Research ArticleEarthquake Response Control of Double-Layer TrussWalls by means of Innovative Fuse Connections

Koichiro Ishikawa

University of Fukui Fukui-shi Japan

Correspondence should be addressed to Koichiro Ishikawa ishikawau-fukuiacjp

Received 8 May 2018 Accepted 8 July 2018 Published 15 August 2018

Academic Editor David M Boyajian

Copyright copy 2018 Koichiro Ishikawais is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

is study deals with partial cylindrical truss walls equipped with damper connections due to horizontal earthquake motions edamper connection consists of an aluminum ball joint an aluminum hub and a steel bolt A ductile elongation of the steel bolt dueto a tensile stress is expected by avoiding the brittle collapse e study proposes a fuse-type connection by means of yield of thesteel bolt due to tension stress realized by the ductile failure collapse mechanism of the wall-type spatial structure e proposedtruss wall with the fuse-type connection can realize a deformation of nodes within the restriction for avoiding a nonstructuralmember damage It is confirmed in the dynamic elastoplastic analysis that the control of the dynamic collapse mechanism such asthe steel bolt elongation can avoid a brittle collapse mechanism such as a chain of member bucklinge evaluation method is alsoproposed by means of the limit displacement considering a ductility factor of the steel bolt within 20

1 Introduction

is study deals with the dynamic elastoplastic analysisconsidering a member buckling and the fuse-type con-nection consists of an aluminum ball joint an aluminumhub and a steel bolt A ductile elongation of the steel boltdue to a tensile stress is expected by avoiding the brittlecollapse in our previous paper [1ndash3] e study proposesa fuse-type connection by means of yield of the steel bolt dueto tension stress realized by the ductile failure collapsemechanism of the wall-type spatial structure

e seismic response characteristics of spatial structuressuch as roof and wall types depend on their form andsupport conditions and several reviews [4 5] and guidelines[6ndash13] quoting many studies have been published dependingon the performance of building structures Several perfor-mance prediction methods have been developed for thispurpose however the earthquake resistance capacity ofspatial structures requires the variation of the form and thesupport condition and it is very difficult to apply them towall-type spatial structures For the performance designseveral prediction methods such as a pushover analysis andan adaptive capacity spectrum method have been developedfor structures such as buildings and bridges [14ndash18]

e control of the dynamic collapse mechanism is alsoproposed to improve the earthquake resistance capacity bya damper connection such as the steel bolt elongation

Effect of the member buckling and yield elongation of thesteel bolt on the seismic response out of the plane is shown incomparison with the response of the wall structure subjected tothe horizontal earthquake motions e earthquake evaluationmethod is also proposed considering the dynamic collapsemechanism A validity of the proposed method is shown bymeans of the accuracy between the analysis and the estimation

2 Examples of Aluminum Truss Structures

Since earthquake resistance standards in Japan were im-proved buildings which were designed on the basis of oldseismic standards before 1981 need to be reinforced quicklyon the basis of the exiting new ones

e aluminum braces are useful for seismic retrofitting ofexisting buildings because they achieve good workability in theerection site and reduce the seismic loading and additional loadson the foundations due to their lightweight and aluminum alloymembers owing to their long-term corrosion resistance

Figure 1 shows double-layer latticed walls and roofsmade of an aluminum alloy truss system and the walls

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 1425672 9 pageshttpsdoiorg10115520181425672

resist in-plane shearing load in an earthquake Figures 1(a)and 1(b) show the entrance canopy of the office and theatrium at the entrance of the railroad station and they areL-shaped application of an aluminum truss wall e trusswalls achieve structural rigidity and strength on seismicloading and the slender members with cladding preventdaylight Figures 1(c) and 1(d) are CG images of seismicretrofit of RC school buildings using the aluminum trusswalls

3 Connection Design of an AluminumTruss Wall

We propose two types of connection systems an aluminumball-jointed truss wall and aluminum pin-connected bracesAs described in more detail below both systems have im-proved in their plastic deformability to resist excessive seismicloads In our previous paper [1] the brittle collapse mecha-nism of the truss wall structure to resist lateral loads has beeninvestigated to evaluate the earthquake resistance capacity

Figure 2 illustrates the aluminum alloy ball-jointed trussconnection used to retrofit this nodal connection consists ofaluminum parts and a steel bolt All aluminum parts areextruded and in heat-treated aluminum alloy 6061-T6 theend plug is welded at its edge to the strut by using a frictionwelding method Friction welding which is one of thevarious welding processes is known for high joint efficiencyand high reliability in comparison withMIG or TIGweldinge collar transfers the compression stress and the steel bolt

transfers the tension stresse bolt is made of high-strengthsteel the figure of the bolt is slimmed in the axle of the bolt asshown in Figure 2

e connection of the truss wall is designed by means ofthe condition such as Ncr gt BNu where Ncr is a memberbuckling or an ultimate strength of the welded joint and BNuis an ultimate strength of the bolt e bolts are able to extendby excessive tensile loading in a major earthquake thereforethe truss wall structure achieves a good hysteretic curve asdescribed in Figure 3 In our previous paper [2] it is in-vestigated that the fuse-type connection realizes the tensionyield of the steel bolt before the member buckling occurs

(a) (b)

(c) (d)

Figure 1 Aluminum truss walls and retrofit

Hub

CollarFricton welding

End plug

BoltStrut

Yield zone

Figure 2 Yielding bolt mechanism

2 Advances in Civil Engineering

4 Truss Members including Jointsand Modeling

e fuse connection consists of two hubs two collars twobolts and a strut as shown in Figure 4 e steel bolt resistsagainst the tension axial stress and the collar resists againstthe compression axial stress as far as the resistancemechanism of the axial stress between the hub and strut isconcerned Figures 5ndash7 show the numerical analysis modelin this study

5 Hysteresis Models of the Truss Member

e present analysis adopts an assumption that struts buckledue to compression and yield under tension Figure 8 showsthe hysteresis curves used for the slenderness ratio ofa member e maximum compressive stress σcr is de-termined using (1) which considers member crookedness

and the residual stresses existing in the strut Figure 9 showsthe hysteresis curves of the steel bolt which yields undertension and slips under compressione hub resists againstthe compression instead of the yielding bolt e yield stressσy and Youngrsquos modulus E are taken to be 210MPa and70GPa respectively e maximum compressive stress σcr iscalculated by (1) and the maximum tension stress of theweld fracture is taken to be 071σy due to a tension axialstress e initial tension stress is not introduced in the steelbolt

λΛle 10 σcr

F

1minus 05(λΛ)21113966 1113967

λΛgt 10 σcr

F

2(λΛ)21113966 1113967

Λ

π2E05F

1113971

3717

F

radic 811

(1)

6 Time-History Analysis of the Truss Wall

Geometric and material nonlinearity is considered in thetime-history analysis of the truss walls subjected to thehorizontal earthquake motion of El Centro NS (PGA561 msec2) e Rayleigh damping matrix is used inthis analysis e damping factor h 002 is used for firstand second vibration modes in the damping matrixe numerical integration method uses the Newmarkmethod β14 is used in this study because β 14will be unconditionally stable for the seismic responseanalysis

61 Analysis Model of the Double-Layer Partial CylindricalTruss Wall e truss wall has a configuration as shownin Figure 10 e length is 14m with 7 grids and theheight is 72 m with 4 grids e bottom nodes are con-strained for all directions e top nodes are free for thehorizontal plane (X direction) ey are restrained for thevertical direction (Y direction) and out of the plane (Zdirection)

An aluminum alloy A6061-T6 is used in the strut anda high tensile strength steel SCM435 with the yieldstrength of 649 Nmm2 is used in the connection steel boltA truss model is used in the analysis e model isa lightweight structure made of an aluminum alloy estructure can bear the dead load which is confirmed as thestatic design

Table 1 shows the member length L (mm) the slen-derness ratio λ the cross-sectional secondary radius i (mm)and the sectional area A (mm2) e member is determinedby the earthquake-proof design using the base shear co-efficient of 10 And the strength of pullout of the bolt such asthe yield axial force is also shown in Table 1

62 Vibration Characteristics and Seismic Responses of theTruss Wall e natural period and the vibration mode of

Horizontal load

Horizontal displacement

Member bucklingFracture of welded joints

Yielding of bolts Fracture of bolts

QcrBQxBQy

Figure 3 Hysteretic curve of the truss wall used to retrofit

Hub Bolt

Strut

End plug

Collar

Figure 4 Truss system

Figure 5 Mechanism of stress transfer

Advances in Civil Engineering 3

the two walls with the 1m and 04mwall depths are obtainedby means of the eigenvalue analysis respectively e firstand third natural periods T1 and T3 are shown in Figure 11e corresponding vibration modes are also shown inFigure 11 respectively It is seen that the shear deformationmode of a wall appears in the first vibration mode of the twowalls and the third mode of the wall with the 1m depth eout-of-plane shape in the third mode of the wall with the04m depth also appears due to the lower bending rigiditythan in the wall with the 1m depth e study focuses on theout-of-plane deformation of the thin depth wall subjected toearthquake motions

63 Dynamic Response Behavior of the Truss Walls SubjectedtoEarthquakeMotions In the present study the earthquakeresistance capacity of the dome is evaluated by in-vestigating the maximum horizontal displacement δmax atthe top of the wall subjected to horizontal earthquakemotions with the peak ground acceleration (PGA) multi-plied by the PGA amplification factor λE e damage limitartificial earthquake motion with a phase characteristic ofthe El Centro NS wave is used in the seismic responseanalysis e PGA is taken to be 112msec2 e re-lationship between λE and δmax of the two walls withdifferent wall depths is shown in Figures 12 and 13 e

location of the steel bolt yield is shown in Figure 14 at thebeginning of the bolt yield and the member bucklingrespectively It is seen in the results that the bolt yieldprecedes the member buckling and the linear relationshipbetween λE and δmax is kept within the plastic region fromthe beginning of the bolt yield to the beginning of themember bucklingis means that the response control canbe feasible by means of the fuse-type connection such as thesteel bolt yielding elongation

e time-history energy response of the restoring forceof the member and the damping of the structure to thein-plane (X) and out-of-plane (Z) directions is shown inFigures 15 and 16 respectively It is seen in the wall withdepths that the structural damping almost absorbs the inputenergy due to the seismic response just before the memberbuckling occursemember buckling induces the absorbedenergy in the case of the wall with 1m depth subjected toearthquake motions with λE 94 e out-of-plane alsoconsumes energy greater due to member buckling as seen inTable 2 On the contrary a sudden dynamic collapse of thewall with the 04m depth occurs just after the memberbuckling because of the bending rigidity out of the planewith the less wall depth

e maximum strains of the steel connection bolt inboth depths are 2 times less than the first yield strain asshown in Figure 17 It is confirmed in the study that allmembers in both walls are also 2 times less than the firstyield strain

7 Evaluation Method of the ResponseEstimation by means of theLimit Displacement

e comparison between the PGA amplification factor λEof the input earthquake motion and the maximum dis-placement δmax to the horizontal in-plane (X) direction atthe top of the wall with the 1m and 04m wall depths isshown in Figure 18 by means of the dynamic analysis Andthe proposed estimation method uses the limit displace-ment e limit displacement δud is defined in the study as12δy1 in the red line in Figure 18 e structural yielddisplacement δy1 is the horizontal in-plane displacement δat the top of the wall just on the first occurrence of the steelbolt yield It is also noticed that a ductility factor of thesteel bolt is taken to be within 20 at the limit displacementδud is is the reason that the limit displacement δud istaken to be 12δy1 e structural buckling displacement

Joint connectionJoint connection

Strut member

Z

Y

X

Figure 6 Components of the member

Figure 7 Truss model of each element for analysis

σσy

071

2

3

4

ndash071

ndash10 10

6

5

εεy

1

Figure 8 Hysteresis model of the aluminum strut

4 Advances in Civil Engineering

δy2 is the horizontal in-plane displacement δ at the top ofthe wall just on the first occurrence of the strut memberbuckling

e evaluation method of the response estimation bymeans of the limit displacement is the first to calculate theδmax using the linear relationship between λE and δmax It canbe evaluated for engineers that the dynamic collapse occursin the case of δmax larger than δud e estimation value λEUis practically calculated by the proposed method using the

response analysis e proposed method can be applied tothe wall with an aspect ratio of the shear-dominant de-formation type

8 Conclusions

is study deals with the partial cylindrical truss wall withthe damper joint connection due to horizontal earthquakemotions It is confirmed in the dynamic elastoplastic analysis

800 ton

001 ton

Constraint for X Y and Z directions

Constraint for Y and Z directions

1 2 3 4 5 6 7 8 9 10 11 12 1314 15

VIIIVIIVIVIVIIIIII

4 un

its (7

2m

)

7 units (140m)

40deg

Y

Z

Z

Y

X

X

Figure 10 Analysis model of the double-layer partial cylindrical truss wall

σ

εB = 016

Bσu = 900Nmm2

Bσy = 640Nmm2

ε

Figure 9 Hysteresis model of the steel bolt

Advances in Civil Engineering 5

that the control of the dynamic collapse mechanism suchas the steel bolt elongation can avoid a brittle collapsemechanism such as a chain of member buckling Effect of themember buckling and yield elongation of the steel bolt onthe seismic response out of the plane is also shown in

comparison with the response of the wall structure subjectedto the horizontal earthquake motions

e evaluation method is also proposed by means of thelimit displacement considering a ductility factor of the steelbolt within 20 is means that the response control can be

(a2) ird mode T3 = 0050s

(a1) First mode T1 = 0234s

(a)

(b2) ird mode T3 = 0049s

(b1) First mode T1 = 0185s

(b)

Figure 11 e first and third vibration modes and natural periods (a) Wall depth 10m (b) Wall depth 04m

TABLE 1 Member characteristics of the truss wallWall depth 10m

Strut (mm) Sectionalarea (mm2)

Cross-sectionalsecondary

radius (mm)

Memberlength (mm)

Slendernessratiolimit

slenderness ratioChord member of X direction ϕ180times t21 104898 567 1705 0367Chord member of Y direction ϕ180times t21 104898 567 1400 0305Web member ϕ150times t12 52025 490 1162 0240

Bolt (mm) Sectionalarea (mm2)

Memberlength (mm)

Minimumelongation ()

Yield axialforce (kN)

Chord member of X direction ϕ300 7069 200 16 4523Chord member of Y direction ϕ300 7069 200 16 4523Web member ϕ150 2545 267 16 1629

Wall depth 04m

Strut (mm) Sectionalarea (mm2)

Cross-sectionalsecondary

radius (mm)

Memberlength (mm)

Slendernessratiolimit

slenderness ratioChord member of X direction ϕ180times t21 101898 567 1705 0367Chord member of Y direction ϕ180times t21 101898 567 1400 0305Web member ϕ150times t12 52025 490 994 0240

Bolt (mm) Sectionalarea (mm2)

Memberlength (mm)

Minimumelongation ()

Yield axialorce (kN)

Chord member of X direction ϕ300 7069 200 16 4523Chord member of Y direction ϕ300 7069 200 16 4523Web member ϕ150 2545 228 16 1629

6 Advances in Civil Engineering

1098765432

01

00 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginningof the bolt

yield λE = 54Beginning ofthe member

bucklingλE = 76

Figure 12 λE and δmax of the wall depth with 1m

(a)

(b)

Figure 14 Continued

10987654321000 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginning ofthe bolt yield

λE = 66Beginning ofthe member

buckling λE = 76

Figure 13 λE and δmax of the wall depth with 04m

(c)

Figure 14 Location of the bolt yield of the wall depth with 1m and04m (a) Case of λE 74 (1m depth) (b) Case of λE 94 (1mdepth) (c) Case of λE 76 (04m depth)

RE

3000

2500

2000

1500

Ener

gy (k

N∙m

)1000

500

00 5 10 15 20

DE

(a)

Ener

gy (k

N∙m

)

3000

2500

2000

1500

1000

500

00 5 10 15 20

RE DE

(b)

Ener

gy (k

N∙m

)

10000

8000

6000

4000

2000

00 5 10 15 20

RE DE

(c)

Figure 15 Time-history energy response of the restoring force ofthe member and the damping of the structure to the in-plane (X)direction component (a) 1m wall depth (λE 74) (b) 04m walldepth (λE 76) (c) 1m wall depth (λE 94) RE restoring forceenergy DE damping energy

Advances in Civil Engineering 7

RE DE

Time (s)

Ener

gy (k

N∙m

)

150

200

100

50

00 5 10 15 20

(a)

Time (s)

200

150

100

50

00 5 10 15 20

Ener

gy (k

N∙m

) RE DE

(b)

Time (s)

Ener

gy (k

N∙m

)

12001000

800600400200

00 5 10 15 20

RE DE

(c)

Figure 16 Time-history energy response to the out-of-plane (Z) direction component (a) 1m wall depth (λE 74) (b) 04m wall depth(λE 76) (c) 1m wall depth (λE 94) RE restoring force energy DE damping energy

Table 2 Ratio of the total energy in the out-of-plane (Z) direction to that in the in-plane (X) direction

Failure type Wall depth (m) λEConsumption energy in the in-plane

direction Ei (kNmiddotm)Consumption energy in the out-of-plane

direction Eo (kNmiddotm) Eo(Ei +Eo) ()

Steel bolt yield 10 74 19378 3033 15404 76 18147 13783 706

Memberbuckling 10 94 55886 79069 1239

Strain (times10ndash3)

Stre

ss (N

mm

2 )

800

400

ndash400

ndash800ndash100 ndash50 00 50 100

0

(a)

Strain (times10ndash3)

800

400

0

ndash400

ndash800ndash100 ndash50 00 50 100

Stre

ss (N

mm

2 )

(b)

Figure 17 Relationship between stress and strain of the web member (a) 1m wall depth before the member buckling (λE 74) (b) 04mwall depth before the collapse (λE 76)

00 100 200 300 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

AnalysisλEy2

λEu

λEy1

δy1 δud δy2

Limit disp

10

75

5

25

0

(a)

10

75

5

25

0

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

00 100 200 300 400

Limit disp

AnalysisλE

uλE

y2

λEy1

δy1 δudδy2

(b)

Figure 18 Comparison between the limit displacement and the analysis (a) 1m wall depth (b) 04m wall depth

8 Advances in Civil Engineering

feasible by the damper connection such as the steel boltelongation due to tension stress

Data Availability

e data used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

e author declares that there are no conflicts of interest

Acknowledgments

is work was supported by JSPS KAKENHI (Grant no18K04427)

References

[1] K Ishikawa S Okubo Y Hiyama and S Kato ldquoEvaluationmethod for predicting dynamic collapse of double layer lat-ticed space truss structures due to earthquake motionrdquo In-ternational Journal of Space Structures vol 15 no 3pp 249ndash257 2000

[2] S Okubo Y Hiyama K Ishikawa R Wendel and L FischerldquoLoad capacity and plastic deformable ability of aluminumalloy double layer latticed wall subjected to plane loadrdquo inProceedings of the IASS Symposium Nagoya Japan 2001

[3] K Ishikawa and S Kato ldquoElastic-plastic buckling analysis ofreticular dome subjected to earthquakemotionrdquo InternationalJournal of Space Structures vol 12 no 3-4 pp 205ndash215 1997

[4] Y Taniguchi P L Gould and M Kurano ldquoEarthquake inputenergy at dynamic collapse for double-layer cylindrical latticeroofsrdquo Journal of the International Association for Shell andSpatial Structures vol 49 no 2 2008

[5] F Fan S Z Shen and G A R Parke ldquoeoretical and ex-perimental study of vibration reduction in braced domesusing a viscous damper systemrdquo International Journal of SpaceStructures vol 19 no 4 pp 195ndash202 2004

[6] M Midorikawa ldquoPerformance-based seismic design pro-visions for buildings in Japanrdquo in Proceedings of the IASS2005 vol 1 pp 307ndash316 Bucharest Romania September2005

[7] G C Giuliani ldquoOverview on the dynamic control of struc-turesrdquo in Proceedings of the IASS 2002 pp 561ndash567 WarsawPoland 2002

[8] Z P Zeng ldquoStructural analysis and design of the latticed shellfor Fujian Gymnasiumrdquo Journal of Spatial Structures vol 13no 2 pp 44ndash48 2007

[9] L Ilzarbe M J Alvarez E Viles and M Tanco ldquoPracticalapplications of design of experiments in the field of engi-neering a bibliographical reviewrdquo Quality and ReliabilityEngineering International vol 24 no 4 pp 417ndash428 2008

[10] European Committee for Standardization (CEN) Eurocode 8Design of Structures for Earthquake Resistance Part 1 GeneralRules Seismic Actions and Rules for Buildings (EN 1998-12004) European Committee for Standardization (CEN)Brussel Belgium 2004

[11] FEMA-356 NEHRP Guidelines for the Seismic Rehabilitationof Buildings Building Seismic Safety Council FEMAWashington DC USA 2000

[12] H G Park T Eom and H Lee ldquoFactored modal combinationfor evaluation of earthquake load profilesrdquo Journal ofStructural Engineering vol 133 no 7 pp 956ndash968 2007

[13] S K Kunnath ldquoIdentification of modal combinations fornonlinear static analysis of building structuresrdquo Computer-Aided Civil and Infrastructure Engineering vol 19 no 4pp 246ndash259 2004

[14] R K Goel and A K Chopra ldquoExtension of modal pushoveranalysis to compute member forcesrdquo Earthquake Spectravol 21 no 1 pp 125ndash139 2005

[15] J C Reyes and A K Chopra ldquoree dimensional modalpushover analysis of buildings subjected to two componentsof ground motion including its evaluation for tall buildingsrdquoEarthquake Engineering and Structural Dynamics vol 40no 7 pp 789ndash806 2011

[16] A K Chopra and R K Goel ldquoA modal pushover analysisprocedure for estimating seismic demands for buildingsrdquoEarthquake Engineering and Structural Dynamics vol 31no 3 pp 561ndash582 2002

[17] G Gupta and S K Kunnath ldquoAdaptive spectra-basedpushover procedure for seismic evaluation of structuresrdquoEarthquake Spectra vol 16 no 2 pp 367ndash392 2000

[18] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 3pp 377ndash390 2007

Advances in Civil Engineering 9

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4 Truss Members including Jointsand Modeling

e fuse connection consists of two hubs two collars twobolts and a strut as shown in Figure 4 e steel bolt resistsagainst the tension axial stress and the collar resists againstthe compression axial stress as far as the resistancemechanism of the axial stress between the hub and strut isconcerned Figures 5ndash7 show the numerical analysis modelin this study

5 Hysteresis Models of the Truss Member

e present analysis adopts an assumption that struts buckledue to compression and yield under tension Figure 8 showsthe hysteresis curves used for the slenderness ratio ofa member e maximum compressive stress σcr is de-termined using (1) which considers member crookedness

and the residual stresses existing in the strut Figure 9 showsthe hysteresis curves of the steel bolt which yields undertension and slips under compressione hub resists againstthe compression instead of the yielding bolt e yield stressσy and Youngrsquos modulus E are taken to be 210MPa and70GPa respectively e maximum compressive stress σcr iscalculated by (1) and the maximum tension stress of theweld fracture is taken to be 071σy due to a tension axialstress e initial tension stress is not introduced in the steelbolt

λΛle 10 σcr

F

1minus 05(λΛ)21113966 1113967

λΛgt 10 σcr

F

2(λΛ)21113966 1113967

Λ

π2E05F

1113971

3717

F

radic 811

(1)

6 Time-History Analysis of the Truss Wall

Geometric and material nonlinearity is considered in thetime-history analysis of the truss walls subjected to thehorizontal earthquake motion of El Centro NS (PGA561 msec2) e Rayleigh damping matrix is used inthis analysis e damping factor h 002 is used for firstand second vibration modes in the damping matrixe numerical integration method uses the Newmarkmethod β14 is used in this study because β 14will be unconditionally stable for the seismic responseanalysis

61 Analysis Model of the Double-Layer Partial CylindricalTruss Wall e truss wall has a configuration as shownin Figure 10 e length is 14m with 7 grids and theheight is 72 m with 4 grids e bottom nodes are con-strained for all directions e top nodes are free for thehorizontal plane (X direction) ey are restrained for thevertical direction (Y direction) and out of the plane (Zdirection)

An aluminum alloy A6061-T6 is used in the strut anda high tensile strength steel SCM435 with the yieldstrength of 649 Nmm2 is used in the connection steel boltA truss model is used in the analysis e model isa lightweight structure made of an aluminum alloy estructure can bear the dead load which is confirmed as thestatic design

Table 1 shows the member length L (mm) the slen-derness ratio λ the cross-sectional secondary radius i (mm)and the sectional area A (mm2) e member is determinedby the earthquake-proof design using the base shear co-efficient of 10 And the strength of pullout of the bolt such asthe yield axial force is also shown in Table 1

62 Vibration Characteristics and Seismic Responses of theTruss Wall e natural period and the vibration mode of

Horizontal load

Horizontal displacement

Member bucklingFracture of welded joints

Yielding of bolts Fracture of bolts

QcrBQxBQy

Figure 3 Hysteretic curve of the truss wall used to retrofit

Hub Bolt

Strut

End plug

Collar

Figure 4 Truss system

Figure 5 Mechanism of stress transfer

Advances in Civil Engineering 3

the two walls with the 1m and 04mwall depths are obtainedby means of the eigenvalue analysis respectively e firstand third natural periods T1 and T3 are shown in Figure 11e corresponding vibration modes are also shown inFigure 11 respectively It is seen that the shear deformationmode of a wall appears in the first vibration mode of the twowalls and the third mode of the wall with the 1m depth eout-of-plane shape in the third mode of the wall with the04m depth also appears due to the lower bending rigiditythan in the wall with the 1m depth e study focuses on theout-of-plane deformation of the thin depth wall subjected toearthquake motions

63 Dynamic Response Behavior of the Truss Walls SubjectedtoEarthquakeMotions In the present study the earthquakeresistance capacity of the dome is evaluated by in-vestigating the maximum horizontal displacement δmax atthe top of the wall subjected to horizontal earthquakemotions with the peak ground acceleration (PGA) multi-plied by the PGA amplification factor λE e damage limitartificial earthquake motion with a phase characteristic ofthe El Centro NS wave is used in the seismic responseanalysis e PGA is taken to be 112msec2 e re-lationship between λE and δmax of the two walls withdifferent wall depths is shown in Figures 12 and 13 e

location of the steel bolt yield is shown in Figure 14 at thebeginning of the bolt yield and the member bucklingrespectively It is seen in the results that the bolt yieldprecedes the member buckling and the linear relationshipbetween λE and δmax is kept within the plastic region fromthe beginning of the bolt yield to the beginning of themember bucklingis means that the response control canbe feasible by means of the fuse-type connection such as thesteel bolt yielding elongation

e time-history energy response of the restoring forceof the member and the damping of the structure to thein-plane (X) and out-of-plane (Z) directions is shown inFigures 15 and 16 respectively It is seen in the wall withdepths that the structural damping almost absorbs the inputenergy due to the seismic response just before the memberbuckling occursemember buckling induces the absorbedenergy in the case of the wall with 1m depth subjected toearthquake motions with λE 94 e out-of-plane alsoconsumes energy greater due to member buckling as seen inTable 2 On the contrary a sudden dynamic collapse of thewall with the 04m depth occurs just after the memberbuckling because of the bending rigidity out of the planewith the less wall depth

e maximum strains of the steel connection bolt inboth depths are 2 times less than the first yield strain asshown in Figure 17 It is confirmed in the study that allmembers in both walls are also 2 times less than the firstyield strain

7 Evaluation Method of the ResponseEstimation by means of theLimit Displacement

e comparison between the PGA amplification factor λEof the input earthquake motion and the maximum dis-placement δmax to the horizontal in-plane (X) direction atthe top of the wall with the 1m and 04m wall depths isshown in Figure 18 by means of the dynamic analysis Andthe proposed estimation method uses the limit displace-ment e limit displacement δud is defined in the study as12δy1 in the red line in Figure 18 e structural yielddisplacement δy1 is the horizontal in-plane displacement δat the top of the wall just on the first occurrence of the steelbolt yield It is also noticed that a ductility factor of thesteel bolt is taken to be within 20 at the limit displacementδud is is the reason that the limit displacement δud istaken to be 12δy1 e structural buckling displacement

Joint connectionJoint connection

Strut member

Z

Y

X

Figure 6 Components of the member

Figure 7 Truss model of each element for analysis

σσy

071

2

3

4

ndash071

ndash10 10

6

5

εεy

1

Figure 8 Hysteresis model of the aluminum strut

4 Advances in Civil Engineering

δy2 is the horizontal in-plane displacement δ at the top ofthe wall just on the first occurrence of the strut memberbuckling

e evaluation method of the response estimation bymeans of the limit displacement is the first to calculate theδmax using the linear relationship between λE and δmax It canbe evaluated for engineers that the dynamic collapse occursin the case of δmax larger than δud e estimation value λEUis practically calculated by the proposed method using the

response analysis e proposed method can be applied tothe wall with an aspect ratio of the shear-dominant de-formation type

8 Conclusions

is study deals with the partial cylindrical truss wall withthe damper joint connection due to horizontal earthquakemotions It is confirmed in the dynamic elastoplastic analysis

800 ton

001 ton

Constraint for X Y and Z directions

Constraint for Y and Z directions

1 2 3 4 5 6 7 8 9 10 11 12 1314 15

VIIIVIIVIVIVIIIIII

4 un

its (7

2m

)

7 units (140m)

40deg

Y

Z

Z

Y

X

X

Figure 10 Analysis model of the double-layer partial cylindrical truss wall

σ

εB = 016

Bσu = 900Nmm2

Bσy = 640Nmm2

ε

Figure 9 Hysteresis model of the steel bolt

Advances in Civil Engineering 5

that the control of the dynamic collapse mechanism suchas the steel bolt elongation can avoid a brittle collapsemechanism such as a chain of member buckling Effect of themember buckling and yield elongation of the steel bolt onthe seismic response out of the plane is also shown in

comparison with the response of the wall structure subjectedto the horizontal earthquake motions

e evaluation method is also proposed by means of thelimit displacement considering a ductility factor of the steelbolt within 20 is means that the response control can be

(a2) ird mode T3 = 0050s

(a1) First mode T1 = 0234s

(a)

(b2) ird mode T3 = 0049s

(b1) First mode T1 = 0185s

(b)

Figure 11 e first and third vibration modes and natural periods (a) Wall depth 10m (b) Wall depth 04m

TABLE 1 Member characteristics of the truss wallWall depth 10m

Strut (mm) Sectionalarea (mm2)

Cross-sectionalsecondary

radius (mm)

Memberlength (mm)

Slendernessratiolimit

slenderness ratioChord member of X direction ϕ180times t21 104898 567 1705 0367Chord member of Y direction ϕ180times t21 104898 567 1400 0305Web member ϕ150times t12 52025 490 1162 0240

Bolt (mm) Sectionalarea (mm2)

Memberlength (mm)

Minimumelongation ()

Yield axialforce (kN)

Chord member of X direction ϕ300 7069 200 16 4523Chord member of Y direction ϕ300 7069 200 16 4523Web member ϕ150 2545 267 16 1629

Wall depth 04m

Strut (mm) Sectionalarea (mm2)

Cross-sectionalsecondary

radius (mm)

Memberlength (mm)

Slendernessratiolimit

slenderness ratioChord member of X direction ϕ180times t21 101898 567 1705 0367Chord member of Y direction ϕ180times t21 101898 567 1400 0305Web member ϕ150times t12 52025 490 994 0240

Bolt (mm) Sectionalarea (mm2)

Memberlength (mm)

Minimumelongation ()

Yield axialorce (kN)

Chord member of X direction ϕ300 7069 200 16 4523Chord member of Y direction ϕ300 7069 200 16 4523Web member ϕ150 2545 228 16 1629

6 Advances in Civil Engineering

1098765432

01

00 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginningof the bolt

yield λE = 54Beginning ofthe member

bucklingλE = 76

Figure 12 λE and δmax of the wall depth with 1m

(a)

(b)

Figure 14 Continued

10987654321000 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginning ofthe bolt yield

λE = 66Beginning ofthe member

buckling λE = 76

Figure 13 λE and δmax of the wall depth with 04m

(c)

Figure 14 Location of the bolt yield of the wall depth with 1m and04m (a) Case of λE 74 (1m depth) (b) Case of λE 94 (1mdepth) (c) Case of λE 76 (04m depth)

RE

3000

2500

2000

1500

Ener

gy (k

N∙m

)1000

500

00 5 10 15 20

DE

(a)

Ener

gy (k

N∙m

)

3000

2500

2000

1500

1000

500

00 5 10 15 20

RE DE

(b)

Ener

gy (k

N∙m

)

10000

8000

6000

4000

2000

00 5 10 15 20

RE DE

(c)

Figure 15 Time-history energy response of the restoring force ofthe member and the damping of the structure to the in-plane (X)direction component (a) 1m wall depth (λE 74) (b) 04m walldepth (λE 76) (c) 1m wall depth (λE 94) RE restoring forceenergy DE damping energy

Advances in Civil Engineering 7

RE DE

Time (s)

Ener

gy (k

N∙m

)

150

200

100

50

00 5 10 15 20

(a)

Time (s)

200

150

100

50

00 5 10 15 20

Ener

gy (k

N∙m

) RE DE

(b)

Time (s)

Ener

gy (k

N∙m

)

12001000

800600400200

00 5 10 15 20

RE DE

(c)

Figure 16 Time-history energy response to the out-of-plane (Z) direction component (a) 1m wall depth (λE 74) (b) 04m wall depth(λE 76) (c) 1m wall depth (λE 94) RE restoring force energy DE damping energy

Table 2 Ratio of the total energy in the out-of-plane (Z) direction to that in the in-plane (X) direction

Failure type Wall depth (m) λEConsumption energy in the in-plane

direction Ei (kNmiddotm)Consumption energy in the out-of-plane

direction Eo (kNmiddotm) Eo(Ei +Eo) ()

Steel bolt yield 10 74 19378 3033 15404 76 18147 13783 706

Memberbuckling 10 94 55886 79069 1239

Strain (times10ndash3)

Stre

ss (N

mm

2 )

800

400

ndash400

ndash800ndash100 ndash50 00 50 100

0

(a)

Strain (times10ndash3)

800

400

0

ndash400

ndash800ndash100 ndash50 00 50 100

Stre

ss (N

mm

2 )

(b)

Figure 17 Relationship between stress and strain of the web member (a) 1m wall depth before the member buckling (λE 74) (b) 04mwall depth before the collapse (λE 76)

00 100 200 300 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

AnalysisλEy2

λEu

λEy1

δy1 δud δy2

Limit disp

10

75

5

25

0

(a)

10

75

5

25

0

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

00 100 200 300 400

Limit disp

AnalysisλE

uλE

y2

λEy1

δy1 δudδy2

(b)

Figure 18 Comparison between the limit displacement and the analysis (a) 1m wall depth (b) 04m wall depth

8 Advances in Civil Engineering

feasible by the damper connection such as the steel boltelongation due to tension stress

Data Availability

e data used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

e author declares that there are no conflicts of interest

Acknowledgments

is work was supported by JSPS KAKENHI (Grant no18K04427)

References

[1] K Ishikawa S Okubo Y Hiyama and S Kato ldquoEvaluationmethod for predicting dynamic collapse of double layer lat-ticed space truss structures due to earthquake motionrdquo In-ternational Journal of Space Structures vol 15 no 3pp 249ndash257 2000

[2] S Okubo Y Hiyama K Ishikawa R Wendel and L FischerldquoLoad capacity and plastic deformable ability of aluminumalloy double layer latticed wall subjected to plane loadrdquo inProceedings of the IASS Symposium Nagoya Japan 2001

[3] K Ishikawa and S Kato ldquoElastic-plastic buckling analysis ofreticular dome subjected to earthquakemotionrdquo InternationalJournal of Space Structures vol 12 no 3-4 pp 205ndash215 1997

[4] Y Taniguchi P L Gould and M Kurano ldquoEarthquake inputenergy at dynamic collapse for double-layer cylindrical latticeroofsrdquo Journal of the International Association for Shell andSpatial Structures vol 49 no 2 2008

[5] F Fan S Z Shen and G A R Parke ldquoeoretical and ex-perimental study of vibration reduction in braced domesusing a viscous damper systemrdquo International Journal of SpaceStructures vol 19 no 4 pp 195ndash202 2004

[6] M Midorikawa ldquoPerformance-based seismic design pro-visions for buildings in Japanrdquo in Proceedings of the IASS2005 vol 1 pp 307ndash316 Bucharest Romania September2005

[7] G C Giuliani ldquoOverview on the dynamic control of struc-turesrdquo in Proceedings of the IASS 2002 pp 561ndash567 WarsawPoland 2002

[8] Z P Zeng ldquoStructural analysis and design of the latticed shellfor Fujian Gymnasiumrdquo Journal of Spatial Structures vol 13no 2 pp 44ndash48 2007

[9] L Ilzarbe M J Alvarez E Viles and M Tanco ldquoPracticalapplications of design of experiments in the field of engi-neering a bibliographical reviewrdquo Quality and ReliabilityEngineering International vol 24 no 4 pp 417ndash428 2008

[10] European Committee for Standardization (CEN) Eurocode 8Design of Structures for Earthquake Resistance Part 1 GeneralRules Seismic Actions and Rules for Buildings (EN 1998-12004) European Committee for Standardization (CEN)Brussel Belgium 2004

[11] FEMA-356 NEHRP Guidelines for the Seismic Rehabilitationof Buildings Building Seismic Safety Council FEMAWashington DC USA 2000

[12] H G Park T Eom and H Lee ldquoFactored modal combinationfor evaluation of earthquake load profilesrdquo Journal ofStructural Engineering vol 133 no 7 pp 956ndash968 2007

[13] S K Kunnath ldquoIdentification of modal combinations fornonlinear static analysis of building structuresrdquo Computer-Aided Civil and Infrastructure Engineering vol 19 no 4pp 246ndash259 2004

[14] R K Goel and A K Chopra ldquoExtension of modal pushoveranalysis to compute member forcesrdquo Earthquake Spectravol 21 no 1 pp 125ndash139 2005

[15] J C Reyes and A K Chopra ldquoree dimensional modalpushover analysis of buildings subjected to two componentsof ground motion including its evaluation for tall buildingsrdquoEarthquake Engineering and Structural Dynamics vol 40no 7 pp 789ndash806 2011

[16] A K Chopra and R K Goel ldquoA modal pushover analysisprocedure for estimating seismic demands for buildingsrdquoEarthquake Engineering and Structural Dynamics vol 31no 3 pp 561ndash582 2002

[17] G Gupta and S K Kunnath ldquoAdaptive spectra-basedpushover procedure for seismic evaluation of structuresrdquoEarthquake Spectra vol 16 no 2 pp 367ndash392 2000

[18] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 3pp 377ndash390 2007

Advances in Civil Engineering 9

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

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Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

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Submit your manuscripts atwwwhindawicom

the two walls with the 1m and 04mwall depths are obtainedby means of the eigenvalue analysis respectively e firstand third natural periods T1 and T3 are shown in Figure 11e corresponding vibration modes are also shown inFigure 11 respectively It is seen that the shear deformationmode of a wall appears in the first vibration mode of the twowalls and the third mode of the wall with the 1m depth eout-of-plane shape in the third mode of the wall with the04m depth also appears due to the lower bending rigiditythan in the wall with the 1m depth e study focuses on theout-of-plane deformation of the thin depth wall subjected toearthquake motions

63 Dynamic Response Behavior of the Truss Walls SubjectedtoEarthquakeMotions In the present study the earthquakeresistance capacity of the dome is evaluated by in-vestigating the maximum horizontal displacement δmax atthe top of the wall subjected to horizontal earthquakemotions with the peak ground acceleration (PGA) multi-plied by the PGA amplification factor λE e damage limitartificial earthquake motion with a phase characteristic ofthe El Centro NS wave is used in the seismic responseanalysis e PGA is taken to be 112msec2 e re-lationship between λE and δmax of the two walls withdifferent wall depths is shown in Figures 12 and 13 e

location of the steel bolt yield is shown in Figure 14 at thebeginning of the bolt yield and the member bucklingrespectively It is seen in the results that the bolt yieldprecedes the member buckling and the linear relationshipbetween λE and δmax is kept within the plastic region fromthe beginning of the bolt yield to the beginning of themember bucklingis means that the response control canbe feasible by means of the fuse-type connection such as thesteel bolt yielding elongation

e time-history energy response of the restoring forceof the member and the damping of the structure to thein-plane (X) and out-of-plane (Z) directions is shown inFigures 15 and 16 respectively It is seen in the wall withdepths that the structural damping almost absorbs the inputenergy due to the seismic response just before the memberbuckling occursemember buckling induces the absorbedenergy in the case of the wall with 1m depth subjected toearthquake motions with λE 94 e out-of-plane alsoconsumes energy greater due to member buckling as seen inTable 2 On the contrary a sudden dynamic collapse of thewall with the 04m depth occurs just after the memberbuckling because of the bending rigidity out of the planewith the less wall depth

e maximum strains of the steel connection bolt inboth depths are 2 times less than the first yield strain asshown in Figure 17 It is confirmed in the study that allmembers in both walls are also 2 times less than the firstyield strain

7 Evaluation Method of the ResponseEstimation by means of theLimit Displacement

e comparison between the PGA amplification factor λEof the input earthquake motion and the maximum dis-placement δmax to the horizontal in-plane (X) direction atthe top of the wall with the 1m and 04m wall depths isshown in Figure 18 by means of the dynamic analysis Andthe proposed estimation method uses the limit displace-ment e limit displacement δud is defined in the study as12δy1 in the red line in Figure 18 e structural yielddisplacement δy1 is the horizontal in-plane displacement δat the top of the wall just on the first occurrence of the steelbolt yield It is also noticed that a ductility factor of thesteel bolt is taken to be within 20 at the limit displacementδud is is the reason that the limit displacement δud istaken to be 12δy1 e structural buckling displacement

Joint connectionJoint connection

Strut member

Z

Y

X

Figure 6 Components of the member

Figure 7 Truss model of each element for analysis

σσy

071

2

3

4

ndash071

ndash10 10

6

5

εεy

1

Figure 8 Hysteresis model of the aluminum strut

4 Advances in Civil Engineering

δy2 is the horizontal in-plane displacement δ at the top ofthe wall just on the first occurrence of the strut memberbuckling

e evaluation method of the response estimation bymeans of the limit displacement is the first to calculate theδmax using the linear relationship between λE and δmax It canbe evaluated for engineers that the dynamic collapse occursin the case of δmax larger than δud e estimation value λEUis practically calculated by the proposed method using the

response analysis e proposed method can be applied tothe wall with an aspect ratio of the shear-dominant de-formation type

8 Conclusions

is study deals with the partial cylindrical truss wall withthe damper joint connection due to horizontal earthquakemotions It is confirmed in the dynamic elastoplastic analysis

800 ton

001 ton

Constraint for X Y and Z directions

Constraint for Y and Z directions

1 2 3 4 5 6 7 8 9 10 11 12 1314 15

VIIIVIIVIVIVIIIIII

4 un

its (7

2m

)

7 units (140m)

40deg

Y

Z

Z

Y

X

X

Figure 10 Analysis model of the double-layer partial cylindrical truss wall

σ

εB = 016

Bσu = 900Nmm2

Bσy = 640Nmm2

ε

Figure 9 Hysteresis model of the steel bolt

Advances in Civil Engineering 5

that the control of the dynamic collapse mechanism suchas the steel bolt elongation can avoid a brittle collapsemechanism such as a chain of member buckling Effect of themember buckling and yield elongation of the steel bolt onthe seismic response out of the plane is also shown in

comparison with the response of the wall structure subjectedto the horizontal earthquake motions

e evaluation method is also proposed by means of thelimit displacement considering a ductility factor of the steelbolt within 20 is means that the response control can be

(a2) ird mode T3 = 0050s

(a1) First mode T1 = 0234s

(a)

(b2) ird mode T3 = 0049s

(b1) First mode T1 = 0185s

(b)

Figure 11 e first and third vibration modes and natural periods (a) Wall depth 10m (b) Wall depth 04m

TABLE 1 Member characteristics of the truss wallWall depth 10m

Strut (mm) Sectionalarea (mm2)

Cross-sectionalsecondary

radius (mm)

Memberlength (mm)

Slendernessratiolimit

slenderness ratioChord member of X direction ϕ180times t21 104898 567 1705 0367Chord member of Y direction ϕ180times t21 104898 567 1400 0305Web member ϕ150times t12 52025 490 1162 0240

Bolt (mm) Sectionalarea (mm2)

Memberlength (mm)

Minimumelongation ()

Yield axialforce (kN)

Chord member of X direction ϕ300 7069 200 16 4523Chord member of Y direction ϕ300 7069 200 16 4523Web member ϕ150 2545 267 16 1629

Wall depth 04m

Strut (mm) Sectionalarea (mm2)

Cross-sectionalsecondary

radius (mm)

Memberlength (mm)

Slendernessratiolimit

slenderness ratioChord member of X direction ϕ180times t21 101898 567 1705 0367Chord member of Y direction ϕ180times t21 101898 567 1400 0305Web member ϕ150times t12 52025 490 994 0240

Bolt (mm) Sectionalarea (mm2)

Memberlength (mm)

Minimumelongation ()

Yield axialorce (kN)

Chord member of X direction ϕ300 7069 200 16 4523Chord member of Y direction ϕ300 7069 200 16 4523Web member ϕ150 2545 228 16 1629

6 Advances in Civil Engineering

1098765432

01

00 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginningof the bolt

yield λE = 54Beginning ofthe member

bucklingλE = 76

Figure 12 λE and δmax of the wall depth with 1m

(a)

(b)

Figure 14 Continued

10987654321000 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginning ofthe bolt yield

λE = 66Beginning ofthe member

buckling λE = 76

Figure 13 λE and δmax of the wall depth with 04m

(c)

Figure 14 Location of the bolt yield of the wall depth with 1m and04m (a) Case of λE 74 (1m depth) (b) Case of λE 94 (1mdepth) (c) Case of λE 76 (04m depth)

RE

3000

2500

2000

1500

Ener

gy (k

N∙m

)1000

500

00 5 10 15 20

DE

(a)

Ener

gy (k

N∙m

)

3000

2500

2000

1500

1000

500

00 5 10 15 20

RE DE

(b)

Ener

gy (k

N∙m

)

10000

8000

6000

4000

2000

00 5 10 15 20

RE DE

(c)

Figure 15 Time-history energy response of the restoring force ofthe member and the damping of the structure to the in-plane (X)direction component (a) 1m wall depth (λE 74) (b) 04m walldepth (λE 76) (c) 1m wall depth (λE 94) RE restoring forceenergy DE damping energy

Advances in Civil Engineering 7

RE DE

Time (s)

Ener

gy (k

N∙m

)

150

200

100

50

00 5 10 15 20

(a)

Time (s)

200

150

100

50

00 5 10 15 20

Ener

gy (k

N∙m

) RE DE

(b)

Time (s)

Ener

gy (k

N∙m

)

12001000

800600400200

00 5 10 15 20

RE DE

(c)

Figure 16 Time-history energy response to the out-of-plane (Z) direction component (a) 1m wall depth (λE 74) (b) 04m wall depth(λE 76) (c) 1m wall depth (λE 94) RE restoring force energy DE damping energy

Table 2 Ratio of the total energy in the out-of-plane (Z) direction to that in the in-plane (X) direction

Failure type Wall depth (m) λEConsumption energy in the in-plane

direction Ei (kNmiddotm)Consumption energy in the out-of-plane

direction Eo (kNmiddotm) Eo(Ei +Eo) ()

Steel bolt yield 10 74 19378 3033 15404 76 18147 13783 706

Memberbuckling 10 94 55886 79069 1239

Strain (times10ndash3)

Stre

ss (N

mm

2 )

800

400

ndash400

ndash800ndash100 ndash50 00 50 100

0

(a)

Strain (times10ndash3)

800

400

0

ndash400

ndash800ndash100 ndash50 00 50 100

Stre

ss (N

mm

2 )

(b)

Figure 17 Relationship between stress and strain of the web member (a) 1m wall depth before the member buckling (λE 74) (b) 04mwall depth before the collapse (λE 76)

00 100 200 300 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

AnalysisλEy2

λEu

λEy1

δy1 δud δy2

Limit disp

10

75

5

25

0

(a)

10

75

5

25

0

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

00 100 200 300 400

Limit disp

AnalysisλE

uλE

y2

λEy1

δy1 δudδy2

(b)

Figure 18 Comparison between the limit displacement and the analysis (a) 1m wall depth (b) 04m wall depth

8 Advances in Civil Engineering

feasible by the damper connection such as the steel boltelongation due to tension stress

Data Availability

e data used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

e author declares that there are no conflicts of interest

Acknowledgments

is work was supported by JSPS KAKENHI (Grant no18K04427)

References

[1] K Ishikawa S Okubo Y Hiyama and S Kato ldquoEvaluationmethod for predicting dynamic collapse of double layer lat-ticed space truss structures due to earthquake motionrdquo In-ternational Journal of Space Structures vol 15 no 3pp 249ndash257 2000

[2] S Okubo Y Hiyama K Ishikawa R Wendel and L FischerldquoLoad capacity and plastic deformable ability of aluminumalloy double layer latticed wall subjected to plane loadrdquo inProceedings of the IASS Symposium Nagoya Japan 2001

[3] K Ishikawa and S Kato ldquoElastic-plastic buckling analysis ofreticular dome subjected to earthquakemotionrdquo InternationalJournal of Space Structures vol 12 no 3-4 pp 205ndash215 1997

[4] Y Taniguchi P L Gould and M Kurano ldquoEarthquake inputenergy at dynamic collapse for double-layer cylindrical latticeroofsrdquo Journal of the International Association for Shell andSpatial Structures vol 49 no 2 2008

[5] F Fan S Z Shen and G A R Parke ldquoeoretical and ex-perimental study of vibration reduction in braced domesusing a viscous damper systemrdquo International Journal of SpaceStructures vol 19 no 4 pp 195ndash202 2004

[6] M Midorikawa ldquoPerformance-based seismic design pro-visions for buildings in Japanrdquo in Proceedings of the IASS2005 vol 1 pp 307ndash316 Bucharest Romania September2005

[7] G C Giuliani ldquoOverview on the dynamic control of struc-turesrdquo in Proceedings of the IASS 2002 pp 561ndash567 WarsawPoland 2002

[8] Z P Zeng ldquoStructural analysis and design of the latticed shellfor Fujian Gymnasiumrdquo Journal of Spatial Structures vol 13no 2 pp 44ndash48 2007

[9] L Ilzarbe M J Alvarez E Viles and M Tanco ldquoPracticalapplications of design of experiments in the field of engi-neering a bibliographical reviewrdquo Quality and ReliabilityEngineering International vol 24 no 4 pp 417ndash428 2008

[10] European Committee for Standardization (CEN) Eurocode 8Design of Structures for Earthquake Resistance Part 1 GeneralRules Seismic Actions and Rules for Buildings (EN 1998-12004) European Committee for Standardization (CEN)Brussel Belgium 2004

[11] FEMA-356 NEHRP Guidelines for the Seismic Rehabilitationof Buildings Building Seismic Safety Council FEMAWashington DC USA 2000

[12] H G Park T Eom and H Lee ldquoFactored modal combinationfor evaluation of earthquake load profilesrdquo Journal ofStructural Engineering vol 133 no 7 pp 956ndash968 2007

[13] S K Kunnath ldquoIdentification of modal combinations fornonlinear static analysis of building structuresrdquo Computer-Aided Civil and Infrastructure Engineering vol 19 no 4pp 246ndash259 2004

[14] R K Goel and A K Chopra ldquoExtension of modal pushoveranalysis to compute member forcesrdquo Earthquake Spectravol 21 no 1 pp 125ndash139 2005

[15] J C Reyes and A K Chopra ldquoree dimensional modalpushover analysis of buildings subjected to two componentsof ground motion including its evaluation for tall buildingsrdquoEarthquake Engineering and Structural Dynamics vol 40no 7 pp 789ndash806 2011

[16] A K Chopra and R K Goel ldquoA modal pushover analysisprocedure for estimating seismic demands for buildingsrdquoEarthquake Engineering and Structural Dynamics vol 31no 3 pp 561ndash582 2002

[17] G Gupta and S K Kunnath ldquoAdaptive spectra-basedpushover procedure for seismic evaluation of structuresrdquoEarthquake Spectra vol 16 no 2 pp 367ndash392 2000

[18] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 3pp 377ndash390 2007

Advances in Civil Engineering 9

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

δy2 is the horizontal in-plane displacement δ at the top ofthe wall just on the first occurrence of the strut memberbuckling

e evaluation method of the response estimation bymeans of the limit displacement is the first to calculate theδmax using the linear relationship between λE and δmax It canbe evaluated for engineers that the dynamic collapse occursin the case of δmax larger than δud e estimation value λEUis practically calculated by the proposed method using the

response analysis e proposed method can be applied tothe wall with an aspect ratio of the shear-dominant de-formation type

8 Conclusions

is study deals with the partial cylindrical truss wall withthe damper joint connection due to horizontal earthquakemotions It is confirmed in the dynamic elastoplastic analysis

800 ton

001 ton

Constraint for X Y and Z directions

Constraint for Y and Z directions

1 2 3 4 5 6 7 8 9 10 11 12 1314 15

VIIIVIIVIVIVIIIIII

4 un

its (7

2m

)

7 units (140m)

40deg

Y

Z

Z

Y

X

X

Figure 10 Analysis model of the double-layer partial cylindrical truss wall

σ

εB = 016

Bσu = 900Nmm2

Bσy = 640Nmm2

ε

Figure 9 Hysteresis model of the steel bolt

Advances in Civil Engineering 5

that the control of the dynamic collapse mechanism suchas the steel bolt elongation can avoid a brittle collapsemechanism such as a chain of member buckling Effect of themember buckling and yield elongation of the steel bolt onthe seismic response out of the plane is also shown in

comparison with the response of the wall structure subjectedto the horizontal earthquake motions

e evaluation method is also proposed by means of thelimit displacement considering a ductility factor of the steelbolt within 20 is means that the response control can be

(a2) ird mode T3 = 0050s

(a1) First mode T1 = 0234s

(a)

(b2) ird mode T3 = 0049s

(b1) First mode T1 = 0185s

(b)

Figure 11 e first and third vibration modes and natural periods (a) Wall depth 10m (b) Wall depth 04m

TABLE 1 Member characteristics of the truss wallWall depth 10m

Strut (mm) Sectionalarea (mm2)

Cross-sectionalsecondary

radius (mm)

Memberlength (mm)

Slendernessratiolimit

slenderness ratioChord member of X direction ϕ180times t21 104898 567 1705 0367Chord member of Y direction ϕ180times t21 104898 567 1400 0305Web member ϕ150times t12 52025 490 1162 0240

Bolt (mm) Sectionalarea (mm2)

Memberlength (mm)

Minimumelongation ()

Yield axialforce (kN)

Chord member of X direction ϕ300 7069 200 16 4523Chord member of Y direction ϕ300 7069 200 16 4523Web member ϕ150 2545 267 16 1629

Wall depth 04m

Strut (mm) Sectionalarea (mm2)

Cross-sectionalsecondary

radius (mm)

Memberlength (mm)

Slendernessratiolimit

slenderness ratioChord member of X direction ϕ180times t21 101898 567 1705 0367Chord member of Y direction ϕ180times t21 101898 567 1400 0305Web member ϕ150times t12 52025 490 994 0240

Bolt (mm) Sectionalarea (mm2)

Memberlength (mm)

Minimumelongation ()

Yield axialorce (kN)

Chord member of X direction ϕ300 7069 200 16 4523Chord member of Y direction ϕ300 7069 200 16 4523Web member ϕ150 2545 228 16 1629

6 Advances in Civil Engineering

1098765432

01

00 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginningof the bolt

yield λE = 54Beginning ofthe member

bucklingλE = 76

Figure 12 λE and δmax of the wall depth with 1m

(a)

(b)

Figure 14 Continued

10987654321000 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginning ofthe bolt yield

λE = 66Beginning ofthe member

buckling λE = 76

Figure 13 λE and δmax of the wall depth with 04m

(c)

Figure 14 Location of the bolt yield of the wall depth with 1m and04m (a) Case of λE 74 (1m depth) (b) Case of λE 94 (1mdepth) (c) Case of λE 76 (04m depth)

RE

3000

2500

2000

1500

Ener

gy (k

N∙m

)1000

500

00 5 10 15 20

DE

(a)

Ener

gy (k

N∙m

)

3000

2500

2000

1500

1000

500

00 5 10 15 20

RE DE

(b)

Ener

gy (k

N∙m

)

10000

8000

6000

4000

2000

00 5 10 15 20

RE DE

(c)

Figure 15 Time-history energy response of the restoring force ofthe member and the damping of the structure to the in-plane (X)direction component (a) 1m wall depth (λE 74) (b) 04m walldepth (λE 76) (c) 1m wall depth (λE 94) RE restoring forceenergy DE damping energy

Advances in Civil Engineering 7

RE DE

Time (s)

Ener

gy (k

N∙m

)

150

200

100

50

00 5 10 15 20

(a)

Time (s)

200

150

100

50

00 5 10 15 20

Ener

gy (k

N∙m

) RE DE

(b)

Time (s)

Ener

gy (k

N∙m

)

12001000

800600400200

00 5 10 15 20

RE DE

(c)

Figure 16 Time-history energy response to the out-of-plane (Z) direction component (a) 1m wall depth (λE 74) (b) 04m wall depth(λE 76) (c) 1m wall depth (λE 94) RE restoring force energy DE damping energy

Table 2 Ratio of the total energy in the out-of-plane (Z) direction to that in the in-plane (X) direction

Failure type Wall depth (m) λEConsumption energy in the in-plane

direction Ei (kNmiddotm)Consumption energy in the out-of-plane

direction Eo (kNmiddotm) Eo(Ei +Eo) ()

Steel bolt yield 10 74 19378 3033 15404 76 18147 13783 706

Memberbuckling 10 94 55886 79069 1239

Strain (times10ndash3)

Stre

ss (N

mm

2 )

800

400

ndash400

ndash800ndash100 ndash50 00 50 100

0

(a)

Strain (times10ndash3)

800

400

0

ndash400

ndash800ndash100 ndash50 00 50 100

Stre

ss (N

mm

2 )

(b)

Figure 17 Relationship between stress and strain of the web member (a) 1m wall depth before the member buckling (λE 74) (b) 04mwall depth before the collapse (λE 76)

00 100 200 300 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

AnalysisλEy2

λEu

λEy1

δy1 δud δy2

Limit disp

10

75

5

25

0

(a)

10

75

5

25

0

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

00 100 200 300 400

Limit disp

AnalysisλE

uλE

y2

λEy1

δy1 δudδy2

(b)

Figure 18 Comparison between the limit displacement and the analysis (a) 1m wall depth (b) 04m wall depth

8 Advances in Civil Engineering

feasible by the damper connection such as the steel boltelongation due to tension stress

Data Availability

e data used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

e author declares that there are no conflicts of interest

Acknowledgments

is work was supported by JSPS KAKENHI (Grant no18K04427)

References

[1] K Ishikawa S Okubo Y Hiyama and S Kato ldquoEvaluationmethod for predicting dynamic collapse of double layer lat-ticed space truss structures due to earthquake motionrdquo In-ternational Journal of Space Structures vol 15 no 3pp 249ndash257 2000

[2] S Okubo Y Hiyama K Ishikawa R Wendel and L FischerldquoLoad capacity and plastic deformable ability of aluminumalloy double layer latticed wall subjected to plane loadrdquo inProceedings of the IASS Symposium Nagoya Japan 2001

[3] K Ishikawa and S Kato ldquoElastic-plastic buckling analysis ofreticular dome subjected to earthquakemotionrdquo InternationalJournal of Space Structures vol 12 no 3-4 pp 205ndash215 1997

[4] Y Taniguchi P L Gould and M Kurano ldquoEarthquake inputenergy at dynamic collapse for double-layer cylindrical latticeroofsrdquo Journal of the International Association for Shell andSpatial Structures vol 49 no 2 2008

[5] F Fan S Z Shen and G A R Parke ldquoeoretical and ex-perimental study of vibration reduction in braced domesusing a viscous damper systemrdquo International Journal of SpaceStructures vol 19 no 4 pp 195ndash202 2004

[6] M Midorikawa ldquoPerformance-based seismic design pro-visions for buildings in Japanrdquo in Proceedings of the IASS2005 vol 1 pp 307ndash316 Bucharest Romania September2005

[7] G C Giuliani ldquoOverview on the dynamic control of struc-turesrdquo in Proceedings of the IASS 2002 pp 561ndash567 WarsawPoland 2002

[8] Z P Zeng ldquoStructural analysis and design of the latticed shellfor Fujian Gymnasiumrdquo Journal of Spatial Structures vol 13no 2 pp 44ndash48 2007

[9] L Ilzarbe M J Alvarez E Viles and M Tanco ldquoPracticalapplications of design of experiments in the field of engi-neering a bibliographical reviewrdquo Quality and ReliabilityEngineering International vol 24 no 4 pp 417ndash428 2008

[10] European Committee for Standardization (CEN) Eurocode 8Design of Structures for Earthquake Resistance Part 1 GeneralRules Seismic Actions and Rules for Buildings (EN 1998-12004) European Committee for Standardization (CEN)Brussel Belgium 2004

[11] FEMA-356 NEHRP Guidelines for the Seismic Rehabilitationof Buildings Building Seismic Safety Council FEMAWashington DC USA 2000

[12] H G Park T Eom and H Lee ldquoFactored modal combinationfor evaluation of earthquake load profilesrdquo Journal ofStructural Engineering vol 133 no 7 pp 956ndash968 2007

[13] S K Kunnath ldquoIdentification of modal combinations fornonlinear static analysis of building structuresrdquo Computer-Aided Civil and Infrastructure Engineering vol 19 no 4pp 246ndash259 2004

[14] R K Goel and A K Chopra ldquoExtension of modal pushoveranalysis to compute member forcesrdquo Earthquake Spectravol 21 no 1 pp 125ndash139 2005

[15] J C Reyes and A K Chopra ldquoree dimensional modalpushover analysis of buildings subjected to two componentsof ground motion including its evaluation for tall buildingsrdquoEarthquake Engineering and Structural Dynamics vol 40no 7 pp 789ndash806 2011

[16] A K Chopra and R K Goel ldquoA modal pushover analysisprocedure for estimating seismic demands for buildingsrdquoEarthquake Engineering and Structural Dynamics vol 31no 3 pp 561ndash582 2002

[17] G Gupta and S K Kunnath ldquoAdaptive spectra-basedpushover procedure for seismic evaluation of structuresrdquoEarthquake Spectra vol 16 no 2 pp 367ndash392 2000

[18] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 3pp 377ndash390 2007

Advances in Civil Engineering 9

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

that the control of the dynamic collapse mechanism suchas the steel bolt elongation can avoid a brittle collapsemechanism such as a chain of member buckling Effect of themember buckling and yield elongation of the steel bolt onthe seismic response out of the plane is also shown in

comparison with the response of the wall structure subjectedto the horizontal earthquake motions

e evaluation method is also proposed by means of thelimit displacement considering a ductility factor of the steelbolt within 20 is means that the response control can be

(a2) ird mode T3 = 0050s

(a1) First mode T1 = 0234s

(a)

(b2) ird mode T3 = 0049s

(b1) First mode T1 = 0185s

(b)

Figure 11 e first and third vibration modes and natural periods (a) Wall depth 10m (b) Wall depth 04m

TABLE 1 Member characteristics of the truss wallWall depth 10m

Strut (mm) Sectionalarea (mm2)

Cross-sectionalsecondary

radius (mm)

Memberlength (mm)

Slendernessratiolimit

slenderness ratioChord member of X direction ϕ180times t21 104898 567 1705 0367Chord member of Y direction ϕ180times t21 104898 567 1400 0305Web member ϕ150times t12 52025 490 1162 0240

Bolt (mm) Sectionalarea (mm2)

Memberlength (mm)

Minimumelongation ()

Yield axialforce (kN)

Chord member of X direction ϕ300 7069 200 16 4523Chord member of Y direction ϕ300 7069 200 16 4523Web member ϕ150 2545 267 16 1629

Wall depth 04m

Strut (mm) Sectionalarea (mm2)

Cross-sectionalsecondary

radius (mm)

Memberlength (mm)

Slendernessratiolimit

slenderness ratioChord member of X direction ϕ180times t21 101898 567 1705 0367Chord member of Y direction ϕ180times t21 101898 567 1400 0305Web member ϕ150times t12 52025 490 994 0240

Bolt (mm) Sectionalarea (mm2)

Memberlength (mm)

Minimumelongation ()

Yield axialorce (kN)

Chord member of X direction ϕ300 7069 200 16 4523Chord member of Y direction ϕ300 7069 200 16 4523Web member ϕ150 2545 228 16 1629

6 Advances in Civil Engineering

1098765432

01

00 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginningof the bolt

yield λE = 54Beginning ofthe member

bucklingλE = 76

Figure 12 λE and δmax of the wall depth with 1m

(a)

(b)

Figure 14 Continued

10987654321000 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginning ofthe bolt yield

λE = 66Beginning ofthe member

buckling λE = 76

Figure 13 λE and δmax of the wall depth with 04m

(c)

Figure 14 Location of the bolt yield of the wall depth with 1m and04m (a) Case of λE 74 (1m depth) (b) Case of λE 94 (1mdepth) (c) Case of λE 76 (04m depth)

RE

3000

2500

2000

1500

Ener

gy (k

N∙m

)1000

500

00 5 10 15 20

DE

(a)

Ener

gy (k

N∙m

)

3000

2500

2000

1500

1000

500

00 5 10 15 20

RE DE

(b)

Ener

gy (k

N∙m

)

10000

8000

6000

4000

2000

00 5 10 15 20

RE DE

(c)

Figure 15 Time-history energy response of the restoring force ofthe member and the damping of the structure to the in-plane (X)direction component (a) 1m wall depth (λE 74) (b) 04m walldepth (λE 76) (c) 1m wall depth (λE 94) RE restoring forceenergy DE damping energy

Advances in Civil Engineering 7

RE DE

Time (s)

Ener

gy (k

N∙m

)

150

200

100

50

00 5 10 15 20

(a)

Time (s)

200

150

100

50

00 5 10 15 20

Ener

gy (k

N∙m

) RE DE

(b)

Time (s)

Ener

gy (k

N∙m

)

12001000

800600400200

00 5 10 15 20

RE DE

(c)

Figure 16 Time-history energy response to the out-of-plane (Z) direction component (a) 1m wall depth (λE 74) (b) 04m wall depth(λE 76) (c) 1m wall depth (λE 94) RE restoring force energy DE damping energy

Table 2 Ratio of the total energy in the out-of-plane (Z) direction to that in the in-plane (X) direction

Failure type Wall depth (m) λEConsumption energy in the in-plane

direction Ei (kNmiddotm)Consumption energy in the out-of-plane

direction Eo (kNmiddotm) Eo(Ei +Eo) ()

Steel bolt yield 10 74 19378 3033 15404 76 18147 13783 706

Memberbuckling 10 94 55886 79069 1239

Strain (times10ndash3)

Stre

ss (N

mm

2 )

800

400

ndash400

ndash800ndash100 ndash50 00 50 100

0

(a)

Strain (times10ndash3)

800

400

0

ndash400

ndash800ndash100 ndash50 00 50 100

Stre

ss (N

mm

2 )

(b)

Figure 17 Relationship between stress and strain of the web member (a) 1m wall depth before the member buckling (λE 74) (b) 04mwall depth before the collapse (λE 76)

00 100 200 300 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

AnalysisλEy2

λEu

λEy1

δy1 δud δy2

Limit disp

10

75

5

25

0

(a)

10

75

5

25

0

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

00 100 200 300 400

Limit disp

AnalysisλE

uλE

y2

λEy1

δy1 δudδy2

(b)

Figure 18 Comparison between the limit displacement and the analysis (a) 1m wall depth (b) 04m wall depth

8 Advances in Civil Engineering

feasible by the damper connection such as the steel boltelongation due to tension stress

Data Availability

e data used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

e author declares that there are no conflicts of interest

Acknowledgments

is work was supported by JSPS KAKENHI (Grant no18K04427)

References

[1] K Ishikawa S Okubo Y Hiyama and S Kato ldquoEvaluationmethod for predicting dynamic collapse of double layer lat-ticed space truss structures due to earthquake motionrdquo In-ternational Journal of Space Structures vol 15 no 3pp 249ndash257 2000

[2] S Okubo Y Hiyama K Ishikawa R Wendel and L FischerldquoLoad capacity and plastic deformable ability of aluminumalloy double layer latticed wall subjected to plane loadrdquo inProceedings of the IASS Symposium Nagoya Japan 2001

[3] K Ishikawa and S Kato ldquoElastic-plastic buckling analysis ofreticular dome subjected to earthquakemotionrdquo InternationalJournal of Space Structures vol 12 no 3-4 pp 205ndash215 1997

[4] Y Taniguchi P L Gould and M Kurano ldquoEarthquake inputenergy at dynamic collapse for double-layer cylindrical latticeroofsrdquo Journal of the International Association for Shell andSpatial Structures vol 49 no 2 2008

[5] F Fan S Z Shen and G A R Parke ldquoeoretical and ex-perimental study of vibration reduction in braced domesusing a viscous damper systemrdquo International Journal of SpaceStructures vol 19 no 4 pp 195ndash202 2004

[6] M Midorikawa ldquoPerformance-based seismic design pro-visions for buildings in Japanrdquo in Proceedings of the IASS2005 vol 1 pp 307ndash316 Bucharest Romania September2005

[7] G C Giuliani ldquoOverview on the dynamic control of struc-turesrdquo in Proceedings of the IASS 2002 pp 561ndash567 WarsawPoland 2002

[8] Z P Zeng ldquoStructural analysis and design of the latticed shellfor Fujian Gymnasiumrdquo Journal of Spatial Structures vol 13no 2 pp 44ndash48 2007

[9] L Ilzarbe M J Alvarez E Viles and M Tanco ldquoPracticalapplications of design of experiments in the field of engi-neering a bibliographical reviewrdquo Quality and ReliabilityEngineering International vol 24 no 4 pp 417ndash428 2008

[10] European Committee for Standardization (CEN) Eurocode 8Design of Structures for Earthquake Resistance Part 1 GeneralRules Seismic Actions and Rules for Buildings (EN 1998-12004) European Committee for Standardization (CEN)Brussel Belgium 2004

[11] FEMA-356 NEHRP Guidelines for the Seismic Rehabilitationof Buildings Building Seismic Safety Council FEMAWashington DC USA 2000

[12] H G Park T Eom and H Lee ldquoFactored modal combinationfor evaluation of earthquake load profilesrdquo Journal ofStructural Engineering vol 133 no 7 pp 956ndash968 2007

[13] S K Kunnath ldquoIdentification of modal combinations fornonlinear static analysis of building structuresrdquo Computer-Aided Civil and Infrastructure Engineering vol 19 no 4pp 246ndash259 2004

[14] R K Goel and A K Chopra ldquoExtension of modal pushoveranalysis to compute member forcesrdquo Earthquake Spectravol 21 no 1 pp 125ndash139 2005

[15] J C Reyes and A K Chopra ldquoree dimensional modalpushover analysis of buildings subjected to two componentsof ground motion including its evaluation for tall buildingsrdquoEarthquake Engineering and Structural Dynamics vol 40no 7 pp 789ndash806 2011

[16] A K Chopra and R K Goel ldquoA modal pushover analysisprocedure for estimating seismic demands for buildingsrdquoEarthquake Engineering and Structural Dynamics vol 31no 3 pp 561ndash582 2002

[17] G Gupta and S K Kunnath ldquoAdaptive spectra-basedpushover procedure for seismic evaluation of structuresrdquoEarthquake Spectra vol 16 no 2 pp 367ndash392 2000

[18] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 3pp 377ndash390 2007

Advances in Civil Engineering 9

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

1098765432

01

00 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginningof the bolt

yield λE = 54Beginning ofthe member

bucklingλE = 76

Figure 12 λE and δmax of the wall depth with 1m

(a)

(b)

Figure 14 Continued

10987654321000 50 100 150 200 250 300 350 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax (mm)

Beginning ofthe bolt yield

λE = 66Beginning ofthe member

buckling λE = 76

Figure 13 λE and δmax of the wall depth with 04m

(c)

Figure 14 Location of the bolt yield of the wall depth with 1m and04m (a) Case of λE 74 (1m depth) (b) Case of λE 94 (1mdepth) (c) Case of λE 76 (04m depth)

RE

3000

2500

2000

1500

Ener

gy (k

N∙m

)1000

500

00 5 10 15 20

DE

(a)

Ener

gy (k

N∙m

)

3000

2500

2000

1500

1000

500

00 5 10 15 20

RE DE

(b)

Ener

gy (k

N∙m

)

10000

8000

6000

4000

2000

00 5 10 15 20

RE DE

(c)

Figure 15 Time-history energy response of the restoring force ofthe member and the damping of the structure to the in-plane (X)direction component (a) 1m wall depth (λE 74) (b) 04m walldepth (λE 76) (c) 1m wall depth (λE 94) RE restoring forceenergy DE damping energy

Advances in Civil Engineering 7

RE DE

Time (s)

Ener

gy (k

N∙m

)

150

200

100

50

00 5 10 15 20

(a)

Time (s)

200

150

100

50

00 5 10 15 20

Ener

gy (k

N∙m

) RE DE

(b)

Time (s)

Ener

gy (k

N∙m

)

12001000

800600400200

00 5 10 15 20

RE DE

(c)

Figure 16 Time-history energy response to the out-of-plane (Z) direction component (a) 1m wall depth (λE 74) (b) 04m wall depth(λE 76) (c) 1m wall depth (λE 94) RE restoring force energy DE damping energy

Table 2 Ratio of the total energy in the out-of-plane (Z) direction to that in the in-plane (X) direction

Failure type Wall depth (m) λEConsumption energy in the in-plane

direction Ei (kNmiddotm)Consumption energy in the out-of-plane

direction Eo (kNmiddotm) Eo(Ei +Eo) ()

Steel bolt yield 10 74 19378 3033 15404 76 18147 13783 706

Memberbuckling 10 94 55886 79069 1239

Strain (times10ndash3)

Stre

ss (N

mm

2 )

800

400

ndash400

ndash800ndash100 ndash50 00 50 100

0

(a)

Strain (times10ndash3)

800

400

0

ndash400

ndash800ndash100 ndash50 00 50 100

Stre

ss (N

mm

2 )

(b)

Figure 17 Relationship between stress and strain of the web member (a) 1m wall depth before the member buckling (λE 74) (b) 04mwall depth before the collapse (λE 76)

00 100 200 300 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

AnalysisλEy2

λEu

λEy1

δy1 δud δy2

Limit disp

10

75

5

25

0

(a)

10

75

5

25

0

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

00 100 200 300 400

Limit disp

AnalysisλE

uλE

y2

λEy1

δy1 δudδy2

(b)

Figure 18 Comparison between the limit displacement and the analysis (a) 1m wall depth (b) 04m wall depth

8 Advances in Civil Engineering

feasible by the damper connection such as the steel boltelongation due to tension stress

Data Availability

e data used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

e author declares that there are no conflicts of interest

Acknowledgments

is work was supported by JSPS KAKENHI (Grant no18K04427)

References

[1] K Ishikawa S Okubo Y Hiyama and S Kato ldquoEvaluationmethod for predicting dynamic collapse of double layer lat-ticed space truss structures due to earthquake motionrdquo In-ternational Journal of Space Structures vol 15 no 3pp 249ndash257 2000

[2] S Okubo Y Hiyama K Ishikawa R Wendel and L FischerldquoLoad capacity and plastic deformable ability of aluminumalloy double layer latticed wall subjected to plane loadrdquo inProceedings of the IASS Symposium Nagoya Japan 2001

[3] K Ishikawa and S Kato ldquoElastic-plastic buckling analysis ofreticular dome subjected to earthquakemotionrdquo InternationalJournal of Space Structures vol 12 no 3-4 pp 205ndash215 1997

[4] Y Taniguchi P L Gould and M Kurano ldquoEarthquake inputenergy at dynamic collapse for double-layer cylindrical latticeroofsrdquo Journal of the International Association for Shell andSpatial Structures vol 49 no 2 2008

[5] F Fan S Z Shen and G A R Parke ldquoeoretical and ex-perimental study of vibration reduction in braced domesusing a viscous damper systemrdquo International Journal of SpaceStructures vol 19 no 4 pp 195ndash202 2004

[6] M Midorikawa ldquoPerformance-based seismic design pro-visions for buildings in Japanrdquo in Proceedings of the IASS2005 vol 1 pp 307ndash316 Bucharest Romania September2005

[7] G C Giuliani ldquoOverview on the dynamic control of struc-turesrdquo in Proceedings of the IASS 2002 pp 561ndash567 WarsawPoland 2002

[8] Z P Zeng ldquoStructural analysis and design of the latticed shellfor Fujian Gymnasiumrdquo Journal of Spatial Structures vol 13no 2 pp 44ndash48 2007

[9] L Ilzarbe M J Alvarez E Viles and M Tanco ldquoPracticalapplications of design of experiments in the field of engi-neering a bibliographical reviewrdquo Quality and ReliabilityEngineering International vol 24 no 4 pp 417ndash428 2008

[10] European Committee for Standardization (CEN) Eurocode 8Design of Structures for Earthquake Resistance Part 1 GeneralRules Seismic Actions and Rules for Buildings (EN 1998-12004) European Committee for Standardization (CEN)Brussel Belgium 2004

[11] FEMA-356 NEHRP Guidelines for the Seismic Rehabilitationof Buildings Building Seismic Safety Council FEMAWashington DC USA 2000

[12] H G Park T Eom and H Lee ldquoFactored modal combinationfor evaluation of earthquake load profilesrdquo Journal ofStructural Engineering vol 133 no 7 pp 956ndash968 2007

[13] S K Kunnath ldquoIdentification of modal combinations fornonlinear static analysis of building structuresrdquo Computer-Aided Civil and Infrastructure Engineering vol 19 no 4pp 246ndash259 2004

[14] R K Goel and A K Chopra ldquoExtension of modal pushoveranalysis to compute member forcesrdquo Earthquake Spectravol 21 no 1 pp 125ndash139 2005

[15] J C Reyes and A K Chopra ldquoree dimensional modalpushover analysis of buildings subjected to two componentsof ground motion including its evaluation for tall buildingsrdquoEarthquake Engineering and Structural Dynamics vol 40no 7 pp 789ndash806 2011

[16] A K Chopra and R K Goel ldquoA modal pushover analysisprocedure for estimating seismic demands for buildingsrdquoEarthquake Engineering and Structural Dynamics vol 31no 3 pp 561ndash582 2002

[17] G Gupta and S K Kunnath ldquoAdaptive spectra-basedpushover procedure for seismic evaluation of structuresrdquoEarthquake Spectra vol 16 no 2 pp 367ndash392 2000

[18] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 3pp 377ndash390 2007

Advances in Civil Engineering 9

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

RE DE

Time (s)

Ener

gy (k

N∙m

)

150

200

100

50

00 5 10 15 20

(a)

Time (s)

200

150

100

50

00 5 10 15 20

Ener

gy (k

N∙m

) RE DE

(b)

Time (s)

Ener

gy (k

N∙m

)

12001000

800600400200

00 5 10 15 20

RE DE

(c)

Figure 16 Time-history energy response to the out-of-plane (Z) direction component (a) 1m wall depth (λE 74) (b) 04m wall depth(λE 76) (c) 1m wall depth (λE 94) RE restoring force energy DE damping energy

Table 2 Ratio of the total energy in the out-of-plane (Z) direction to that in the in-plane (X) direction

Failure type Wall depth (m) λEConsumption energy in the in-plane

direction Ei (kNmiddotm)Consumption energy in the out-of-plane

direction Eo (kNmiddotm) Eo(Ei +Eo) ()

Steel bolt yield 10 74 19378 3033 15404 76 18147 13783 706

Memberbuckling 10 94 55886 79069 1239

Strain (times10ndash3)

Stre

ss (N

mm

2 )

800

400

ndash400

ndash800ndash100 ndash50 00 50 100

0

(a)

Strain (times10ndash3)

800

400

0

ndash400

ndash800ndash100 ndash50 00 50 100

Stre

ss (N

mm

2 )

(b)

Figure 17 Relationship between stress and strain of the web member (a) 1m wall depth before the member buckling (λE 74) (b) 04mwall depth before the collapse (λE 76)

00 100 200 300 400

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

AnalysisλEy2

λEu

λEy1

δy1 δud δy2

Limit disp

10

75

5

25

0

(a)

10

75

5

25

0

PGA

ampl

ifica

tion

fact

or λ

E

Maximum disp δmax

00 100 200 300 400

Limit disp

AnalysisλE

uλE

y2

λEy1

δy1 δudδy2

(b)

Figure 18 Comparison between the limit displacement and the analysis (a) 1m wall depth (b) 04m wall depth

8 Advances in Civil Engineering

feasible by the damper connection such as the steel boltelongation due to tension stress

Data Availability

e data used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

e author declares that there are no conflicts of interest

Acknowledgments

is work was supported by JSPS KAKENHI (Grant no18K04427)

References

[1] K Ishikawa S Okubo Y Hiyama and S Kato ldquoEvaluationmethod for predicting dynamic collapse of double layer lat-ticed space truss structures due to earthquake motionrdquo In-ternational Journal of Space Structures vol 15 no 3pp 249ndash257 2000

[2] S Okubo Y Hiyama K Ishikawa R Wendel and L FischerldquoLoad capacity and plastic deformable ability of aluminumalloy double layer latticed wall subjected to plane loadrdquo inProceedings of the IASS Symposium Nagoya Japan 2001

[3] K Ishikawa and S Kato ldquoElastic-plastic buckling analysis ofreticular dome subjected to earthquakemotionrdquo InternationalJournal of Space Structures vol 12 no 3-4 pp 205ndash215 1997

[4] Y Taniguchi P L Gould and M Kurano ldquoEarthquake inputenergy at dynamic collapse for double-layer cylindrical latticeroofsrdquo Journal of the International Association for Shell andSpatial Structures vol 49 no 2 2008

[5] F Fan S Z Shen and G A R Parke ldquoeoretical and ex-perimental study of vibration reduction in braced domesusing a viscous damper systemrdquo International Journal of SpaceStructures vol 19 no 4 pp 195ndash202 2004

[6] M Midorikawa ldquoPerformance-based seismic design pro-visions for buildings in Japanrdquo in Proceedings of the IASS2005 vol 1 pp 307ndash316 Bucharest Romania September2005

[7] G C Giuliani ldquoOverview on the dynamic control of struc-turesrdquo in Proceedings of the IASS 2002 pp 561ndash567 WarsawPoland 2002

[8] Z P Zeng ldquoStructural analysis and design of the latticed shellfor Fujian Gymnasiumrdquo Journal of Spatial Structures vol 13no 2 pp 44ndash48 2007

[9] L Ilzarbe M J Alvarez E Viles and M Tanco ldquoPracticalapplications of design of experiments in the field of engi-neering a bibliographical reviewrdquo Quality and ReliabilityEngineering International vol 24 no 4 pp 417ndash428 2008

[10] European Committee for Standardization (CEN) Eurocode 8Design of Structures for Earthquake Resistance Part 1 GeneralRules Seismic Actions and Rules for Buildings (EN 1998-12004) European Committee for Standardization (CEN)Brussel Belgium 2004

[11] FEMA-356 NEHRP Guidelines for the Seismic Rehabilitationof Buildings Building Seismic Safety Council FEMAWashington DC USA 2000

[12] H G Park T Eom and H Lee ldquoFactored modal combinationfor evaluation of earthquake load profilesrdquo Journal ofStructural Engineering vol 133 no 7 pp 956ndash968 2007

[13] S K Kunnath ldquoIdentification of modal combinations fornonlinear static analysis of building structuresrdquo Computer-Aided Civil and Infrastructure Engineering vol 19 no 4pp 246ndash259 2004

[14] R K Goel and A K Chopra ldquoExtension of modal pushoveranalysis to compute member forcesrdquo Earthquake Spectravol 21 no 1 pp 125ndash139 2005

[15] J C Reyes and A K Chopra ldquoree dimensional modalpushover analysis of buildings subjected to two componentsof ground motion including its evaluation for tall buildingsrdquoEarthquake Engineering and Structural Dynamics vol 40no 7 pp 789ndash806 2011

[16] A K Chopra and R K Goel ldquoA modal pushover analysisprocedure for estimating seismic demands for buildingsrdquoEarthquake Engineering and Structural Dynamics vol 31no 3 pp 561ndash582 2002

[17] G Gupta and S K Kunnath ldquoAdaptive spectra-basedpushover procedure for seismic evaluation of structuresrdquoEarthquake Spectra vol 16 no 2 pp 367ndash392 2000

[18] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 3pp 377ndash390 2007

Advances in Civil Engineering 9

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

feasible by the damper connection such as the steel boltelongation due to tension stress

Data Availability

e data used to support the findings of this studyare available from the corresponding author upon request

Conflicts of Interest

e author declares that there are no conflicts of interest

Acknowledgments

is work was supported by JSPS KAKENHI (Grant no18K04427)

References

[1] K Ishikawa S Okubo Y Hiyama and S Kato ldquoEvaluationmethod for predicting dynamic collapse of double layer lat-ticed space truss structures due to earthquake motionrdquo In-ternational Journal of Space Structures vol 15 no 3pp 249ndash257 2000

[2] S Okubo Y Hiyama K Ishikawa R Wendel and L FischerldquoLoad capacity and plastic deformable ability of aluminumalloy double layer latticed wall subjected to plane loadrdquo inProceedings of the IASS Symposium Nagoya Japan 2001

[3] K Ishikawa and S Kato ldquoElastic-plastic buckling analysis ofreticular dome subjected to earthquakemotionrdquo InternationalJournal of Space Structures vol 12 no 3-4 pp 205ndash215 1997

[4] Y Taniguchi P L Gould and M Kurano ldquoEarthquake inputenergy at dynamic collapse for double-layer cylindrical latticeroofsrdquo Journal of the International Association for Shell andSpatial Structures vol 49 no 2 2008

[5] F Fan S Z Shen and G A R Parke ldquoeoretical and ex-perimental study of vibration reduction in braced domesusing a viscous damper systemrdquo International Journal of SpaceStructures vol 19 no 4 pp 195ndash202 2004

[6] M Midorikawa ldquoPerformance-based seismic design pro-visions for buildings in Japanrdquo in Proceedings of the IASS2005 vol 1 pp 307ndash316 Bucharest Romania September2005

[7] G C Giuliani ldquoOverview on the dynamic control of struc-turesrdquo in Proceedings of the IASS 2002 pp 561ndash567 WarsawPoland 2002

[8] Z P Zeng ldquoStructural analysis and design of the latticed shellfor Fujian Gymnasiumrdquo Journal of Spatial Structures vol 13no 2 pp 44ndash48 2007

[9] L Ilzarbe M J Alvarez E Viles and M Tanco ldquoPracticalapplications of design of experiments in the field of engi-neering a bibliographical reviewrdquo Quality and ReliabilityEngineering International vol 24 no 4 pp 417ndash428 2008

[10] European Committee for Standardization (CEN) Eurocode 8Design of Structures for Earthquake Resistance Part 1 GeneralRules Seismic Actions and Rules for Buildings (EN 1998-12004) European Committee for Standardization (CEN)Brussel Belgium 2004

[11] FEMA-356 NEHRP Guidelines for the Seismic Rehabilitationof Buildings Building Seismic Safety Council FEMAWashington DC USA 2000

[12] H G Park T Eom and H Lee ldquoFactored modal combinationfor evaluation of earthquake load profilesrdquo Journal ofStructural Engineering vol 133 no 7 pp 956ndash968 2007

[13] S K Kunnath ldquoIdentification of modal combinations fornonlinear static analysis of building structuresrdquo Computer-Aided Civil and Infrastructure Engineering vol 19 no 4pp 246ndash259 2004

[14] R K Goel and A K Chopra ldquoExtension of modal pushoveranalysis to compute member forcesrdquo Earthquake Spectravol 21 no 1 pp 125ndash139 2005

[15] J C Reyes and A K Chopra ldquoree dimensional modalpushover analysis of buildings subjected to two componentsof ground motion including its evaluation for tall buildingsrdquoEarthquake Engineering and Structural Dynamics vol 40no 7 pp 789ndash806 2011

[16] A K Chopra and R K Goel ldquoA modal pushover analysisprocedure for estimating seismic demands for buildingsrdquoEarthquake Engineering and Structural Dynamics vol 31no 3 pp 561ndash582 2002

[17] G Gupta and S K Kunnath ldquoAdaptive spectra-basedpushover procedure for seismic evaluation of structuresrdquoEarthquake Spectra vol 16 no 2 pp 367ndash392 2000

[18] C Casarotti and R Pinho ldquoAn adaptive capacity spectrummethod for assessment of bridges subjected to earthquakeactionrdquo Bulletin of Earthquake Engineering vol 5 no 3pp 377ndash390 2007

Advances in Civil Engineering 9

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Active and Passive Electronic Components

VLSI Design

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Shock and Vibration

Hindawiwwwhindawicom Volume 2018

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018

SensorsJournal of

Hindawiwwwhindawicom Volume 2018

International Journal of

RotatingMachinery

Hindawiwwwhindawicom Volume 2018

Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Navigation and Observation

International Journal of

Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom