments

is research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education(2017R1D1A3B03032854) and by Ministry of public Ad-ministration and Security as Disaster Prevention SafetyHuman resource development Project and was also a part ofthe project titled ldquoDevelopment of performance-basedseismic design technologies for advancement in design codesfor port structuresrdquo funded by the Ministry of Oceans andFisheries Korea

References

[1] G H Powell Static Pushover Methods-Explanation Com-parison and Implementation 2013 httpswikicsiamericacomdisplayperformStatic+pushover+methods+-+explanation2C+comparison+and+implementation

[2] ATC 40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood CA USA 1996

[3] ASCESEI 41 Seismic Evaluation and Retrofit of ExistingBuildings American Society of Civil Engineers Reston VAUSA 2013

[4] Eurocode 8 Design of Structures for Earthquake ResistancePart 1 General Rules Seismic Actions and Rules for BuildingsEN 1998 European Committee for Standardization (CEN)Brussels Belgium 2004

[5] FEMA 440 Improvement of Nonlinear Static Seismic AnalysisProcedures Applied Technology Council (ATC-55 Project)Federal Emergency Management Agency Washington DCUSA 2006

[6] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 4pp 377ndash390 2007

[7] P Fajfar ldquoCapacity spectrum method based on inelasticdemand spectrardquo Earthquake Engineering and StructuralDynamics vol 28 no 9 pp 979ndash993 1999

[8] Y-Y Lin and K Chang ldquoAn improved capacity spectrummethod for ATC 40rdquo Earthquake Engineering and StructuralDynamics vol 32 no 13 pp 2013ndash2025 2003

[9] X Mingkui D Yinfeng L Gang and C Guangjun ldquoAnimproved capacity spectrum method based on inelastic de-mand spectrardquo in Proceedings of 4th International Conferenceon Earthquake Engineering Taipei Taiwan October 2006

[10] A Chopra and R Goel ldquoEvaluation of NSP to estimateseismic deformation SDF systemsrdquo Journal of StructuralEngineering vol 126 no 4 pp 482ndash490 2000

[11] S Freeman ldquoDevelopment and use of capacity spectrummethodrdquo in Proceedings of 6th US NCEE Conference onEarthquake Engineering pp 1ndash12 SeattleWA USA June 1998

[12] H Sucuoglu and M S Gunay ldquoGeneralized force vectors formulti-mode pushover analysisrdquo Earthquake Engineering andStructural Dynamics vol 40 no 1 pp 55ndash74 2011

[13] E Kalkan and S K Kunnath ldquoAdaptive modal combinationprocedure for nonlinear static analysis of building structuresrdquoJournal of Structural Engineering vol 132 no 11 pp 1721ndash1731 2006

[14] M Cosic and S Brcic ldquoIterative displacement coefficientmethod mathematical formulation and numerical analysesrdquoGraCevinar vol 65 no 3 pp 199ndash211 2013

12 Advances in Civil Engineering

levels for steel container cranes (considering as steel momentframe SMF) are shown in Table 4 In previous studiesderailment defined as the reduction of the axial reaction ofat least one leg base to be zero due to sufficient lateral loadswas considered as a damage state [28] However it is re-ported that a crane was repaired by repositioning it on therails by jacking systems and mobile crane when it wasderailed without any damage to the upper structure that isthe repair of a Krupp crane at the Port of Oakland in the pastin this way [29] Hence derailment is assumed to be the onlyform of the cranersquos movement without damage of thestructure and the portal frame is still considered to beelastic Consideration of slight derailment is not consideredas a damage state in this study e damage state consideredin this study focuses only on the structural behavior of theportal frame Several other damage criteria for STS containercranes were suggested in previous studies [28 30] as brieflysummarized in Tables 5 and 6 based on observations ofdamages of container cranes subjected to past earthquakestesting of scaled models on shaking table and analyses of FEmodels

For the NSA procedures a concentrated force was ap-plied at the boom level as illustrated in Figure 7 underdisplacement-controlled analyses e results of pushoveranalyses indicate that both columns reach the limit states atthe same portal drift level even when the concentrated forceis applied in the seaward or landward direction In additionsince the cross sections of the waterside and landside legs areslightly different they are expected to have similar stiffnessand strength As a result Figure 7 indicates that both col-umns reach the immediate occupancy (IO) life safety (LS)and collapse prevention (CP) levels at a portal drift of ap-proximately 16 18 and 22 respectively In this study

the complex stiffened box sections of the portal columns havebeen converted into unstiffened box section for simplicitye section of the top of the portal columns is illustrated inFigure 8 e x-axis and y-axis are the trolley-travel directionand gantry-travel direction (along the rails) respectively It isnoted that the hollow box sections at the top of the portalcolumns of the Korean crane are smaller than those of craneJ100 as mentioned in Table 6 Even the overall height of theKorean crane is greater than that of the J100 Past recordsindicate that there were few moderate to large earthquakes inKorea us an optimization of the general stiffness of thewhole structure of a crane with less emphasis on the seismiceffect can reduce the initial cost for the owner

e ADRS diagrams consisting of both capacity andseismic demand are shown in Figure 9 e CSM and ELMwere performed under the seismic demand of KBC 2016with a selected damping ratio of 15 as suggested byKosbab for a jumbo container crane [28 31] e resultsfrom both pushover methods are similar e performancepoint of CSM indicates that the total base shear and max-imum horizontal displacement at the top of the portal frameare 169182 kN and 106 cm respectively e total baseshear and maximum displacement obtained from ELM are169186 kN and 106 cm respectively with a ductility ratioμ 10 and the modification factor M 1

34 Dynamic Analyses For the input ground motions theeffect of vertical excitation is high when the spectral accel-eration Sa of the crane (with a natural period of 03 s) is greaterthan 05 g as observed in the experimental study by KosbabFor lower Sa the effect of vertical excitation on the portal driftis around 01 [28] In this study the vertical groundmotionsare neglected with the assumption that their amplitudes areattenuated by the effect of quay wall and local site

e nonlinear modal THAwas considered incorporatingthe P-Δ effect e Rayleigh damping β which relates to themass and stiffness matrix was calculated by (15) and (16)considering mode 1 (boom torsion) and mode 3 (portalsway) as shown in Figure 5

β a01

2ωn

+ a1ωn

2 (15)

Mode 1 T = 382 s f = 026 Hz

(a)

Mode 3 T = 135 s f = 074 Hz

(b)

Figure 5 Numerical fundamental periods and modal shapes (a) boom torsion and (b) portal sway

Table 2 Soil investigation at a seaport in South Korea

Boreholes Shear wave velocity GL minus30m vs (ms) Soil typesBH-1 406 SCBH-2 252 SDBH-3 447 SCBH-4 247 SDBH-5 337 SD

6 Advances in Civil Engineering

Assuming that the frequencies of the two modes are ωi

and ωj having an equal damping ratio of 15 the co-efficients a0 and a1 can be obtained as follows

a0 β2ωiωj

ωi + ωj

a1 β2

ωi + ωj

(16)

During the operation the crane is not fixed to rails orquay wall For nonlinear THA therefore a gap link elementis used to simulate the contact between trucks and rails egap element is activated when structures come closer anddeactivated when they go far away [23] e axial force willbe set to zero when the portal leg is upliftede gap elementdoes not disengage in the horizontal direction duringuplifting It is also the limit of this support boundary asdiscussed in detail by Kosbab [28] However a gap element(or a similar type called no tension element) was proven tobe suitable to assess the uplift response as proposed byChaudhuri et al [32] e results of the THA together withthe NSA methods are discussed in detail in Section 4

4 Results and Discussions

41 Drift Response In contrast to the global drift analysis ofa building at the roof level most of the plastic hinges were

observed to be developed in the portal frame of the craneduring past earthquakes Furthermore the portal frame isthe main structure to support the whole upper structuresus the horizontal displacement or drift at the top of theportal frame is commonly considered [33 34] as shown inFigure 10e drift at the top of the portal frame (denoted asportal drift) of a container crane provides information onhow much of the horizontal deformation occurs at thefundamental mode in the trolley travel direction Besidesmeasuring the portal drift the drift at the top of upper legsand apex is monitored along with the corresponding heightas shown in Figure 10 e average drift of the portal frametop of upper leg and apex are estimated to be 061 026and 018 corresponding to heights of 166m 471m and766m respectively in the trolley travel direction from THAunder nine ground motions with scaled PGA ranging from010 g to 032 g e results of both pushover analyses usingCSM and ELM shown in Figure 9 are in good agreementwith that of THA In particular the average portal drift of064 is 003 larger than that of THA On the other handby using the deformation of the fundamental mode thedisplacements of the apex obtained from pushover analysesare significantly larger compared to the time-history ana-lyses with an error of over 16 e portal drifts obtainedfrom time-history and pushover analyses indicate that thecrane behaviors are in the elastic state under seismic exci-tations based on the performance levels in Figure 7According to other performance levels and damage criteria

Table 3 Site classification of KBC 2016

Soil types Soil profile nameAverage properties on the upper 30m of the site profile

Shear wavevelocity vs (ms)

Standard penetrationresistance N (blows30 cm)

Soil undrained shearstrength su (times10minus3MPa)

SA Hard rock gt1500 mdash mdashSB Rock 760 to 1500 mdash mdashSC Very dense soil and soft rock 360 to 760 gt50 gt100SD Stiff soil 180 to 360 15 to 50 50 to 100SE Soft soil lt180 lt15 lt50

00

02

04

06

08

10

12

00 05 10 15 20 25

Spec

tral

acce

lera

tion

Sa (

g)

Period T (s)

Design RS (KBC2016)Individual GMMean of GMs

Fundamental period

Figure 6 Scaled response spectra at the fundamental period

000

005

010

015

020

025

030

035

040

00 05 10 15 20 25 30

V bm

g

Portal dri ()Waterside legLandside leg

Imm

edia

te o

ccup

ancy

(IO

)

Life

safe

ty (L

S)

Colla

pse p

reve

ntio

n (C

P)

Hinge assignments

Figure 7 Pushover curve and limit states for typical Koreancontainer crane

Advances in Civil Engineering 7

as summarized in Tables 5 and 6 the cranemight work in thedamage degree I as defined by PIANC and between DR andIU levels according to Kosbabrsquos proposal

42 Total Base Shear e total base shears obtained fromCSM and ELM analyses are plotted in Figure 11 e totalbase shear is observed to be almost unrelated to the scaled

Table 4 Structural performance levels and damage based on ASCESEI 41-13 [3]

Elements Immediate occupancy (IO) Life safety (LS) Collapse prevention (CP)

For vertical elements of SMFs (ie portal columns of the crane)

Minor local yielding at a fewplaces No fractures Minorbuckling or observablepermanent distortion of

members

Hinges form Local buckling ofsome beam elements Severejoint distortion but shear

connections remain intact A fewelements may experience partial

fracture

Extensive distortion of beamsand column panels Many

fractures at momentconnections but shear

connections remain intact

Overall damage Light Moderate Severe

Table 5 Damage criteria for cranes according to PIANC [30]

Level of damage Degree I Degree II Degree III Degree IV

Displacement Withoutderailment With derailment Without overturning Overturning

Peak response stressesstrains(i) Upperstructures Elastic Elastic Plastic (ltμεmax for upper

structure)Plastic (geμεmax for upper

structure)

(ii) Portal frame Elastic Plastic (ltμεmax for portalframe) Without collapse Collapse

(iii) Toe Elastic Damage to toe (including pull-out of vehicle fracture of anchorbrakes)Note μ and εmax are the ductility factor and strain limit for the structure respectively

Table 6 Performance levels and limit states proposed by Kosbab [28]

Level ofdamageelements Derailment (DR) Immediate use (IU) Structural damage (SD) Complete collapse (CC)

Whole structures Derailed without anydamage to the structure

Minor structural damage(not significantly impacts its

operational capacity)Derailment may or may not

have occurred

Extensive damage and will notbe suitable for use without

major repairs but not collapse

Local buckling near theportal joints can quickly

lead to global instability andeventual collapse

Portal frame Elastic

Lower limit elastic Highlimit some minor bucklingof hollow sections (withinthe portal frame or not)

A portaldeformationlt deformation atmax load capacity up to thepoint of ultimate ductility

Portal deformationsurpasses the estimatedpoint of max ductility

Overall damage Derailed Minor damage Major damage CollapseLimit state in terms of portal drift (for reference)(i) Crane J100 13 20 30 45(ii) Crane LD100 mdash 15 20 30(iii) Crane LD50 15 19 25 35

182c

m

190cm 190cm

182c

m

Waterside leg tf = 20cmLandside leg tf = 16cm

Waterside leg tw = 16cm Landside leg tw = 12cm Flange

Web

(a) (b)

x

y

Figure 8 Hollow box elements (a) original stiffened section and (b) simplified unstiffened section

8 Advances in Civil Engineering

PGA magnitude and rupture distance For an example themaximum total base shear is obtained from a minimumPGA ground motion which is the Landers earthquake atYermo Fire station in 1992 (GM-4) with a PGA of 01 g orthe earthquake with a relatively high PGA value of around024 g (GM-2) at a short rupture distance (14 km) generatesa lower structural response of 141573 kN compared withthe average value of 167493 kN for the nine ground motionexcitations e total base shears obtained from pushovermethods show higher values than the average obtained fromTHA In particular the results for CSM and ELM are169182 kN and 169186 kN respectively as mentioned inthe previous section From this observation it can beconcluded that the pushover methods are suitable forseismic analysis of a STS container crane

43Uplift Behavior e uplifting of a crane will result in theredistribution of the load and will change the horizontal

displacement of the whole structure e uplift is defined bytwo conditions (1) the vertical displacement of the upliftedleg should be a positive value or zero (a negative value meansthe gap element is still ldquocloserdquo) and (2) the vertical reactionof the uplifted leg is zero In this study four portal legs twolandside legs (node 10 and 20) and two waterside legs (node30 and 40) as shown in Figure 1 are considered to studyuplift responses Figure 12 shows the potential uplift (interms of vertical responsedisplacement) and the time ofoccurrence of the landside leg (node 20) and waterside leg(node 30) It is noted that the term ldquopotential upliftrdquo is usedbecause the full uplift was not occurred under the earth-quake demand as discussed in Section 32 just a slight upliftmight happen in this study e full uplift of a crane leg isconsidered when a leg totally wins against the initial gravityload which meets both conditions as mentioned above Itcan be observed that the potential uplift of landside leg willoccur sooner than that of the waterside leg except for GM-3GM-8 and GM-9e reason could be that the center of total

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20

Hei

ght o

f cra

ne H

(m)

Horizontal displacement (cm)

Individual GMAverage of GMsPushover

Apex (3)

Top of upper leg (2)

Top of portalleg (1)

(3)

(1)

(2)

δ

(a)

0

10

20

30

40

50

60

70

80

90

0 02 04 06 08

Hei

ght o

f cra

ne H

(m)

Dri ()

Apex (3)

Top of upper leg (2)

Individual GMAverage of GMsPushover

Top of portalleg (1)

(b)

Figure 10 Height of crane versus (a) horizontal displacement and (b) drift

0

02

04

06

08

T=

05s

T = 10s

T = 15s

T = 20s

1

0 10 20 30 40

Spec

tral

acce

lera

tion

Sa (

g)

Spectral displacement Sd (cm)

15 dampingdemand spectrum

Capacity spectrum

(a)

T=

05s

T = 10s

T = 15s

T = 20s

Spec

tral

acce

lera

tion

Sa (

g)

0 10 20 30 40Spectral displacement Sd (cm)

Capacity spectrum

0

02

04

06

08

1

15 dampingdemand spectrum

(b)

Figure 9 Pushover analyses (a) CSM of ATC-40 and (b) ELM of FEMA 440

Advances in Civil Engineering 9

mass is not at the center of the two portal legs e total massconcentrates closer to the waterside legs than the landsidelegsus the first uplift will occur at the landside legs Whena leg is uplifted the axial force of the opposite leg will increasesignificantly In particular in this study it is observed that themaximum axial compressive force increases up to 120496 kNon the landside leg (node 10) due to the upward verticalresponsedisplacement of the waterside leg when excited bythe Landers earthquake (GM-4) at Yermo Fire station It isinteresting to note that the increase of the axial force of node10 is approximately 495 compared with the initial gravityforce of that node of around 243486 kN

On the other hand the vertical response of crane leg isobserved to be strongly influenced by the ground motionsrsquocharacteristics Figure 13 indicates that the amplitude of

vertical responsedisplacement decays significantly withtime after reaching the peak value when subjected to short-duration earthquakes such as GM-2 GM-5 GM-6 and GM-8 However the vertical response maintains large amplitudefor a long time when excited by long-duration earthquakeseven when the acceleration amplitude is not as high as inGM-4 GM-7 and GM-9 It can be stated that a long-duration earthquake may generate uplift and for a longperiod of time even when the input ground motion is of lowamplitude Assessment of the uplift behavior is an importantissue that should be considered in the seismic design ofa container crane to predict the overloading on the portallegs It is noted that a positive value of the vertical responseshown in Figure 13 means that the cranersquos leg moves upwardwhereas a negative value indicates a compression (downward

1300

1400

1500

1600

1700

1800

1900

2000

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tota

l bas

e she

ar V

b (k

N)

Earthquakes

Total base shear of each GMAverage of total base shear

Pushover-CSMPushover-ELM

Scaled PGA (g)Magnitude

02569561

02465314

025728350

010728240

032693100

01866959

01666954

01969010

02176206Rup distance (km)

Figure 11 Total base shear versus earthquakes

0

10

20

30

40

50

60

0

001

002

003

004

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tim

e of o

ccur

renc

e (s)

Upw

ard

vert

ical

resp

onse

(cm

)

Earthquakes

Time of occurrence (node 20)Time of occurrence (node 30)

Landside leg (node 20)Waterside leg (node 30)

Figure 12 Upward vertical responsesdisplacements of the landside and waterside legs versus time of occurrence due to dynamic analysis(gravity analysis not included)

10 Advances in Civil Engineering

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(a)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(b)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(c)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(d)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(e)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(f )

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(g)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(h)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(i)

Figure 13 Time-history vertical response of the landside leg (node 20) (a) Imperial Valley-02 (GM-1) (b) Imperial Valley-06 (GM-2) (c)Landers Barstow (GM-3) (d) Landers Yermo Fire Station (GM-4) (e) Loma Prieta (GM-5) (f ) Northridge-01 Newhall (GM-6) (g)Northridge-01 Sylmar (GM-7) (h) Kobe Japan (GM-8) (i) Chi-Chi Taiwan (GM-9)

Advances in Civil Engineering 11

movement) comparing with the state after analyzing gravityload When taking into account both static analysis (gravityload analysis) and dynamic analysis the value of verticaldisplacement is still negative in all cases indicating no fulluplift occurrence For example under subjected by theearthquake GM-4 (Landers at Yermo fire station) thelandside leg (node 20) results in a positive value of 0034 cmfor dynamic analysis and a negative value of minus0058 cm forgravity load analysis thus the value considering both cases ofanalysis is approximately minus0024 cm by summation ismeans that the crane might be slightly uplifted and will befully uplifted if the value of displacement reaches zero and thevertical reaction of the crane leg is zero as well

5 Conclusions

is study represents a preliminary investigation for theseismic behavior of a typical Korean STS container cranee complex seismic response of the crane is estimated byrepresenting it by a 3D FE model Nonlinear time-historyanalysis and both CSM and ELM pushover analyses methodsare used to analyze the crane and compare the resultsSeveral key observations can be made based on the resultsobtained from this study ey are as follows

e conventional CSM and ELM are found to be suf-ficient to analyze a STS container crane In particular therelative errors of the portal drift and total base shearobtained from pushover methods are 46 and 10 re-spectively comparing with those using the nonlinear time-history analyses However the horizontal displacements ofthe apex of the crane obtained from CSM and ELM appear tobe overestimated because these methods consider only thefundamental mode whereas the nonlinear time-historyanalysis uses the superposition principle of multiple modes

Assessment of uplift response is an important issue thatshould be considered in the seismic analysis of a containercrane It is clearly seen in this study that the axial force of thelandside legs increases nearly 50 of the initial gravity forceas the waterside legs are slightly uplifted us a gap ele-ment which is integrated into most of the commercialsoftware is appropriate for modeling base support to studythe uplift behavior On the other hand the uplift response isstrongly influenced by the characteristics of the groundmotions e potential uplift can have large amplitude fora long time when excited by long-duration earthquakes evenwhen the acceleration amplitude may not be high

e portal drifts of the typical Korean STS containercrane corresponding to performance levels of IO LS andCP as defined in ASCESEI 41-13 are 16 18 and 22respectively ese values can be used as damage limits forthe fragility analysis

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflict of interest

Acknowledgments

is research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education(2017R1D1A3B03032854) and by Ministry of public Ad-ministration and Security as Disaster Prevention SafetyHuman resource development Project and was also a part ofthe project titled ldquoDevelopment of performance-basedseismic design technologies for advancement in design codesfor port structuresrdquo funded by the Ministry of Oceans andFisheries Korea

References

[1] G H Powell Static Pushover Methods-Explanation Com-parison and Implementation 2013 httpswikicsiamericacomdisplayperformStatic+pushover+methods+-+explanation2C+comparison+and+implementation

[2] ATC 40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood CA USA 1996

[3] ASCESEI 41 Seismic Evaluation and Retrofit of ExistingBuildings American Society of Civil Engineers Reston VAUSA 2013

[4] Eurocode 8 Design of Structures for Earthquake ResistancePart 1 General Rules Seismic Actions and Rules for BuildingsEN 1998 European Committee for Standardization (CEN)Brussels Belgium 2004

[5] FEMA 440 Improvement of Nonlinear Static Seismic AnalysisProcedures Applied Technology Council (ATC-55 Project)Federal Emergency Management Agency Washington DCUSA 2006

[6] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 4pp 377ndash390 2007

[7] P Fajfar ldquoCapacity spectrum method based on inelasticdemand spectrardquo Earthquake Engineering and StructuralDynamics vol 28 no 9 pp 979ndash993 1999

[8] Y-Y Lin and K Chang ldquoAn improved capacity spectrummethod for ATC 40rdquo Earthquake Engineering and StructuralDynamics vol 32 no 13 pp 2013ndash2025 2003

[9] X Mingkui D Yinfeng L Gang and C Guangjun ldquoAnimproved capacity spectrum method based on inelastic de-mand spectrardquo in Proceedings of 4th International Conferenceon Earthquake Engineering Taipei Taiwan October 2006

[10] A Chopra and R Goel ldquoEvaluation of NSP to estimateseismic deformation SDF systemsrdquo Journal of StructuralEngineering vol 126 no 4 pp 482ndash490 2000

[11] S Freeman ldquoDevelopment and use of capacity spectrummethodrdquo in Proceedings of 6th US NCEE Conference onEarthquake Engineering pp 1ndash12 SeattleWA USA June 1998

[12] H Sucuoglu and M S Gunay ldquoGeneralized force vectors formulti-mode pushover analysisrdquo Earthquake Engineering andStructural Dynamics vol 40 no 1 pp 55ndash74 2011

[13] E Kalkan and S K Kunnath ldquoAdaptive modal combinationprocedure for nonlinear static analysis of building structuresrdquoJournal of Structural Engineering vol 132 no 11 pp 1721ndash1731 2006

[14] M Cosic and S Brcic ldquoIterative displacement coefficientmethod mathematical formulation and numerical analysesrdquoGraCevinar vol 65 no 3 pp 199ndash211 2013

12 Advances in Civil Engineering

Assuming that the frequencies of the two modes are ωi

and ωj having an equal damping ratio of 15 the co-efficients a0 and a1 can be obtained as follows

a0 β2ωiωj

ωi + ωj

a1 β2

ωi + ωj

(16)

During the operation the crane is not fixed to rails orquay wall For nonlinear THA therefore a gap link elementis used to simulate the contact between trucks and rails egap element is activated when structures come closer anddeactivated when they go far away [23] e axial force willbe set to zero when the portal leg is upliftede gap elementdoes not disengage in the horizontal direction duringuplifting It is also the limit of this support boundary asdiscussed in detail by Kosbab [28] However a gap element(or a similar type called no tension element) was proven tobe suitable to assess the uplift response as proposed byChaudhuri et al [32] e results of the THA together withthe NSA methods are discussed in detail in Section 4

4 Results and Discussions

41 Drift Response In contrast to the global drift analysis ofa building at the roof level most of the plastic hinges were

observed to be developed in the portal frame of the craneduring past earthquakes Furthermore the portal frame isthe main structure to support the whole upper structuresus the horizontal displacement or drift at the top of theportal frame is commonly considered [33 34] as shown inFigure 10e drift at the top of the portal frame (denoted asportal drift) of a container crane provides information onhow much of the horizontal deformation occurs at thefundamental mode in the trolley travel direction Besidesmeasuring the portal drift the drift at the top of upper legsand apex is monitored along with the corresponding heightas shown in Figure 10 e average drift of the portal frametop of upper leg and apex are estimated to be 061 026and 018 corresponding to heights of 166m 471m and766m respectively in the trolley travel direction from THAunder nine ground motions with scaled PGA ranging from010 g to 032 g e results of both pushover analyses usingCSM and ELM shown in Figure 9 are in good agreementwith that of THA In particular the average portal drift of064 is 003 larger than that of THA On the other handby using the deformation of the fundamental mode thedisplacements of the apex obtained from pushover analysesare significantly larger compared to the time-history ana-lyses with an error of over 16 e portal drifts obtainedfrom time-history and pushover analyses indicate that thecrane behaviors are in the elastic state under seismic exci-tations based on the performance levels in Figure 7According to other performance levels and damage criteria

Table 3 Site classification of KBC 2016

Soil types Soil profile nameAverage properties on the upper 30m of the site profile

Shear wavevelocity vs (ms)

Standard penetrationresistance N (blows30 cm)

Soil undrained shearstrength su (times10minus3MPa)

SA Hard rock gt1500 mdash mdashSB Rock 760 to 1500 mdash mdashSC Very dense soil and soft rock 360 to 760 gt50 gt100SD Stiff soil 180 to 360 15 to 50 50 to 100SE Soft soil lt180 lt15 lt50

00

02

04

06

08

10

12

00 05 10 15 20 25

Spec

tral

acce

lera

tion

Sa (

g)

Period T (s)

Design RS (KBC2016)Individual GMMean of GMs

Fundamental period

Figure 6 Scaled response spectra at the fundamental period

000

005

010

015

020

025

030

035

040

00 05 10 15 20 25 30

V bm

g

Portal dri ()Waterside legLandside leg

Imm

edia

te o

ccup

ancy

(IO

)

Life

safe

ty (L

S)

Colla

pse p

reve

ntio

n (C

P)

Hinge assignments

Figure 7 Pushover curve and limit states for typical Koreancontainer crane

Advances in Civil Engineering 7

as summarized in Tables 5 and 6 the cranemight work in thedamage degree I as defined by PIANC and between DR andIU levels according to Kosbabrsquos proposal

42 Total Base Shear e total base shears obtained fromCSM and ELM analyses are plotted in Figure 11 e totalbase shear is observed to be almost unrelated to the scaled

Table 4 Structural performance levels and damage based on ASCESEI 41-13 [3]

Elements Immediate occupancy (IO) Life safety (LS) Collapse prevention (CP)

For vertical elements of SMFs (ie portal columns of the crane)

Minor local yielding at a fewplaces No fractures Minorbuckling or observablepermanent distortion of

members

Hinges form Local buckling ofsome beam elements Severejoint distortion but shear

connections remain intact A fewelements may experience partial

fracture

Extensive distortion of beamsand column panels Many

fractures at momentconnections but shear

connections remain intact

Overall damage Light Moderate Severe

Table 5 Damage criteria for cranes according to PIANC [30]

Level of damage Degree I Degree II Degree III Degree IV

Displacement Withoutderailment With derailment Without overturning Overturning

Peak response stressesstrains(i) Upperstructures Elastic Elastic Plastic (ltμεmax for upper

structure)Plastic (geμεmax for upper

structure)

(ii) Portal frame Elastic Plastic (ltμεmax for portalframe) Without collapse Collapse

(iii) Toe Elastic Damage to toe (including pull-out of vehicle fracture of anchorbrakes)Note μ and εmax are the ductility factor and strain limit for the structure respectively

Table 6 Performance levels and limit states proposed by Kosbab [28]

Level ofdamageelements Derailment (DR) Immediate use (IU) Structural damage (SD) Complete collapse (CC)

Whole structures Derailed without anydamage to the structure

Minor structural damage(not significantly impacts its

operational capacity)Derailment may or may not

have occurred

Extensive damage and will notbe suitable for use without

major repairs but not collapse

Local buckling near theportal joints can quickly

lead to global instability andeventual collapse

Portal frame Elastic

Lower limit elastic Highlimit some minor bucklingof hollow sections (withinthe portal frame or not)

A portaldeformationlt deformation atmax load capacity up to thepoint of ultimate ductility

Portal deformationsurpasses the estimatedpoint of max ductility

Overall damage Derailed Minor damage Major damage CollapseLimit state in terms of portal drift (for reference)(i) Crane J100 13 20 30 45(ii) Crane LD100 mdash 15 20 30(iii) Crane LD50 15 19 25 35

182c

m

190cm 190cm

182c

m

Waterside leg tf = 20cmLandside leg tf = 16cm

Waterside leg tw = 16cm Landside leg tw = 12cm Flange

Web

(a) (b)

x

y

Figure 8 Hollow box elements (a) original stiffened section and (b) simplified unstiffened section

8 Advances in Civil Engineering

PGA magnitude and rupture distance For an example themaximum total base shear is obtained from a minimumPGA ground motion which is the Landers earthquake atYermo Fire station in 1992 (GM-4) with a PGA of 01 g orthe earthquake with a relatively high PGA value of around024 g (GM-2) at a short rupture distance (14 km) generatesa lower structural response of 141573 kN compared withthe average value of 167493 kN for the nine ground motionexcitations e total base shears obtained from pushovermethods show higher values than the average obtained fromTHA In particular the results for CSM and ELM are169182 kN and 169186 kN respectively as mentioned inthe previous section From this observation it can beconcluded that the pushover methods are suitable forseismic analysis of a STS container crane

43Uplift Behavior e uplifting of a crane will result in theredistribution of the load and will change the horizontal

displacement of the whole structure e uplift is defined bytwo conditions (1) the vertical displacement of the upliftedleg should be a positive value or zero (a negative value meansthe gap element is still ldquocloserdquo) and (2) the vertical reactionof the uplifted leg is zero In this study four portal legs twolandside legs (node 10 and 20) and two waterside legs (node30 and 40) as shown in Figure 1 are considered to studyuplift responses Figure 12 shows the potential uplift (interms of vertical responsedisplacement) and the time ofoccurrence of the landside leg (node 20) and waterside leg(node 30) It is noted that the term ldquopotential upliftrdquo is usedbecause the full uplift was not occurred under the earth-quake demand as discussed in Section 32 just a slight upliftmight happen in this study e full uplift of a crane leg isconsidered when a leg totally wins against the initial gravityload which meets both conditions as mentioned above Itcan be observed that the potential uplift of landside leg willoccur sooner than that of the waterside leg except for GM-3GM-8 and GM-9e reason could be that the center of total

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20

Hei

ght o

f cra

ne H

(m)

Horizontal displacement (cm)

Individual GMAverage of GMsPushover

Apex (3)

Top of upper leg (2)

Top of portalleg (1)

(3)

(1)

(2)

δ

(a)

0

10

20

30

40

50

60

70

80

90

0 02 04 06 08

Hei

ght o

f cra

ne H

(m)

Dri ()

Apex (3)

Top of upper leg (2)

Individual GMAverage of GMsPushover

Top of portalleg (1)

(b)

Figure 10 Height of crane versus (a) horizontal displacement and (b) drift

0

02

04

06

08

T=

05s

T = 10s

T = 15s

T = 20s

1

0 10 20 30 40

Spec

tral

acce

lera

tion

Sa (

g)

Spectral displacement Sd (cm)

15 dampingdemand spectrum

Capacity spectrum

(a)

T=

05s

T = 10s

T = 15s

T = 20s

Spec

tral

acce

lera

tion

Sa (

g)

0 10 20 30 40Spectral displacement Sd (cm)

Capacity spectrum

0

02

04

06

08

1

15 dampingdemand spectrum

(b)

Figure 9 Pushover analyses (a) CSM of ATC-40 and (b) ELM of FEMA 440

Advances in Civil Engineering 9

mass is not at the center of the two portal legs e total massconcentrates closer to the waterside legs than the landsidelegsus the first uplift will occur at the landside legs Whena leg is uplifted the axial force of the opposite leg will increasesignificantly In particular in this study it is observed that themaximum axial compressive force increases up to 120496 kNon the landside leg (node 10) due to the upward verticalresponsedisplacement of the waterside leg when excited bythe Landers earthquake (GM-4) at Yermo Fire station It isinteresting to note that the increase of the axial force of node10 is approximately 495 compared with the initial gravityforce of that node of around 243486 kN

On the other hand the vertical response of crane leg isobserved to be strongly influenced by the ground motionsrsquocharacteristics Figure 13 indicates that the amplitude of

vertical responsedisplacement decays significantly withtime after reaching the peak value when subjected to short-duration earthquakes such as GM-2 GM-5 GM-6 and GM-8 However the vertical response maintains large amplitudefor a long time when excited by long-duration earthquakeseven when the acceleration amplitude is not as high as inGM-4 GM-7 and GM-9 It can be stated that a long-duration earthquake may generate uplift and for a longperiod of time even when the input ground motion is of lowamplitude Assessment of the uplift behavior is an importantissue that should be considered in the seismic design ofa container crane to predict the overloading on the portallegs It is noted that a positive value of the vertical responseshown in Figure 13 means that the cranersquos leg moves upwardwhereas a negative value indicates a compression (downward

1300

1400

1500

1600

1700

1800

1900

2000

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tota

l bas

e she

ar V

b (k

N)

Earthquakes

Total base shear of each GMAverage of total base shear

Pushover-CSMPushover-ELM

Scaled PGA (g)Magnitude

02569561

02465314

025728350

010728240

032693100

01866959

01666954

01969010

02176206Rup distance (km)

Figure 11 Total base shear versus earthquakes

0

10

20

30

40

50

60

0

001

002

003

004

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tim

e of o

ccur

renc

e (s)

Upw

ard

vert

ical

resp

onse

(cm

)

Earthquakes

Time of occurrence (node 20)Time of occurrence (node 30)

Landside leg (node 20)Waterside leg (node 30)

Figure 12 Upward vertical responsesdisplacements of the landside and waterside legs versus time of occurrence due to dynamic analysis(gravity analysis not included)

10 Advances in Civil Engineering

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(a)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(b)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(c)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(d)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(e)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(f )

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(g)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(h)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(i)

Figure 13 Time-history vertical response of the landside leg (node 20) (a) Imperial Valley-02 (GM-1) (b) Imperial Valley-06 (GM-2) (c)Landers Barstow (GM-3) (d) Landers Yermo Fire Station (GM-4) (e) Loma Prieta (GM-5) (f ) Northridge-01 Newhall (GM-6) (g)Northridge-01 Sylmar (GM-7) (h) Kobe Japan (GM-8) (i) Chi-Chi Taiwan (GM-9)

Advances in Civil Engineering 11

movement) comparing with the state after analyzing gravityload When taking into account both static analysis (gravityload analysis) and dynamic analysis the value of verticaldisplacement is still negative in all cases indicating no fulluplift occurrence For example under subjected by theearthquake GM-4 (Landers at Yermo fire station) thelandside leg (node 20) results in a positive value of 0034 cmfor dynamic analysis and a negative value of minus0058 cm forgravity load analysis thus the value considering both cases ofanalysis is approximately minus0024 cm by summation ismeans that the crane might be slightly uplifted and will befully uplifted if the value of displacement reaches zero and thevertical reaction of the crane leg is zero as well

5 Conclusions

is study represents a preliminary investigation for theseismic behavior of a typical Korean STS container cranee complex seismic response of the crane is estimated byrepresenting it by a 3D FE model Nonlinear time-historyanalysis and both CSM and ELM pushover analyses methodsare used to analyze the crane and compare the resultsSeveral key observations can be made based on the resultsobtained from this study ey are as follows

e conventional CSM and ELM are found to be suf-ficient to analyze a STS container crane In particular therelative errors of the portal drift and total base shearobtained from pushover methods are 46 and 10 re-spectively comparing with those using the nonlinear time-history analyses However the horizontal displacements ofthe apex of the crane obtained from CSM and ELM appear tobe overestimated because these methods consider only thefundamental mode whereas the nonlinear time-historyanalysis uses the superposition principle of multiple modes

Assessment of uplift response is an important issue thatshould be considered in the seismic analysis of a containercrane It is clearly seen in this study that the axial force of thelandside legs increases nearly 50 of the initial gravity forceas the waterside legs are slightly uplifted us a gap ele-ment which is integrated into most of the commercialsoftware is appropriate for modeling base support to studythe uplift behavior On the other hand the uplift response isstrongly influenced by the characteristics of the groundmotions e potential uplift can have large amplitude fora long time when excited by long-duration earthquakes evenwhen the acceleration amplitude may not be high

e portal drifts of the typical Korean STS containercrane corresponding to performance levels of IO LS andCP as defined in ASCESEI 41-13 are 16 18 and 22respectively ese values can be used as damage limits forthe fragility analysis

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflict of interest

Acknowledgments

is research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education(2017R1D1A3B03032854) and by Ministry of public Ad-ministration and Security as Disaster Prevention SafetyHuman resource development Project and was also a part ofthe project titled ldquoDevelopment of performance-basedseismic design technologies for advancement in design codesfor port structuresrdquo funded by the Ministry of Oceans andFisheries Korea

References

[1] G H Powell Static Pushover Methods-Explanation Com-parison and Implementation 2013 httpswikicsiamericacomdisplayperformStatic+pushover+methods+-+explanation2C+comparison+and+implementation

[2] ATC 40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood CA USA 1996

[3] ASCESEI 41 Seismic Evaluation and Retrofit of ExistingBuildings American Society of Civil Engineers Reston VAUSA 2013

[4] Eurocode 8 Design of Structures for Earthquake ResistancePart 1 General Rules Seismic Actions and Rules for BuildingsEN 1998 European Committee for Standardization (CEN)Brussels Belgium 2004

[5] FEMA 440 Improvement of Nonlinear Static Seismic AnalysisProcedures Applied Technology Council (ATC-55 Project)Federal Emergency Management Agency Washington DCUSA 2006

[6] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 4pp 377ndash390 2007

[7] P Fajfar ldquoCapacity spectrum method based on inelasticdemand spectrardquo Earthquake Engineering and StructuralDynamics vol 28 no 9 pp 979ndash993 1999

[8] Y-Y Lin and K Chang ldquoAn improved capacity spectrummethod for ATC 40rdquo Earthquake Engineering and StructuralDynamics vol 32 no 13 pp 2013ndash2025 2003

[9] X Mingkui D Yinfeng L Gang and C Guangjun ldquoAnimproved capacity spectrum method based on inelastic de-mand spectrardquo in Proceedings of 4th International Conferenceon Earthquake Engineering Taipei Taiwan October 2006

[10] A Chopra and R Goel ldquoEvaluation of NSP to estimateseismic deformation SDF systemsrdquo Journal of StructuralEngineering vol 126 no 4 pp 482ndash490 2000

[11] S Freeman ldquoDevelopment and use of capacity spectrummethodrdquo in Proceedings of 6th US NCEE Conference onEarthquake Engineering pp 1ndash12 SeattleWA USA June 1998

[12] H Sucuoglu and M S Gunay ldquoGeneralized force vectors formulti-mode pushover analysisrdquo Earthquake Engineering andStructural Dynamics vol 40 no 1 pp 55ndash74 2011

[13] E Kalkan and S K Kunnath ldquoAdaptive modal combinationprocedure for nonlinear static analysis of building structuresrdquoJournal of Structural Engineering vol 132 no 11 pp 1721ndash1731 2006

[14] M Cosic and S Brcic ldquoIterative displacement coefficientmethod mathematical formulation and numerical analysesrdquoGraCevinar vol 65 no 3 pp 199ndash211 2013

12 Advances in Civil Engineering

as summarized in Tables 5 and 6 the cranemight work in thedamage degree I as defined by PIANC and between DR andIU levels according to Kosbabrsquos proposal

42 Total Base Shear e total base shears obtained fromCSM and ELM analyses are plotted in Figure 11 e totalbase shear is observed to be almost unrelated to the scaled

Table 4 Structural performance levels and damage based on ASCESEI 41-13 [3]

Elements Immediate occupancy (IO) Life safety (LS) Collapse prevention (CP)

For vertical elements of SMFs (ie portal columns of the crane)

Minor local yielding at a fewplaces No fractures Minorbuckling or observablepermanent distortion of

members

Hinges form Local buckling ofsome beam elements Severejoint distortion but shear

connections remain intact A fewelements may experience partial

fracture

Extensive distortion of beamsand column panels Many

fractures at momentconnections but shear

connections remain intact

Overall damage Light Moderate Severe

Table 5 Damage criteria for cranes according to PIANC [30]

Level of damage Degree I Degree II Degree III Degree IV

Displacement Withoutderailment With derailment Without overturning Overturning

Peak response stressesstrains(i) Upperstructures Elastic Elastic Plastic (ltμεmax for upper

structure)Plastic (geμεmax for upper

structure)

(ii) Portal frame Elastic Plastic (ltμεmax for portalframe) Without collapse Collapse

(iii) Toe Elastic Damage to toe (including pull-out of vehicle fracture of anchorbrakes)Note μ and εmax are the ductility factor and strain limit for the structure respectively

Table 6 Performance levels and limit states proposed by Kosbab [28]

Level ofdamageelements Derailment (DR) Immediate use (IU) Structural damage (SD) Complete collapse (CC)

Whole structures Derailed without anydamage to the structure

Minor structural damage(not significantly impacts its

operational capacity)Derailment may or may not

have occurred

Extensive damage and will notbe suitable for use without

major repairs but not collapse

Local buckling near theportal joints can quickly

lead to global instability andeventual collapse

Portal frame Elastic

Lower limit elastic Highlimit some minor bucklingof hollow sections (withinthe portal frame or not)

A portaldeformationlt deformation atmax load capacity up to thepoint of ultimate ductility

Portal deformationsurpasses the estimatedpoint of max ductility

Overall damage Derailed Minor damage Major damage CollapseLimit state in terms of portal drift (for reference)(i) Crane J100 13 20 30 45(ii) Crane LD100 mdash 15 20 30(iii) Crane LD50 15 19 25 35

182c

m

190cm 190cm

182c

m

Waterside leg tf = 20cmLandside leg tf = 16cm

Waterside leg tw = 16cm Landside leg tw = 12cm Flange

Web

(a) (b)

x

y

Figure 8 Hollow box elements (a) original stiffened section and (b) simplified unstiffened section

8 Advances in Civil Engineering

PGA magnitude and rupture distance For an example themaximum total base shear is obtained from a minimumPGA ground motion which is the Landers earthquake atYermo Fire station in 1992 (GM-4) with a PGA of 01 g orthe earthquake with a relatively high PGA value of around024 g (GM-2) at a short rupture distance (14 km) generatesa lower structural response of 141573 kN compared withthe average value of 167493 kN for the nine ground motionexcitations e total base shears obtained from pushovermethods show higher values than the average obtained fromTHA In particular the results for CSM and ELM are169182 kN and 169186 kN respectively as mentioned inthe previous section From this observation it can beconcluded that the pushover methods are suitable forseismic analysis of a STS container crane

43Uplift Behavior e uplifting of a crane will result in theredistribution of the load and will change the horizontal

displacement of the whole structure e uplift is defined bytwo conditions (1) the vertical displacement of the upliftedleg should be a positive value or zero (a negative value meansthe gap element is still ldquocloserdquo) and (2) the vertical reactionof the uplifted leg is zero In this study four portal legs twolandside legs (node 10 and 20) and two waterside legs (node30 and 40) as shown in Figure 1 are considered to studyuplift responses Figure 12 shows the potential uplift (interms of vertical responsedisplacement) and the time ofoccurrence of the landside leg (node 20) and waterside leg(node 30) It is noted that the term ldquopotential upliftrdquo is usedbecause the full uplift was not occurred under the earth-quake demand as discussed in Section 32 just a slight upliftmight happen in this study e full uplift of a crane leg isconsidered when a leg totally wins against the initial gravityload which meets both conditions as mentioned above Itcan be observed that the potential uplift of landside leg willoccur sooner than that of the waterside leg except for GM-3GM-8 and GM-9e reason could be that the center of total

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20

Hei

ght o

f cra

ne H

(m)

Horizontal displacement (cm)

Individual GMAverage of GMsPushover

Apex (3)

Top of upper leg (2)

Top of portalleg (1)

(3)

(1)

(2)

δ

(a)

0

10

20

30

40

50

60

70

80

90

0 02 04 06 08

Hei

ght o

f cra

ne H

(m)

Dri ()

Apex (3)

Top of upper leg (2)

Individual GMAverage of GMsPushover

Top of portalleg (1)

(b)

Figure 10 Height of crane versus (a) horizontal displacement and (b) drift

0

02

04

06

08

T=

05s

T = 10s

T = 15s

T = 20s

1

0 10 20 30 40

Spec

tral

acce

lera

tion

Sa (

g)

Spectral displacement Sd (cm)

15 dampingdemand spectrum

Capacity spectrum

(a)

T=

05s

T = 10s

T = 15s

T = 20s

Spec

tral

acce

lera

tion

Sa (

g)

0 10 20 30 40Spectral displacement Sd (cm)

Capacity spectrum

0

02

04

06

08

1

15 dampingdemand spectrum

(b)

Figure 9 Pushover analyses (a) CSM of ATC-40 and (b) ELM of FEMA 440

Advances in Civil Engineering 9

mass is not at the center of the two portal legs e total massconcentrates closer to the waterside legs than the landsidelegsus the first uplift will occur at the landside legs Whena leg is uplifted the axial force of the opposite leg will increasesignificantly In particular in this study it is observed that themaximum axial compressive force increases up to 120496 kNon the landside leg (node 10) due to the upward verticalresponsedisplacement of the waterside leg when excited bythe Landers earthquake (GM-4) at Yermo Fire station It isinteresting to note that the increase of the axial force of node10 is approximately 495 compared with the initial gravityforce of that node of around 243486 kN

On the other hand the vertical response of crane leg isobserved to be strongly influenced by the ground motionsrsquocharacteristics Figure 13 indicates that the amplitude of

vertical responsedisplacement decays significantly withtime after reaching the peak value when subjected to short-duration earthquakes such as GM-2 GM-5 GM-6 and GM-8 However the vertical response maintains large amplitudefor a long time when excited by long-duration earthquakeseven when the acceleration amplitude is not as high as inGM-4 GM-7 and GM-9 It can be stated that a long-duration earthquake may generate uplift and for a longperiod of time even when the input ground motion is of lowamplitude Assessment of the uplift behavior is an importantissue that should be considered in the seismic design ofa container crane to predict the overloading on the portallegs It is noted that a positive value of the vertical responseshown in Figure 13 means that the cranersquos leg moves upwardwhereas a negative value indicates a compression (downward

1300

1400

1500

1600

1700

1800

1900

2000

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tota

l bas

e she

ar V

b (k

N)

Earthquakes

Total base shear of each GMAverage of total base shear

Pushover-CSMPushover-ELM

Scaled PGA (g)Magnitude

02569561

02465314

025728350

010728240

032693100

01866959

01666954

01969010

02176206Rup distance (km)

Figure 11 Total base shear versus earthquakes

0

10

20

30

40

50

60

0

001

002

003

004

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tim

e of o

ccur

renc

e (s)

Upw

ard

vert

ical

resp

onse

(cm

)

Earthquakes

Time of occurrence (node 20)Time of occurrence (node 30)

Landside leg (node 20)Waterside leg (node 30)

Figure 12 Upward vertical responsesdisplacements of the landside and waterside legs versus time of occurrence due to dynamic analysis(gravity analysis not included)

10 Advances in Civil Engineering

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(a)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(b)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(c)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(d)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(e)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(f )

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(g)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(h)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(i)

Figure 13 Time-history vertical response of the landside leg (node 20) (a) Imperial Valley-02 (GM-1) (b) Imperial Valley-06 (GM-2) (c)Landers Barstow (GM-3) (d) Landers Yermo Fire Station (GM-4) (e) Loma Prieta (GM-5) (f ) Northridge-01 Newhall (GM-6) (g)Northridge-01 Sylmar (GM-7) (h) Kobe Japan (GM-8) (i) Chi-Chi Taiwan (GM-9)

Advances in Civil Engineering 11

movement) comparing with the state after analyzing gravityload When taking into account both static analysis (gravityload analysis) and dynamic analysis the value of verticaldisplacement is still negative in all cases indicating no fulluplift occurrence For example under subjected by theearthquake GM-4 (Landers at Yermo fire station) thelandside leg (node 20) results in a positive value of 0034 cmfor dynamic analysis and a negative value of minus0058 cm forgravity load analysis thus the value considering both cases ofanalysis is approximately minus0024 cm by summation ismeans that the crane might be slightly uplifted and will befully uplifted if the value of displacement reaches zero and thevertical reaction of the crane leg is zero as well

5 Conclusions

is study represents a preliminary investigation for theseismic behavior of a typical Korean STS container cranee complex seismic response of the crane is estimated byrepresenting it by a 3D FE model Nonlinear time-historyanalysis and both CSM and ELM pushover analyses methodsare used to analyze the crane and compare the resultsSeveral key observations can be made based on the resultsobtained from this study ey are as follows

e conventional CSM and ELM are found to be suf-ficient to analyze a STS container crane In particular therelative errors of the portal drift and total base shearobtained from pushover methods are 46 and 10 re-spectively comparing with those using the nonlinear time-history analyses However the horizontal displacements ofthe apex of the crane obtained from CSM and ELM appear tobe overestimated because these methods consider only thefundamental mode whereas the nonlinear time-historyanalysis uses the superposition principle of multiple modes

Assessment of uplift response is an important issue thatshould be considered in the seismic analysis of a containercrane It is clearly seen in this study that the axial force of thelandside legs increases nearly 50 of the initial gravity forceas the waterside legs are slightly uplifted us a gap ele-ment which is integrated into most of the commercialsoftware is appropriate for modeling base support to studythe uplift behavior On the other hand the uplift response isstrongly influenced by the characteristics of the groundmotions e potential uplift can have large amplitude fora long time when excited by long-duration earthquakes evenwhen the acceleration amplitude may not be high

e portal drifts of the typical Korean STS containercrane corresponding to performance levels of IO LS andCP as defined in ASCESEI 41-13 are 16 18 and 22respectively ese values can be used as damage limits forthe fragility analysis

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflict of interest

Acknowledgments

is research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education(2017R1D1A3B03032854) and by Ministry of public Ad-ministration and Security as Disaster Prevention SafetyHuman resource development Project and was also a part ofthe project titled ldquoDevelopment of performance-basedseismic design technologies for advancement in design codesfor port structuresrdquo funded by the Ministry of Oceans andFisheries Korea

References

[1] G H Powell Static Pushover Methods-Explanation Com-parison and Implementation 2013 httpswikicsiamericacomdisplayperformStatic+pushover+methods+-+explanation2C+comparison+and+implementation

[2] ATC 40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood CA USA 1996

[3] ASCESEI 41 Seismic Evaluation and Retrofit of ExistingBuildings American Society of Civil Engineers Reston VAUSA 2013

[4] Eurocode 8 Design of Structures for Earthquake ResistancePart 1 General Rules Seismic Actions and Rules for BuildingsEN 1998 European Committee for Standardization (CEN)Brussels Belgium 2004

[5] FEMA 440 Improvement of Nonlinear Static Seismic AnalysisProcedures Applied Technology Council (ATC-55 Project)Federal Emergency Management Agency Washington DCUSA 2006

[6] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 4pp 377ndash390 2007

[7] P Fajfar ldquoCapacity spectrum method based on inelasticdemand spectrardquo Earthquake Engineering and StructuralDynamics vol 28 no 9 pp 979ndash993 1999

[8] Y-Y Lin and K Chang ldquoAn improved capacity spectrummethod for ATC 40rdquo Earthquake Engineering and StructuralDynamics vol 32 no 13 pp 2013ndash2025 2003

[9] X Mingkui D Yinfeng L Gang and C Guangjun ldquoAnimproved capacity spectrum method based on inelastic de-mand spectrardquo in Proceedings of 4th International Conferenceon Earthquake Engineering Taipei Taiwan October 2006

[10] A Chopra and R Goel ldquoEvaluation of NSP to estimateseismic deformation SDF systemsrdquo Journal of StructuralEngineering vol 126 no 4 pp 482ndash490 2000

[11] S Freeman ldquoDevelopment and use of capacity spectrummethodrdquo in Proceedings of 6th US NCEE Conference onEarthquake Engineering pp 1ndash12 SeattleWA USA June 1998

[12] H Sucuoglu and M S Gunay ldquoGeneralized force vectors formulti-mode pushover analysisrdquo Earthquake Engineering andStructural Dynamics vol 40 no 1 pp 55ndash74 2011

[13] E Kalkan and S K Kunnath ldquoAdaptive modal combinationprocedure for nonlinear static analysis of building structuresrdquoJournal of Structural Engineering vol 132 no 11 pp 1721ndash1731 2006

[14] M Cosic and S Brcic ldquoIterative displacement coefficientmethod mathematical formulation and numerical analysesrdquoGraCevinar vol 65 no 3 pp 199ndash211 2013

12 Advances in Civil Engineering

PGA magnitude and rupture distance For an example themaximum total base shear is obtained from a minimumPGA ground motion which is the Landers earthquake atYermo Fire station in 1992 (GM-4) with a PGA of 01 g orthe earthquake with a relatively high PGA value of around024 g (GM-2) at a short rupture distance (14 km) generatesa lower structural response of 141573 kN compared withthe average value of 167493 kN for the nine ground motionexcitations e total base shears obtained from pushovermethods show higher values than the average obtained fromTHA In particular the results for CSM and ELM are169182 kN and 169186 kN respectively as mentioned inthe previous section From this observation it can beconcluded that the pushover methods are suitable forseismic analysis of a STS container crane

43Uplift Behavior e uplifting of a crane will result in theredistribution of the load and will change the horizontal

displacement of the whole structure e uplift is defined bytwo conditions (1) the vertical displacement of the upliftedleg should be a positive value or zero (a negative value meansthe gap element is still ldquocloserdquo) and (2) the vertical reactionof the uplifted leg is zero In this study four portal legs twolandside legs (node 10 and 20) and two waterside legs (node30 and 40) as shown in Figure 1 are considered to studyuplift responses Figure 12 shows the potential uplift (interms of vertical responsedisplacement) and the time ofoccurrence of the landside leg (node 20) and waterside leg(node 30) It is noted that the term ldquopotential upliftrdquo is usedbecause the full uplift was not occurred under the earth-quake demand as discussed in Section 32 just a slight upliftmight happen in this study e full uplift of a crane leg isconsidered when a leg totally wins against the initial gravityload which meets both conditions as mentioned above Itcan be observed that the potential uplift of landside leg willoccur sooner than that of the waterside leg except for GM-3GM-8 and GM-9e reason could be that the center of total

0

10

20

30

40

50

60

70

80

90

0 5 10 15 20

Hei

ght o

f cra

ne H

(m)

Horizontal displacement (cm)

Individual GMAverage of GMsPushover

Apex (3)

Top of upper leg (2)

Top of portalleg (1)

(3)

(1)

(2)

δ

(a)

0

10

20

30

40

50

60

70

80

90

0 02 04 06 08

Hei

ght o

f cra

ne H

(m)

Dri ()

Apex (3)

Top of upper leg (2)

Individual GMAverage of GMsPushover

Top of portalleg (1)

(b)

Figure 10 Height of crane versus (a) horizontal displacement and (b) drift

0

02

04

06

08

T=

05s

T = 10s

T = 15s

T = 20s

1

0 10 20 30 40

Spec

tral

acce

lera

tion

Sa (

g)

Spectral displacement Sd (cm)

15 dampingdemand spectrum

Capacity spectrum

(a)

T=

05s

T = 10s

T = 15s

T = 20s

Spec

tral

acce

lera

tion

Sa (

g)

0 10 20 30 40Spectral displacement Sd (cm)

Capacity spectrum

0

02

04

06

08

1

15 dampingdemand spectrum

(b)

Figure 9 Pushover analyses (a) CSM of ATC-40 and (b) ELM of FEMA 440

Advances in Civil Engineering 9

mass is not at the center of the two portal legs e total massconcentrates closer to the waterside legs than the landsidelegsus the first uplift will occur at the landside legs Whena leg is uplifted the axial force of the opposite leg will increasesignificantly In particular in this study it is observed that themaximum axial compressive force increases up to 120496 kNon the landside leg (node 10) due to the upward verticalresponsedisplacement of the waterside leg when excited bythe Landers earthquake (GM-4) at Yermo Fire station It isinteresting to note that the increase of the axial force of node10 is approximately 495 compared with the initial gravityforce of that node of around 243486 kN

On the other hand the vertical response of crane leg isobserved to be strongly influenced by the ground motionsrsquocharacteristics Figure 13 indicates that the amplitude of

vertical responsedisplacement decays significantly withtime after reaching the peak value when subjected to short-duration earthquakes such as GM-2 GM-5 GM-6 and GM-8 However the vertical response maintains large amplitudefor a long time when excited by long-duration earthquakeseven when the acceleration amplitude is not as high as inGM-4 GM-7 and GM-9 It can be stated that a long-duration earthquake may generate uplift and for a longperiod of time even when the input ground motion is of lowamplitude Assessment of the uplift behavior is an importantissue that should be considered in the seismic design ofa container crane to predict the overloading on the portallegs It is noted that a positive value of the vertical responseshown in Figure 13 means that the cranersquos leg moves upwardwhereas a negative value indicates a compression (downward

1300

1400

1500

1600

1700

1800

1900

2000

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tota

l bas

e she

ar V

b (k

N)

Earthquakes

Total base shear of each GMAverage of total base shear

Pushover-CSMPushover-ELM

Scaled PGA (g)Magnitude

02569561

02465314

025728350

010728240

032693100

01866959

01666954

01969010

02176206Rup distance (km)

Figure 11 Total base shear versus earthquakes

0

10

20

30

40

50

60

0

001

002

003

004

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tim

e of o

ccur

renc

e (s)

Upw

ard

vert

ical

resp

onse

(cm

)

Earthquakes

Time of occurrence (node 20)Time of occurrence (node 30)

Landside leg (node 20)Waterside leg (node 30)

Figure 12 Upward vertical responsesdisplacements of the landside and waterside legs versus time of occurrence due to dynamic analysis(gravity analysis not included)

10 Advances in Civil Engineering

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(a)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(b)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(c)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(d)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(e)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(f )

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(g)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(h)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(i)

Figure 13 Time-history vertical response of the landside leg (node 20) (a) Imperial Valley-02 (GM-1) (b) Imperial Valley-06 (GM-2) (c)Landers Barstow (GM-3) (d) Landers Yermo Fire Station (GM-4) (e) Loma Prieta (GM-5) (f ) Northridge-01 Newhall (GM-6) (g)Northridge-01 Sylmar (GM-7) (h) Kobe Japan (GM-8) (i) Chi-Chi Taiwan (GM-9)

Advances in Civil Engineering 11

movement) comparing with the state after analyzing gravityload When taking into account both static analysis (gravityload analysis) and dynamic analysis the value of verticaldisplacement is still negative in all cases indicating no fulluplift occurrence For example under subjected by theearthquake GM-4 (Landers at Yermo fire station) thelandside leg (node 20) results in a positive value of 0034 cmfor dynamic analysis and a negative value of minus0058 cm forgravity load analysis thus the value considering both cases ofanalysis is approximately minus0024 cm by summation ismeans that the crane might be slightly uplifted and will befully uplifted if the value of displacement reaches zero and thevertical reaction of the crane leg is zero as well

5 Conclusions

is study represents a preliminary investigation for theseismic behavior of a typical Korean STS container cranee complex seismic response of the crane is estimated byrepresenting it by a 3D FE model Nonlinear time-historyanalysis and both CSM and ELM pushover analyses methodsare used to analyze the crane and compare the resultsSeveral key observations can be made based on the resultsobtained from this study ey are as follows

e conventional CSM and ELM are found to be suf-ficient to analyze a STS container crane In particular therelative errors of the portal drift and total base shearobtained from pushover methods are 46 and 10 re-spectively comparing with those using the nonlinear time-history analyses However the horizontal displacements ofthe apex of the crane obtained from CSM and ELM appear tobe overestimated because these methods consider only thefundamental mode whereas the nonlinear time-historyanalysis uses the superposition principle of multiple modes

Assessment of uplift response is an important issue thatshould be considered in the seismic analysis of a containercrane It is clearly seen in this study that the axial force of thelandside legs increases nearly 50 of the initial gravity forceas the waterside legs are slightly uplifted us a gap ele-ment which is integrated into most of the commercialsoftware is appropriate for modeling base support to studythe uplift behavior On the other hand the uplift response isstrongly influenced by the characteristics of the groundmotions e potential uplift can have large amplitude fora long time when excited by long-duration earthquakes evenwhen the acceleration amplitude may not be high

e portal drifts of the typical Korean STS containercrane corresponding to performance levels of IO LS andCP as defined in ASCESEI 41-13 are 16 18 and 22respectively ese values can be used as damage limits forthe fragility analysis

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflict of interest

Acknowledgments

is research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education(2017R1D1A3B03032854) and by Ministry of public Ad-ministration and Security as Disaster Prevention SafetyHuman resource development Project and was also a part ofthe project titled ldquoDevelopment of performance-basedseismic design technologies for advancement in design codesfor port structuresrdquo funded by the Ministry of Oceans andFisheries Korea

References

[1] G H Powell Static Pushover Methods-Explanation Com-parison and Implementation 2013 httpswikicsiamericacomdisplayperformStatic+pushover+methods+-+explanation2C+comparison+and+implementation

[2] ATC 40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood CA USA 1996

[3] ASCESEI 41 Seismic Evaluation and Retrofit of ExistingBuildings American Society of Civil Engineers Reston VAUSA 2013

[4] Eurocode 8 Design of Structures for Earthquake ResistancePart 1 General Rules Seismic Actions and Rules for BuildingsEN 1998 European Committee for Standardization (CEN)Brussels Belgium 2004

[5] FEMA 440 Improvement of Nonlinear Static Seismic AnalysisProcedures Applied Technology Council (ATC-55 Project)Federal Emergency Management Agency Washington DCUSA 2006

[6] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 4pp 377ndash390 2007

[7] P Fajfar ldquoCapacity spectrum method based on inelasticdemand spectrardquo Earthquake Engineering and StructuralDynamics vol 28 no 9 pp 979ndash993 1999

[8] Y-Y Lin and K Chang ldquoAn improved capacity spectrummethod for ATC 40rdquo Earthquake Engineering and StructuralDynamics vol 32 no 13 pp 2013ndash2025 2003

[9] X Mingkui D Yinfeng L Gang and C Guangjun ldquoAnimproved capacity spectrum method based on inelastic de-mand spectrardquo in Proceedings of 4th International Conferenceon Earthquake Engineering Taipei Taiwan October 2006

[10] A Chopra and R Goel ldquoEvaluation of NSP to estimateseismic deformation SDF systemsrdquo Journal of StructuralEngineering vol 126 no 4 pp 482ndash490 2000

[11] S Freeman ldquoDevelopment and use of capacity spectrummethodrdquo in Proceedings of 6th US NCEE Conference onEarthquake Engineering pp 1ndash12 SeattleWA USA June 1998

[12] H Sucuoglu and M S Gunay ldquoGeneralized force vectors formulti-mode pushover analysisrdquo Earthquake Engineering andStructural Dynamics vol 40 no 1 pp 55ndash74 2011

[13] E Kalkan and S K Kunnath ldquoAdaptive modal combinationprocedure for nonlinear static analysis of building structuresrdquoJournal of Structural Engineering vol 132 no 11 pp 1721ndash1731 2006

[14] M Cosic and S Brcic ldquoIterative displacement coefficientmethod mathematical formulation and numerical analysesrdquoGraCevinar vol 65 no 3 pp 199ndash211 2013

12 Advances in Civil Engineering

mass is not at the center of the two portal legs e total massconcentrates closer to the waterside legs than the landsidelegsus the first uplift will occur at the landside legs Whena leg is uplifted the axial force of the opposite leg will increasesignificantly In particular in this study it is observed that themaximum axial compressive force increases up to 120496 kNon the landside leg (node 10) due to the upward verticalresponsedisplacement of the waterside leg when excited bythe Landers earthquake (GM-4) at Yermo Fire station It isinteresting to note that the increase of the axial force of node10 is approximately 495 compared with the initial gravityforce of that node of around 243486 kN

On the other hand the vertical response of crane leg isobserved to be strongly influenced by the ground motionsrsquocharacteristics Figure 13 indicates that the amplitude of

vertical responsedisplacement decays significantly withtime after reaching the peak value when subjected to short-duration earthquakes such as GM-2 GM-5 GM-6 and GM-8 However the vertical response maintains large amplitudefor a long time when excited by long-duration earthquakeseven when the acceleration amplitude is not as high as inGM-4 GM-7 and GM-9 It can be stated that a long-duration earthquake may generate uplift and for a longperiod of time even when the input ground motion is of lowamplitude Assessment of the uplift behavior is an importantissue that should be considered in the seismic design ofa container crane to predict the overloading on the portallegs It is noted that a positive value of the vertical responseshown in Figure 13 means that the cranersquos leg moves upwardwhereas a negative value indicates a compression (downward

1300

1400

1500

1600

1700

1800

1900

2000

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tota

l bas

e she

ar V

b (k

N)

Earthquakes

Total base shear of each GMAverage of total base shear

Pushover-CSMPushover-ELM

Scaled PGA (g)Magnitude

02569561

02465314

025728350

010728240

032693100

01866959

01666954

01969010

02176206Rup distance (km)

Figure 11 Total base shear versus earthquakes

0

10

20

30

40

50

60

0

001

002

003

004

GM-1 GM-2 GM-3 GM-4 GM-5 GM-6 GM-7 GM-8 GM-9

Tim

e of o

ccur

renc

e (s)

Upw

ard

vert

ical

resp

onse

(cm

)

Earthquakes

Time of occurrence (node 20)Time of occurrence (node 30)

Landside leg (node 20)Waterside leg (node 30)

Figure 12 Upward vertical responsesdisplacements of the landside and waterside legs versus time of occurrence due to dynamic analysis(gravity analysis not included)

10 Advances in Civil Engineering

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(a)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(b)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(c)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(d)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(e)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(f )

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(g)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(h)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(i)

Figure 13 Time-history vertical response of the landside leg (node 20) (a) Imperial Valley-02 (GM-1) (b) Imperial Valley-06 (GM-2) (c)Landers Barstow (GM-3) (d) Landers Yermo Fire Station (GM-4) (e) Loma Prieta (GM-5) (f ) Northridge-01 Newhall (GM-6) (g)Northridge-01 Sylmar (GM-7) (h) Kobe Japan (GM-8) (i) Chi-Chi Taiwan (GM-9)

Advances in Civil Engineering 11

movement) comparing with the state after analyzing gravityload When taking into account both static analysis (gravityload analysis) and dynamic analysis the value of verticaldisplacement is still negative in all cases indicating no fulluplift occurrence For example under subjected by theearthquake GM-4 (Landers at Yermo fire station) thelandside leg (node 20) results in a positive value of 0034 cmfor dynamic analysis and a negative value of minus0058 cm forgravity load analysis thus the value considering both cases ofanalysis is approximately minus0024 cm by summation ismeans that the crane might be slightly uplifted and will befully uplifted if the value of displacement reaches zero and thevertical reaction of the crane leg is zero as well

5 Conclusions

is study represents a preliminary investigation for theseismic behavior of a typical Korean STS container cranee complex seismic response of the crane is estimated byrepresenting it by a 3D FE model Nonlinear time-historyanalysis and both CSM and ELM pushover analyses methodsare used to analyze the crane and compare the resultsSeveral key observations can be made based on the resultsobtained from this study ey are as follows

e conventional CSM and ELM are found to be suf-ficient to analyze a STS container crane In particular therelative errors of the portal drift and total base shearobtained from pushover methods are 46 and 10 re-spectively comparing with those using the nonlinear time-history analyses However the horizontal displacements ofthe apex of the crane obtained from CSM and ELM appear tobe overestimated because these methods consider only thefundamental mode whereas the nonlinear time-historyanalysis uses the superposition principle of multiple modes

Assessment of uplift response is an important issue thatshould be considered in the seismic analysis of a containercrane It is clearly seen in this study that the axial force of thelandside legs increases nearly 50 of the initial gravity forceas the waterside legs are slightly uplifted us a gap ele-ment which is integrated into most of the commercialsoftware is appropriate for modeling base support to studythe uplift behavior On the other hand the uplift response isstrongly influenced by the characteristics of the groundmotions e potential uplift can have large amplitude fora long time when excited by long-duration earthquakes evenwhen the acceleration amplitude may not be high

e portal drifts of the typical Korean STS containercrane corresponding to performance levels of IO LS andCP as defined in ASCESEI 41-13 are 16 18 and 22respectively ese values can be used as damage limits forthe fragility analysis

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflict of interest

Acknowledgments

is research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education(2017R1D1A3B03032854) and by Ministry of public Ad-ministration and Security as Disaster Prevention SafetyHuman resource development Project and was also a part ofthe project titled ldquoDevelopment of performance-basedseismic design technologies for advancement in design codesfor port structuresrdquo funded by the Ministry of Oceans andFisheries Korea

References

[1] G H Powell Static Pushover Methods-Explanation Com-parison and Implementation 2013 httpswikicsiamericacomdisplayperformStatic+pushover+methods+-+explanation2C+comparison+and+implementation

[2] ATC 40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood CA USA 1996

[3] ASCESEI 41 Seismic Evaluation and Retrofit of ExistingBuildings American Society of Civil Engineers Reston VAUSA 2013

[4] Eurocode 8 Design of Structures for Earthquake ResistancePart 1 General Rules Seismic Actions and Rules for BuildingsEN 1998 European Committee for Standardization (CEN)Brussels Belgium 2004

[5] FEMA 440 Improvement of Nonlinear Static Seismic AnalysisProcedures Applied Technology Council (ATC-55 Project)Federal Emergency Management Agency Washington DCUSA 2006

[6] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 4pp 377ndash390 2007

[7] P Fajfar ldquoCapacity spectrum method based on inelasticdemand spectrardquo Earthquake Engineering and StructuralDynamics vol 28 no 9 pp 979ndash993 1999

[8] Y-Y Lin and K Chang ldquoAn improved capacity spectrummethod for ATC 40rdquo Earthquake Engineering and StructuralDynamics vol 32 no 13 pp 2013ndash2025 2003

[9] X Mingkui D Yinfeng L Gang and C Guangjun ldquoAnimproved capacity spectrum method based on inelastic de-mand spectrardquo in Proceedings of 4th International Conferenceon Earthquake Engineering Taipei Taiwan October 2006

[10] A Chopra and R Goel ldquoEvaluation of NSP to estimateseismic deformation SDF systemsrdquo Journal of StructuralEngineering vol 126 no 4 pp 482ndash490 2000

[11] S Freeman ldquoDevelopment and use of capacity spectrummethodrdquo in Proceedings of 6th US NCEE Conference onEarthquake Engineering pp 1ndash12 SeattleWA USA June 1998

[12] H Sucuoglu and M S Gunay ldquoGeneralized force vectors formulti-mode pushover analysisrdquo Earthquake Engineering andStructural Dynamics vol 40 no 1 pp 55ndash74 2011

[13] E Kalkan and S K Kunnath ldquoAdaptive modal combinationprocedure for nonlinear static analysis of building structuresrdquoJournal of Structural Engineering vol 132 no 11 pp 1721ndash1731 2006

[14] M Cosic and S Brcic ldquoIterative displacement coefficientmethod mathematical formulation and numerical analysesrdquoGraCevinar vol 65 no 3 pp 199ndash211 2013

12 Advances in Civil Engineering

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(a)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(b)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(c)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(d)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(e)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(f )

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 10 20 30 40 50

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(g)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(h)

ndash040

ndash020

000

020

040

ndash004

ndash002

000

002

004

0 20 40 60 80 100

Acc

eler

atio

n (g

)

Ver

tical

resp

onse

(cm

)

Time (s)

Vertical response (landside leg)Acceleration (g)

(i)

Figure 13 Time-history vertical response of the landside leg (node 20) (a) Imperial Valley-02 (GM-1) (b) Imperial Valley-06 (GM-2) (c)Landers Barstow (GM-3) (d) Landers Yermo Fire Station (GM-4) (e) Loma Prieta (GM-5) (f ) Northridge-01 Newhall (GM-6) (g)Northridge-01 Sylmar (GM-7) (h) Kobe Japan (GM-8) (i) Chi-Chi Taiwan (GM-9)

Advances in Civil Engineering 11

movement) comparing with the state after analyzing gravityload When taking into account both static analysis (gravityload analysis) and dynamic analysis the value of verticaldisplacement is still negative in all cases indicating no fulluplift occurrence For example under subjected by theearthquake GM-4 (Landers at Yermo fire station) thelandside leg (node 20) results in a positive value of 0034 cmfor dynamic analysis and a negative value of minus0058 cm forgravity load analysis thus the value considering both cases ofanalysis is approximately minus0024 cm by summation ismeans that the crane might be slightly uplifted and will befully uplifted if the value of displacement reaches zero and thevertical reaction of the crane leg is zero as well

5 Conclusions

is study represents a preliminary investigation for theseismic behavior of a typical Korean STS container cranee complex seismic response of the crane is estimated byrepresenting it by a 3D FE model Nonlinear time-historyanalysis and both CSM and ELM pushover analyses methodsare used to analyze the crane and compare the resultsSeveral key observations can be made based on the resultsobtained from this study ey are as follows

e conventional CSM and ELM are found to be suf-ficient to analyze a STS container crane In particular therelative errors of the portal drift and total base shearobtained from pushover methods are 46 and 10 re-spectively comparing with those using the nonlinear time-history analyses However the horizontal displacements ofthe apex of the crane obtained from CSM and ELM appear tobe overestimated because these methods consider only thefundamental mode whereas the nonlinear time-historyanalysis uses the superposition principle of multiple modes

Assessment of uplift response is an important issue thatshould be considered in the seismic analysis of a containercrane It is clearly seen in this study that the axial force of thelandside legs increases nearly 50 of the initial gravity forceas the waterside legs are slightly uplifted us a gap ele-ment which is integrated into most of the commercialsoftware is appropriate for modeling base support to studythe uplift behavior On the other hand the uplift response isstrongly influenced by the characteristics of the groundmotions e potential uplift can have large amplitude fora long time when excited by long-duration earthquakes evenwhen the acceleration amplitude may not be high

e portal drifts of the typical Korean STS containercrane corresponding to performance levels of IO LS andCP as defined in ASCESEI 41-13 are 16 18 and 22respectively ese values can be used as damage limits forthe fragility analysis

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflict of interest

Acknowledgments

is research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education(2017R1D1A3B03032854) and by Ministry of public Ad-ministration and Security as Disaster Prevention SafetyHuman resource development Project and was also a part ofthe project titled ldquoDevelopment of performance-basedseismic design technologies for advancement in design codesfor port structuresrdquo funded by the Ministry of Oceans andFisheries Korea

References

[1] G H Powell Static Pushover Methods-Explanation Com-parison and Implementation 2013 httpswikicsiamericacomdisplayperformStatic+pushover+methods+-+explanation2C+comparison+and+implementation

[2] ATC 40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood CA USA 1996

[3] ASCESEI 41 Seismic Evaluation and Retrofit of ExistingBuildings American Society of Civil Engineers Reston VAUSA 2013

[4] Eurocode 8 Design of Structures for Earthquake ResistancePart 1 General Rules Seismic Actions and Rules for BuildingsEN 1998 European Committee for Standardization (CEN)Brussels Belgium 2004

[5] FEMA 440 Improvement of Nonlinear Static Seismic AnalysisProcedures Applied Technology Council (ATC-55 Project)Federal Emergency Management Agency Washington DCUSA 2006

[6] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 4pp 377ndash390 2007

[7] P Fajfar ldquoCapacity spectrum method based on inelasticdemand spectrardquo Earthquake Engineering and StructuralDynamics vol 28 no 9 pp 979ndash993 1999

[8] Y-Y Lin and K Chang ldquoAn improved capacity spectrummethod for ATC 40rdquo Earthquake Engineering and StructuralDynamics vol 32 no 13 pp 2013ndash2025 2003

[9] X Mingkui D Yinfeng L Gang and C Guangjun ldquoAnimproved capacity spectrum method based on inelastic de-mand spectrardquo in Proceedings of 4th International Conferenceon Earthquake Engineering Taipei Taiwan October 2006

[10] A Chopra and R Goel ldquoEvaluation of NSP to estimateseismic deformation SDF systemsrdquo Journal of StructuralEngineering vol 126 no 4 pp 482ndash490 2000

[11] S Freeman ldquoDevelopment and use of capacity spectrummethodrdquo in Proceedings of 6th US NCEE Conference onEarthquake Engineering pp 1ndash12 SeattleWA USA June 1998

[12] H Sucuoglu and M S Gunay ldquoGeneralized force vectors formulti-mode pushover analysisrdquo Earthquake Engineering andStructural Dynamics vol 40 no 1 pp 55ndash74 2011

[13] E Kalkan and S K Kunnath ldquoAdaptive modal combinationprocedure for nonlinear static analysis of building structuresrdquoJournal of Structural Engineering vol 132 no 11 pp 1721ndash1731 2006

[14] M Cosic and S Brcic ldquoIterative displacement coefficientmethod mathematical formulation and numerical analysesrdquoGraCevinar vol 65 no 3 pp 199ndash211 2013

12 Advances in Civil Engineering

movement) comparing with the state after analyzing gravityload When taking into account both static analysis (gravityload analysis) and dynamic analysis the value of verticaldisplacement is still negative in all cases indicating no fulluplift occurrence For example under subjected by theearthquake GM-4 (Landers at Yermo fire station) thelandside leg (node 20) results in a positive value of 0034 cmfor dynamic analysis and a negative value of minus0058 cm forgravity load analysis thus the value considering both cases ofanalysis is approximately minus0024 cm by summation ismeans that the crane might be slightly uplifted and will befully uplifted if the value of displacement reaches zero and thevertical reaction of the crane leg is zero as well

5 Conclusions

is study represents a preliminary investigation for theseismic behavior of a typical Korean STS container cranee complex seismic response of the crane is estimated byrepresenting it by a 3D FE model Nonlinear time-historyanalysis and both CSM and ELM pushover analyses methodsare used to analyze the crane and compare the resultsSeveral key observations can be made based on the resultsobtained from this study ey are as follows

e conventional CSM and ELM are found to be suf-ficient to analyze a STS container crane In particular therelative errors of the portal drift and total base shearobtained from pushover methods are 46 and 10 re-spectively comparing with those using the nonlinear time-history analyses However the horizontal displacements ofthe apex of the crane obtained from CSM and ELM appear tobe overestimated because these methods consider only thefundamental mode whereas the nonlinear time-historyanalysis uses the superposition principle of multiple modes

Assessment of uplift response is an important issue thatshould be considered in the seismic analysis of a containercrane It is clearly seen in this study that the axial force of thelandside legs increases nearly 50 of the initial gravity forceas the waterside legs are slightly uplifted us a gap ele-ment which is integrated into most of the commercialsoftware is appropriate for modeling base support to studythe uplift behavior On the other hand the uplift response isstrongly influenced by the characteristics of the groundmotions e potential uplift can have large amplitude fora long time when excited by long-duration earthquakes evenwhen the acceleration amplitude may not be high

e portal drifts of the typical Korean STS containercrane corresponding to performance levels of IO LS andCP as defined in ASCESEI 41-13 are 16 18 and 22respectively ese values can be used as damage limits forthe fragility analysis

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflict of interest

Acknowledgments

is research was supported by Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Education(2017R1D1A3B03032854) and by Ministry of public Ad-ministration and Security as Disaster Prevention SafetyHuman resource development Project and was also a part ofthe project titled ldquoDevelopment of performance-basedseismic design technologies for advancement in design codesfor port structuresrdquo funded by the Ministry of Oceans andFisheries Korea

References

[1] G H Powell Static Pushover Methods-Explanation Com-parison and Implementation 2013 httpswikicsiamericacomdisplayperformStatic+pushover+methods+-+explanation2C+comparison+and+implementation

[2] ATC 40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood CA USA 1996

[3] ASCESEI 41 Seismic Evaluation and Retrofit of ExistingBuildings American Society of Civil Engineers Reston VAUSA 2013

[4] Eurocode 8 Design of Structures for Earthquake ResistancePart 1 General Rules Seismic Actions and Rules for BuildingsEN 1998 European Committee for Standardization (CEN)Brussels Belgium 2004

[5] FEMA 440 Improvement of Nonlinear Static Seismic AnalysisProcedures Applied Technology Council (ATC-55 Project)Federal Emergency Management Agency Washington DCUSA 2006

[6] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 4pp 377ndash390 2007

[7] P Fajfar ldquoCapacity spectrum method based on inelasticdemand spectrardquo Earthquake Engineering and StructuralDynamics vol 28 no 9 pp 979ndash993 1999

[8] Y-Y Lin and K Chang ldquoAn improved capacity spectrummethod for ATC 40rdquo Earthquake Engineering and StructuralDynamics vol 32 no 13 pp 2013ndash2025 2003

[9] X Mingkui D Yinfeng L Gang and C Guangjun ldquoAnimproved capacity spectrum method based on inelastic de-mand spectrardquo in Proceedings of 4th International Conferenceon Earthquake Engineering Taipei Taiwan October 2006

[10] A Chopra and R Goel ldquoEvaluation of NSP to estimateseismic deformation SDF systemsrdquo Journal of StructuralEngineering vol 126 no 4 pp 482ndash490 2000

[11] S Freeman ldquoDevelopment and use of capacity spectrummethodrdquo in Proceedings of 6th US NCEE Conference onEarthquake Engineering pp 1ndash12 SeattleWA USA June 1998

[12] H Sucuoglu and M S Gunay ldquoGeneralized force vectors formulti-mode pushover analysisrdquo Earthquake Engineering andStructural Dynamics vol 40 no 1 pp 55ndash74 2011

[13] E Kalkan and S K Kunnath ldquoAdaptive modal combinationprocedure for nonlinear static analysis of building structuresrdquoJournal of Structural Engineering vol 132 no 11 pp 1721ndash1731 2006

[14] M Cosic and S Brcic ldquoIterative displacement coefficientmethod mathematical formulation and numerical analysesrdquoGraCevinar vol 65 no 3 pp 199ndash211 2013

12 Advances in Civil Engineering

[15] S Taghavipour T Majid and T Lau ldquoAssessment of non-linear static (pushover) procedures using time-history directintegration analysisrdquo Australian Journal of Basic and AppliedSciences vol 7 no 8 pp 468ndash479 2013

[16] S Freeman J Nicoletti and J Tyrell ldquoEvaluations of existingbuildings for seismic riskmdasha case study of Puget Sound NavalShipyard BremertonWashingtonrdquo in Proceedings of the 1stUS National Conference on Earthquake Engineering OaklandCA USA June 1975

[17] FEMA 274 NEHRP Commentary on the Guidelines for theSeismic Rehabilitation of Buildings Federal EmergencyManagement Agency Washington DC USA 1997

[18] A Guyader and W Iwan Automated Capacity SpectrumMethod of Analysis California Institute of TechnologyPasadena CA USA 2004

[19] A K Chopra and R K Goel ldquoCapacity-demand-diagrammethods based on inelastic design spectrumrdquo EarthquakeSpectra vol 15 no 4 pp 637ndash656 1999

[20] B Gencturk and A S Elnashai ldquoDevelopment and applica-tion of an advanced capacity spectrum methodrdquo EngineeringStructures vol 30 no 11 pp 3345ndash3354 2008

[21] M Causevic and S Mitrovic ldquoComparison between non-linear dynamic and static seismic analysis of structuresaccording to European and US provisionsrdquo Bulletin ofEarthquake Engineering vol 9 no 2 pp 467ndash489 2011

[22] M Ferraioli A Lavino and A Mandara ldquoAn adaptive ca-pacity spectrum method for estimating seismic response ofsteel moment-resisting framesrdquo International Journal ofEarthquake Engineering Anno XXXIII Speciale CTA 2015no 1-2 pp 47ndash60 2015 httpingegneriasismicaorgwp-contentuploads201609Ferraioli-Nuova-impaginazionepdf

[23] SAP2000 Linear and Nonlinear Static and Dynamic Analysisand Design of 3D Structures Basic Analysis Reference ManualCSI Berkeley CA USA 2006

[24] E WilsonHree-Dimensional Static and Dynamic Analysis ofStructures A Physical Approach with Emphasis on EarthquakeEngineering CSI Berkeley CA USA 2002

[25] J Huh A Haldar and S Yim ldquoEffect of uncertainty infrequency content and strong motion duration on structuralseismic risksrdquo International Journal of Ocean System Engi-neering vol 2 no 1 pp 25ndash37 2012

[26] Architectural Institute of Korea Korean Building Code Ar-chitectural Institute of Korea Seoul Republic of Korea 2016

[27] J Huh Q H Tran A Haldar I Park and J-H Ahn ldquoSeismicvulnerability assessment of a shallow two-story undergroundRC box structurerdquo Applied Sciences vol 7 no 7 p 735 2017

[28] B D Kosbab Seismic Performance Evaluation of Port Con-tainer Cranes Allowed to Uplift Georgia Institute of Tech-nology Atlanta GA USA 2010

[29] Liftech On the Mend Liftech Consultants Inc Oakland CAUSA 2008

[30] PIANC Seismic Desing Guidelines for Port Structures AABalkema Leiden e Netherlands 2001

[31] L Jacobs B Kosbab R Leon and R DesRoches ldquoSeismicbehavior of a jumbo container crane including upliftrdquoEarthquake Spectra vol 27 no 3 pp 745ndash773 2011

[32] S Chaudhuri D Karmakar U Na and M ShinozukaldquoSeismic performance evaluation of container cranesrdquo inProceedings of ATC amp SEI 2009 Conference on Improving theSeismic Performance of Existing Buildings and OtherStructures San Francisco CA USA December 2009

[33] L Jacobs Shake Table Experiments for the Determination ofthe Seismic Response of Jumbo Container Cranes GeorgiaInstitute of Technology Atlanta GA USA 2010

[34] T Kanayama and A Kashiwazaki ldquoAn evaluation of upliftingbehavior of container cranes under strong earthquakesrdquoTransactions of the Japan Society of Mechanical Engineersvol 64 no 618 pp 100ndash106 1998 in Japanese

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