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Journal of Earthquake Engineering, Vol. 8, No. 3 (2004) 457496c
Imperial College Press
SEISMIC BEHAVIOUR OF PERIMETER AND
SPATIAL STEEL FRAMES
ELENA MELE, LUIGI DI SARNO and ANTONELLO DE LUCA
Department of Structural Analysis and Design,
University of Naples Federico II,
P.le V.Tecchio, 80,
80125 Naples, Italy
Received 6 May 2002Revised 26 August 2002Accepted 11 June
2003
The present study deals with the seismic performance of partial
perimeter and spatialmoment resisting frames (MRFs) for
low-to-medium rise buildings. It seeks to establishperimeter
configuration systems and hence the lack of redundancy can
detrimentallyaffect the seismic response of framed buildings. The
paper tackles this key issue by com-paring the performance of a set
of perimeter and spatial MRFs, which were consistentlydesigned. The
starting point is the set of low- (three-storey) and medium-rise
(nine-storey) perimeter frames designed within the SAC Steel
Project for the Los Angeles,Seattle and Boston seismic zones.
Extensive design analyses (static and multi-modal)of the perimeter
frame buildings and consistent design of spatial frame systems, as
analternative to the perimeter configuration, were conducted within
this analytical study.The objectives of the consistent design are
two-fold, i.e. obtaining fundamental periodssimilar to those of the
perimeter frames, i.e. same lateral stiffness under design
horizon-tal loads, and supplying similar yield strength. The
seismic behaviour of perimeter andspatial configuration structures
was evaluated by means of push-over non-linear staticanalyses and
inelastic dynamic analyses (non linear time histories). Comparisons
be-tween analysis results were developed in a well defined
framework since a clear schemeto define and evaluate relevant limit
states is suggested. The failure modes, either localor global, were
computed and correlated to design choices, particularly those
concerningthe strength requirements (column overstrength factors)
and stiffness (elastic stabilityindexes). The inelastic response
exhibited by the sample MRFs under severe groundmotions was
assessed in a detailed fashion. Conclusions are drawn in terms of
localand global performance, namely global and inter-storey drifts,
beam and column plas-tic rotations, hysteretic energy. The finding
is that the seismic response of perimeterand spatial MRFs is fairly
similar. Therefore, an equivalent behaviour between the
twoconfigurations can be obtained if the design is consistent.
Keywords: Seismic design; steel frames; perimeter; spatial;
pushover; dynamic analysis.
1. Introduction
The design criteria to obtain satisfactory seismic performance
of steel moment re-
sisting frame (MRF) buildings is a major research issue which
has been deeply
discussed during recent years (e.g. Luco and Cornell [2000], Yun
et al. [2002],
among others). Building damage survey carried out in the
aftermath of the 1994
457
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458 E. Mele, L. Di Sarno & A. De Luca
Northridge (California) and 1995 Hyogoken-Nanbu (Japan)
earthquakes showed
clearly widespread and unexpected damage modes in steel
structures. Several
types of brittle fractures were, indeed, found at welded
connections in MRFs.
As a consequence, a great deal of research in USA, Japan and
Europe has
been devoted to understand and prevent the causes of the
observed poor per-
formance of steel structures. For example, in the USA, the SAC
Joint Venture
was formed with the specific goal of investigating the damage to
welded steel
moment frame buildings in the 1994 Northridge earthquake and
developing re-
pair techniques and new design approaches to minimise damage to
steel moment
frame buildings in future earthquakes [SAC, 1995]. In the first
part of the research
program (SAC Steel Project) interim design guidelines [FEMA 267,
1995; FEMA
267A, 1997; FEMA 267B, 1999] were developed and two sets of nine
frame build-
ings (low-, medium- and high-rise) were designed in compliance
with both pre-
Northridge design practice [UBC, 1994] and the Interim
Guidelines. The structural
systems of these nine model buildings are perimeter MRFs,
designed for three dif-
ferent earthquake prone zones. Such structures were considered
as benchmarks in
order to carry out analytical investigations on the seismic
performance, with the
aim of:
Developing concepts and information needed to identify and
predict local and
global seismic demand parameters which have a significant effect
on the seismic
response of steel moment resisting frames;
Identifying the effect on seismic performance of the strength,
stiffness and
hysteretic characteristics of realistic alternative connection
types as well as of
the system configuration and proportioning.
In the present study, the SAC low- and medium-rise buildings
were selected and
assessed to establish the governing parameters in the seismic
design and hence eval-
uate the response of MRFs under severe earthquakes, varying the
design criteria
and the design parameter values. This paper focuses, however, on
the influence of
the configuration layout and redundancy of the lateral resisting
system on the seis-
mic performance of framed buildings. The SAC perimeter
structures are analysed
and contrasted to alternative structural configurations, i.e.
spatial MRFs.
2. Object and Layout of the Paper
This analytical study deals with the seismic performance of
partial perimeter and
spatial MRFs for low-to-medium rise buildings. Its aim is to
establish if the de-
sign choice of employing perimeter configuration system, namely
the lack of high
redundancy, has detrimental effects on the seismic response of
framed buildings.
The effect of redundant seismic framing is a major topic, often
appointed by the
engineering community as one of the possible causes of the poor
seismic performance
[FEMA 350, 2000; Whittaker et al., 1999]. Nevertheless, few
studies have been
conducted so far to quantify systematically such an effect.
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Seismic Behaviour of Perimeter and Spatial Steel Frames 459
The framework employed within this study is based upon the
comparison of
the seismic performance of perimeter and spatial MRFs, which are
consistently
designed. Thus, the set of low- (three-storey) and medium-rise
(nine-storey)
perimeter frames designed within the SAC Steel Project for the
Los Angeles, Seattle
and Boston seismic zones was considered as a benchmark. The
scheme of the study
carried out can be summarised as follows:
Definition of the design parameters for steel MRF systems. A
critical assessment
of MRF design procedures and approaches is carried out in order
to establish the
structural parameters governing the seismic design.
Elastic analyses (static and multi-modal) of the SAC perimeter
frame buildings
under design load distributions and evaluation of major design
parameters.
Consistent design of spatial frame systems, as alternative
structural configuration
for the SAC model buildings. The design is consistent because it
is carried out
with two specific objectives: (i) obtaining the same period as
the perimeter frame
building, i.e. same lateral stiffness under design horizontal
loads; (ii) supplying
the same yield strength as perimeter frame building. It is also
worth mentioning
that the total weight of both configurations does not differ
significantly.
Assessment of the inelastic behaviour of perimeter and spatial
frames and
comparisons.
Evaluation of the seismic performance and inelastic demands
under severe
earthquakes of perimeter and spatial frames and comparisons.
The seismic behaviour of perimeter and spatial configuration
structures was
evaluated by means of push-over non-linear static analyses and
inelastic dynamic
analyses. Comparisons between analysis results were developed in
a well defined
framework. A clear scheme to define and evaluate relevant limit
states (LSs) is
suggested in agreement with a similar proposal available in the
literature [Broderick
and Elnashai, 1996; Elnashai et al., 1998]. Thus, the failure
modes, either local or
global, were computed and correlated to design choices,
particularly concerning
strength requirements (column overstrength factors) and
stiffness (elastic stability
indexes). Moreover, the inelastic response exhibited by
perimeter and spatial MRFs
under severe ground motions was assessed. Conclusions are drawn
in terms of local
and global performance, namely (i) global and inter-storey
drifts, (ii) beam and
column plastic rotations and (iii) hysteretic energy.
3. Structural Systems
3.1. Description
The assessed structures are three- and nine-storey office
buildings, designed
according to the UBC 1994 provisions for three different seismic
zones, respectively
Los Angeles (LA), seismic zone 4, Seattle (SE), seismic zone 3
and Boston (BO),
seismic zone 2A. They were designed by three U.S. professional
firms, i.e. Brandow
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460 E. Mele, L. Di Sarno & A. De Luca
and Johnston Associates (three- and nine-storey LA buildings),
KPFF Consulting
Engineers (three- and nine-storey SE buildings) and LeMessurier
Consultants
(three- and nine-storey BO buildings). These MRFs have been
extensively anal-
ysed by Gupta and Krawinkler [1998a, 1998b, 2000a, 2000b] within
SAC studies on
structural system performance, and other Researchers [e.g.
Maison and Bonowitz,
1999; Mele et al., 2000].
Low-rise buildings have a rectangular floor plan 56.08 37.80 m
(Fig. 1). The
structural configuration consists of six 9.15 m bays along the
major side and four
9.15 m bays in the orthogonal direction. The inter-storey height
is 3.96 m. The
lateral load resisting system consists of two four-bays
perimeter moment frames in
both principal directions, thus providing torsional resistance,
and interior gravity
frames with simple shear connections. In the LA perimeter frame
there are only
three moment resisting bays; the fourth bay includes pinned
beams connected to
weak axis columns. At the first and second floor, beam span
loads (dead and live)
are equal to 14.88 kN/m and joint vertical loads are equal to
158 kN and 107 kN
at interior and perimeter joints, respectively. Beam loads of
12.65 kN/m and joint
vertical loads of 140 kN (interior joints) and 92 kN (exterior
joints) were respectively
considered at the roof. At each storey level the slab consists
of 76.2 mm metal
decking with 63.5 mm of normal weight concrete (NWC). The latter
is stiff enough
to ensure the diaphragm (rigid) action. The total seismic load
of the building is
Wtot = 29 500 kN.
The nine-storey buildings (Fig. 2) have a square floor plan 45.7
45.7 m, with
five 9.15 m bays along both sides. The inter-storey height is
5.49 m at the first
storey and 3.96 m at all other storeys, whilst the basement
level is 3.66 m in height.
Four MRFs are located along the perimeter of the buildings, two
for both principal
directions to provide lateral and torsion resistance, similarly
to low-rise frames.
Perimeter systems consist of four bays with strong axis columns
rigidly connected
to the girders plus an external bay where the girder is shear
connected to the corner
columns, thus biaxial bending is prevented in all building
corner columns. Beam
span loads and joint vertical loads are similar to the
three-storey counterparts. The
slab is a floor system (rigid plane) of composite metal deck
(76.2 mm thick), with
63.5 mm of NWC fill. The total seismic load of the building is
Wtot = 90 140 kN.
Element cross sections of perimeter and spatial frames employed
in three- and
nine-storey buildings are provided in Table 1 and Table 6,
respectively.
Nominal yield strength equal to 345 MPa (50 ksi) was used for
girders and
columns of all perimeter frames, except for LA frames, in which
nominal yield
strength equal to 248 MPa (36 ksi) was adopted for girders.
Similar yield stress
values were employed either for low- or medium-rise, spatial
MRFs.
In the following, low- and medium-rise perimeter frames are
appointed as:
LA-3P, SE-3P, BO-3P and LA-9P, SE-9P, BO-9P. Similarly, the
spatial frames
are appointed as: LA-3S, SE-3S, BO-3S and LA-9S, SE-9S, BO-9S.
For example,
LA-3P means that the frame is located in Los Angeles, it has
three-storeys and
perimeter configuration.
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Seismic Behaviour of Perimeter and Spatial Steel Frames 461
Fig
.1.
Geo
met
ryofth
ree-
store
yM
RFs:
pla
nla
yout
(lef
t)and
ver
tica
lse
ctio
n(r
ight)
.
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Fig. 2. Geometry of nine-storey MRFs: plan layout (left) and
vertical section (right).
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Seism
icBehavio
ur
ofPerim
ete
rand
Spatia
lStee
lFra
mes
463
Table 1. Beam and column cross sections (three- and nine-storey
perimeter MRFs).
Beams Internal Columns External ColumnsFrame
Storey LA SE BO LA SE BO LA SE BO
01 W33 118 W24 76 W21 62 W14 311 W14 176 W14 99 W14 257 W14 159
W14 74
Three-Storey 12 W30 116 W24 84 W21 57 W14 311 W14 176 W14 99 W14
257 W14 159 W14 74
23 W24 68 W18 40 W18 35 W14 311 W14 176 W14 99 W14 257 W14 159
W14 74
01 W36 160 W30 108 W24 68 W14 500 W24 229 W14 233 W14 370 W24
229 W14 159
12 W36 160 W30 108 W36 135 W14 500 W24 229 W14 233 W14 370 W24
229 W14 159
23 W36 160 W30 116 W33 118 W14 455 W24 229 W14 233 W14 370 W24
229 W14 159
34 W36 135 W30 108 W30 116 W14 455 W24 229 W14 233 W14 370 W24
229 W14 159
Nine-Storey 45 W36 135 W27 94 W30 116 W14 370 W24 207 W14 211
W14 283 W24 207 W14 132
56 W36 135 W27 94 W30 108 W14 370 W24 207 W14 211 W14 283 W24
207 W14 132
67 W36 135 W24 76 W30 99 W14 283 W24 162 W14 176 W14 257 W24 162
W14 99
78 W30 99 W24 76 W27 94 W14 283 W24 162 W14 176 W14 257 W24 162
W14 99
89 W27 84 W24 62 W24 76 W14 257 W24 131 W14 120 W14 233 W24 131
W14 68
910 W24 68 W24 62 W18 40 W14 257 W24 131 W14 120 W14 233 W24 131
W14 68
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464 E. Mele, L. Di Sarno & A. De Luca
3.2. Modelling
The structural analysis was performed through two finite element
method codes.
Elastic analyses were carried out by means of SAP2000 [SAP2000,
1999], while
the computer code DRAIN-2DX [Prakash et al., 1993] was used to
evaluate the
responses of both perimeter and spatial MRFs beyond the elastic
limit (inelastic
static and non linear dynamic analyses). Moreover, DRAIN-2DX
models were cali-
brated on the basis of the SAP2000 counterparts. Bare frames,
employing centreline
dimensions, were modelled as two-dimensional assemblages of
plastic hinge (lumped
plasticity) beam and beam-column elements. The latter account
for bending-axial
interaction, through a linearised biaxial plastic domain
(bending moment-axial
load), characterised by horizontal and vertical straight lines
corresponding to 10% of
adimensionalised bending and axial capacity, with reference to
full plastic bending
moment and squash load, respectively. Bilinear elastic plastic
behaviour with strain
hardening of 1% was adopted to model plastic hinges. Shear
behaviour of beams and
columns was assumed to remain linearly elastic. Geometric
non-linearities, i.e. P
effects, were included within elastic and inelastic analyses.
Panel zone yielding and
deformation were not considered. Moreover, the additional
stiffness and strength
due to the presence of the concrete deck slab were not accounted
for in the analysed
plane systems. Dynamic elastic analyses were based upon a 5%
equivalent viscous
damping, whilst the latter was not accounted for in the
inelastic analyses since
dissipative sources other than material plasticity were not
considered.
4. Design Analyses of Perimeter Frames
The design choices adopted for perimeter framed buildings were
investigated with
respect to the main structural properties, namely stiffness
(fundamental period and
lateral stiffness), strength (design stress level, column
over-strength factor, yield
strength) and stability (sensitivity to P effects). These
analyses were based upon
UBC94 seismic provisions [UBC, 1994], which defines the seismic
base shear V as
follows:
V = C(T ) W , (1)
where the seismic coefficient (C) is a function of the period (T
):
C =1.25ZIS
RwT2
3
, (2)
where Z = zone factor, I = importance factor, S = soil response
factor, Rw =
response modification or force reduction factor.
4.1. Period and design forces
The design period at which the static lateral forces are
computed deserves particu-
lar attention and has been subjected to several adjustments in
the Codes of Practice
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Seismic Behaviour of Perimeter and Spatial Steel Frames 465
during recent years [Chopra and Goel, 2000]. However, it is
common among pro-
fessionals to adopt empirical formulas like that proposed by UBC
(Method A):
TA = Ct (Htot)3
4 (3)
(with Ct = 0.035 for steel frames and Htot is the global height
in feet), albeit
the code specifically advises the adoption of a more refined,
Rayleigh type formula
(Method B). In such case, as an upper limit of the period to be
used in the as-
sessment of structural deformations, the code requires, for high
seismicity areas
(Zone 4):
TB,max = 1.30 TA , (4)
whilst a longer value, i.e.
TB,max = 1.40 TA (5)
is allowed for low-to-intermediate seismicity, namely Zones 1, 2
and 3.
For the assessed buildings Methods A and B were used to
determine the design
base shears. The period values computed by means of Eq. (3) and
either Eqs. (4)
or (5), depending on seismic zone, along with the actual values
of the structure
fundamental periods, are provided in Table 2 for three- and
nine-storey perimeter
MRFs. In these tables the design base shear (VUBC-A and VUBC-B)
and maximum
inter-storey and roof drift ratios (d/h and Dtop/H), computed by
means of elastic
analyses, are also given. For the sake of completeness, base
shears corresponding to
wind forces and the relative deformation parameters were
evaluated; the latter are
included in the above mentioned table. To evaluate wind actions
and effects, wind
speeds of 70 mph (LA) and 80 mph (BO and SE) and Exposure B were
assumed.
Large scatters can be observed between the actual natural
periods and the
counterparts based upon code equations. Standardised
semi-empirical formulae are
calibrated to account for the contribution of in-filled non
structural elements. The
latter increase the frame lateral stiffness. These contributions
are, however, usually
neglected in preliminary design models. For the set of SAC
buildings, elastic anal-
yses performed on 3D FEM frame models showed that, due to the
contribution of
the internal frames (gravity load system), the period values
decrease by less than
5% for the three-storey buildings and by approximately 10% for
the nine-storey
buildings. Thus, unless very stiff non-structural elements are
adopted, empirical
code formulas provide too low an estimate of the fundamental
period. This finding
is in agreement with previous studies [Gupta and Krawinkler,
1998b, 2000a].
4.2. Lateral stiffness
Elastic deformation parameters, i.e. inter-storey and global
drifts, were computed
through static analyses employing Methods A and B (UBC, 1994)
horizontal force
distributions, as well as through response spectrum analysis
(Table 2).
It is instructive to note that in steel MRF design, stiffness
requirements, ex-
pressed as either maximum inter-storey or roof drift
limitations, are usually more
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Table 2. Fundamental period, base shear, maximum drift index and
roof drift (three- and nine-storey perimeter MRFs).
Method A Method B Wind Loads Dynamic Analysis
T V/W d/h Dtop/H T V/W d/h Dtop/H V/W d/h Dtop/H T Dtop/H
Frame [sec] [%] [%] [%] [sec] [%] [%] [%] [%] [%] [%] [sec]
[%]
LA-3P 7.64 0.30 0.26 0.72 6.26 0.25 0.22 2.36 0.07 0.06 0.99
0.14
SE-3P 0.55 5.73 0.38 0.33 0.77 4.48 0.30 0.26 3.08 0.15 0.13
1.31 0.09
BO-3P 2.87 0.35 0.30 0.77 2.24 0.29 0.24 3.08 0.27 0.23 1.76
0.09
LA-9P 4.04 0.30 0.28 1.79 3.39 0.25 0.24 2.53 0.18 0.13 2.53
0.12
SE-9P 1.38 3.04 0.41 0.36 1.93 2.42 0.33 0.29 3.32 0.35 0.27
3.30 0.10
BO-9P 1.51 0.28 0.21 1.93 1.21 0.22 0.18 3.32 0.59 0.32 3.63
0.10
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Seismic Behaviour of Perimeter and Spatial Steel Frames 467
stringent than strength. For code compliant design [UBC, 1994]
the inter-storey
drift limitation is equal to either 1/300 or 1/400 for
structures with fundamen-
tal period respectively either lower or higher than 0.7 sec.
Thus, for three-storey
buildings, 1/300 applies when Method A is used, since Eq. (3)
provides a period
value equal to 0.55 sec; on the other hand, 1/400 applies if
Method B or spectrum
analysis are adopted.
Inter-storey drift ratios computed for low-rise frames show that
code limits
are exactly fulfilled only in LA-3P, while they are slightly
exceeded in SE-3P and
BO-3P. However, for such buildings, the roof drift is
respectively less than 1/300
and 1/400 under Methods A and B design loads. Roof drift values
obtained through
response spectrum analyses are even smaller than the latter
ones.
It should be pointed out that for the BO-3P building the base
shear due to wind
actions is larger than the seismic shear. Nevertheless, the
maximum deformations
occur under the seismic force distribution, due to a larger
overturning moment.
Thus, it is likely that member proportioning was governed by the
seismic load
condition.
With regard to the medium-rise buildings, the design load due to
wind actions
is higher than the seismic ones for BO-9P and SE-9P. It is
interesting to note
that whereas for BO-9P the effects due to wind actions (d/h and
Dtop/H) are
also greater than the seismic loads, for the SE-9P building the
roof and inter-storey
drifts induced by wind actions are slightly smaller than those
induced by earthquake
loading.
The LA-9P building fully satisfies the drift limitation (1/400)
under Method B
design loads, while SE-9P and BO-9P slightly exceed it. However,
the nine-storey
buildings spectrum analysis provides values of the deformation
parameters which
are also by and large within code limitations.
Concerning stiffness distribution, the structures exhibit a
quite smooth variation
of global stiffness over the height. In the low-rise frames
while the beam cross
sections are reduced over the frame height (with the exception
of the SE-3P frame,
which has second floor beams stiffer than first storey ones),
the columns cross
sections are the same. In the medium-rise frames both columns
and beams are
varied throughout the building height. Column splices are
generally located at every
third storey, and beams are consistently reduced. In SE-9P, as
for SE-3P, second
floor beams are stiffer than first storey ones.
4.3. Design stress level and yield strength
The stress level in structural members under gravity and seismic
lateral loads
(Methods A and B of UBC) was evaluated and very low stress
values were obtained.
Thus, the base shear Vy corresponding to first yield, i.e. onset
of yield strength
in the most stressed section, was evaluated. Values of Vy ,
normalised to seismic
weight W and to the seismic base shears (VUBC-A and VUBC-B), are
provided for
three- and nine-storey buildings in Table 3; the values for wind
actions are also
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Table 3. Non-dimensional base shear (three- and nine-storey
perimeter MRFs).
VUBC-M.A/W VUBC-M.B/W VWIND/W Vy-triang./W Vy-unif./W
Vy-triang./ Vy-triang./ Vy-unif./
Frame [%] [%] [%] [%] [%] VUBC-M.A VUBC-M.B VWIND
LA-3P 7.64 6.26 2.36 20.1 22.79 2.63 3.23 9.66
SE-3P 5.73 4.48 3.08 18.59 21.02 3.24 4.15 6.82
BO-3P 2.87 2.24 3.08 10.89 11.25 3.79 4.86 3.65
LA-9P 4.04 3.39 2.53 10.18 10.61 2.52 3.00 4.19
SE-9P 3.04 2.42 3.32 8.06 8.43 2.65 3.33 2.54
BO-9P 1.51 1.21 3.32 7.53 7.79 4.99 6.22 2.35
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Seismic Behaviour of Perimeter and Spatial Steel Frames 469
included. Design over-strength factors, herein defined as the
ratio Vy/VUBC, are
high. They range between 2.52 and 3.25, except where the design
was governed by
wind (BO frames). These large values are due to several
features: (i) the ratio of
yield-to-allowable stress (about 1.5), (ii) the compliance to
drift limitations, (iii)
the compliance of SCWB requirement and (iv) the different
susceptibility to second
order effects. The latter is significant for BO MRFs whose
Vy/VUBC represent an
outlier when compared to the mean values.
It is worth mentioning that the design of BO-3P as well as SE-9P
and
BO-9P, which exhibit over-strengths equal to 3.80, 2.65 and
4.97, respectively, were
governed by wind loading. Thus, the computed Vy/VUBC factors do
not refer to the
actual design condition.
Finally, it is interesting to note that for BO frames (both low-
and medium-
rise), as well as for SE medium-rise frames, the over-strength
factors due to the
wind are lower than the seismic counterparts. By contrast, LA
frames (three- and
nine-storeys) and SE low-rise frame, exhibit design
over-strength for wind greater
than for earthquake loads.
4.4. Column over-strength factor
Column over-strength factors (COF s) were computed at each frame
joint using the
following standardised relationship [UBC, 1994]:
COF =Zc(fyc fa)
Zbfyb(6)
in order to verify the fulfilment of the strong column weak beam
(SCWB) re-
quirement (COF 1). In the above equation Zc, Zb and fyc, fyb are
section plastic
modulus and yield stress respectively for columns and beams
framing into the joint,
while fa is the axial stress in column members. An adequate
column over-strength
factor gives rise to a configuration where columns are protected
from plastic hinge
formation. Hence, inelastic deformations should occur in
beams.
It is worth mentioning that COF s in three-storey frames (Table
4) are greater
than unity, minimum values being 1.06, 1.23 and 1.94,
respectively, for BO-3P,
Table 4. COF s (three- and nine-storeyperimeter MRFs).
Frame Minimum Maximum
LA-3P 1.94 (1) 3.77 (3)
SE-3P 1.23 (2) 3.60 (3)
BO-P 1.06 (1) 1.87 (2)
LA-9P 1.39 (7) 4.89 (8)
SE-9P 1.17 (9) 3.66 (1)
BO-9P 0.68 (2) 2.04 (1)
Keys: Bracketed values show the floors.
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470 E. Mele, L. Di Sarno & A. De Luca
SE-3P and LA-3P buildings. Moreover, for BO-3P nearly 80% of the
total number
of beam-to-column connections exhibit COF s between 1.0 and
1.50, thus show-
ing high risk of extensive column hinging. Indeed, recent
studies [Nakashima and
Sawaizumi, 2000] showed that plastic hinges in columns cannot be
prevented by
simply satisfying the requirement COF 1. Minimum COF values
strongly de-
pend on ground motions and importance of higher vibration modes
of vibration. As
rule of thumb, COF s ranging from 1.5 to 2 are required to
ensure elastic response of
column members. As a consequence, for low-rise buildings, the
adequate fulfilment
of SCWB can be predicted only for LA-3P.
Values of COF vary quite significantly for medium-rise buildings
(Table 4) as
a function of seismic hazard. Indeed, for LA-9P, values ranging
from 1.4 to 1.9
occur between the fourth and sixth floor, while values greater
than 2 can be found
elsewhere. In BO-9P building, COF values smaller than 1
characterise all beam-to-
column joints from the third to seventh floor. Values equal to
unity (eighth floor)
or greater can be found in the remaining floors. An intermediate
situation can be
observed for SE-9P, exhibiting COF between 1.4 and 1.6 (first
and third floor) or
1.7 and 2.1 (fourth and seventh floor); values greater than 2
are located at the
eighth floor. Thus, for LA-9P a SCWB behaviour is expected,
while for BO-9P a
weak column strong beam (WCSB) behaviour at intermediate
storeys, with col-
umn plastic hinges, seems to be unavoidable. Finally, in SE-9P,
plastic hinges are
expected mainly in beam members, although some column plastic
deformations are
likely to occur.
4.5. Stability
The design criteria for MRFs are based also on specific checks
for second or-
der effects at each storey and overall stability. P effects can
be approximately
evaluated through the stability index () expressed as
follows:
=Ptot drVtot h
, (7)
where Ptot is the total gravity storey load, Vtot the total
seismic storey design shear,
whilst dr and h are, respectively, the design inter-storey drift
and relative height.
The stability index expressed by Eq. (7) may be assumed
approximately equiv-
alent, for framed structures, to the elastic critical vertical
load ratio [Horne, 1975],
defined as the ratio (P/Pcr) in which P is the total vertical
load and Pcr is the
elastic critical load value for failure in a sway mode.
Therefore, it represents a
measure of the sensitivity to P effects. In International
Standards [UBC, 1994;
1997; EC8, 1998], it is required that the ratio should not to
exceed 0.10 in order
to neglect P effects. On the other hand, if 0.10 < 0.30, then
P effects
should be accounted for; the upper bound for is, however,
assumed equal to 0.30.
The -value was computed for all floors in low- and medium-rise
frames, under
seismic actions. The maximum values, along with the storey level
where they are
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Seismic Behaviour of Perimeter and Spatial Steel Frames 471
Table 5. Stability index (three- and nine-storey perimeter
MRFs).
Method A Wind
Frame Minimum Maximum Minimum Maximum
LA-3P 0.017 (3) 0.026 (2) 0.021 (3) 0.026 (2)
SE-3P 0.029 (3) 0.043 (2) 0.038 (3) 0.044 (2)
BO-P 0.049 (3) 0.039 (2) 0.064 (3) 0.080 (2)
LA-9P 0.022 (9) 0.065 (1) 0.046 (7) 0.065 (1)
SE-9P 0.030 (9) 0.096 (1) 0.057 (9) 0.097 (2)
BO-9P 0.049 (9) 0.154 (1) 0.069 (7) 0.146 (1)
Keys: Bracketed values show the floors.
found, were also evaluated (Table 5). The values corresponding
to wind effects were
included for comparative purposes.
For low-rise MRFs, the stability check is greatest at the second
floor, indepen-
dently of seismic region. The maximum values for are always
lower than 0.10, with
the highest value for BO-3P frame (max = 0.080), whilst the
greatest safety margin
for stability checks is exhibited by LA-3P (max = 0.026).
Intermediate behaviour
characterises the SE-3P building (max = 0.044).
For nine-storey buildings the variation of stability index
heightwise is more
pronounced than in low-rise frames, with the highest values are
at either the
first or second floor, and a nearly linear reduction from the
base to roof level.
The most critical stability indexes were found for the BO-9P
building (max =
0.154), whilst greater safety margin for stability checks is
exhibited by LA-9P frame
(max = 0.065). An intermediate behaviour characterises the SE-9P
frame (max =
0.097).
As a result, second-order effects can be significant for BO-9P
and, to a lesser
extent, SE-9P. These frames possess the highest values of the
stability index; similar
results were found for BO-9S and SE-9S. However, the latter are
characterised by
lower values than the perimeter frames, thus rendering the onset
of instability
more unlikely.
5. Design of Spatial Frames and Comparison to Perimeter
Frames
Spatial MRF buildings possess the same layout as their perimeter
counterparts,
see for example Fig. 1 (low-rise) and Fig. 2 (medium-rise). For
such structures, it
was assumed that all frames along the North-South direction are
special moment
resisting frames. Braced frames are assumed to resist earthquake
loads in the
orthogonal direction.
Floor masses for spatial MRFs were computed by considering 1/7
floor tributary
area (low-rise) or 1/6 (medium-rise). The total seismic load of
a three-storey
building is Wtot = 29 500 kN; thus for spatial MRF is: WMRF-S =
4214 kN
versus WMRF-P = 14750 kN for the perimeter MRF. For nine-storey
buildings
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472 E. Mele, L. Di Sarno & A. De Luca
it is Wtot = 90 140 kN, thus for spatial MRF is: WMRF-S = 15023
kN versus
WMRF-P = 45 070 kN for the perimeter MRF.
The design of buildings with spatial frames was carried out
according to UBC
seismic provisions [UBC, 1994]. The design target was to match
the stiffness
and strength properties of their perimeter counterparts. Member
cross sections
employed are provided in Table 6.
The results of comparative analyses for the design parameters of
both spatial
and perimeter frames are discussed hereafter.
5.1. Period and design forces
The fundamental periods of low- and medium-rise spatial frames
are provided in
Table 7. The values computed by means of code equations are
equal to perimeter
values because the building height does not change. Similarly,
for the design base
shears, which are based on the spectral ordinates.
Negligible variations of the fundamental period were found for
low-to-moderate
seismic zone (BO and SE). Spatial frames are slightly stiffer
than perimeter frames;
however, variations do not exceed 8%. Similarly, medium-rise
frames show roughly
the same periods for either perimeter or spatial
configurations.
Finally, modal masses relative to the first vibration mode were
computed for the
assessed buildings; such values were then compared. Two points
are worth noting:
(i) all frames possess a modal mass nearly equal to 85% and (ii)
modal masses of
perimeter structures are roughly equal to spatial ones; the
variations are, in fact,
within 3%. As a result, a dynamic response correspondent to a
single degree of
freedom system (SDOF) may be predicted for the set of frames,
either three- or
nine-storeys.
5.2. Lateral stiffness
Table 7 provides maximum values of elastic deformation
parameters (inter-storey
and roof drift ratios) under design loads for low- and
medium-rise spatial structures.
Values relative to low-rise frames are compliant with code
limitations, for either
Method A (d/h 1/300) or Method B (d/h 1/400). This is not the
case for SE-
3S; however, the exceedence is around about 5% and hence is
negligible. By contrast,
the spatial nine-storey frame design gave rise to structures
(LA-9S and BO-9S)
exceeding slightly standardised values, namely 1/400; higher d/h
were found for SE-
9P. Maximum inter-storey drifts are not found at the same floor,
being the second
for BO-9S and fourth for LA-9S. Drift ratios computed for
spatial configurations
replicate the response established for perimeter frames.
5.3. Design stress level and yield strength
Base shears Vy corresponding to first yield, normalised to
seismic weight (W),
i.e. Vy/W , and to seismic base shears (VUBC-A and VUBC-B), are
given in Table 8
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Table 6. Beam and column cross sections (three- and nine-storey
spatial MRFs).
Beams Internal Columns External Columns
Frame Storey LA SE BO LA SE BO LA SE BO
01 W18 71 W14 48 W14 26 W14 120 W14 99 W14 61 W14 120 W14 99 W14
61
Three-Storey 12 W18 65 W14 48 W14 26 W14 120 W14 99 W14 61 W14
120 W14 99 W14 61
23 W18 55 W14 26 W14 22 W14 120 W14 99 W14 61 W14 120 W14 99 W14
61
01 W24 104 W18 71 W18 60 W14 283 W14 211 W14 211 W14 283 W14 211
W14 211
12 W24 117 W18 71 W18 60 W14 283 W14 211 W14 211 W14 283 W14 211
W14 211
23 W24 117 W18 71 W18 60 W14 211 W14 211 W14 211 W14 211 W14 211
W14 211
34 W24 84 W18 71 W18 60 W14 211 W14 211 W14 211 W14 211 W14 211
W14 211
Nine-Storey 45 W24 84 W18 76 W18 55 W14 159 W14 193 W14 193 W14
159 W14 193 W14 193
56 W24 84 W18 76 W18 55 W14 159 W14 193 W14 193 W14 159 W14 193
W14 193
67 W24 84 W18 76 W18 50 W14 120 W14 176 W14 176 W14 120 W14 176
W14 176
78 W24 62 W18 71 W18 50 W14 120 W14 176 W14 176 W14 120 W14 176
W14 176
89 W24 62 W18 71 W18 50 W14 90 W14 159 W14 159 W14 90 W14 159
W14 159
910 W24 62 W18 71 W18 50 W14 90 W14 159 W14 159 W14 90 W14 159
W14 159
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Table 7. Fundamental period, base shear, maximum drift index and
roof drift (three- and nine-storey spatial MRFs).
Method A Method B Wind Loads Dynamic Analysis
T V/W d/h Dtop/H T V/W d/h Dtop/H V/W d/h Dtop/H T Dtop/H
Frame [sec] [%] [%] [%] [sec] [%] [%] [%] [%] [%] [%] [sec]
[%]
LA-3S 7.64 0.30 0.25 0.72 6.24 0.25 0.20 2.36 0.07 0.06 0.99
0.15
SE-3S 0.55 5.73 0.35 0.29 0.77 4.48 0.27 0.23 3.08 0.13 0.11
1.22 0.10
BO-3S 2.87 0.32 0.26 0.77 2.24 0.25 0.21 3.08 0.25 0.20 1.63
0.10
LA-9S 4.04 0.29 0.27 1.79 3.39 0.26 0.24 2.53 0.18 0.14 2.52
0.14
SE-9S 1.38 3.04 0.40 0.33 1.93 2.42 0.27 0.23 3.32 0.39 0.27
3.30 0.10
BO-9S 1.51 0.25 0.21 1.93 1.21 0.21 0.17 3.32 0.49 0.34 3.56
0.10
Table 8. Non-dimensional base shear (three- and nine-storey
spatial MRFs).
VUBC-M.A/W VUBC-M.B/W VWIND/W Vy-triang./W Vy-unif./W
Vy-triang./ Vy-triang./ Vy-unif./
Frame [%] [%] [%] [%] [%] VUBC-M.A VUBC-M.B VWIND
LA-3S 7.64 6.26 2.36 22.94 26.88 3.00 3.68 11.39
SE-3S 5.73 4.48 3.08 22.38 30.23 3.91 5.00 9.81
BO-3S 2.87 2.24 3.08 9.74 11.33 3.39 4.35 3.68
LA-9S 4.04 3.39 2.53 7.32 11.44 1.81 2.16 4.52
SE-9S 3.04 2.42 3.32 10.36 11.08 3.41 4.28 3.34
BO-9S 1.51 1.21 3.32 7.85 8.80 5.20 6.49 2.65
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Seismic Behaviour of Perimeter and Spatial Steel Frames 475
for three- and nine-storey spatial buildings; values due to wind
actions are also
provided.
Slightly higher yield thresholds Vy/W were estimated for LA-3S,
SE-3S and
SE-9S. By contrast, smaller values arise for BO-3S and
LA-9S.
Over-strength factors (Vy/VUBC-A) for the spatial configuration
exceeds
perimeter values; this is not the case for BO-3S and LA-9S. Such
design
values range between 2.68 and 3.90 (low-rise), 1.81 and 5.20
(medium-rise).
However, referring to the over-strength factor Vy/VWIND , where
the design is
governed by wind (SE-9S and BO-9S), the range upper bound is
3.34.
Yield stress level in LA-9S drops off by about 40% with respect
to LA-9P, while
SE-9S gives rise to a Vy/VUBC-A that is nearly 30% higher than
SE-9P.
As a result, it can be argued that the design of spatial MRFs is
governed by
stiffness rather than strength requirements similar to perimeter
configurations (see
Sec. 5.2).
5.4. Column over-strength factor
To check SCWB fulfillment, COF s were computed by means of Eq.
(7); minimum
and maximum values are given in Table 9 for low-to-medium
rise.
Column over-strength factors in spatial frames are greater than
unity, the mini-
mum values being between 1.28 and 2.07 and the maximum varying
between 4.3 and
8.1. The latter occur at beam-to-external-column joints and can
be explained by
the design choice of adopting equal sections for either external
or internal columns.
However, three-storey frames exhibit on average higher COF s: in
SE-3S these
factors are at least 2.07, so that the occurrence of plastic
hinges in beams can be
safely predicted. Moreover, SCWB-type behaviour is likely to
occur in LA-3S and
BO-3S. COF s greater than 2 were computed at all beam-to-column
connections
in the first two storeys. Therefore, it can be stated that
low-storey spatial frames
were designed relying on high COF s in such a way as to
guarantee plastification in
beams; for perimeter frames this response can be predicted only
for LA.
In medium-rise frames, COF s are greater than 2 for BO-9S,
except at the roof
floor (1.38), thus the SCWB design was fulfilled. However, LA-9S
and SE-9S are
Table 9. COF s (three- and nine-storeyspatial MRFs).
Frame Minimum Maximum
LA-3S 1.28 (3) 4.29 (2)
SE-3S 2.07 (3) 5.42 (2)
BO-3S 1.76 (3) 5.87 (2)
LA-9S 1.42 (1) 6.16 (8)
SE-9S 1.25 (9) 5.50 (7)
BO-9S 1.38 (9) 5.59 (1)
Keys: Bracketed values show the floors.
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February 11, 2004 15:47 WSPC/124-JEE 00136
476 E. Mele, L. Di Sarno & A. De Luca
characterised by intermediate floors where column over-strength
drops below 2.
Indeed, LA-9S, between the first and fifth floor, has COF s
slightly lower than
2, with minimum equal to 1.42 (Table 9). SE-9S shows values
ranging between
1.25 (roof level) and 5.50 (seventh floor); average values are,
however, nearly 2.
Maximum values of the column over-strength factor are generally
higher than for
the perimeter due to the design choice of employing similar
column sections, either
for interior or exterior bays.
5.5. Elastic stability
Stability indexes for spatial frames were evaluated through Eq.
(8); the most critical
values and the storey levels at which they occur are given in
Table 10.
For three-storey frames, -values were generally found to be more
critical for
perimeter rather than spatial configurations. Wind loads give
rise to stability in-
dexes as for seismic actions; the criticality is yet to be found
at the second storeys.
For BO-3P (Table 5) the maximum (0.080) is computed under wind
loads; in
BO-3S the same value ( = 0.069) was evaluated for earthquake and
wind.
On the other hand, nine-storey frames exhibit the highest
-values (Table 10)
either at ground (LA-3S) or second storeys (SE-9S and BO-9S);
lower -values char-
acterise spatial configurations. The variation of stability
index throughout the build-
ing height is more pronounced than in low-storey frames: a
nearly linear variation,
from ground floor to roof, is observed.
Similarly to low-rise frames, higher -values characterise
perimeter rather than
spatial frames. Indeed a, stability index equal to 0.154 was
computed for BO-9P
when the seismic force distribution (Method A) is considered. By
contrast, in LA-9S,
the sensitivity to second order effects is negligible under both
environmental actions,
since = 0.065.
The lowest elastic critical multiplier (1/) for medium-rise
building was found
for BO, namely 7.5 (6.5 in BO-9P); whilst a 1/ equal to 16.3
renders the LA
structure safe for stability checks.
Table 10. Stability index (three- and nine-storey spatial
MRFs).
Method A Wind
Frame Minimum Maximum Minimum Maximum
LA-3S 0.015 (3) 0.026 (3) 0.020 (1) 0.025 (2)
SE-3S 0.026 (3) 0.039 (2) 0.027 (1) 0.039 (2)
BO-3S 0.044 (3) 0.069 (2) 0.048 (1) 0.069 (2)
LA-9S 0.018 (9) 0.061 (1) 0.042 (8) 0.061 (1)
SE-9S 0.018 (9) 0.098 (2) 0.034 (9) 0.109 (2)
BO-9S 0.029 (9) 0.134 (2) 0.053 (9) 0.123 (2)
Keys: Bracketed values show the floors.
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February 11, 2004 15:47 WSPC/124-JEE 00136
Seismic Behaviour of Perimeter and Spatial Steel Frames 477
Therefore, the computed figures (Table 5 for perimeter and Table
10 for spa-
tial frames), highlight a large increase of susceptibility to
second order effects for
medium rather than low rise frames, either perimeter or
spatial.
6. Inelastic Static Pushover Analyses
Non linear static push-over analysis is a simplified but
powerful tool [Krawinkler
and Seneviratna, 1998; Mwafy and Elnashai, 2000]. It enables the
assessment of the
structural behaviour in the elastic and inelastic range and
hence the strength and
deformation capacity can be estimated. Therefore, the structural
models described
in Sec. 3.1 were implemented and global load-deformation curves
were obtained for
perimeter and spatial MRFs.
0
1000
2000
3000
4000
5000
0.00 1.00 2.00 3.00 4.00 5.00 6.00
LA-3P LA-3S UBC (MET.A) YLS ULS
VB (kN)
dtop / Htot (%)
1/400
0
10
20
30
40
50
0.00 1.00 2.00 3.00 4.00 5.00 6.00
LA-3P LA-3S UBC (MET.A) YLS ULS
VB / W
tot (%)
dtop / Htot (%)
1/400
0
1000
2000
3000
4000
5000
0.00 1.00 2.00 3.00 4.00 5.00 6.00
SE-3P SE-3S UBC (MET.A) YLS ULS
VB (kN)
dtop / Htot (%)
1/400
0
1000
2000
3000
4000
5000
0.00 1.00 2.00 3.00 4.00 5.00 6.00
LA-3P LA-3S UBC (MET.A) YLS ULS
VB (
kN
)
dtop / Htot (%)
1/4
00
0
10
20
30
40
50
0.00 1.00 2.00 3.00 4.00 5.00 6.00
LA-3P LA-3S UBC (MET.A) YLS ULS
VB /
Wto
t (%
)
dtop / Htot (%)
1/4
00
0
1000
2000
3000
4000
5000
0.00 1.00 2.00 3.00 4.00 5.00 6.00
SE-3P SE-3S UBC (MET.A) YLS ULS
VB (
kN
)
dtop / Htot (%)
1/4
00
0
10
20
30
40
50
0.00 1.00 2.00 3.00 4.00 5.00 6.00
SE-3P SE-3S UBC (MET.A) YLS ULS
VB /
Wto
t (%
)
dtop / Htot (%)
1/4
00
0
1000
2000
3000
4000
5000
0.00 1.00 2.00 3.00 4.00 5.00 6.00
BO-3P BO-3S UBC (MET.A) YLS ULS
VB (
kN
)
dtop / Htot (%)
1/4
00
0
10
20
30
40
50
0.00 1.00 2.00 3.00 4.00 5.00 6.00
BO-3P BO-3S UBC (MET.A) YLS ULS
VB /
Wto
t (%
)
dtop / Htot (%)
1/4
00
Figure 3. - Push-over curves with triangular distribution
(3-story MRFs): single frames (left) and buildings (right).
0
1000
2000
3000
4000
5000
0.00 1.00 2.00 3.00 4.00 5.00 6.00
BO-3P BO-3S UBC (MET.A) YLS ULS
VB (kN)
dtop / Htot (%)
1/400
0
10
20
30
40
50
0.00 1.00 2.00 3.00 4.00 5.00 6.00
BO-3P BO-3S UBC (MET.A) YLS ULS
VB / W
tot (%)
dtop / Htot (%)
1/400
Fig. 3. Push-over curves with triangular distribution
(three-storey MRFs): single frames (left)and buildings (right).
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February 11, 2004 15:47 WSPC/124-JEE 00136
478 E. Mele, L. Di Sarno & A. De Luca
Figures 3 and 4 provide the results of the analyses carried out
on three- and
nine-storey frames, respectively. The results of perimeter and
spatial frames, are
contrasted in the same plot. They are expressed in terms of base
shear divided
by tributary seismic weight, V/W , versus top displacement
normalised to build-
ing height (dtop/Htot). It is deemed useful for comparative
purposes to include in
Figs. 3 and 4, plots with curves employing the dimensional base
shear V as or-
dinates. Similarly, vertical lines corresponding to the code
inter-storey drift limit
[UBC, 1994)], i.e. d/h = 1/400, are also drawn.
In order to assess strength and deformation capacities of MRF
systems, two
limit conditions, namely yield limit state (YLS) and ultimate
limit state (ULS), were
defined and relevant points are indicated on the curve response.
These LS definitions
were chosen consistently with (i) international codes and
recommendations [UBC,
0
2000
4000
6000
8000
0.00 1.00 2.00 3.00 4.00 5.00 6.00
LA-9P LA-9S UBC (MET. A) YLS ULS
dtop / Htot (%)
VB (kN)
1/400
0
10
20
30
40
50
0.00 1.00 2.00 3.00 4.00 5.00 6.00
LA-9P LA-9S UBC (MET. A) YLS ULS
dtop / Htot (%)
VB / W
tot (%) 1/400
0
2000
4000
6000
8000
0.00 1.00 2.00 3.00 4.00 5.00 6.00
SE-9P SE-9S UBC (MET. A) YLS ULS
dtop / Htot (%)
VB (kN)
1/400
0
10
20
30
40
50
0.00 1.00 2.00 3.00 4.00 5.00 6.00
SE-9P SE-9S UBC (MET. A) YLS ULS
dtop / Htot (%)
VB / W
tot (%) 1/400
0
2000
4000
6000
8000
0.00 1.00 2.00 3.00 4.00 5.00 6.00
BO-9P BO-9S UBC (MET. A) YLS ULS
dtop / Htot (%)
VB (kN)
1/400
0
10
20
30
40
50
0.00 1.00 2.00 3.00 4.00 5.00 6.00
BO-9P BO-9S UBC (MET. A) YLS ULS
dtop / Htot (%)
VB / W
tot (%) 1/400
Fig. 4. Push-over curves with triangular distribution
(nine-storey MRFs): single frames (left)and buildings (right).
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February 11, 2004 15:47 WSPC/124-JEE 00136
Seismic Behaviour of Perimeter and Spatial Steel Frames 479
1997; EC8, 1998; FEMA 350, 2000] and (ii) experimental and
numerical studies
available in the inherent literature [Elnashai et al., 1998;
Mwafi and Elnashai, 2000].
Performance criteria used to define the two LSs are briefly
described in the following
paragraph; then a detailed discussion of push-over results is
provided.
6.1. Yield and ultimate limit states definition
YLS corresponds to the state at which inelastic deformations
begin to contribute
to the energy absorption. It can be reliably evaluated by means
of static analyses
and corresponds to the onset of the yield at the member far
ends.
The ULS definition appears more complex and controversial than
YLS, since it
deals with the structure collapse condition, which is always
conventionally defined.
In this paper different structural failure modes, both local and
global, were con-
sidered, and the corresponding performance criteria were
defined. In the following
section, local and global failure sources are described and the
corresponding limit
values of relevant performance parameters are provided.
Local failure modes include either member or connection failure.
In this paper
only connection failure, due to the attainment of plastic
rotation capacity for welded
connections (set equal to SAC target plastic rotation 3%), was
accounted for as a
local failure mode. Moreover, base column rotations were also
considered to detect
the LSs.
The global failure modes were defined either at the attainment
of a collapse
mechanism formation or when a specific threshold value of
inter-storey drift,
stability index, lateral resistance reduction, were
attained.
The inter-storey drift ratio (IDR) is an adequate structural
parameter to assess
the MRF performance. Indeed, it can be checked easily by field
evidence in the
aftermath of earthquakes as well as in experimental tests. So
far, several researchers
[Leelataviwat et al., 1999, Maison and Bonowitz, 1999] have
proposed different IDR
values, as a function of the probability of exceedance and the
acceptable damage.
In this paper the IDR value of 4% [FEMA 350, 2000] was assumed
as a rational
and reliable limit for structural integrity.
The overall stability under seismic loading implies that the
structural system
may preserve its vertical load-bearing capacity at the
occurrence of an input ground
motion that provokes both horizontal and vertical vibrations and
hence correspon-
dent inertial forces. Indeed, P effects of each storey of the
structure can be
evaluated by means of the stability index ; in the present study
the limit value of
0.30 was assumed to be the critical threshold for .
The occurrence of both local (i.e. soft storey) and global
mechanisms was also
checked. It is worth pointing out that, while a global mechanism
failure mode can
occur if there is not a concentration of deformation and
strength demand anywhere
in the frame (thus both IDR and -values are less than the limit
values), the local
mechanism is likely to be associated with the achievement of the
ULSs specified
above, e.g. inter-storey drift and storey stability index.
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February 11, 2004 15:47 WSPC/124-JEE 00136
480 E. Mele, L. Di Sarno & A. De Luca
Finally, a strength degradation criterion, corresponding to a
drop of 10% in
the frame lateral resistance, was also considered. It is well
known that a global
force-displacement response characterised by a final negative
slope occurs when
P effects significantly affect the structural behaviour. Despite
the decrease in
the lateral resistance which does not imply failure in itself,
the response tends to
be unstable and unreliable, thus the above limit criterion was
assumed and checked
for the MRFs.
6.2. Analysis results
Pushover curves provided in Figs. 3 and 4 for low- and
medium-rise frames respec-
tively, confirm that frame designs were governed primarily by
stiffness requirements.
Indeed, UBC inter-storey drift limit, e.g. 1/400, intercepts the
curves at base shears
equal or greater than design values (VUBC). Furthermore,
pushover curves provide
information on structural over-strengths, deformation capacity
and importance of
P effects.
Values of design, yield and ultimate base shear (respectively
VUBC, Vy , Vu) are
depicted on the curves by means of triangular, square, and
circular markers, respec-
tively; the same shear values, normalised to the tributary
seismic weight, W , are
reported in Table 11 for perimeter and spatial frames, together
with the coefficients:
y (design over-strength, equal to the ratio Vy/VUBC), u (global
over-strength,
equal to the ratio Vu/VUBC), and u/y (system over-strength).
The ultimate strength, Vu, is the value of base shear
corresponding to the struc-
tural collapse, which has been conventionally defined as the
minimum of a set of
ULSs, as presented earlier.
For all MRF buildings, particularly the spatial ones, a
significant over-strength
above the design base shear VUBC (allowable stress design level)
can be observed.
In particular, a global over-strength u, ranging between 3.55
(LA-3P) and 5.81
(SE-3S) for three-storey buildings and between 3.13 (SE-9P) 7.59
(BO-9S) for
nine-storey buildings can be derived from the curves.
Global over-strength, given by the u coefficient, arises from
different sources
which can be quantified through the coefficients y and u/y. The
contribution
quantified by the y multiplier, which has been appointed as
design over-strength,
is partially related to the ratio of yield to allowable stress
(about 1.5) and partially
related to the fulfilment of drift limitations as well as to
SCWB requirements.
Furthermore, stress redistribution within member cross sections,
which can be
related to section shape factor (plastic-to-elastic modulus
ratio, approximately 1.15
for wide flange sections) is also to be considered. For
over-strength contribution
quantified by u/y, appointed as system over-strength,
redistribution of internal
forces among the structural system members is the primary
source.
By comparing the push-over curve response and the values
provided in Table 11,
it may be concluded that global and system over-strengths,
namely u and u/y,
for spatial frames are higher than for their perimeter
counterparts.
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Table 11. Results from push-over curves (Triangular
Distribution).
Perimeter Spatial
Frame du/dy Vy/VUBC Vu/Vy Vu/VUBC ULS du/dy Vy/VUBC Vu/Vy
Vu/VUBC ULS
LA-3 4.71 2.63 1.35 3.55 Mech. (g) 4.48 3.00 1.97 5.27 Mech.
(g)SE-3 2.64 3.24 1.24 4.03 Mech. (g) 2.86 3.91 1.49 5.81 3%
(b)BO-3 2.76 3.79 1.26 4.77 3% (c) 3.21 3.39 1.64 5.60 3% (b)
LA-9 4.10 2.52 1.40 3.54 3% (b) 3.77 1.81 2.12 3.84 3% (b)SE-9
3.53 2.65 1.18 3.13 3% (b) 2.55 3.41 1.27 4.37 3% (b)BO-9 1.52 4.99
1.07 5.30 4% (1) 2.73 5.20 1.47 7.59 3% (b)
Keys: 3% = TPR; 4% = IDR; (b) = beam; (c) = column; g = global;
(1) = first storey.
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482 E. Mele, L. Di Sarno & A. De Luca
It is also interesting to note that, although the two
alternative configurations
exhibit nearly similar yield strength, i.e. similar design
over-strength y, perime-
ter frame curves possess a sharp transition between elastic
branch and the sub-
sequent yield plateau. By contrast, such a transition is quite
smooth for spatial
configurations. As was observed in recent studies [Gupta and
Krawinkler, 2000a],
such a sharp transition is a consequence of the low relative
importance of gravity
moments in the beams of perimeter frames (high ratio of seismic
to gravity loads). It
is worth mentioning that the smoother the transition, the higher
is the probability
of high local ductility demands.
The deformation parameters identified on pushover curves are
roof drift val-
ues at the onset of yield (dy) and at ULS (du), respectively.
Both perimeter and
spatial frames are characterised by a similar translation
ductility (du/dy), with val-
ues ranging between 2.64 (SE-3P) and 4.71 (LA-3P) for low-rise
frames, and 1.52
(BO-9P) and 4.10 (LA-9P) for medium rise frames. Furthermore,
the storey drifts
experienced by nine-storey perimeter and spatial frames at
similar values of dtopcan be explained on the basis of their
different deformed shapes estimated at dyand du, respectively.
For spatial frames, the fulfilment of SCWB requirement was a
specific design
target which led to a limitation of negative stiffness branch in
the push over curves
(reduced P sensitivity). Indeed, the comparison between
perimeter and spatial
BO frames, show that the latter reaches higher ultimate
displacements than the
former, without showing significant strength loss. This result
relates to low- and
medium-rise frames; nevertheless, it is critical in medium-rise
frames (Fig. 4).
A further comparison of inelastic static performance for
perimeter and spatial
frames may be derived by considering the governing ULSs, as
listed respectively in
the sixth and eleventh columns of Table 11. Such ULSs are the
onset of 3% plastic
rotations in beams and global mechanisms for perimeter and
spatial typologies;
BO-3P exhibits 3% rotation in the columns, whilst BO-9P is
characterised by a
high IDR.
It is instructive to correlate the values of the elastic
critical multiplier for vertical
loads to the slope of the descending branch of push-over curves
(Figs. 3 and 4).
As already observed, low-rise perimeter and spatial structures
(three-storey) do
not suffer any instability problem since the critical multiplier
of vertical loads is
consistently greater than 10. By contrast, some differences
arise for the medium rise
frames (nine-storey). LA-9P and LA-9S possess nearly the same
critical multiplier
(15.5 versus 16.5, respectively), thus negligible P effects are
expected in both
cases. For BO-9S a significant improvement in the P resistance
with respect to
the perimeter frame can be observed. Indeed, a comparison
between the slope of the
softening branch of the perimeter and spatial curves shows a
significantly reduced
slope for the BO-9S, corresponding to the increase in the
critical multiplier value
from about 6 (perimeter) to about 8 (spatial). This improved
structural response
is also confirmed by inelastic dynamic analyses, as discussed in
the next section.
Although perimeter and spatial configurations behave in a
similar fashion in terms
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Seismic Behaviour of Perimeter and Spatial Steel Frames 483
of global behaviour, e.g. same top displacement, the
inter-storey drifts and plastic
rotation demands in beams and columns are lower for the spatial
than for the
perimeter solution.
7. Inelastic Time History Analysis
The present study was focused on the non-linear global response
and behaviour of
the structure rather than on the detailed performance of any of
its elements. To
this end, emphasis was placed on investigating the beam and
column maximum ro-
tations, storey displacements and storey drift ratios. Inelastic
time history analyses
were performed on the set of three-storey and nine-storey
perimeter and spatial
frames by means of the computer program DRAIN 2DX [Prakash et
al., 1993]. The
aim is to evaluate and compare the seismic demand along the
height for the sample
structures. The analyses were carried out by employing three
acceleration histories
with different characteristics. The latter were derived from
actual records of the El
Centro, Northridge and Kobe earthquakes.
It is worth mentioning that the design seismic loads adopted for
the buildings
at three locations (LA, SE, BO) were quite different, since they
correspond to three
different seismic hazard zones (namely, Z = 0.40 for LA, Z =
0.30 for SE, and
Z = 0.15 for BO). Nevertheless, the same ground motions,
representative of severe
seismic input, were used for the seismic performance evaluation
of the three sets of
buildings. The choice of this approach in the analyses is
related to several reasons,
as specified in the following.
The choice of an accelerogram is a very complex task due to the
uncertainties
involved. At the same site, as a result of the same source, the
ground motions may
be very different in character for different events. The use of
artificial ground mo-
tions, which can be generated with peak ground acceleration
(PGA) matching those
specified for the seismic zone, may be questionable due to the
poor frequency con-
tent of the generated acceleration history when compared to
actual seismic records
[Broderick and Elnashai, 1996]. Furthermore, the use of scaled
natural records,
obtained by either amplifying or reducing the PGA without
changing other char-
acteristics (periods, duration, velocities, etc.) is also
debatable [Bommer and Scott,
2000].
Finally, the analysis of the MRF design process, carried out in
Secs. 4 and
5, has shown that stiffness, SCWB and stability, rather than
strength (i.e. value
of the design base shear), are the governing design issues.
Thus, a satisfactory
performance even under severe earthquakes, can be expected for
MRF buildings
when the above design issues have been addressed, independently
of the seismic
zone. Due to the fundamental period of vibration, i.e. 0.99 sec
to 3.56 sec, a set
of accelerograms with near- and far-field effects were selected
for the nonlinear
dynamic analyses. The latter were, however, conducted by using
the same un-scaled
historical records for all MRF buildings.
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484 E. Mele, L. Di Sarno & A. De Luca
Table 12. Characteristics of ground motions.
Earthquake Date Station Component Duration (sec) PGA (g)
Imperial Valley 18.5.40 El Centro S00E 53.80 0.348
Northridge 17.1.94 Newhall 340N/118W 59.98 0.583
Hyogoken-Nanbu 17.1.95 Kobe EW3 56.40 0.834
7.1. Ground motions
The main properties of the ground motions adopted in the
time-history analyses
are summarised in Table 12. The selected ground motions cover a
wide earthquake
scenario because of their different characteristics in terms of
frequency content
and peak ground accelerations. The classical El Centro record
exhibits a broad
frequency range, whilst the Northridge and Kobe ground motions
are representative
of near-fault effects, especially in their few large pulses with
a short duration.
By superimposing the 5% damping elastic spectra upon the
acceleration spectra
of the considered records (Fig. 5) it may be observed that the
UBC-94 spectrum
(soil type S2, relative to LA) under-estimates the ordinates
derived from Northridge
and Kobe between 0.25 and 0.40 sec. By contrast, the smoothed
spectra is more
conservative in the long period range (specifically for T >
2.0 sec).
7.2. Analysis results
7.2.1. Global drifts
Comparisons between maximum top displacements (adimensionalised
to the total
building height, H) of perimeter and spatial frames computed via
time history
analyses are provided in Fig. 6. Low-storey frames exhibit drift
ratios greater than
1%; in fact, the values range between 1.16% and 3.75%. Perimeter
MRFs are less
flexible than their spatial counterparts; the latter are
characterised by an average
Dtot/H value equal to 2.44% versus 1.83% computed for the
former. The drift ratios
vary as a function of the earthquake, El Centro and Kobe being
respectively the
least and the most demanding. The values of Dtot/H for
medium-rise perimeter
configurations range between 0.95% (LA-9P), and 1.55% (SE-9P).
These values are
much smaller than the three-storey counterparts due to the
longer periods of the
nine-storey frames and the shape of the spectral acceleration
curves of the given
records.
It is interesting to point out that, except for LA, the maximum
nondimensional
top displacements exceeds 1.00%. The highest values for the BO
and SE frames are
induced by Newhall, whilst by Kobe for the LA frame. The drifts
tend to be more
uniform and hence less dependent upon the input earthquake than
the three-storey
frames. The range of variability is relatively narrow (1% to
1.5%).
The spatial configuration is characterised by roof displacements
similar to
perimeter frames; by comparing the average values the difference
is around 5%. The
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0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 1.0 2.0 3.0 4.0 5.0
ElCentro Kobe New ha ll UBC (Z= 0.40)
T(sec)
S
a
(
g
)
0.0
0.5
1.0
1.5
2.0
0.0 1.0 2.0 3.0 4.0 5.0
ElCentro Kobe New hall UBC (Z=0.40)
T(sec)
S
V
(
m
/
s
e
c
)
Fig. 5. Acceleration (left) and velocity (right) spectra.
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486
E.M
ele,L.D
iSarn
o&
A.D
eLuca
0.00
1.00
2.00
3.00
4.00
5.00
6.00
LA -3P LA -3S SE-3P SE-3S BO-3P BO-3S
ElCentro
Newhall
Kobe
Three- Storey
D
t
o
p
/
H
t
o
t
(
%
)
! ! ! !
! ! ! !
! ! ! !
" " " "
" " " "
" " " "
# # # #
# # # #
# # # #
$ $ $ $
$ $ $ $
$ $ $ $
% % % %
% % % %
% % % %
& & & &
& & & &
& & & &
& & & &
0.00
1.00
2.00
3.00
4.00
5.00
6.00
LA -9P LA -9S SE-9P SE-9S BO-9P BO-9S
' ' ' '
ElCentro
( ( (
Newhall
) ) )
Kobe
Nine-Storey
D
t
o
p
/
H
t
o
t
(
%
)
Fig. 6. Roof drifts for perimeter and spatial MRFs: three-storey
(left) and nine-storey (right).
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February 11, 2004 15:47 WSPC/124-JEE 00136
Seismic Behaviour of Perimeter and Spatial Steel Frames 487
minimum and maximum values are 0.84% (LA-9S) and 1.52% (SE-9S),
which are
comparable with the narrow range, e.g. 1% to 1.5%, evaluated
earlier for perimeter
frames.
7.2.2. Inter-storey drifts
A comparison of inter-storey displacements is provided in
bar-chart format in Fig. 7.
Inter-storey drift is adimensionalised with regard to
inter-storey height (d/h).
The results show that the maximum drifts are generally lower
than the thresh-
old value of 4%, corresponding to an inter-storey drift capacity
(IDC) for MRFs
classified as special [FEMA 350, 2000]. Values beyond 4% occur
for the Kobe earth-
quake, which frequently gives rise to high values of inelastic
deformation demand.
The major issues mentioned earlier for top displacements are
confirmed from the
drift results. However, a critical assessment of inter-storey
drift values can pro-
vide further information on the localisation of the plastic
demand throughout the
structural system.
Medium-rise spatial frames exhibit d/h values (Fig. 7) on
average lower than
the perimeter ones. The results for the LA frame do not follow
the same trend. The
inter-storey drifts computed for spatial configurations are
always lower than for the
perimeter (except for LA). The scatter is lower for the spatial
frames (1.40% and
3.50% are the minimum and maximum values of d/h) than for
perimeter frames
(1.36% and 4.66% are the correspondent minimum and maximum
d/h).
It is remarkable to highlight that in high (LA) and medium (SE)
seismic areas,
the demand tends to be uniformly distributed, whilst a large
variation characterises
the response of BO frames (low seismicity). The latter is due to
the assumptions
adopted in the design. In the case of BO perimeter frames the
SCWB require-
ments are not fulfilled, but they are fulfilled for the spatial
configuration. Thus,
different plastic rotation demands are expected for such
alternative configurations.
The envelope of the distribution of the plastic rotations along
the height of BO-9P
shows that a concentration of plastic demand affects the first
floor, thus leading to
a soft storey mechanism. Similar envelopes, for the other
frames, demonstrate that
no soft mechanisms occur and the maximum plastic excursions
affect the upper
storeys, without any detrimental effect on the global hysteretic
dissipation.
The maximum inter-storey drifts for low-rise buildings are
provided in Fig. 7.
By comparing the results, it may be observed that spatial frames
exhibit higher
values of inter-storey drift (minimum d/h = 1.62% and maximum
d/h = 5.06%);
the highest values, greater than 4.5%, occurs for the Kobe
record. For the perimeter
frames a reduced variation of drift values is found. LA-3P
experiences d/h = 1.70%
for the El Centro record, whilst the maximum value is 3.83% and
is due to BO-3P
(Kobe ground motion).
7.2.3. Plastic rotations
Maximum plastic rotations for both perimeter and spatial
typologies and low-to-
medium rise buildings are provided below with regard to the
beams (Fig. 8) and
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< < < > > >
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M M M
M M M
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N N N N
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LA -9P LA -9S SE-9P SE-9S BO-9P BO-9S
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R R R R
Newhall
S S S
Kobe
IDCNine-Storey
d
i
n
t
/
h
i
n
t
(
%
)
Fig. 7. Inter-storey drifts for perimeter and spatial MRFs:
three-storey (left) and nine-storey (right).
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T T T T
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LA -3P LA -3S SE-3P SE-3S BO-3P BO-3S
f f f
ElCentro
g g g g
Newhall
h h h
Kobe
m
a
x
(
r
a
d
)
TPRThree-Storey
i i i i
i i i i
i i i i
j j j j
j j j j
j j j j
j j j j
j j j j
k k k k
k k k k
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l l l l
l l l l
l l l l
l l l l
m m m m
m m m m
m m m m
n n n n
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o o o o
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o o o o
p p p p
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r r r r
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s s s s
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t t t t
t t t t
t t t t
u u u u
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u u u u
u u u u
v v v v
v v v v
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x x x
x x x
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x x x
x x x
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z z z z
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0.00
0.01
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LA -9P LA -9S SE-9P SE-9S BO-9P BO-9S
{ { {
ElCentro
| | |
Newhall
} } }
Kobe
TPR
Nine-Storey
m
a
x
(
r
a
d
)
Fig. 8. Beam plastic rotations for perimeter and spatial MRFs:
three-storey (left) and nine-storey (right).
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February 11, 2004 15:47 WSPC/124-JEE 00136
490 E. Mele, L. Di Sarno & A. De Luca
columns (Fig. 9). In all bar charts the threshold of 0.03 rad
(3%), target plastic
rotation (TPR) of beam-to-column connections as defined within
the SAC Steel
Project [FEMA 350, 2000], is drawn.
The end beam rotations for medium rise perimeter frames (Fig. 8)
range from
a lower bound of 1.01% (LA-El Centro) to an upper limit of 3.33%
(BO-Kobe).
Kobe is the most severe earthquake case: for all seismic zones
the beams undergo
plastic rotations greater than 2%. By contrast, the least
demanding record is El
Centro; it gives rise to plastic rotations of 1.07% on BO, 1.01%
for LA and 1.12%
in SE frame. Intermediate values ranging between 1.25% (LA) and
2.22% (SE) are
induced by Newhall ground motion.
A smoothed variation characterises the plastic demands on
nine-storey spatial
frames. The minimum plastic rotation was computed for BO-El
Centro (1.23%)
while the maximum (3.15%) is reached in the LA frame when the
Kobe record is
considered. The two sets of values show that, except for Kobe,
the plastic rotation
demands are lower than the 3% TPR required by SAC. The latter is
a direct
consequence of the SCWB fulfilment, adopted as a specific design
target for spatial
frames.
Maximum plastic rotations in low-rise perimeter and spatial MRFs
are also
provided (Fig. 8). The values of inelastic demands in the beams
of perimeter and
spatial MRFs are quite close and do not generally overcome the
3% limit value.
The Kobe earthquake provokes the largest plasticity in the beams
of BO and SE
frames (respectively 5.13% and 5.50%). These results may be
justified in the light
of the frequency content of Kobe. It is particularly severe in
the neighbourhood of
natural periods of low-rise frames. High values of beam
rotations can be found in
the case of perimeter as well as spatial frames; they were
deliberately designed with
similar fundamental periods.
For the sake of completeness, the maximum plastic rotations in
the column
elements of the nine- and three-storey frames, both perimeter
and spatial, are also
considered. In the case of perimeter configurations (Fig. 9) the
nine-storey Boston
frame is characterised by relevant plastic demands, especially
with regard to the case
of the Newhall record (maximum rotation 3.53%), that corresponds
to the highest
demand for the perimeter configuration. The behaviour of the
column elements
of the LA perimeter frame is almost elastic, since the maximum
value is equal to
0.08%. The comparison with the spatial configurations suggests
that for all but the
LA and SE frames under the Kobe ground motion, the columns are
in the elastic
range.
The values for the column plastic rotations of the three-storey
frames are also
shown in Fig. 9. The scenario outlined is quite different from
the aforementioned,
with regard to the spatial frames where the adopted design
philosophy is slightly
different from that adopted for the nine-storey spatial frames.
While the plastic
rotations required in the columns of the spatial configuration
are lower than in
perimeter layouts, some plastifications in the columns occur.
Nevertheless, since
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Feb
ruary
11,2004
15:4
7W
SP
C/124-J
EE
00136
Seism
icBehavio
ur
ofPerim
ete
rand
Spatia
lStee
lFra
mes
491
~ ~ ~ ~
0.00
0.01
0.02
0.03
0.04
0.05
0.06
LA -3P LA -3S SE-3P SE-3S BO-3P BO-3S
ElCentro
Newhall
Kobe
m
a
x
(
r
a
d
)
TPR
Three-Storey
0.00
0.01
0.02
0.03
0.04
0.05
0.06
LA -9P LA -9S SE-9P SE-9S BO-9P BO-9S
ElCentro
Newhall
Kobe
TPR
Nine-Storey
m
a
x
(
r
a
d
)
Fig. 9. Column plastic rotations perimeter and spatial MRFs:
three-storey (left) and nine-storey (right).
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February 11, 2004 15:47 WSPC/124-JEE 00136
492 E. Mele, L. Di Sarno & A. De Luca
the design was based upon the fulfilment of SCWB, the maximum
plastic rotations
take place in the base column ends.
The comparison between inter-storey drifts (Fig. 7) and beam
plastic rotations
(Fig. 8) shows close values for both set of data (low-to-medium
rise and perimeter-
spatial), especially for SCWB frames. It is, therefore,
confirmed, as in previous
studies [Mele et al., 1995], that plastic rotation can be
predicted via the inter-
storey drift index. Inelastic inter-storey drift can be related
to the elastic inter-
storey drift by means of the displacement amplification factor
Cd, thus a reasonable
prediction of plastic rotation demands can be obtained by means
of a simple elastic
analysis.
7.2.4. Hysteretic energy
Inelastic time history analyses also indicate the hysteretic
energy dissipated during
the ground motions. In Fig. 10 the energy time histories for
perimeter and spatial
Fig. 10. Hysteretic energy diagrams: three-storey (left) and
nine-storey (right) MRF buildings.
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February 11, 2004 15:47 WSPC/124-JEE 00136
Seismic Behaviour of Perimeter and Spatial Steel Frames 493
MRF buildings, under the El Centro, Newhall and Kobe seismic
inputs, are pro-
vided. They were computed by considering the energy dissipated
by each MRFs and
accounting for the actual number of frames used to withstand
horizontal forces.
It can be observed that the energy dissipated by the three pairs
(LA, SE and BO)
of buildings configurations (perimeter, spatial) is quite close.
The total dissipated
energy is a function of the building natural period and of the
earthquake ground
motion.
With regard to the ground motion, Newhall represents the worst
case scenario
for the set of assessed buildings: the energy varies in the
range 5000 kNm (BO-
3) and 10 000 kNm (LA-9). Due to the higher values of beam
plastic rotations
(greater than 4%) and inter-storey drifts (around 3%) SE-3 MRFs
dissipate a large
amount of energy; the maximum values are comparable to the LA
counterparts.
These results were also found for medium-rise buildings; in this
case, though, the
influence of higher-mode effects gives rise to more complex
responses. Concerning
the dependence of the hysteretic energy on the building natural
period, it may be
observed that lower energy values can be found for longer period
buildings (e.g.:
BO-9 versus LA-9), as a consequence of a sort of self-isolation
effect. As a result,
the energy dissipated by the three pairs (LA, SE and BO) of
buildings configurations
(perimeter, spatial) is quite close. Therefore, it can be argued
also that in terms of
hysteretic energy, the dynamic response of the perimeter and
spatial MRFs is fairly
similar; thus, their equivalent behaviour is confirmed.