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Proceedings fib Symposium PRAGUE 2011
ISBN 978-80-87158-29-6 Session 1-2: New Model Code
1
FLOOR HORIZONTAL ACCELERATION DEMAND IN
REINFORCED CONCRETE FRAMES
Fabrizio
Mollaioli
Andrea
Lucchini
Paolo
Bazzurro
Silvia
Bruno
Adriano
De Sortis
Abstract
The response of acceleration-sensitive non-structural components in buildings is directly affected
by the peak absolute floor acceleration that they experience during the ground shaking. The design
of reinforced concrete buildings in highly seismic areas often results in very strong frames that
withstand well the seismic loading but induce extremely high floor accelerations. The consequence
of such strong-frame design philosophy is that contents and many non-structural components,
which make for most of the replacement value of the building, suffer a disproportionately high
amount of damage if not properly restrained.
Purpose of this paper is to study how the peak floor acceleration demand varies along the
height of different reinforced concrete frame buildings. This study will consider 4-, 6- and 8-storey
reinforced concrete frames characterized by different masonry infill walls configurations, subjected
to earthquakes of different intensities. The most meaningful parameters influencing the peak floor
acceleration demand distribution will be discussed. Comparisons with the predictions obtained
using the Eurocode 8 equation will be also described.
Keywords: Floor Acceleration, Infilled Frames, Reinforced Concrete, Strong Ground Motions
1 Introduction
Purpose of this paper is to study how the Peak Floor Acceleration (PFA) demand varies along the
height of different reinforced concrete frame buildings (Fig. 1). In particular, the response of
simple 2-bay 4-storey, 6-storey and 8-storey frames with regular stiffness and mass distribution
fib Symposium PRAGUE 2011 Proceedings
Session 1-2: New Model Code ISBN 978-80-87158-29-6
2
designed according to current (post 2003) Italian seismic codes is investigated. All the selected
case studies are characterized by a base shear seismic coefficient Cy (that is, a ratio of the
maximum base shear to the weight of the building) equal to 0.35. For each building, three different
masonry infill wall configurations (see Fig. 2) are considered: a) no walls (i.e., bare frame), b)
frame with masonry infills at all stories, and c) frame with infills at all stories but the ground level.
In total, 9 different reinforced concrete frames (3 heights x 3 wall configurations) are analyzed.
PFA
PGA
PFA / PGA
PGA
Fig. 1 Definition of the Peak Floor Acceleration (PFA) demand normalized with respect to the Peak Ground
Acceleration (PGA).
Bare frame Infilled frame Pilotis frame
w = 5.0 m
h = 3.2 m
a) b) c)
Fig. 2 Investigated reinforced concrete frame typologies (from Decanini et al. 2004):
a) bare, b) infilled and c) pilotis
The seismic response of the buildings is evaluated using FE models built in OpenSees (McKenna et
al. 2007), with elastic beams and nonlinear column elements (based on a force formulation and
with distributed inelasticity). A system of equivalent diagonal struts is used to model the infill walls
(see Fig. 3, a). Each wall strut element is supposed to carry the load only in compression. The
ultimate lateral strength is selected as the minimum value among the strut capacities associated
with the four possible in-plane failure modes: diagonal tension, diagonal compression, shear failure
at the horizontal wall-to-frame interface, and crushing of the wall corners in contact with the frame.
This model excludes out-of-plane failure modes. The hysteretic behaviour of the strut considers
stiffness degradation, strength deterioration, and loop pinching. Fig. 3 shows the backbone curve
(b) and a typical base shear vs. horizontal displacement cyclic loop (c) of the strut model.
Proceedings fib Symposium PRAGUE 2011
ISBN 978-80-87158-29-6 Session 1-2: New Model Code
3
Hm
Hmfc
Hmf
Hmr
0.02- 0.04 Kmfc
urufcuf u
1
1Kmfc
FCF
-120
-100
-80
-60
-40
-20
0
20
40
60
80
100
120
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
y
H (kN)
u (cm)
a) b) c)
Fig. 3 Infill wall model (from Decanini et al. 2004): a) strut system representing the wall; b) backbone curve
and hysteretic behaviour c) of the force-displacement (that is, base shear H vs. horizontal displacement
u) model adopted for the strut
The PFA demands are computed via nonlinear dynamic analysis by applying to the buildings
a large ensemble of strong ground motions. In particular, 98 records from 41 different earthquakes
representative of both moderate and extreme events are used to evaluate the buildings response in
both the elastic and the nonlinear range. The moment magnitude of the selected ground motions
ranges between 5.0 and 7.6, while the closest distance from the causative fault ranges from 0.7 to
21 km. Several records are near-fault, including both forward and backward directivity regions.
Recording stations are located on C-D NEHRP soil type. Finally peak ground acceleration varies
between 150 and 1200 cm/s2, and peak ground velocity ranges from 10 to 170 cm/s.
In each time-history analysis, in addition to the floor acceleration demands the Maximum
Inter-storey Drift Ratio (MIDR) is also recorded. Such parameter is used to identify the following
three ranges for the nonlinear structural response of the buildings: limited damage (MIDR<1%),
significant (1%<MIDR<2.5%), and severe (MIDR>2.5%). Because in the latter one the damage
level of the non-structural components is not of big interest, the floor accelerations recorded in this
range will be not discussed.
2 PFA demand distribution
In Fig. 4, the PFA demand distributions (normalized with respect to the Peak Ground Accelerations
PGA) recorded in the limited structural damage range of all the studied buildings are shown. In
each plot both the mean PFAs (denoted with a bold line), and the mean + or – one standard
deviation (solid lines) are reported. It can be observed that in all the cases the PFA distribution is
actually a bilinear curve. The maximum peak floor acceleration, in fact, is reached at a floor level
in general lower than the roof. This observation (which will be better discussed in the following) is
actually in contrast with many prediction equations proposed by codes which usually assume
simple linear in-elevation distribution of the PFAs. It is also interesting to observe that the
maximum amplification of the peak floor accelerations with respect to the ground is always lower
than 2.5.
In order to explain the observed bilinear shape of the PFA distribution, it can be noted that
the floor above which the acceleration values remain approximately constant, correspond, in the
studied buildings, to the elevation level where the second mode contribute result higher. In general,
in fact, when the participating mass of the higher modes is not negligible (that is the case of the
studied mid-rise buildings), the response in acceleration (more than the displacement demand) is
significantly affected by their contribute. This is due to the fact that in many cases the acceleration
spectral ordinates of the higher modes are higher than that of the first one. This is clearly shown,
for example, in the plots of Fig. 6 and Fig. 7 which report the spectral accelerations and the
corresponding modal shapes of the first and second mode of the 6-storey infilled frame.
Comparing the responses of the bare, infilled and pilotis buildings, it can be observed that
the floor levels where the accelerations reach the maximum values are not significantly influenced
fib Symposium PRAGUE 2011 Proceedings
Session 1-2: New Model Code ISBN 978-80-87158-29-6
4
by the infill walls configuration. This can be easily explained if it is noted that in the studied cases
the infills do not significantly change the second mode shape. The only differences can be found in
the 4-storey infilled buildings where the maximum accelerations occur at a lower floor level than
the bare frame. With the increase of the number of storeys the influence of the infill walls on the
shape of the PFA distribution decreases. In particular, in all the three 6-storey the floor level above
which the PFA remain approximately constant is the third, while in 8-sorey is the forth.
No such big differences can be observed in the shape of the PFA distributions if the response
in the significant damage range is considered (see the plots reported in Fig. 5). Actually, the PFAs
profiles tend in general to become more linear. This is more evident in some cases, e.g. in the 6-and
8-storey bare frames. Again, this can be explained by the fact that getting deeper into the nonlinear
range, with the elongation of the period values the spectral acceleration ordinates of the higher
modes decrease in general more than that of the first.
1 2 3
1
2
3
4
PFA/PGA
Flo
or
Bare
1 2 3
1
2
3
4
PFA/PGA
Flo
or
Infilled
1 2 3
1
2
3
4
PFA/PGA
Flo
or
Pilotis
1 2 3
2
4
6
PFA/PGA
Flo
or
1 2 3
2
4
6
PFA/PGA
Flo
or
1 2 3
2
4
6
PFA/PGA
Flo
or
1 2 3
2
4
6
8
PFA/PGA
Flo
or
1 2 3
2
4
6
8
PFA/PGA
Flo
or
1 2 3
2
4
6
8
PFA/PGA
Flo
or
Fig. 4 PFA/PGA demand distribution obtained only from the records exciting the buildings in the limited
damage range (MIDR<1%); in each plot both the mean (bold line) and the mean + and – one standard
deviation (solid lines) is reported
Proceedings fib Symposium PRAGUE 2011
ISBN 978-80-87158-29-6 Session 1-2: New Model Code
5
1 2 3
1
2
3
4
PFA/PGA
Flo
or
Bare
1 2 3
1
2
3
4
PFA/PGA
Flo
or
Infilled
1 2 3
1
2
3
4
PFA/PGA
Flo
or
Pilotis
1 2 3
2
4
6
PFA/PGA
Flo
or
1 2 3
2
4
6
PFA/PGA
Flo
or
1 2 3
2
4
6
PFA/PGA
Flo
or
1 2 3
2
4
6
8
PFA/PGA
Flo
or
1 2 3
2
4
6
8
PFA/PGA
Flo
or
1 2 3
2
4
6
8
PFA/PGA
Flo
or
Fig. 5 PFA/PGA demand distribution obtained only from the records exciting the buildings in the significant
damage range (1%<MIDR<2.5%); in each plot both the mean (bold line) and the mean + and – one standard
deviation (solid lines) is reported
0 0.5 1 1.5 20
0.5
1
T [s]
Sa
[g
]
T1
T2
-1 -0.5 0 0.5 10
2
4
6
s
Flo
or
Mode 1
Mode 2
Fig. 6 Mean spectrum of the records exciting the 6-storey
infilled frame in the limited damage range; two point
markers denote the spectral ordinate corresponding to the
first two mode periods of the building
Fig. 7 First two mode shapes of the 6-storey
infilled frame
fib Symposium PRAGUE 2011 Proceedings
Session 1-2: New Model Code ISBN 978-80-87158-29-6
6
In order to compare the PFA distributions obtained in this study with respect to the floor
acceleration demand given by the Eurocode 8 (2004), the following equation prescribed by the
code has to be used:
Sa = α S [3(1+z/H)/(1+(1-Ta/T1)2) -0.5] (1)
where
α is the ratio of the ground acceleration on type-A ground to the acceleration of gravity
S is the soil factor
Ta is the fundamental vibration period of the non-structural element
T1 is the fundamental vibration period of the building
z is the height of the non-structural element
H is the building height
The PFA demand can then be derived from the previous equation as follows:
PFA/PGA = Sa(Ta/T1=0) /(α S) = 1+(3/2)z/H (2)
which represents a simple linear profile for the PFA distribution. It is interesting to note that such
equation is simply based on two important assumptions on the acceleration demands: the maximum
peak floor acceleration is fixed to be equal to 2.5 the PGA, which corresponds to the maximum
amplification value of the elastic response spectrum proposed by the code; the maximum floor
acceleration is reached at the roof of the building, and does not depend on the building properties or
its dynamic behaviour.
3 Conclusions and further investigations
From the observation of the results obtained in the analyses on the investigated buildings the
following main conclusions can be drawn:
• in the mid-rise buildings (and so probably in the high-rise also) the profile of the PFA
distribution tend to be bilinear, rather than simply linear, because of the contribute at the middle
floor levels of the higher modes;
• the floor level above which the PFA remain almost constant in general moves up toward the
roof when the structural damage increases; this can be explained with the reduction of the
higher modes influence produced by the elongation of the periods;
• in order to measure the importance of the higher modes contribute, functional for identifying the
cases where the PFA distribution of the building becomes more bilinear, the participating
masses weighted by the spectral acceleration ordinates can be used;
• the influence of the infill walls decreases as the number of storeys increases.
Based on the obtained findings the following further investigations are already underway by the
authors with the objective of:
• evaluating the correlation between the inter-storey drifts and the peak floor accelerations, in
order to check if an eventual concentration of damage can become a filter for the response at the
high frequencies through the height of the building;
• confirming the obtained results, namely the importance of higher modes effect on the PFAs
distribution, also for other type of buildings: wall or dual systems, buildings designed using
different seismic codes and also for vertical loads only;
• checking the need of changing the linear PFAs distribution proposed by the Eurocode 8 into a
bilinear one with the constant PFA part of the distribution starting at lower floor levels than the
roof. It would be interesting to study the behaviour of mid- or high-rise buildings (for example
with lateral load wall resisting system) with a fundamental period in the acceleration-sensitive
region of the spectrum and with significant contribute of the higher modes, that could produce a
maximum PFA amplification also at the middle floor levels (not only at the roof). It is important
to underline that in this period region the amplification of the PFA with respect to the PGA
reach its maximum, which is identified by the code with a value of 2.5.
Proceedings fib Symposium PRAGUE 2011
ISBN 978-80-87158-29-6 Session 1-2: New Model Code
7
The financial support of the Italian Ministry of the Instruction, University and Research (MIUR) is
gratefully acknowledged.
References
[1] Decanini, L., Mollaioli, F., Mura, A., Saragoni, R.: Seismic Performance of Masonry Infilled
R/C frames. Proc. of 13th WCEE, Paper 165, Vancouver, 2004.
[2] McKenna, F., Fenves, G.L., Scott, M.H.: OpenSees: open system for earthquake engineering
simulation”. http://opensees.berkeley.edu, PEER, University of California, Berkeley, CA,
2007.
[3] ENV 1998-1, Eurocode 8: Design of structures for earthquake resistance - Part 1: General
rules, seismic actions and rules for buildings, 2004.
Prof. Fabrizio Mollaioli, C.Eng. � Sapienza University of Rome
Faculty of Architecture
Department of Structural and
Geotechnical Engineering
Via Gramsci 53
00197 Rome, Italy
� +390 649 919 186
� +390 632 214 49
URL http://w3.disg.uniroma1.it/mollaioli/
Andrea Lucchini, Ph.D. � Sapienza University of Rome
Faculty of Architecture
Department of Structural and
Geotechnical Engineering
Via Gramsci 53
00197 Rome, Italy
� +390 649 919 149
� +390 649 919 192
URL www.disg.uniroma1.it/
Paolo Bazzurro, Ph.D. � Engineering Analysis and Research
AIR Worldwide
San Francisco, CA 94111, USA
� +1 415 912 311 1
Silvia Bruno, Ph.D. � PROGER SpA
Via Gaeta 15
00185 Rome, Italy
� +390 644 877 432
Adriano De Sortis, Ph.D. � Department of Civil Protection
Via Vitorchiano 2-4
00189 Rome, Italy
� +390 668 204 181
