* Co esponding au ho . Tel.: +34 93 4016316, +34 606807733; ax: +34 934016096. E-mail add ess: [email p o ec ed]
(F. López-Almansa).
SEISMIC PERFORMANCE OF
BUILDINGS WITH THIN RC BEARING WALLS
H. Gonzales a, F. López-Almansa b*
a Technical Uni e si y o Ca alonia, Geo echnical Enginee ing and Geosciences Depa men , Jo di Gi ona 18, 08034 Ba celona, Spain
b Technical Uni e si y o Ca alonia, A chi ec u e S uc u es Depa men , A da. Diagonal 649, 08028 Ba celona, Spain
ABSTRACT
In La in Ame ica he e is an u gen need o housing; hus, du ing he las ew yea s a ele an numbe o mid-heigh buildings (usually,
up o i e s o ies) wi h hin RC shea -walls ha e been cons uc ed o low-cos dwellings in Boli ia, Colombia, Ecuado , Mexico, Pe u,
Venezuela, and o he coun ies loca ed in seismic-p one egions. These walls a e 10 cm hick and hei ein o cemen consis s mainly o
a single laye o welded wi e mesh. This cons uc ion echnology o e s wo main ad an ages: economy and apidi y o cons uc ion.
These buildings do no ul ill he in e na ional seismic codes bu some na ional egula ions a e less demanding, no p e en ing he use o
hin bea ing walls. These buildings migh be ulne able o ea hquakes because o hei low duc ili y, he insu iciency o he
expe imen al in o ma ion, he absence o obse ed damages and, in some cases, poo cons uc ion quali y. This wo k desc ibes he ini ial
s eps o a wide esea ch aiming a p o iding eliable seismic design guidelines o hin-wall buildings; he ini ial objec i es a e
analyzing he seismic pe o mance o hese buildings, p oposing p elimina y design c i e ia and iden i ying u he esea ch needs. This
esea ch ocuses on buildings loca ed in Pe u, being ep esen a i e o he si ua ions in he o he coun ies. The ulne abili y is
nume ically e alua ed by push-o e and nonlinea ime his o y analyses; he s uc u al pa ame e s a e ob ained om a ailable es ing
in o ma ion. The ob ained esul s show ha he seismic s eng h o he analyzed buildings is insu icien ; howe e , mino changes in he
s uc u al design migh imp o e signi ican ly hei seismic pe o mance. Economical and easy- o-implemen design ecommenda ions
a e issued.
KEY WORDS: seismic ulne abili y, hin suppo ing walls, ein o ced conc e e, push-o e analysis, nonlinea ime his o y analysis.
1. In oduc ion
Due o se e al easons, in mos o he ci ies o La in Ame ica he e is an u gen need o housing. Con e sely, he
in ol ed coun ies do no ha e he capaci y o cons uc ing he equi ed numbe o buildings, p o ided hey ha e
o be designed and buil o ul ill he usual s anda ds o de eloped coun ies. Gi en his si ua ion, du ing he las
ew yea s a ele an numbe o mid-heigh buildings (usually, up o i e s o ies) wi h hin shea -walls made o
ein o ced conc e e ha e been cons uc ed o low-cos dwellings in Colombia [1], Mexico [2], Pe u [3],
Venezuela [4], and o he de eloping coun ies loca ed in seismic-p one egions o La in Ame ica. These walls a e
he only e ical ca ying-load membe s; no mally hey a e 10 cm hick and hei ein o cemen consis s basically
o a single laye o cold- olled welded wi e mesh. This cons uc ion echnology o e s wo main ad an ages:
economy (because o li le consump ion o ma e ials and o wo k o ce) and apidi y o cons uc ion. Nowadays,
many hin shea -wall buildings a e unde cons uc ion in Pe u and o he close coun ies.
These buildings do no ul ill he majo in e na ional seismic design codes, as [5] and [6], among o he s.
Con e sely some na ional codes [7–9] a e less demanding, hus do no p e en he use o 10 cm hick bea ing
walls; e.g. he Mexican Me opoli an code [10] allows he use o 10 cm hick suppo ing walls o up o wo s o ies.
Conce ns abou he seismic pe o mance o hese buildings migh a ise; beyond he high s i ness, hus leading o
high base-shea coe icien s, main sou ces o seismic ulne abili y a e: appa en low duc ili y, sca ci y o
expe imen al in o ma ion, no pas expe ience o beha io unde s ong ea hquakes, use o low-s eng h conc e e,
and, in some cases, poo cons uc ion quali y. Acco dingly, Muñoz e al. [3] ha e shown ha hese buildings
migh be ulne able.
This wo k belongs o a wide esea ch p ojec aiming o p o ide seismic design guidelines o hin-wall buildings.
Tha p ojec consis s o he ollowing non-consecu i e s ages:
 Nume ical seismic e alua ion o a numbe o exis ing hin-wall buildings.
2
 Full-scale es ing o indi idual walls and o wall-slab assemblies.
 Fo mula ion o design guidelines.
 Pa ame ical nume ical s udy o he seismic e iciency o buildings ha ul ill hese equi emen s.
 P oposal o e o i s a egies.
This wo k desc ibes he i s s age o he esea ch p ojec . The objec i es o his pape a e: analyzing he seismic
pe o mance o a numbe o exis ing buildings, p oposing p elimina y design c i e ia and iden i ying u he
esea ch needs, use ul o he nex s ages. This wo k ocuses on buildings loca ed in Pe u, being ep esen a i e o
he si ua ions in he o he coun ies.
The i s s ep o he esea ch desc ibed in his pape consis s o selec ing se en ep esen a i e hin-wall buildings.
Then, hei ulne abili y is assessed by nume ical simula ion using he PERFORMD-3D p og am [11,12]; bo h
s a ic nonlinea (push-o e ) and nonlinea ime-his o y analyses a e ca ied ou . Fo he dynamic analyses, he
inpu s a e selec ed o ep esen he highes seismici y in Pe u, mainly in he Paci ic coas al egions; bo h
impulsi e and ib a o y accele og ams a e conside ed. Gi en he high s i ness o he buildings, he soil-s uc u e
in e ac ion has been conside ed; he beha io o he soil has been desc ibed by nonlinea e ical sp ings. The
esul s o he push-o e and dynamic analyses allow assessing he ulne abili y o he conside ed buildings and
o mula ing p elimina y design guidelines. As well, some emaining esea ch needs a e iden i ied.
2. Conside ed buildings
2.1 Thin-wall buildings in Pe u
O e 2500 hin-wall buildings ha e been cons uc ed in Pe u o low-cos housing, mainly a e 2001 [13]. This
subsec ion con ains a desc ip ion o such buildings and a selec ion o se en ep esen a i e ones.
As discussed p e iously, he main ein o cemen o he walls consis s me ely o a single laye o cold- olled
welded wi e mesh; howe e , in he mos ecen buildings, in he lowes loo s such mesh is made wi h ho - olled
ba s. The bounda y elemen s a he ends o he walls consis simply o addi ional ein o cemen ba s, wi hou any
con inemen e ec . Gi en he a he educed size o he ooms, he wall densi y is usually o e 3% in each
di ec ion, and he span-leng hs a e sho , a e aging 3.5 m and gene ally do no exceed 6 m; hence, he loo slabs
a e no mally 12 cm hick RC pla es. The clea heigh anges usually be ween 2.40 m and 2.65 m. Commonly,
he e a e no basemen s and he ounda ion consis s o a conc e e ma whose dep h anges be ween 20 and 25 cm.
Fig. 1(a) displays a pic u e o a ypical building and Fig. 1(b) shows a plan iew o one o hei loo s. Fig. 1(a)
shows ha he e a e coupling beams among neighbo ing walls. Howe e , such beams do no ul ill he
equi emen s s a ed egula ly in he design codes (e.g. hickness and ein o cemen de ails).
(a) Image o a building (b) Plan loo
Fig. 1. Building wi h hin walls
Se en exis ing buildings ha e been selec ed o ep esen he as majo i y o he ac ual buildings wi h hin walls in
Pe u. The main cha ac e is ics o hese buildings a e desc ibed in Table 1. Buildings C1 and C2 a e loca ed in
3
Chiclayo (no he n Pe u) and buildings L1 o L5 a e loca ed in Lima; bo h ci ies belong o he zone wi h highes
seismici y in Pe u. The soil has been classi ied acco ding o he Pe u ian seismic design code [8]. The wall
densi y in each di ec ion is de ined as he a io be ween he a eas o he walls (in such di ec ion) and he plan a ea;
he connec ed walls a e spli in indi idual ones assigned o hei co esponding di ec ions. The di ec ions wi h he
maximum and minimum wall densi ies a e e e ed as X (s ong) and Y (weak), espec i ely. In he connec ed
walls, hei momen s o ine ia ha e been calcula ed accoun ing o he con ibu ion o he langes; he e ec i e
wid hs ha e been de e mined acco ding o [14]. Nin h column con ains he a ios be ween he momen s o ine ia
o he walls and hose o he plan a ea. Fig. 1 co esponds o building C2. The las wo columns con ain he plan
egula i y and he esponse educ ion ac o assumed by he designe s.
Table 1. Main cha ac e is ics o he ep esen a i e buildings
Bldng. S o ies /
heigh
(m)
Soil
ype Yea Plan a ea
(m2) Wall a eas
(m2)
Wall
densi ies
(%)
Wall
momen s o
ine ia (m4)
Ra io o
momen s o
ine ia (‰)
Assumed
plan
con ig.
Red.
ac o
(R)
C1 5 / 13.10 So 2005 14.5  14.9 5.91 / 4.34 3.82 / 2.42 21.71 / 4.04 9.02 / 1.98 I egula 3
C2 5 / 13.75 So 2004 9.70  19.4 6.80 / 3.20 4.24 / 2.38 22.57 / 1.59 4.55 / 1.56 Regula 4
L1 5 / 12.75 In . 2002 21.8  19.8 10.51 / 9.18 3.25 / 2.75 43.16 / 14.85 3.81 / 1.33 Regula 6
L2 4 / 10.20 S i 2004 24.6  15.0 12.50 / 6.33 4.36 / 2.11 68.71 / 10.97 12.07 / 0.93 Regula 4
L3 5 / 12.75 S i 2004 24.9  10.0 11.69 / 3.32 5.44 / 1.39 43.25 / 2.99 22.91 / 0.34 I egula 3
L4 5 / 12.10 S i 2003 16.6  12.1 5.95 / 5.88 3.78 / 3.74 8.75 / 12.62 4.41 / 3.86 Regula 5
L5 5 / 12.10 S i 2003 15.1  28.0 11.35 / 10.12 3.49 / 3.11 24.83 / 12.72 1.25 / 2.95 Regula 5
Buildings in Table 1 do no ha e any basemen , ha e plan symme y (e.g. he mass and s i ness cen e s a e nea
coinciden ) and a e ully uni o m along hei heigh . In spi e ha he e a e some ac ual buildings ha do no
exhibi hese cha ac e is ics, ha e no been conside ed in his s udy since hey ep esen only a small pe cen age.
2.2 Code- ype seismic design o he conside ed buildings
The buildings lis ed in Table 1 we e designed acco ding o he Pe u ian seismic code [8]; i is based on UBC [15]
and p o ides mainly c i e ia o de e mine he base-shea coe icien . Tha egula ion was i s issued in 2003,
wi hou any speci ic p o ision ega ding hin shea -wall buildings. A ele an amendmen dealing wi h hese
ypes o buildings was published in 2004 [16]; no iceably, in ha documen hey a e e e ed as “limi ed duc ili y
wall buildings” (EMDL). The amendmen consis ed basically o de ining he alues o he esponse educ ion
coe icien R: R = 4 and R = 3 we e chosen o egula and i egula buildings, espec i ely (see he las wo
columns o Table 1); he p e ious code [8] s a ed R = 6 ( o shea -wall buildings). O he ecommenda ions a e
simila o he usual equi emen s [14] o shea -wall buildings; wo issues a e pa icula ly ele an o sho o
mid-heigh buildings simila o hose lis ed in Table 1: (i) he la e al beha io o hin shea -wall buildings could be
desc ibed wi h equi alen ame models accoun ing o he lange s i ening e ec o he in e sec ing o hogonal
walls, and (ii) he maximum allowed in e -s o y d i is 0.005. The EMDL code s a es ha he con inemen
bounda y elemen s in he wall ends a e equi ed only i he well known inequali y linking he neu al axis posi ion
and he ho izon al displacemen o he op loo [14,17] is no ul illed; acco ding o his c i e ion, in mos o he
cases such con inemen is no needed. In spi e o he cons uc ion yea s indica ed in Table 1, hese buildings ul ill
only some o he equi emen s o EMDL code.
2.3 Nume ical modeling o he s uc u al beha io
The s uc u al beha io o he conside ed hin-wall buildings is desc ibed by ini e-elemen models whose
pa ame e s a e ob ained mainly om expe imen s ca ied ou in Pe u [18–20]. The es ed specimens we e bo h
ull-scale indi idual walls and ull-scale single-s o ey wall assemblies; he expe imen s consis ed basically o
imposing cyclic ho izon al displacemen laws o hese specimens un il ailu e. The e ec o he uppe loo s was
ep esen ed by cons an e ical o ces.
The s a ic and dynamic nonlinea s uc u al beha io s o he ep esen a i e buildings (Table 1) a e desc ibed by a
4
1
s o de , h ee-dimensional ini e-elemen model implemen ed in he PERFORM-3D p og am [11,12]. Fig. 2
depic s such a model o building L1.
Fig. 2. Fini e-elemen model o building L1
Two ypes o ins abili ies migh a ise in he s uc u al beha io o he conside ed buildings: global buckling o he
building and local buckling o he hin walls. Abou he i s ype, he global second o de e ec s a e no
conside ed because he a ios be ween he ac ual e ical loads and hei c i ical alues a e small [21,22]. Abou
he second ype o ins abili y, undoub edly he isk o local buckling o he walls migh be se ious, gi en hei
slende ness; ema kably, o clea heigh equal o 2.40 m mos o he seismic design codes [5,6,23–25] p e en he
use o hickness smalle han abou 12 cm. Howe e , he s uc u al analyses ca ied ou inside his s udy ha e
shown ha , excep o he impulsi e eco ds (see subsec ion 4.1), he e ical s esses in he conc e e o he walls
a e su icien ly lowe han he allowable alue (see Fig. 3(b)); consequen ly, i is un easible ha any local
ins abili y could ampli y i un il eaching such le el. Mo eo e , he plan layou o he conside ed buildings (see
Fig. 1) shows ha mos o he un langed wall ends co espond o inne pa s o he buildings, whe e he expec able
cyclic inc eases o e ical s esses a e smalle .
As shown in Fig. 2, he walls a e disc e ized by quad angula 4-node shell elemen s. The in-plane nonlinea
beha io o he walls is desc ibed by a plas ic hinge loca ed in hei base: he e ical leng h o each hinge is
selec ed as sugges ed in [26]; in mos o he cases, such heigh is equal o hal o he ho izon al leng h o he wall.
The ou -o -plane bending is assumed o be linea . The coupling beams a e desc ibed by 3-D 2-node ame
elemen s. The con ibu ion o he slabs o such beams is ep esen ed by an e ec i e wid h de e mined acco ding
o [14]. No o he con ibu ion o he slabs o he la e al s eng h o he building is conside ed; howe e , hei
diaph agm e ec is included. In building C1 (Table 1), a mo e de ailed model disc e izing he slabs wi h pla e
elemen s was also gene a ed; he esul s o he analyses we e simila o bo h cases. Fo he modal and dynamic
analyses he masses a e concen a ed, ollowing a lumped-masses app oach, in he cen oid o e e y loo ; he
o a ional ine ia has been also conside ed.
The lexu al beha io o he walls is desc ibed by a ibe model as shown in Fig. 3(a); he beha io o conc e e is
ep esen ed by he s ess-s ain cons i u i e law shown in Fig. 3(b). This law is aken om [27] by neglec ing he
ensile s eng h; his model has been chosen since i desc ibes accu a ely he s uc u al beha io o uncon ined
conc e e [28]. The cha ac e is ic alue ’
c o he conc e e comp essi e s eng h is es ima ed om ield ebound
hamme es s ca ied ou by one o he au ho s; he de o ma ion modulus Ec is de e mined om ’c acco ding o
[14]. The beha io o he ein o cemen s eel is desc ibed by an uniaxial i-linea law [29]; hei modulus o
elas ici y, hei yielding poin , and hei ul ima e s ess and s ain a e aken om es s desc ibed in [30].
No iceably, he pa ame e s o he cold- olled and he ho - olled s eels a e di e en .
5
(a) Fibe model (b) Uniaxial cons i u i e law o conc e e
Fig. 3. Flexu al model o he hin walls
The shea beha io o he walls is desc ibed by a composi e s eel-conc e e model; Fig. 4(b) shows i s i-linea
cons i u i e law [31]. Fo shea s ains no highe han abou 0.005, his law is he en elope (back-bone cu e) o
he expe imen al s ess-s ain cu es (Fig. 4(a)) ob ained in [20] om uniaxial cyclic es ing o a single-s o ey
ull-scale housing model and se en single squa walls (heigh -leng h a io < 1.5); o shea s ains highe han
abou 0.005, he s i ness and s eng h deg ada ions a e accoun ed o by dec easing b anches. Fig. 4(a) displays
he cu es conside ed in [32–34] oge he wi h he cu e p oposed in his s udy, which is also plo ed in Fig. 4(b).
The p oposed cu e is de i ed acco ding he ecommenda ions in [33].
(a) Expe imen al loops [20] (b) Back-bone en elope
Fig. 4. Shea model o he hin walls
The hys e e ic beha io o he coupling beams is desc ibed by igid-plas ic shea hinges [35] loca ed in hei mid
span. The ans e sal (ho izon al) bending and he o sion a e assumed o be linea .
The s i ness and s eng h deg ada ion a e u he accoun ed o by speci ying ene gy deg ada ion ac o s o
conc e e and s eel [36]. These ac o s a e he a ios be ween he a eas o he deg aded and non-deg aded hys e esis
loops, espec i ely.
The accu acy o his model is checked by compa ison wi h quasi-s a ic in-plane shea cyclic es s o indi idual
squa walls [19]. Fig. 5 p esen s compa isons be ween nume ical and expe imen al hys e esis loops [19].

=+
Ac ual c oss sec ion
Conc e e ibe s
S eel ibe s
0
5
10
15
20
25
30
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
S ain ε
c
S ess σ
c
(MPa)
-60 -40 -20 0 20 40 60
-600
-450
-300
-150
0
150
300
450
600
Tes da a
P oposed backbone cu e
ASCE 41 Sup#1
FEMA 356
Top displacemen (mm)
La e al load (kN)
-0.018 -0.012 -0.006 0.000 0.006 0.012 0.018
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Shea s ess  (MPa)
Shea s ain 

6
(a) Obse ed esponse [19] (b) Calcula ed esponse
Fig. 5. Compa ison o expe imen al and nume ical esponses
2.4 Measu emen s on he ep esen a i e buildings
No empi ical exp essions o he undamen al pe iod o hin-wall buildings ha e been p oposed in he echnical
li e a u e; i simpli ied exp essions de i ed o egula shea -wall buildings [5,6,8,23] a e used ins ead, high
sca e ing is ob ained. The e o e, ambien ib a ion measu emen s we e conduc ed on buildings L4 and L5 o
es ima e i s undamen al pe iod; o he p oo s ca ied ou on simila buildings in Lima p o ided close esul s.
Table 2 displays he ob ained esul s, oge he wi h he esul s de e mined acco ding o he Eu opean and Pe u ian
egula ions and wi h alues p o ided by modal analyses using he PERFORM-3D p og am [11,12]; SSI accoun s
o soil-s uc u e in e ac ion. Two di e en exp essions om he EC-8 [6] ha e been used; exp ession (1)
accoun s only o he heigh o he building while exp ession (2) conside s also o he pa ame e s such as he wall
densi y and hei e ical slende ness ( ela ed o he momen o ine ia o he wall, wi hou accoun ing o he
con ibu ion o he langes). Fo he o he conside ed egula ions [5,23], he esul s a e simila .
Table 2. Fundamen al pe iods (s) o he ep esen a i e buildings
Bldng.
Di ec ion X Di ec ion Y
Exp. EC-8
(1) EC-8
(2) E.030 Num.
(w/o
SSI)
Num.
(w
SSI) Exp. EC-8
(1) EC-8
(2) E.030 Num.
(w/o
SSI)
Num.
(w
SSI)
C1 – 0.34 0.39 0.22 0.08 0.19 – 0.34 0.71 0.22 0.12 0.20
C2 – 0.36 0.39 0.23 0.11 0.21 – 0.36 1.03 0.23 0.17 0.24
L1 – 0.34 0.38 0.21 0.11 0.14 – 0.34 0.69 0.21 0.15 0.17
L2 – 0.29 0.14 0.17 0.07 0.10 – 0.29 0.41 0.17 0.14 0.16
L3 – 0.34 0.38 0.21 0.07 0.10 – 0.34 0.69 0.21 0.23 0.25
L4 0.14 0.32 0.50 0.20 0.11 0.15 0.12 0.32 0.42 0.20 0.10 0.16
L5 0.12 0.32 0.31 0.20 0.11 0.13 0.13 0.32 0.37 0.20 0.12 0.14
Resul s om Table 2 allow de i ing he ollowing gene al conclusions: (i) he design codes o e es ima e he
na u al pe iods, (ii) he EC-8 [6] p o ides signi ican ly highe pe iods han he E.030 [8], (iii) in he weak
di ec ion, he exp ession (2) o EC-8 [6] p o ides ex emely long pe iods, and (i ) he ag eemen be ween he
expe imen al esul s and hose p o ided by nume ical simula ion (accoun ing o he soil-s uc u e) in e ac ion is
sa is ac o y.
3. Push-o e analyses
3.1 Push-o e analyses o he ep esen a i e buildings
The seismic pe o mance o he ep esen a i e buildings (Table 1) has been assessed by 2D nonlinea s a ic
analyses (push-o e ) by using he PERFORM-3D p og am [11,12]; he model desc ibed in subsec ion 2.3 has
-25 -20 -15 -10 -5 0 5 10 15 20 25
-300
-200
-100
0
100
200
300
A
La e al displacemen (mm)
La e al load (kN)
Fo ce
(
kN
)
Displacemen (mm)
7
been conside ed o desc ibe i s s uc u al beha io . In he push-o e analyses wo pa e ns ha e been conside ed
o he la e al o ces: iangula and i s modal shape; since he con ibu ion o he highe modes is small, hey
ha e no been accoun ed o [37]. The analyses a e s opped when any o he se o p ede e mined ul ima e s a es o
he walls is eached; in his s udy h ee bounds a e s a ed: conc e e e ical comp essi e s ain (
c = 0.015, see Fig.
3(b)), axial s ain o he e ical s eel ein o cemen (s = 0.2 o con en ional ba s and s = 0.065 o wi e mesh),
and global shea s ain ( = 0.02, see Fig. 4(b)). Such bounds a e sugges ed in [29,30]. No limi has been
es ablished o he coupling beams since hei ailu e is ea lie han he shea ailu e on he walls.
Figs. 6 o 12 show he capaci y cu es o he selec ed buildings C1, C2, L1, L2, L3, L4 and L5, espec i ely; in
hose Figs., he soil-s uc u e in e ac ion is no conside ed. The la e al o ces pa e n is iangula ; simila esul s
a e ob ained o he o he conside ed pa e n. Fo compa ison pu poses, he d i limi equal o 0.5% [16] is also
plo ed. Th ee Damage Limi S a es (DLS) co esponding o di e en Pe o mance Objec i es (o Le els) [33]
a e conside ed: “Immedia e Occupancy” (IO), “Li e Sa e y” (LS) and “Collapse P e en ion” (CP); o each o
hem, h ee h esholds a e es ablished: lexu al and shea beha io o he walls and shea beha io o he coupling
beams. The lexu al h esholds o he walls a e de ined in e ms o he o a ions in he plas ic hinges [26]; he
bounds a e 0.002 ad (IO), 0.004 ad (LS) and 0.008 ad (CP). Such alues a e es ablished as ecommended in
[33]. The o e all Damage Limi S a es o each building ha e been conse a i ely de ined as he mos c i ical o
hose o he membe s ha he s uc u e is composed o . The shea h esholds o he walls a e de ined in e ms o
he shea s ains; he bounds a e 0.0025 (IO), 0.00375 (LS) and 0.005 (CP), see Fig. 4(b). Such alues a e
es ablished based on expe imen s ca ied ou on squa hin walls whose ein o cemen s a e simila o hose in he
conside ed buildings [20]. The h esholds o he coupling beams a e de ined in e ms o he cho d o a ion [32];
he bounds a e 0.005 (IO), 0.01 (LS) and 0.02 (CP). Such alues a e es ablished based on [32]. In he coupling
beams he ailu e o he diagonal s u s migh be ele an , gi en ha he web is hin and he conc e e s eng h is
low; his ailu e mode has been e i ied acco ding o Eu opean egula ions [38]. The “Coe icien Me hod” is
used o de e mine he Ta ge D i (TD) poin s; i is assumed ha C2 = 1 [32]. The buildings in Table 1 a e
conside ed as basic acili ies; he e o e, IO co esponds o he Occasional Inpu ( e u n pe iod 72 yea s), LS
co esponds o he Ra e Inpu ( e u n pe iod 475 yea s) and CP co esponds o he Ve y Ra e Inpu ( e u n pe iod
975 yea s) [39].
Fig. 6. Capaci y cu es o building C1
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
TD (IO)
TD (IO)
TD (IO)
TD (LS) TD (CP)
Di ec ion X+
Di ec ion X-
Di ec ion Y
Max. d i 0.5%
TD (CP)
TD (LS)
TD (CP)
TD (LS)
IO Flexu al (walls)
IO Shea (walls)
IO Shea (beams)
LS Flexu al (walls)
LS Shea (walls)
LS Shea (beams)
CP Flexu al (walls)
CP Shea (walls)
CP Shea (beams)
Base shea coe icien ( V / W )
Roo d i
(
%
)
8
Fig. 7.
Capaci y cu es o building
C2
Fig. 8.
Capaci y cu es o building
L1
0.00.20.40.60.81.01.21.4
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
TD (IO)
TD (IO)
TD (IO)
Di ec ion X
Di ec ion Y+
Di ec ion Y-
Max. d i 0.5%
TD (CP)
TD (LS)
TD (CP)
TD (LS)
TD (CP)
TD (LS)
Base shea coe icien ( V / W )
Roo d i (%)
IO Flexu al (walls)
IO Shea (walls)
IO Shea (beams)
LS Flexu al (walls)
LS Shea (walls)
LS Shea (beams)
CP Flexu al (walls)
CP Shea (walls)
CP Shea (beams)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0.0
0.2
0.4
0.6
0.8
1.0
TD (IO)
TD (IO)
TD (IO)
Max. d i 0.5%
TD (LS) TD (CP)
TD (LS)
TD (CP)
TD (LS)
Di ec ion X+
Di ec ion X-
Di ec ion Y
Base shea coe icien ( V / W )
Roo d i (%)
IO Flexu al (walls)
IO Shea (walls)
IO Shea (beams)
LS Flexu al (walls)
LS Shea (walls)
LS Shea (beams)
CP Flexu al (walls)
CP Shea (walls)
CP Shea (beams)
TD (CP)
9
Fig. 9. Capaci y cu es o building L2
Fig. 10. Capaci y cu es o building L3
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
TD (IO)
TD (IO)
TD (IO)
Di ec ion X+
Di ec ion X-
Di ec ion Y
Max. d i 0.5%
TD (CP)
TD (LS)
TD (CP)
TD (LS)
TD (CP)
TD (LS)
Base shea coe icien (
V
/ W )
Roo d i (%)
IO Flexu al (walls)
IO Shea (walls)
IO Shea (beams)
LS Flexu al (walls)
LS Shea (walls)
LS Shea (beams)
CP Flexu al (walls)
CP Shea (walls)
CP Shea (beams)
0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
TD (IO)
TD (IO)
TD (IO)
Di ec ion X+
Di ec ion X-
Di ec ion Y
Max. d i 0.5%
TD (LS) TD (CP)
TD (CP)
TD (LS)
TD (CP)
TD (LS)
Base shea coe icien (
V
/ W )
Roo d i (%)
IO Flexu al (walls)
IO Shea (walls)
IO Shea (beams)
LS Flexu al (walls)
LS Shea (walls)
LS Shea (beams)
CP Flexu al (walls)
CP Shea (walls)
CP Shea (beams)
16
Moquegua [54] and o he 15-Aug-2007 Pisco [55,56] ea hquakes, espec i ely; he a i icial accele og ams a e
e med EQ-SII-01 o EQ-SII-05. Abou he scaling o he his o ical eco ds, ASCE 7-05 [50] s a es ha each pai
o mo ions should be scaled such ha o each pe iod be ween 0.2 T and 1.5 T, he a e age o he SRSS spec a
om all ho izon al componen pai s does no all below 1.3 imes he co esponding o dina e o he design
esponse spec um by mo e han 10%; T being he undamen al pe iod o he s uc u e. Since he conside ed
buildings a e ema kably s i (Table 2), only sho pe iod anges a e conside ed in he scaling o he inpu s;
hence, elsewhe e he spec a o he his o ical eco ds migh di e signi ican ly om he design one. Fig. 16 shows
ha , o he mid and long pe iod anges, he spec al o dina es o he his o ical inpu s a e highe han hose o he
design spec um and o he syn he ic ones; gi en he leng hening o he undamen al pe iod due o he nonlinea
beha io , hese eco ds may be signi ican ly mo e damaging. Some au ho s [57–59] ha e poin ed ou limi a ions
o he scaling c i e ion by ASCE 7-05 [50] and ha e p oposed al e na i e p ocedu es.
Fig. 16. Response spec a o he scaled accele og ams co esponding o in e media e soil
The second g oup o inpu s consis s o six unscaled, wo-componen s, nea - aul eco ds: San Fe nando 1971
(Pacoima Dam s a ion, e med EQ-SF-PD), Loma P ie a 1989 (Los Ga os s a ion, e med EQ-LP-LG, and
Lexing on Dam s a ion, e med EQ-LP-LD), Lande s 1992 (Luce ne s a ion, e med EQ-LA-LU), Kobe 1995
(JMA s a ion, e med EQ-KO-JMA), and Quindío 1999 (CFLAN s a ion, e med EQ-QU-CF).
The hi d g oup o inpu s includes wo unscaled Chilean eco ds: Viña del Ma 1985 (Llolleo s a ion, e med
EQ-VM-LL) and Concepción 2010 (CCSP s a ion, e med EQ-CO-CC). These accele og ams ha e been
in oduced because hei in ensi ies and subduc i e mechanisms a e simila o hose in Pe u [54].
4.2 Resul s o he dynamic analyses
Nonlinea dynamic analyses ha e been ca ied ou on he buildings lis ed in Table 1 by using he PERFORM-3D
p og am [11,12]. The wo componen s o each inpu a e applied simul aneously; he mos damaging componen s
o each inpu a e assumed o shake he buildings in hei weak di ec ions. The s uc u al beha io o he buildings
is simula ed by he model desc ibed in subsec ion 2.3. The damping is ep esen ed by a Rayleigh model; as
sugges ed in he e e ences [60,61] he assumed damping a io is 2.5%.
Fig. 17 displays he maximum in e -s o ey d i s o di ec ions X and Y o building L1 o he i s g oup o
(scaled) inpu s; he d i limi equal o 0.5% [16] is also plo ed o compa ison pu poses. Since he damage
h esholds and he Ta ge D i s o di ec ions X+ and X– a e a he simila (see Fig. 8 and Table 3), Fig. 17(a)
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0
0,0
0,4
0,8
1,2
1,6
2,0
2,4
2,8
3,2
3,6
Sa (g)
T (s)
E.030-SII
EQ-SII-Moq
EQ-SII-Pis
EQ-SII-01
EQ-SII-02
EQ-SII-03
EQ-SII-04
EQ-SII-05

17
shows only he absolu e maximum alues.
(a) Di ec ion X (b) Di ec ion Y
Fig. 17. Maximum in e -s o ey d i s o building L1 o he scaled inpu s (1s g oup)
The esul s displayed in Fig. 17 show ha he a i icial inpu s (EQ-SII-01 o EQ-SII-05) g ossly unde es ima e he
esponse o he eco ded inpu s (EQ-SI-Moq and EQ-SI-Pis). As discussed p e iously, his di e ence can be
explained by hei highe spec al ampli udes (Fig. 16) due o he scaling c i e ion in ASCE 7-05 [50]. This end
is also obse ed o he o he buildings lis ed in Table 1, hough less in ensely.
Fig. 18 displays he maximum in e -s o ey d i s in di ec ions X and Y o building C1 o he second g oup o
inpu s; he d i limi equal o 0.5% [16] is also plo ed o compa ison pu poses. As in Fig. 17, only he absolu e
maximum alues a e shown.
(a) Di ec ion X (b) Di ec ion Y
Fig. 18. Maximum in e
-s o ey d i s o building C1 o he nea
-sou ce inpu s (2nd g oup)
The esul s om Fig. 18 show ha building C1 is se e ely damaged in he weak di ec ion; his ac is expec able
because o mos o he inpu s he obse ed d i s exceed he Damage Limi S a es [32,33] co esponding o Li e
Sa e y (LS) (see Fig. 6). As well, in he weak di ec ion he wo mos damaging inpu s p o ide d i s o e 0.5%.
These p elimina y esul s highligh he high damage po en ial o he conside ed impulsi e inpu s.
Fig. 19 displays he maximum in e -s o ey d i s in di ec ions X and Y o building C1 o he hi d g oup o inpu s.
As in Figs. 17 and 18, only he absolu e maximum alues a e shown.
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
1
2
3
4
5
S o ey
In e -s o ey d i (%)
EQ-SII-Moq
EQ-SII-Pis
EQ-SII-01
EQ-SII-02
EQ-SII-03
EQ-SII-04
EQ-SII-05
A e age
Di ec ion X
Max. d i 0.5%
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
1
2
3
4
5
S o ey
In e -s o ey d i (%)
EQ-SII-Moq
EQ-SII-Pis
EQ-SII-01
EQ-SII-02
EQ-SII-03
EQ-SII-04
EQ-SII-05
A e age
Di ec ion Y
Max. d i 0.5%
0.0 0.1 0.2 0.3 0.4 0.5
0
1
2
3
4
5
Max. d i 0.5%
S
o ey
In e -s o ey d i (%)
EQ-SF-PD
EQ-LP-LG
EQ-LP-LD
EQ-LA-LU
EQ-KO-JMA
EQ-QU-CF
Di ec ion X
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0
1
2
3
4
5
Max. d i 0.5%
S o ey
In e -s o ey d i (%)
EQ-SF-PD
EQ-LP-LG
EQ-LP-LD
EQ-LA-LU
EQ-KO-JMA
EQ-QU-CF
Di ec ion Y
18
(a) Di ec ion X (b) Di ec ion Y
Fig. 19. Maximum in e -s o ey d i s o building C1 o he Chilean inpu s (3 d g oup)
Compa ison wi h Fig. 18 shows ha hese inpu s a e signi ican ly less demanding. Mo eo e , he esul s om Fig.
19 allow de i ing he ollowing conclusions:
 In he weak di ec ion he Viña del Ma ea hquake gene a es se e e damage in he coupling beams, since he
shea demand exceeds he Damage Limi S a es co esponding o Li e Sa e y (LS) (see Fig. 6).
 The ension s ain co esponding o he Viña del Ma ea hquake is mo e han wice he maximum alue
speci ied (1%) [29,42]. I may gene a e a signi ican hinging in he base o he walls.
5. Compa ison be ween push-o e and dynamic esul s
This sec ion p esen s a compa ison be ween he esul s o he s a ic push-o e and dynamic analyses o he scaled
inpu s ( i s g oup). Table 7 displays he Ta ge D i s (co esponding o “Li e Sa e y”) ob ained om bo h
analyses.
Table 7. Compa ison be ween he LS Ta ge D i s (%) om s a ic and dynamic analyses
Building Di ec ion X+ Di ec ion X– Di ec ion Y+ Di ec ion Y–
S a ic / dynamic S a ic / dynamic S a ic / dynamic S a ic / dynamic
C1 0.288 / 0.165 0.264 / 0.137 0.453 / 0.246 0.453 / 0.260
C2 0.442 / 0.219 0.414 / 0.184 0.348 / 0.244 0.348 / 0.197
L1 0.173 / 0.194 0.160 / 0.155 0.324 / 0.406 0.324 / 0.366
L2 0.072 / 0.069 0.092 / 0.064 0.342 / 0.251 0.342 / 0.234
L3 0.083 / 0.050 0.069 / 0.045 0.522 / 0.298 0.522 / 0.284
L4 0.136 / 0.078 0.127 / 0.083 0.176 / 0.120 0.180 / 0.122
L5 0.207 / 0.157 0.180 / 0.154 0.177 / 0.138 0.181 / 0.131
Resul s om Table 7 show ha , apa om building L1, he d i s ob ained om he push-o e analyses a e la ge
han hose a ising om he dynamic analyses; he a ios ange om 2.25 (building C2, di ec ion X–) o 1.04
(building L2, di ec ion X+). These di e ences can be explained by he simpli ied conse a i e assump ions in he
push-o e analyses; being pa icula ly ele an o wall buildings [62]. The excep ion o building L1 migh be
due o he ex ao dina ily high esponse o he wo his o ical inpu s (Fig. 17).
6. P elimina y design ecommenda ions
The esul s o his s udy allow concluding ha he hin shea -wall buildings designed wi h he p e ious e sion o
he Pe u ian seismic design code [8] may ha e an inadequa e seismic beha io ; e en, he conside a ion o he las
e sion o such code [16], migh be insu icien . The ollowing p elimina y design ecommenda ions a e
o mula ed:
0.00 0.03 0.06 0.09 0.12 0.15
0
1
2
3
4
5
S o ey
In e -s o ey d i (%)
EQ-VM-LL
EQ-CO-CC
Di ec ion X
0.00 0.09 0.18 0.27 0.36 0.45
0
1
2
3
4
5
S o ey
In e -s o e
y
d i
(
%
)
EQ-VM-LL
EQ-CO-CC
Di ec ion Y
19
 The wall densi y in any di ec ion should be, a leas , equal o abou 4%. As well, he momen s o ine ia
(including he con ibu ion o he langes), should be, a leas , 4‰ o hose o he plan a ea.
 The coupling beams should be designed ollowing usual seismic guidelines. In such a case, e en keeping hei
wid h equal o he one o he wall, he bene i s migh be ele an .
 The soil-s uc u e in e ac ion is ele an and should be accoun ed o .
 The accu a e calcula ion o he na u al pe iods is o li le in e es because hese buildings all usually in o he
cons an accele a ion b anch o he design spec um. Mo eo e , he ea ly onse o c acking in he walls
gene a es leng hening o such pe iod e en o low seismici y egions.
Only economical and easible design ecommenda ions a e o mula ed since nowadays mass high-quali y
cons uc ion is no a o dable by he in ol ed coun ies, as discussed p e iously.
7. Conclusions
This wo k p esen s a nume ical seismic assessmen o se en exis ing ep esen a i e hin shea -wall and
mid-heigh buildings loca ed in Pe u. Bo h s a ic and dynamic nonlinea analyses ha e been conduc ed. Apa
om he pa icula in e p e a ions o he esul s included in he ex , he o e all conclusions a ising om his
esea ch a e:
 The seismic s eng hs o all he analyzed buildings a e insu icien . Fo he Immedia e Occupancy (IO)
pe o mance le el, i e o he se en conside ed buildings exhibi inadequa e beha io , a leas in one
di ec ion. Fo he Li e Sa e y (LS) and Collapse P e en ion (CP) le els, he numbe s o buildings ha beha e
unaccep ably a e se en and ou , espec i ely.
 The be e pe o mances, in e ms o he a ios be ween he Ta ge D i s and he co esponding Damage Limi
S a es, co espond o he s ong di ec ions ( hose wi h highes densi ies o walls).
 In mos o he cases he Damage Limi S a es o Immedia e Occupancy, Li e Sa e y and Collapse P e en ion
a e achie ed i s in he coupling beams. The nex ailu e mode co esponds o he lexu e o he walls.
 Mino and easible modi ica ions in he coupling beams migh p o ide ele an imp o emen s in he seismic
pe o mance o hese buildings.
The ex ension o hese conclusions o he majo i y o hin-wall buildings can be done only wi h ex eme cau ion,
gi en he p elimina y cha ac e o his esea ch.
One o he majo bene i s a ising om his esea ch is a deepe knowledge abou he seismic beha io o hese
buildings. This unde s anding allows iden i ying u he esea ch needs, use ul o he nex s ages.
ACKNOWLEDGEMENTS
This wo k has ecei ed inancial suppo om he Spanish Go e nmen unde p ojec CGL2008-00869/BTE. The s ay o H. Gonzales in Ba celona has
been suppo ed by he Ca alan Agency o Managemen o Uni e si y and Resea ch G an s (AGAUR), g an # DEBEQ-10020. The au ho s a e also
hank ul o Eng. Gab iela Medina o p o iding expe imen al in o ma ion.
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