Numerical simulation of ceiling collapse in full-scale gymnasium specimen using ASIGauss technique
11th World Congress on Computational Mechanics (WCCM XI)

5th European Conference on Computational Mechanics (ECCM V)
6th European Conference on Computational Fluid Dynamics (ECFD VI)
E. Oñate, J. Oliver and A. Huerta (Eds)

NUMERICAL SIMULATION OF CEILING COLLAPSE IN FULLSCALE GYMNASIUM SPECIMEN USING ASI–GAUSS TECHNIQUE
H. Tagawa1, T. Yamamoto2, T. Yamashita1, T. Sasaki1 and D. Isobe31

Hyogo Earthquake Engineering Research Center
National Institute for Earth Science and Disaster Prevention (NIED)
1501-21 Nishikameya, Mitsuda, Shijimi-cho, Miki, Hyogo 673-0515, Japane-mail: tagawa@bosai.go.jp, tyamashi@bosai.go.jp,
tomo_s@bosai.go.jp, www.bosai.go.jp/hyogo/
2

Graduate School, University of Tsukuba
1-1-1 Tennodai, Tsukuba-shi, Ibaraki 305-8573, Japane-mail: s1320975@u.tsukuba.ac.jp, www.kz.tsukuba.ac.jp
3

Division of Engineering Mechanics and Energy, University of Tsukuba
1-1-1 Tennodai, Tsukuba-shi, Ibaraki 305-8573, Japane-mail: isobe@kz.tsukuba.ac.jp, www.kz.tsukuba.ac.jp/~isobe/

Key Words: Ceiling Collapse, Gymnasium, ASI–Gauss Technique, Finite Element Method
Abstract. Many ceiling collapse accidents were observed during the 2011 Great East Japan
earthquake and have been observed during other earthquakes in Japan. A numerical seismic
simulation of the collapse of the ceiling in a full-scale gymnasium specimen, which was tested
at the E-Defense shaking table facility in 2014 [1], was conducted. The numerical model
represented steel structural frames and a suspended ceiling. All of the members were modeledusing linear Timoshenko beam elements. The adaptively shifted integration–Gauss technique,which shifts the numerical integration point adaptively to an appropriate position, was applied
to a nonlinear finite element analysis of this structurally discontinuous problem. The
preliminary simulation results showed that ceiling collapse progressed owing to detachmentof the clips that connected the ceiling joists to the ceiling joist receivers and eventually
resulted in the ceiling falling down.
1

INTRODUCTION

A large-space building, such as a school gymnasium, which is typically used as a shelter
during major earthquakes, must maintain its ability to function after an earthquake disasterand withstand aftershocks. After the main shock of the 2011 Great East Japan earthquake, aseries of aftershocks occurred, and it was reported that, in addition to the human casualties
suffered, many school gymnasiums failed to function as shelters because of the structural
damage that they suffered, including column–base damage, brace buckling, and damage
caused by falling nonstructural elements such as ceiling components and lighting equipment.
To address these problems, design guidelines for suspended ceilings have been issued by

1398

H TaagawH.
wa, T. Yam
Y mam
motoo, T
T. Yama
Y ashiita, T. Sasa
S aki andd D. Isoobe

onss. Thes
T se guig idellinees area baasedd on
o inveestiigationns of ceiilinng dam
d mag
ge oobsserv
vedd
severral insstituutio
ng prep evioous eaarth
hquuakees anda d exxpeerimmenntal datad a obbtaiineed fromf m scas ale moodels ofo ceiilings,
duurinwhhich area nott neecessaarilyy deriv
vedd frrom
m thhe aactu
ual behhavviorr off coollaapseed ceiilings.
To
o ex
xam
minne thee coollaapsse me
m chaanissm off a su
uspendded
d ceeiliing, a thhreee-dimeenssionnal (33D)
shhakiingg taablee testt t wasw s cond
ducctedd on
o a fulll-sscalle schhoool gymg mnaasiuum
m sp
peccimmen withw h asuuspeendded ceeilin
ng at
a the
t E-Deefennse shakiing tab
ble facciliity in 201
2 14 [1]. A nuum
mericcal sim
mulatiionn
off the collc apsse ofo thet ceeilin
ng in thet e gyymnnassium
m specs cim
menn, obseo erv
ved in thee shhakkingg taablee teest,
waas conc ndu
ucteed. Th
he simus ulaation was
w s baasedd oon non
n nlinnearr finnitee ellemmen
nt anala lysiis utili
u izinng lineearr
Tiimooshenkko bbeaam eleemeents annd thee ad
dapptivvely
y shhifteed integrration (AASI))–GGau
uss tecchniquue [2],[[3]. TheT e modem elinng memethood anda d prreliimin
narry ssim
mulaatioon rresu
ultss arre presp senttedd in thiis pap
p er.
2 MOD
M DE
ELIING
G OF
O AG
GY
YM
MNA
ASIIUM
M SP
PEC
CIM
ME
EN W
WIITH
H A SUS
SPE
END
DE
ED CE
EIL
LIN
NG
2.1 GyG mnnassiumm Spe
S ecimmenn
A piccturre oof thet speecim
meen is shhow
wn in Figgurre 1.
1 The
T e plan of thee firrst flooor is 30.
3 0 m × 18
8.6
m an
nd thet topp ofo thet sloopeed roo
r of iss 9.099 m abbovve thet grrounnd. Thhe speecim
men hash 6 spaans inn
booth thee X annd Y dired ectiion
ns. TheT e piitchh of thhe roo
r of iss 3//10
0 (== 3..6/1
12). Thhe speecim
meen is tyypicall
off thhe conc nstrructtionn ofo aan elem
e meentaary or m
midddle--schhoool gym
g mnaasiu
um inn Jaapan. Thhe ccoluumns,
girrdeers, beeam
ms, andd roooff pu
urlins aree stteell mmemmberrs withw h widw de-fflan
nge or chhann
nel sectioonss. The
T
girrdeers aree ffram
medd into
i o thhe coolum
mnss byb weeldiing. T
Thee brracces aree rou
r und steeel baars withw hturrnbbucklees. T
Thee beam
ms, ex
xcep
pt thot se ini thet braceed framf mess, area connneecteed tto thet colum
mnss withw hboolts, annd thet e rooof purp rlinns area connneecteed tot tthe girrderrs w
withh boltb s.
Th
he nummerricaal moodel ofo thet gy
ymnassiummenn, inccludding its
i su speend
ded ceeilinng, ism speecim
illlusttratted in Fig
gurre 2.
2 A
All off thhe memm mberss, in
ncluudiing thee plasp sterr bo
oardd oon thet ceeilinng, weere
moodeeledd usinu ng lineoshhenkko beaam
m ellemmentts. In thiis prelp limminaary sim
ulatiionn, aall ofo thet
l ear Tiimomucoonn
necttionns weere moodeeledd usinu ng rig
gid coonn
necttionns, wherw reas bolt
b tedd coonn
necctions wiill bemoodeeledd usinu ng pin
onnecttion
ns in
i futuf ure sim
Thee ASI–
A –Gausss techt hniquee reequuirees th
hatt
p co
mullatiionss. T
onne memm mb
ber be moodeeledd withw h onnly twwo eleme men
nts to acccurrateely reppressennt pplastic behavvior. For
F rthiis rear sonn, nnod
des weere plaaceed ata thhe endd aandd ceenteer ppoinnts off alll off thhe m
Thee tootall
meembberss. T
nuumb
berr off eleem
mentts was
w s 177,900,, annd thet tottal nuumb
ber of noodess wasw 133,7336. Alll of thhe nod
n des
onn thhe first
f t flooorr weree fixxedd, annd thee grrou
und mootio
on acca celeerattionn was
w inpput at theese noddess.

Figgurre 1:
G mnaasiuum
m sppeciimeen
1 Gym

Figu
o gym
g mnaasiuum speecimmenn
F ure 2: Moodeel of

2.22 Sus
S speendded Ceeiling
A typpicaal ccon
nfig
guraatioon of a sus
s pen
ndeed cceilingg is illlusstraatedd inn FiguF ure 3. Pllastter boaard
d isatttachhed
d too thhe ceiilinng jjoisst wit
w h scres ewss, tthe ceeilinng joiists arre atta
a acheed to thee ceili
c ing
g jo
oistt

2
1399

H TaagawH.
wa, T. Yam
Y mam
motoo, T
T. Yama
Y ashiita, T. Sasa
S aki andd D. Isoobe

w th clip
c ps, annd thet ceeilin
ng joiist recceivverrs aare attacched
d to thet haangging
g bboltt withw hrecceiverrs wit
haangerss. Inn pprev
viouus earrthq
quaakes, mamany ceeilinng colllappse accciddentts hav
h ve bbeeen cau
c usedd byb thet
deetacchm
mennt oof thhe ceiilinng joist cllipss annd hanngeers,, resullting in
n thhe plaasteer bboard, ceilinng jois
j sts,
annd ceil
c lingg jooistt reeceiivers fall
f lingg dow
d wn. Thhereeforre, in thee modm del, thee clip
c s anda haangeers weere
moodeeledd usinu ng beamb m eleme ment tha
t at caan sim
mulaate fraactu
ure.
Th
he susps penndeed ceil
c lingg was
w moodeeledd acccuurattelyy, accoa ord
ding
g too drraw
winggs oof thee deesiggn ofo thet
sppeciimeen. A piccturre ofo tthe suspeend
ded ceiilinng ini thet gyymnnasiiumm sp
peccimmenn is shoow
wn inn Figu
F ure
4(a), annd thet nuumeericcal moodeel ofo thet enntiree su
usp
pendedd ceiliingg is shhowwn iin Fig
F guree 44(b)). The
T
nuumeericcal moodeel ofo a paart ofo thet ceeilinng is
i sshoownn inn Fiiguure 4(c4 c), alona ng wiith thee deetaiils of
o the
t
eleem
mentt asssemmbblag
ge. Thhe han
h nginng bollt wer
w re spas aced
d 1,0000 mm
mm apara rt ini tthe X--dirrectionn and
a d
1,147
7 mm
m aloongg th
he slops pe ini thet Y--dirrecttionn. The
T e haangging
g bo
oltss werew e 1,,5000 mm
mm loong,, annd thet
cliip heig
h ghtt waas 25
2 mmm.

G obaal(b)( Deetail(aa) Glo
3 T
Typpicaal conc nfiguraatioon ofs pennded ceili
c ing
g (p
persspecctiv
ve)
Fiigurre 3:o susp

Fiiguure 4: Mo
Modeel off suusp
penddedd ceeilinng

4 AN
NA
ALY
YSIS ME
ET
THO
OD
D
Th
he ASI
A I–G
uss tecchnniquue [2][ , [33], whwhichh wast nuumeericcal integrratiion po
ointt
Gau
w useed to shiift theaddapttiveely to an
n ap
ppro
oprriatte posi
p itioon, waas eempployyedd inn a no
onliineaar finif ite eleemeent anaaly
ysis off

3
1400

H. Tagawa, T. Yamamoto, T. Yamashita, T. Sasaki and D. Isobe

the structure. The locations of the numerical integration and stress evaluation points used in
the ASI–Gauss technique are illustrated in Figure 5. Two consecutive elements forming amember are considered to be a subset, and the numerical integration points of an elastically
deformed member are placed such that the stress evaluation points are coincident with theGaussian integration points of the member. Therefore, stresses and strains are evaluated at theGaussian integration points of elastically deformed members, and the accuracy of the bending
deformation is guaranteed even using one-point integration.
The updated Lagrangian method was used to consider geometric nonlinearity in theincremental analysis. The conjugate gradient (CG) method was used to solve the linear
equations. The Newmark– method was used for implicit time integration. The time step of
the analysis was 1.0 × 10-3 s. The numerical simulation of the ceiling collapse was considereda structurally discontinuous problem. The detachments of the ceiling joists and ceiling joist
receivers were considered by setting the sectional forces of the clips and hangers to be zero
once the axial forces acting on these members exceeded the maximum strength. The contact
of members with the ground was also considered.

Figure 5 Location of numerical integration and stress evaluation points considered with the
ASI–Gauss technique5

PRELIMINARY SIMULATION RESULTS

A nonlinear time history simulation was conducted for the model of the full-scale
gymnasium specimen with its suspended ceiling. The ground motion acceleration K-NET
Sendai, which was observed during the 2011 Great East Japan earthquake and is shown in
Figure 6, was scaled by 0.5 and input at all nodes on the first floor. The maximum strength of
all of the clips was set to be 0.4 kN [4], and that of all the hangers was set to be 2.8 kN [5], tomodel the detachment of these elements.
The simulation results are shown in Figure 7. The ceiling joists and plaster boards on theright side of the suspended ceiling started to fall down approximately 72.5 s after thecommencement of the simulation, as shown in Figure 7(a). The ceiling collapse commenced
at 72.95 s, as shown in Figure 7(b). The clips became detached from the ceiling joist receivers,
and the ceiling joists and plaster boards fell down at 74.2 s, as shown in Figure 7(c). Finally,
the suspended ceiling had fallen completely at 75.2 s, as shown in Figure 7(d). The ceilingjoists and plaster boards were all piled on the first floor. These results show that the numericalsimulation of the ceiling collapse could be successfully conducted using the ASI–Gauss
technique.

41401

H TaagawH.
wa, T. Yam
Y mam
motoo, T
T. Yama
Y ashiita, T. Sasa
S aki andd D. Isoobe

Fiigurre 6:
6 Gro
G oun
nd motm tionn accceelerratioon (K-NE
ET Seenddai)(a)) Thhreeshooldd off ceilinng collc lap
pse (722.5 s) (bb) Prog
P greession of ceiilinng ccolllapsse(772..95 s)(c)) Prrogrressio
on ofo cceiliing
g coollaapsee (774.22 s)) (dd) CCommplletee fallin
ng-ddowwn (755.2 s)Figgurre 77: Simuulaation resu
ults
MP
PR
ROV
ME
ENTS
S IN
N FUT
F TUR
RE
E SIIM
LA
ATIO
ON
NS
6 IM
VEM
MUL
Th
he numn merricaal mod
m del shoown
n inn Figu
ure 2 is beinng impprov
ved
d annd cali
c ibraate d so thhatt thee modm delondds bbettter to thet e gyymn
nassiumm specs cim
n an
nd bettb ter simmullatees th
he behb havviorr obbserrveed incoorreespomen
the 3D sha
s akinng tab
t t. TheT isssuess too bee adddrresssedd in futturee siimu
ulattionns aare as folllow
ws.
t le test
 The
T e beeamo bee conn
necctedd too thhe ccoluum
mns wiith bollts, annd thet rooof purrlin
ns aare to be
ms aree toconc nneccted tot giirdeers wiith boolts.. Cc necctio
ons arre mod
gidd
t the
Currrenttly,, thhesee conn
m deled as rig
conc nnecctioonss. In
I adddition,, bracces wiith tu
urnbbuccklees area e cuurreenttly moodeeledd usin
u ng beaammelem
e mennts. The
w bee adddrresssed
d byy usin
u ng trus
t ss elem
e meentss too modms,
T se issuess will
m del thee beeambrab cess, annd rooof pur
p linss.
s penndeed ceil
c lingg iss ussuaallyy suurroounnded byb out
o ter waalls. In
n th
he gymg mnasiuum
m sppecimeen, A susp

51402

H TaagawH.
wa, T. Yam
Y mam
motoo, T
T. Yama
Y ashiita, T. Sasa
S aki andd D. Isoobelatel erall jooistss arre set
s on
n th
he perip imeeterrs sso thatt t thhe cceillingg caan be in conntaact wit
w th tthe ou
uterr
wal
w lls, as shhow
wn in Fig
gure 8.
8 The
T e coontaact off th
he ssusppen
ndeed ceil
c lingg w
withh thhe outter waallsshos ouldd bee coonssideeredd inn fu
uturre sims mulaatioons.
InI thet cuurreent moodeel, thet ceeilin
ng joists annd ceilc lingg jooistt reeceiiveers aree coontiinuuous. In
I the
t
gym
g mnaasiuum
m sp
peciimeen, theese meem
mberrs hhavve splis cess th
hat maay bec
b com
me ssep
paraatedd annd cauusepart
p tiall coollaapse ofo tthe ceeilinng joiistss annd ceiilinng jjoisst recer eiv
verss, asa oobservvedd inn th
he 3D
3
sha
s akinng ttab
ble tesst. M
Moodelingg ofo thest se meembberss w
withh sppliccess may
m bee reequuireed iin futu
f ure
sim
s mulaatioons.

E vattion
n (X
X-Z
Z)
(bb) Elev
E vationn (YY-ZZ)(aa) Elev
F
Fig
guree 8:: Laaterral joiists to be in conntaact wit
w th ceil
c lingg

7 CON
C NC
CLU
USIONSS
A nu
umeericcal sim
mullatioon of thee coollaapse oof thhe ceiilinng in a fuull-sscaale gym
mnnasium
m sppecimeen,
whhich was
w s teested at
a th
he E
E-D
Deffennse shaakinng tab
ble faccilitty in
i 201
2 14, waas succ
s cesssfuully
y coondducttedd
utiilizzing
g liinear Tim
moosheenk
ko beaam elem
mentts and
d th
he AS
SI–
–Gaausss teechhniqquee. A prep limminaaryysimmuulatiionn shhowwedd th
hat tthee ceeilinng colllappse prrogrresssedd ow
win
ng to
t the
t deetacchm
mennt ofo cclip
ps th
hatt
coonn
nectted thee ceiliing
g joistss too thhe ceil
c lingg jooistt haanggerss annd ulttim
mateely ressultted in thee ceiliingg
falllinng dowd wn.. The isssues to
o be
b add
a dresssedd inn futu
mullatiionss, incl
i luddingg th
he conc ntacct ofo thetf ure sim
suuspeendded ceilinng witw th thhe outter waalls,, arre aaddressed
d.

RE
EF
FER
REN
NC
S
CES
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waraa, A.
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T gaw
wa, T. Arrai, T. Kaanaai, M.
M Taakaookaa, Y
Y. IIwaashiita,
K Kaj
[2]]
[3]]
[4]]
[5]]

E-D
E Deffensse Shakee T
Tab
ble Exxperrimmen
nts on Wide
W e-aareaa Susp
S pen
nsio
on Ceeilinng Syysteemss, AIJ
AJKin
K nki--Brrancch Ann
A nuaal Mee
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61403