Intersections V05 No03 03
10
33 Seismic Analysis ISSN 1582-3024 http://www.intersections.ro Seismic analysis using Robot Millennium Mihai Nedelcu Department of Structural Mechanics , Technical University of Cluj-Napoca, 400020, Romania Summary The paper presents the modelling and structural analysis of a complex structure under seismic loads using the Robot Millennium software package. In order to test the output results, the author chose a building already designed in the documentation [1]. The above mentioned documentation was created as a guideline for applying the design standard P100-1/2006. Following the given structure architecture and loads, the author of this paper remodelled the structure using Robot Millennium v.20.1. The objective of the paper is to show: 1. the Robot Millennium instruments used for modelling this type of structures 2. various modelling ways for the same structure highlighting the most convenient one (in the author’s opinion) 3. the results accuracy of the analysis in comparison with the output given by the work of Professor Tudor Postelnicu KEYWORDS: seismic analysis, modal analysis, stories, rigid links, panel cut, reinforced concrete walls. Article No.3, Intersections/IntersecĠii, Vol.5, 2008, No.3, “Seismic Analysis”
description
Intersections V05 No03 03
Transcript of Intersections V05 No03 03
33
Seis
mic
Ana
lysi
s
ISS
N 1
582-
3024
http
://w
ww
.inte
rsec
tions
.ro
Seis
mic
ana
lysi
s usi
ng R
obot
Mill
enni
um
Mih
ai N
edel
cu
Dep
artm
ent o
f Str
uctu
ral M
echa
nics
, Te
chni
cal U
nive
rsity
of C
luj-N
apoc
a, 4
0002
0, R
oman
ia
Sum
mar
y Th
e pa
per
pres
ents
the
mod
ellin
g an
d st
ruct
ural
ana
lysi
s of
a c
ompl
ex s
truc
ture
un
der
seis
mic
load
s us
ing
the
Robo
t Mill
enni
um s
oftw
are
pack
age.
In o
rder
to te
st
the
outp
ut
resu
lts,
the
auth
or
chos
e a
build
ing
alre
ady
desi
gned
in
th
e do
cum
enta
tion
[1].
The
abov
e m
entio
ned
docu
men
tatio
n w
as c
reat
ed a
s a
guid
elin
e fo
r ap
plyi
ng th
e de
sign
sta
ndar
d P1
00-1
/200
6. F
ollo
win
g th
e gi
ven
stru
ctur
e ar
chite
ctur
e an
d lo
ads,
the
auth
or o
f thi
s pa
per
rem
odel
led
the
stru
ctur
e us
ing
Robo
t Mill
enni
um
v.20
.1.
The
obje
ctiv
e of
the
pape
r is t
o sh
ow:
1.th
e Ro
bot
Mill
enni
um
inst
rum
ents
us
ed
for
mod
ellin
g th
is
type
of
st
ruct
ures
2.va
riou
s m
odel
ling
way
s fo
r th
e sa
me
stru
ctur
e hi
ghlig
htin
g th
e m
ost
conv
enie
nt o
ne (i
n th
e au
thor
’s o
pini
on)
3.th
e re
sults
acc
urac
y of
the
anal
ysis
in c
ompa
riso
n w
ith th
e ou
tput
giv
en b
y th
e w
ork
of P
rofe
ssor
Tud
or P
oste
lnic
u
KEY
WO
RD
S: s
eism
ic a
naly
sis,
mod
al a
naly
sis,
stor
ies,
rigid
lin
ks,
pane
l cu
t, re
info
rced
con
cret
e w
alls
.
Artic
le N
o.3,
Inte
rsec
tions
/Inte
rsec
ii, V
ol.5
, 200
8, N
o.3,
“Se
ism
ic A
naly
sis”
Mih
ai N
edel
cu
34
Seis
mic
Ana
lysi
s
ISS
N 1
582-
3024
http
://w
ww
.inte
rsec
tions
.ro
1. I
NTR
OD
UC
TIO
N
The
chos
en b
uild
ing
is fu
lly d
escr
ibed
in th
e 3rd
exa
mpl
e of
a v
ery
prof
essi
onal
and
us
eful
doc
umen
tatio
n: “
P100
-1/ B
uild
ing
seis
mic
des
ign,
vol
ume
2-B
. Com
men
ts
and
calc
ulus
exa
mpl
es”,
re
spon
sibl
e au
thor
: Tu
dor
Post
elni
cu,
Ph.D
., Pr
of.,
U.T
.C.B
. Fo
r th
e se
ism
ic
anal
ysis
, th
e au
thor
s of
th
e ab
ove
men
tione
d do
cum
enta
tion
used
the
lat
eral
for
ce m
etho
d an
d 3D
lin
ear-e
last
ic c
ompu
tatio
n ge
nera
ted
by m
eans
of t
he E
TAB
S pr
ogra
m. T
he a
utho
r of t
his p
aper
wan
ted
to se
e if
the
Rob
ot M
illen
nium
sof
twar
e pa
ckag
e co
uld
be a
goo
d al
tern
ativ
e in
this
kin
d of
stru
ctur
es a
naly
sis.
The
anal
yzed
bui
ldin
g is
loca
ted
in B
ucha
rest
and
has
: •
3 un
derg
roun
d le
vels
(h=3
m) +
gro
und
floor
(h=6
m) a
nd 1
0 st
orie
s (h=
3m)
•5
long
itudi
nal s
pans
x 8
m a
nd 5
tran
sver
sal s
pans
2x7
+1x4
+2x7
m
The
stru
ctur
al c
hara
cter
istic
s:
•R
.C.
wal
ls (
both
unc
oupl
ed a
nd c
oupl
ed b
y sp
andr
el w
alls
), co
lum
ns a
nd
beam
s •
conc
rete
cla
ss C
25/3
0
•st
eel P
C52
•
a g=0
.24g
, Tc=
1.6s
ec, d
uctil
ity c
lass
H, i
mpo
rtanc
e co
effic
ient
g1=
1.2
A c
urre
nt fl
oor p
lan
is sh
own
in F
igur
e 1.
2. M
OD
ELLI
NG
PR
ESEN
TATI
ON
For t
he s
eism
ic a
naly
sis,
the
stru
ctur
e is
con
side
red
fixed
at t
he g
roun
d flo
or b
ase.
U
sing
Rob
ot M
illen
nium
v.2
0.1,
the
aut
hor
mod
eled
the
stru
ctur
e us
ing
bars
for
co
lum
ns/b
eam
s an
d pa
nels
for s
labs
/ R.C
. wal
ls (s
ee F
igur
e 2)
. Of c
ours
e af
ter t
he
mes
h ge
nera
tion
(eve
n w
ith la
rge
finite
ele
men
ts) t
he g
reat
num
ber o
f equ
atio
ns (o
f or
der 1
0^5)
led
to a
sign
ifica
nt sl
owin
g do
wn
of th
e an
alys
is. A
s a g
ood
alte
rnat
ive
the
Rig
id L
inks
add
ition
al a
ttrib
ute
can
be u
sed
inst
ead
of p
anel
s fo
r th
e sl
abs
mod
elin
g. B
y in
trodu
cing
the
Mem
bran
e rig
id li
nk, t
he u
ser c
an c
onne
ct th
e no
des
of e
ach
floor
acc
ordi
ng to
any
DO
F, in
this
cas
e th
e X
,Y d
ispl
acem
ents
and
the
RZ
rota
tion.
And
so
the
slab
eff
ect a
s a
rigid
bod
y is
fully
cov
ered
. At t
he s
ame
time
the
beam
s ha
ve to
be
mod
eled
as
T-se
ctio
n, ta
king
into
acc
ount
the
corr
espo
ndin
g sl
ab ri
gidi
ty. A
sla
b w
idth
of 3
xhp
(the
slab
thic
knes
s) w
as ta
ken
on e
ach
side
for
the
inte
rior b
eam
s and
of 2
xhp
on e
ach
side
for t
he m
argi
nal b
eam
s. H
avin
g no
slab
fin
ite e
lem
ents
red
uces
con
side
rabl
y th
e an
alys
is ti
me
with
abs
olut
ely
no d
amag
e to
the
resu
lts. T
he m
odel
is p
rese
nted
in F
igur
e 3.
Artic
le N
o.3,
Inte
rsec
tions
/Inte
rsec
ii, V
ol.5
, 200
8, N
o.3,
“Se
ism
ic A
naly
sis”
Seis
mic
ana
lysi
s usi
ng R
obot
Mill
enni
um
35
Seis
mic
Ana
lysi
s
ISS
N 1
582-
3024
http
://w
ww
.inte
rsec
tions
.ro
Figu
re 1
. The
bui
ldin
g cu
rren
t flo
or p
lan
Figu
re 2
. The
stru
ctur
e m
odel
show
ing:
a) s
ectio
n sh
apes
, b) r
igid
link
s
Follo
win
g th
e in
stru
ctio
ns o
f P1
00-2
006,
the
rig
idity
of
the
elem
ents
is
take
n di
ffer
ently
, dep
endi
ng o
n th
e ty
pe o
f ana
lysi
s. Fi
rst,
the
goal
is to
mak
e th
e m
odal
an
alys
is, i
n w
hich
the
rigid
ity o
f wal
ls, c
olum
ns a
nd b
eam
s is
take
n EI
=0.5
E cI c.
As
for
the
span
drel
wal
ls, t
heir
You
ng m
odul
us i
s E s
pand
rel =0
.4*
E wal
ls an
d th
e ot
her
Artic
le N
o.3,
Inte
rsec
tions
/Inte
rsec
ii, V
ol.5
, 200
8, N
o.3,
“Se
ism
ic A
naly
sis”
Mih
ai N
edel
cu
36
Seis
mic
Ana
lysi
s
ISS
N 1
582-
3024
http
://w
ww
.inte
rsec
tions
.ro
sect
iona
l cha
ract
eris
tics:
A=0
.2A
c, I=
0.2I
c. R
educ
ing
the
rigid
ity o
f th
e el
emen
ts,
the
elem
ents
are
con
side
red
in a
pla
stic
sta
ge a
nd s
o th
e bu
ildin
g be
havi
or d
urin
g an
ear
thqu
ake
is w
ell a
ppro
xim
ated
acc
ordi
ng to
P10
0-20
06. T
o ac
hiev
e th
at th
e us
er c
an d
efin
e a
new
mat
eria
l with
a m
odifi
ed Y
oung
mod
ulus
, in
this
cas
e na
med
C
25/3
0_0.
5 (J
ob P
refe
renc
es/M
ater
ials
/Mod
ifica
tion)
. Th
e ch
arac
teris
tics
of a
lo
ngitu
dina
l w
all
are
set
as p
rese
nted
in
Figu
re 3
. As
for
the
span
drel
wal
ls t
he
doub
le r
educ
tion
is a
chie
ved
by m
ultip
lyin
g th
e th
ickn
ess
of 5
0cm
with
the
0.2
fa
ctor
.
Figu
re 3
. Def
inin
g th
e se
ctio
n pr
oper
ties o
f: a)
long
itudi
nal w
alls
, b) s
pand
rel w
alls
As
for
the
bar
elem
ents
, the
re is
an
alte
rnat
ive.
The
pro
gram
allo
ws
the
redu
ctio
n of
mom
ent o
f ine
rtia
acco
rdin
g to
loca
l axe
s x, y
, z (s
ee F
igur
e 4)
.
Artic
le N
o.3,
Inte
rsec
tions
/Inte
rsec
ii, V
ol.5
, 200
8, N
o.3,
“Se
ism
ic A
naly
sis”
Seis
mic
ana
lysi
s usi
ng R
obot
Mill
enni
um
37
Seis
mic
Ana
lysi
s
ISS
N 1
582-
3024
http
://w
ww
.inte
rsec
tions
.ro
Figu
re 4
. Def
inin
g th
e pr
oper
ties o
f: a)
col
umns
70x
70cm
, b) b
eam
s 30x
70cm
Ano
ther
pr
oble
m
in
the
mod
al
anal
ysis
is
th
e m
odel
ing
of
the
addi
tiona
l ec
cent
riciti
es: ±
5%
in e
ach
dire
ctio
n. T
he c
ode
expl
ains
in d
etai
l how
thei
r eff
ect
has
to b
e ta
ken
into
acc
ount
. The
lev
el s
eism
ic f
orce
s, co
mpu
ted
by h
and
or b
y so
me
user
def
ined
com
pute
r pro
gram
hav
e to
be
appl
ied
to th
e re
sist
ance
ele
men
ts
depe
ndin
g on
the
ir rig
idity
. Bec
ause
the
re a
re 2
mai
n di
rect
ions
, for
eac
h on
e 2
sign
s an
d th
e m
ass
ecce
ntric
ities
can
als
o be
pos
itive
or
nega
tive,
the
re a
re 8
co
mbi
natio
ns to
be
mad
e. T
his
wor
k is
tim
e co
nsum
ing
and
the
prob
abili
ty o
f use
r er
rors
is
high
ly i
ncre
ased
. A
goo
d al
tern
ativ
e se
ems
to b
e th
e M
odal
Ana
lysi
s Pa
ram
eter
s/D
efin
ition
of m
ass e
ccen
tric
ities
that
the
prog
ram
off
ers (
see
Figu
re 5
). Th
e si
gn o
f ecc
entri
city
can
be
chan
ged
but i
s im
poss
ible
to h
ave
both
sig
ns in
the
sam
e m
odel
. So,
diff
eren
t mod
els
have
to b
e m
ade.
Of
cour
se, i
f th
e st
ruct
ure
is
som
eway
sym
met
rical
, the
wor
k is
muc
h re
duce
d.
Figu
re 5
. Int
rodu
cing
the
addi
tiona
l mas
s ecc
entri
citie
s
In th
e 3rd
exa
mpl
e th
e lo
ads
are
gene
rally
giv
en. B
ecau
se o
f th
is “
gene
ralit
y” th
e re
sults
of
this
pap
er a
re n
ot id
entic
al to
the
orig
inal
one
s, bu
t the
diff
eren
ces
are
acce
ptab
le. G
iven
the
loa
ds, t
he l
oad
to m
ass
conv
ersi
on i
s m
ade
auto
mat
ical
ly.
The
size
of
FE-s
sho
uld
be s
et a
s bi
g as
pos
sibl
e, s
ince
fro
m th
e m
odal
ana
lysi
s po
int o
f vie
w th
e m
esh
refin
emen
t will
not
cha
nge
the
resu
lts. D
oing
that
the
mod
al
anal
ysis
was
mad
e in
a fe
w s
econ
ds. T
he re
sults
are
com
pare
d to
the
orig
inal
one
s (s
ee F
igur
es 6
and
7).
Als
o th
e sh
ape
of th
e ei
genv
ecto
rs f
or th
e fir
st 3
mod
es is
sh
own
in X
Y v
iew
(se
e Fi
gure
8).
The
addi
tiona
l ecc
entri
citie
s ef
fect
for
the
first
tw
o m
odes
can
be
seen
.
Figu
re 6
. The
Rob
ot M
illen
nium
mod
al a
naly
sis r
esul
ts
Artic
le N
o.3,
Inte
rsec
tions
/Inte
rsec
ii, V
ol.5
, 200
8, N
o.3,
“Se
ism
ic A
naly
sis”
Mih
ai N
edel
cu
38
Seis
mic
Ana
lysi
s
ISS
N 1
582-
3024
http
://w
ww
.inte
rsec
tions
.ro
Figu
re 7
. The
orig
inal
mod
al a
naly
sis r
esul
ts
Figu
re 8
. The
shap
e of
the
eige
nvec
tors
for t
he fi
rst 3
mod
es in
XY
vie
w
The
next
ste
p is
to d
efin
e th
e se
ism
ic a
naly
sis
(see
Fig
ure
9). T
he b
ehav
ior f
acto
r (q
) has
diff
eren
t val
ues
acco
rdin
g di
rect
ion
X a
nd Y
. For
the
duct
ility
cla
ss H
, on
X-lo
ngitu
dina
l di
rect
ion,
the
wal
ls a
re c
onsi
dere
d as
can
tilev
ers
()
whi
le o
n Y
-tran
sver
sal d
irect
ion,
the
wal
ls a
re c
oupl
ed, a
nd s
o re
sults
a h
ighe
r q
().
1/
4u
q
1/
4u
q
Figu
re 9
. Int
rodu
cing
the
seis
mic
ana
lysi
s par
amet
ers
Sinc
e th
e se
ism
ic a
naly
sis
is c
once
rned
, on
ly t
he s
peci
al l
oad
com
bina
tions
are
in
trodu
ced.
To
asse
ss th
e de
form
atio
ns, n
o ch
ange
s ar
e m
ade
to th
e FE
mes
h or
to
Artic
le N
o.3,
Inte
rsec
tions
/Inte
rsec
ii, V
ol.5
, 200
8, N
o.3,
“Se
ism
ic A
naly
sis”
Seis
mic
ana
lysi
s usi
ng R
obot
Mill
enni
um
39
Seis
mic
Ana
lysi
s
ISS
N 1
582-
3024
http
://w
ww
.inte
rsec
tions
.ro
the
sect
iona
l rig
iditi
es.
The
allo
wed
dis
plac
emen
ts a
re g
iven
by
P100
-200
6 in
re
latio
n to
the
elas
tic d
rift.
The
prog
ram
off
ers
anot
her u
sefu
l too
l by
allo
win
g th
e us
er to
def
ine
the
stor
ies
of
the
build
ing:
Geo
met
ry/C
ode
Para
met
ers/
Stor
ies.
The
elem
ents
of e
ach
stor
ey a
re
pres
ente
d in
a d
iffer
ent c
olor
in th
e Fi
gure
10.
The
wal
ls a
re n
ot c
olor
ed b
ecau
se o
f th
e la
rge
FE m
esh.
Figu
re 1
0. T
he st
orie
s dis
play
The
char
acte
ristic
s of
eac
h st
orey
can
be
seen
by
the
Stor
y Ta
ble/
Valu
es o
ptio
n. In
th
e Fi
gure
11,
are
pre
sent
ed th
e m
ass,
the
grav
ity a
nd to
rsio
n ce
nter
s, ec
cent
ricity
e 0
and
the
appl
ied
addi
tiona
l ecc
entri
citie
s e2.
Figu
re 1
1. S
tory
Tab
le: V
alue
s
Usi
ng S
tory
Tab
le/D
ispl
acem
ents
opt
ion,
the
sto
ries
max
imum
abs
olut
e an
d re
lativ
e di
spla
cem
ents
(dre) c
an b
e se
en (F
igur
e 12
).
Artic
le N
o.3,
Inte
rsec
tions
/Inte
rsec
ii, V
ol.5
, 200
8, N
o.3,
“Se
ism
ic A
naly
sis”
Mih
ai N
edel
cu
40
Seis
mic
Ana
lysi
s
ISS
N 1
582-
3024
http
://w
ww
.inte
rsec
tions
.ro
Figu
re 1
1. S
tory
Tab
le: V
alue
s
And
so
the
elas
tic a
nd i
nela
stic
drift
can
be
com
pute
d. T
able
1 i
s sh
owin
g a
com
paris
on b
etw
een
the
resu
lts o
f thi
s pap
er a
nd th
e or
igin
al o
nes f
or X
dire
ctio
n.
Tabl
e 1.
Nam
e of
the
tabl
e R
obot
Mill
enni
um
Exam
ple
3 Le
vel
dreX
dr
iftSL
S dr
iftU
LS
drift
SLS
drift
ULS
(cm
) <0
.005
<0.0
25<0
.005
<0.0
25G
F 0.
1470
0.
0009
0.
0042
0.
0009
0.
0040
E1
0.13
09
0.00
16
0.00
75
0.00
15
0.00
70
E20.
1590
0.
0020
0.
0091
0.
0018
0.
0084
E3
0.18
01
0.00
22
0.01
03
0.00
20
0.00
95
E40.
1948
0.
0024
0.
0111
0.
0022
0.
0102
E5
0.20
41
0.00
25
0.01
16
0.00
23
0.01
05
E60.
2086
0.
0026
0.
0119
0.
0023
0.
0107
E7
0.20
90
0.00
26
0.01
19
0.00
23
0.01
06
E80.
2063
0.
0025
0.
0118
0.
0022
0.
0104
E9
0.20
18
0.00
25
0.01
15
0.00
22
0.01
02
E10
0.19
40
0.00
24
0.01
11
0.00
21
0.00
98
The
next
ste
p is
to c
alcu
late
the
inte
rnal
for
ces.
The
elem
ents
rig
iditi
es a
re to
be
chan
ged.
For
wal
ls a
nd b
ar e
lem
ents
CR
2-1
-1.1
giv
es E
I= E
cI c a
nd fo
r the
span
drel
w
alls
EI=
0.4
(EcI c
). A
s the
bui
ldin
g fle
xibi
lity
is d
ecre
asin
g, th
e in
tern
al fo
rces
will
be
cal
cula
ted
on th
e hy
poth
esis
of
the
uncr
acke
d se
ctio
ns a
nd s
o th
ey a
re h
ighe
r th
en th
e m
ost p
roba
ble
ones
. The
FE
mes
h of
the
wal
ls w
as n
ow r
efin
ed u
p to
a
50cm
siz
e. F
urth
er r
efin
emen
t gav
e no
sub
stan
tial m
odifi
catio
n of
the
resu
lts. O
f co
urse
the
cha
lleng
e is
to
find
the
inte
rnal
for
ces
conc
erni
ng t
he w
alls
and
the
sp
andr
el w
alls
. Fo
r th
is r
easo
n th
e pr
ogra
m h
as t
he o
ptio
n Re
duce
d Re
sults
for
Pa
nels.
With
the
sign
con
vent
ion
from
Fig
ure
12 th
e us
er c
an c
hoos
e th
e se
ctio
n (th
e cu
t) w
here
mom
ents
, she
ar f
orce
s an
d st
ress
es w
ill b
e di
spla
yed
(see
Fig
ure
13).
Artic
le N
o.3,
Inte
rsec
tions
/Inte
rsec
ii, V
ol.5
, 200
8, N
o.3,
“Se
ism
ic A
naly
sis”
Seis
mic
ana
lysi
s usi
ng R
obot
Mill
enni
um
41
Seis
mic
Ana
lysi
s
ISS
N 1
582-
3024
http
://w
ww
.inte
rsec
tions
.ro
Figu
re 1
2. S
ign
conv
entio
n
Figu
re 1
3. C
hoos
ing
a) th
e cu
t pos
ition
, b) t
he re
duce
d fo
rces
to b
e di
spla
yed
Ther
e ar
e tw
o po
ssib
ilitie
s fo
r m
odel
ing
the
wal
l co
lum
ns. U
ntil
now
the
y w
ere
mod
eled
as
bars
. In
this
cas
e, f
or a
RC
wal
l the
inte
rnal
for
ces
of b
oth
wal
l and
w
all
colu
mns
mus
t be
com
bine
d in
ord
er t
o ha
ve t
he r
esul
t fo
r th
e en
tire
wal
l se
ctio
n. A
sec
ond
poss
ibili
ty i
s to
elim
inat
e th
e w
all
colu
mns
and
to
use
an
equi
vale
nt w
all
sect
ion
from
the
prim
ary
mom
ent
of i
nerti
a po
int
of v
iew
. Th
e bu
ildin
g st
iffne
ss w
ill s
light
ly d
ecre
ase
due
to t
he l
ack
of c
ompr
essi
on/te
nsio
n ab
sorb
ed b
y th
e w
all
colu
mns
. Com
paris
on o
f th
e 2
mod
elin
g m
etho
ds w
ith th
e or
igin
al re
sults
is g
iven
for a
long
itudi
nal w
all (
Tabl
e 2)
. The
forc
es a
re c
alcu
late
d at
the
gro
und
floor
lev
el f
rom
one
sei
smic
com
bina
tion
on X
dire
ctio
n. T
he
diff
eren
ce b
etw
een
the
axia
l for
ces
has
to c
ome
from
the
lack
of k
now
ledg
e in
the
load
s di
strib
utio
n ov
er e
ach
stor
ey s
ince
the
eval
uatio
n of
the
build
ing
tota
l wei
ght
was
che
cked
and
alm
ost p
erfe
ct si
mila
rity
was
ach
ieve
d.
Artic
le N
o.3,
Inte
rsec
tions
/Inte
rsec
ii, V
ol.5
, 200
8, N
o.3,
“Se
ism
ic A
naly
sis”
Mih
ai N
edel
cu
42
Seis
mic
Ana
lysi
s
ISS
N 1
582-
3024
http
://w
ww
.inte
rsec
tions
.ro
Tabl
e 2.
Fin
al in
tern
al fo
rces
for a
long
itudi
nal w
all
Wal
l PL1
N
(kN
) M
(kN
m)
T (k
N)
Wal
l -7
741.
22
-326
48.3
29
86.1
5 W
all c
olum
n 1
-276
0.13
-1
78.8
1 32
4W
all c
olum
n 2
5175
.29
-251
.61
389
Fina
l for
ces
-101
56.4
64
389.
96
3699
.15
Wal
l with
out c
olum
ns
-993
9.21
-6
3955
.5
3468
.02
Exam
ple
3 -1
1456
65
463
3778
3. C
ON
CLU
SIO
NS
The
Rob
ot M
illen
nium
sof
twar
e pa
ckag
e gi
ves
us a
relia
ble
and
eleg
ant a
ltern
ativ
e fo
r sei
smic
ana
lysi
s. Its
feat
ures
fully
cov
er th
e de
man
ds o
f P10
0-20
06. H
owev
er,
care
ful
exam
inat
ion
of i
ts to
ols
has
to b
e do
ne i
n or
der
to c
hoos
e th
e op
timal
m
odel
ing
stra
tegy
.
Ref
eren
ces
1.Po
stel
nicu
Tud
or,
P100
-1/P
roie
ctar
ea S
eism
ica
a cl
adir
ilor
vol.2
-B.
Com
enta
rii
si e
xem
ple
de
calc
ul –
ctr
. U.T
.C.B
. nr.
158/
02.0
8.20
05 M
.T.C
.T.
2.R
obot
Mill
enni
um v
.20.
1.Au
tode
sk In
c, 2
008
3.C
R 2
-1-1
.1,C
od d
e pr
oiec
tare
a c
onst
ruct
iilor
cu
pere
ti st
ruct
ural
i de
beto
n ar
mat
4.P1
00-1
/200
6,C
od d
e pr
oiec
tare
seis
mic
a
Artic
le N
o.3,
Inte
rsec
tions
/Inte
rsec
ii, V
ol.5
, 200
8, N
o.3,
“Se
ism
ic A
naly
sis”
