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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Porto, Portugal, 30 June - 2 July 2014
A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.)
ISSN: 2311-9020; ISBN: 978-972-752-165-4
The assessment of an existing RC framed structure: a case study on a collapsed
building
M. G. Mulas1, R. Pantalena2, C. Smerzini3, D. Coronelli1
DICA, Department of Civil and Environmental Eng., Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano, Italy
2
Consultant Engineer, Corso Lodi 78, 20139 Milano, Italy
3
D’Appolonia S.p.A., Via S. Nazaro 19, 16145, Genova, formerly DICA
email: [email protected], [email protected], [email protected],[email protected]
1
ABSTRACT: The total collapse of a building in L’Aquila, Via D’Annunzio (D’Annunzio Street), located at about 6 km from
the epicenter of the earthquake of April 6 2009, is here analyzed. The reinforced concrete moment-resisting frames were
designed in the 1961 according to the Italian Seismic Code of 1937, and failed with a “pancake-type collapse”, with a very high
death toll of 13 casualties. At the beginning of 2013, the first Author was appointed by the legal authority to investigate the
reasons for the collapse. Studies were partly based on the on-site investigations performed during the summer 2009, including
tests on the concrete properties, analysis of the ground properties and exam of parts of the collapsed structure recovered from the
debris. Due to the lack of a complete set of design blueprints, the dimensions and positions of the columns, as well as the
geometry of the reinforcement, were obtained by an on-site series of measurements during 2013. The range of variation of
natural periods and modal shapes depending on the modeling assumptions have been determined through numerical analyses.
The seismic excitation at the site, determined from the earthquake records and the ground properties coming from down-hole
tests, has been provided in terms of time history and response spectrum. When all the factors affecting the seismic behavior are
taken into account, the collapse of the building can be explained; the collapse mechanism resembles the modal shape of the first
mode. The flaws of the original design, brought to light with this study, can be assumed as typical for the design time and
provide clear indications on the critical points to be checked when assessing an RC frame of the sixties.
KEY WORDS: Dynamic global collapse; Non-ductile resisting frame; Torsional mode; Site analysis.
1
INTRODUCTION
A magnitude Mw6.3 earthquake struck the city of L’Aquila, in
Central Italy, at 3.32 am of April 6 2009. Among the various
cases of failure of reinforced concrete (RC) buildings in the
urban area of L’Aquila, the event caused the total collapse of
a building in Via D’Annunzio (D’Annunzio Street) located at
about 6 km from the epicenter. Death toll was very high with
thirteen people killed and three suffering serious injury. The
building, designed in 1961 according to the Italian Seismic
Code of 1937, was a 5-story (including one underground
floor) RC framed structure having a C-shaped plan. The
structural collapse, of a “pancake type”, involved all the floors
of the buildings, with columns failing at nodes, and was
accompanied by a large rotation motion of the whole building.
The first author was appointed by the legal authority to
investigate the reasons for the collapse. The studies,
performed with the co-authors, were based on the results of
on-site investigations performed in the months following the
collapse, concerning the soil properties and the mechanical
properties of the concrete adopted in construction. A
campaign of measures on the geometry of the small survived
part of the basement structure helped in establishing the
geometry of the building. The on-field tests were supplemented with numerical studies, necessary to characterize the
dynamic behavior of the building and its earthquake response.
The flaws of the original design, that was affected by the
lack of efficient computational tool, reflect in the dynamic
behavior of the building. The first natural mode resembles the
collapse mechanism; the situation is worsened by a design
characterized by a large overstrength in beams, with relatively
slender columns, and by a poor quality of the concrete. All
these factors lead to the explanation of the collapse. The paper
briefly describes both the investigation performed and the
results found, pointing out the critical points to be checked for
structures built according to obsolete codes.
2
2.1
THE STRUCTURE AT STUDY
Geometry
A general view of the building at study is shown in Figure 1.
The building, designed at the beginning of the sixties, was a 5floor building with a basement. The plan of the typical floor is
shown in Figure 2, one of the original drawings of the
buildings. A roof was on the top of the building. The Cshaped building had a symmetry axis approximately parallel
to the street. A small RC core for the elevator was placed
along the symmetry axis. The resisting system was composed
of moment-resisting frames. The horizontal structure of the
floors was realized with precast inverted T-beams interlocked
in situ with rows of bricks; an upper RC slab, cast in situ,
connected the two parts to form a composite slab. Two 6-bay
frames were perpendicular to the symmetry axis, while six 2bay frames were approximately parallel to the symmetry axis
(three on each side), each rotated by a small angle. The
direction of floors, depicted in Figure 2, is coherent with the
geometry of frames. The foundations, still in place, are
composed of inverted beams connecting the columns along
the directions of the main frames; no transverse connections
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
have been found on the site, even though a mention of them
was present in the general relation accompanying the project.
A second jacketing intervention was performed in 2002 on
six columns at the basement level, as shown in Figure 3, to the
aim of fixing a problem of concrete carbonation and light
corrosion of bars. The jacket was placed from the column base
up to the height of approximately 3,10 m for perimeter
columns and 1,80
m for central columns.
PIANTA SEMINTERRATO
32
31
33
30
29
25
24
o
Via D'Annunzi
Since the building collapsed totally during the seismic event
of April 6 2009, the geometry definition was based on the few
original documents still available, a large number of pictures
and several on-site measurements on the remaining of the
basement. The following Table 1 summarizes the typical
dimensions of columns and beams at each level (GF stands for
ground floor).
Table 1. Geometry of columns and beams
L-1 - GF
GF – L+1
L1 – L2
L2 - L3
L3 - L4 (under the roof)
L4 (under the roof) - Roof
Column [cm]
40x50
30x50
30x40
30x40
30x40
30x40
Beam [cm]
40x60
30x55
30x55
30x55
30x55
30x55
Figure 2 - Typical plan: beams, columns and floors.
Three parts of jacketed columns were found among the debris
of the collapsed building, and were recovered in a separate
place. The geometry of the steel reinforcement within the
jacket suggest that the jacketing was performed during the
initial construction works. In fact, both the longitudinal and
the transverse reinforcement are composed of smooth bars,
having the same cross-section of the ones of the columns core.
However, since the building totally collapsed, it was
impossible to ascertain the exact position of the jacketed
columns within the structure, and to establish how many
jacketed columns were present.
246
1
27
19
18
20
17
16
8
Figure 1- General view of the building, street on the right.
26
23
22
34
9
10
11
12
13
2
3
4
5
6
21
14
7
Figure 3 – Basement plan. Geometry and position of columns,
units[cm], from measurements; jacketed columns are circled.
2.2
The structural design
The structural design report of the building was issued on
1961; the reference code adopted by the designer was the
Italian seismic code in force at that time, the RD (“Regio
Decreto”) n. 2105/1937 [1]. The seismic design was
essentially based, in RD 2105, on the following principles.
 Application at each floor centroid of an equivalent static
force equal to 5% of permanent loads plus 1/3 of variable
loads; this force must be applied both in transverse and
longitudinal direction.
 Application of vertical loads equal to the minimum
between 1) 1.25 times the sum of permanent loads plus 1/3
of variable loads, 2) the sum of permanent loads plus
variable loads.
The above criteria were used for designing the 6-bay frame
located in the central part of the building (within the red
dotted box in Figure 3). The loads acting on the frame were
apparently derived according to tributary areas and to criteria
that were typical, at that time, for designing vertical load
carrying systems. The contribution of the mass of columns
and perimeter walls was not taken into account, with an
underestimation of the horizontal forces of about 20%. This
flaw was partially mitigated by the fact that, as found from
measurements on the remaining of the columns on site and on
the parts of structure recovered in a separate place, the
diameter of bars of the longitudinal reinforcement was larger
than the required value (18mm instead of 16mm)
This 6-bay frame was considered as representative of all of
the other frames in the structure, so that the same cross
sections were assumed both for the second 6-bay frames and
for the six 2-bay frames, in spite of the difference in the beam
length and in the load situation. Each frame is designed to
resist only in-plane forces; the longitudinal steel
reinforcement is placed in the cross-sections to resist only inplane actions. The foundation beams are designed according
to the same approach. The design of RC cross-sections
follows the prescription of the Italian Code of 1939 [2].
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Mechanical properties of the structural materials
The allowable stress values used in the calculations were
obtained examining the design documents. On the basis of the
regulations there quoted, it is possible to estimate that the
concrete specified by the designer would correspond to
strength class C16/20 (cylinder strength 16MPa, cubic
strength 20 MPa), according to the classes defined in UNI-EN
13791 [3]. An experimental campaign was carried out based
on 16 concrete cores taken from the column stubs remaining
standing at the basis of the collapsed building, after removing
the ruins and debris. Four bar samples were cut for the
reinforcement.
To establish the strength of the in-situ cast concrete, the
concrete cores were subject to the standard compression
strength test according to UNI-EN 12390-3 [4], including the
measurement of density. Table 1 lists the statistical parameters
of interest herein. The mean cylinder compressive strength
fcm,is value is 14,1 MPa. The coefficient of variation COV,
computed as σ/fcm,is, is equal to 0,39. The characteristic “in
situ” cylinder strength fck,is can be computed [4] as:
fck,is = fcm,is – k2 σ = 13,3 – 1,48 x 5,4 = 6,0 MPa
The results can be explained in terms of a low quality
construction process, concrete mixing casting and curing,
aiming at a concrete quality higher than that obtained in most
cases. This is also indicated by the high scatter of the strength
(COV=0.39) typical of low-strength concrete and deficient
construction practices.
The correlation of strength with density is shown in Figure
5. The concrete density mean value is 2245 Kg/m3. All values
are in the lower part of the range considered for normal
strength concrete (2200-2500 kg/m3), with 31% of the values
out of this range, below 2200 kg/m3. The increase of strength
with density shown in the results (Figure 5) is coherent with a
theoretical model [5], considering the variation of strength
with the compaction of concrete for a given mix-design.
30.0
25.0
strength (MPa)
2.3
(1)
where:
- k2 is a statistical coefficient for the calculation of fck,is, when
the characteristic value is estimated on the basis of a sample
of test results. The value k2= 1,48 is indicated by EN 13791
when the sample is made of at least 15 test results;
- σ is the standard deviation of fc,is.
14.1
5.4
0.39
6.0
5.9
26.7
The histogram of core cylinder strength is depicted in Figure
4. The strength values are quite low; according to the classes
defined in [3] the standard class is C8/10, lower than the class
required in design. The shape of the histogram shows a rather
dispersed distribution of strength, with a peak of probability
density at 15 MPa, close to the mean value of 14.1MPa, a
considerable number of results in the range between 9 and 12
MPa, and scattered values higher than the mean.
number of results / total number
0.2
0.18
0.16
0.14
0.06
0.04
0.02
0
0 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 30
core strength fc (MPa)
Figure 4 - Hystogram of core cylinder strength.
range for normal concrete
0.0
2100.0 2150.0 2200.0 2250.0 2300.0 2350.0 2400.0 2450.0 2500.0
density (Kg/m3)
Figure 5 - Correlation of strength with density.
For these results, the value of R2, equal to 0.459, is
relatively low due to the high scatter in the measured values of
strength related to density. This can be considered the
consequence of a poor construction process with low control
in the mix-design and curing. The coefficient of determination
R2 of the model in Figure 5 was computed according to the
well-known expression:

R 2  1   f ci  f cimod
i

2
2
  f ci  f cm 
(2)
i
where fci = measured values; fcimod = modelled values; fcm =
mean value of measured strength.
Four steel samples were taken from the collapsed part of the
building, three for smooth reinforcement and one deformed
bar. The tension tests for the smooth bars measured mean
yield strength 312 MPa with a rather high scatter (range of
values 281-344 MPa), average elongation at failure 32% (2836%). These values are in good agreement with design values.
3.1
0.1
0.08
10.0
R² = 0.4957
3
0.12
15.0
5.0
Table 1. Properties of concrete from core drilled tests.
Cylinder Compressive Concrete Strenght
Mean value (MPa)
Standard Dev. (MPa)
COV (dimensionless)
Characteristic strength (MPa)
Minimum (MPa)
Maximum (MPa)
20.0
THE SEISMIC EXCITATION AT THE SITE
The earthquake records
The April 6th 2009, MW 6.3, L'Aquila earthquake represents
the third strongest event recorded by strong-motion
instruments in Italy, after the 1980, MW 6.9, Irpinia and the
1976, MW 6.4, Friuli earthquakes, but it is the best
documented from an instrumental viewpoint. As a matter of
fact, during the earthquake, the Italian Strong-Motion
Network (Rete Accelerometrica Nazionale, RAN), operated
by the Italian Department of Civil Protection (DPC), provided
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
an unprecedented dataset of digital strong-motion recordings.
All the records are available on the web portal of the ITalian
ACcelerometric Archive (ITACA: http://itaca.mi.ingv.it). In
particular, the high-quality recordings obtained at three
stations, AQV, AQA and AQG, located along a seismic
transect in the upper Aterno valley, and at two stations, AQK
and AQU, located at L’Aquila downtown, are of particular
interest. The observed Peak Ground Acceleration (PGA)
ranges from about 0.25-0.35g in downtown L'Aquila to 0.400.60g along the Aterno river valley.
Among the available data, the records provided by AQK,
located behind the L’Aquila Bus Station in the immediate
perimeter of the historical center of L’Aquila, and by AQU,
located in an underground vault of the L’Aquila historic
castle, are the most interesting ones for the purpose of this
work. They are, in fact, located at small distances from the
building under investigation, as shown in Figure 6.
Furthermore, only for AQK, the profile of the shear wave
velocity (VS) with depth is available.
To define the geotechnical model to be used in the site
response analyses, reference is made to the site investigations
carried out in the framework of the Microzonation studies
(http://www.protezionecivile.gov.it/jcms/it/microzonazione_a
quilano.wp), i.e., DownHole (DH) and MASW data. The VS
profiles as obtained from both investigations are shown in
Figure 7 along with the one for station AQK. Significant
discrepancies are found between the DH (in red) and MASW
(in green) results. Based on the comparison with empirical
amplification curves, computed from the recordings of
aftershocks collected in the framework of the microzonation
project (not shown herein for brevity), the MASW profile was
regarded as the most representative and, hence, taken as
reference subsoil model for the analyses.
Figure 7. Lhs: geological map of the historical center of
L’Aquila (“macroarea 1”, adapted from [6]). Rhs: VS profile
at AQK (black line) and at the site in Via D’Annunzio.
Figure 6. Location of stations AQK and AQU with respect to
the building under investigation in via D’Annunzio 24-26.
3.2
Evaluation of ground motion at the site
The epicentral area of L’Aquila earthquake corresponds to the
upper and middle Aterno valley, which is characterized by a
complex tectonic evolution reflected by the high variability of
the geologic and geomorphologic patterns.
The building of Via D’Annunzio lies in the southern sector
of the alluvial terrace, some tens of meters thick, on which the
historical center of L’Aquila is built (Figure 7). As described
in [6], this terrace consists of calcareous breccias and conglomerates with limestone clasts in a marly matrix, superimposed
in the southern part to lacustrine sediments, mainly consisting
of silty and sandy layers (referred to as “limi rossi”),
characterized typically by lower shear-wave velocity.
The ground motion at the site in Via D’Annunzio has been
evaluated by performing local site response analyses, based on
the available information on the local geological and
topographic features. The AQK record was considered as the
seismic input in the analyses. It was preferred to the AQU
record, located in the L’Aquila Castle, owing to: (i) the small
distances (about 400 m, see Figure 6) with respect to the
building; (ii) similarity of geological conditions (both the
building and AQK station lie within the zone of “limi rossi” in
L’Aquila downtown).
248
From [7], the procedure to evaluate the earthquake ground
motion at the D’Annunzio site can be summarized as follows:
 the AQK record was deconvolved considering the 1D
stratigraphy available at the ITACA website (black line
in Figure 7);
 to quantify the site amplification effects, the base motion
obtained at the previous step was used as seismic input
for 1D equivalent-linear local response analyses by using
the software EERA
(http://gees.usc.edu/GEES/Software/EERA2000);
 no topography amplification effects were considered due
to the limited slopes in the study area, as confirmed by
2D numerical simulations of SH wave propagation;
 the horizontal, NS and EW, accelerograms obtained at
the ground surface were rotated clockwise by 20.5° to
compute the ground motion along the principal
directions of the building;
 the 5% damped elastic response spectra for both horizontal components, 20.5° N and 110.5° N, were computed
(Figure 8).
The resulting elastic response spectra show that ground
motion along the 20.5°N direction is predominant over a wide
range of vibration periods. This effect is related to the
directionality of earthquake ground motion in the L’Aquila
records along the fault normal direction, which corresponds
approximately to the direction rotated by an angle of about
20° with respect to the North (see e.g. [8]).
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Figure 8. Elastic response spectra, rotated components.
4
THE COLLAPSE DESCRIPTION
Only few pictures witness the conditions of the building after
the collapse. As it appears from Figure 9 and Figure 10, both
showing a view from the hillside of D’Annunzio Street, the
building is totally collapsed, with the failure of all the
columns at all the floors. Some of the elements in the
basement failed too.
Figure 11 - Aerial view of the building, within the red circle,
before the earthquake.
Figure 12 - Aerial view of the building, within the red circle,
after the April 6 2009 earthquake.
Figure 9 - View of the collapsed building, roof well visible.
The situation after the earthquake is depicted in Figure 12,
where both the translation in the direction perpendicular to the
street and the rotation of the plan are well apparent. The
translation towards the right in the picture moves the building
away from the street (also visible in Figure 10). The in-plane
rotation takes place about the lower corner on the left. It is
worth noting that the other buildings around, even though
damaged at different extent, are still standing.
5
Figure 10 - The collapsed building (a rescuers’ picture).
The floors stacked one over the other, with a “pancaketype” of collapse. From Figure 9 it can be seen that the
undamaged roof was found practically at the street level.
Figure 11 shows an aerial view of the building in the
original configuration before the earthquake, with the C-shape
well apparent.
THE NUMERICAL MODEL
A series of finite element numerical models of the structure
were set up using SAP2000 v.14 [9]. These reproduce the
geometry and loads of the building both in the configuration
at the end of the construction, corresponding to the original
design, and at the date of April 6th 2009. The typical
approximations and assumptions for building structures were
adopted. The geometry of beams and columns was determined
on the basis of the comparison of the on site measurements –
extended to the basement only, due to the total collapse of the
building, and to the parts recovered in a separate place - with
all the documents available, namely the design relation,
architectural drawings and floor plans. The geometry of the
floors was not completely specified in the design documents
and there were not drawings of floors, apart from Figure 2.
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Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Only two or three parts of floors were recovered from the
debris. The following assumptions were made for all models:
 The x and y axes of the reference system are orthogonal
and parallel to D’Annunzio Street, with a vertical z axis.
 The beams and columns in the frames have been modeled
with two-node beam elements. Four-node shell elements
were used for the core walls and the RC walls along the
basement perimeter. The stone and masonry perimeter
walls in the basement were not modeled.
 The elements were placed along the centroidal axes of the
members, neglecting small misalignments.
 Fixed ends were placed at the base of the columns and
wall elements, corresponding to the extrados of the
foundations.
 The columns in the 2-bay frames were modeled taking
into account the 8° in-plane rotation of the cross-sections.
 The floors were modeled as loads acting on the beams on
their perimeter, and the balconies as loads on the
corresponding external side beams. This assumption
neglects the in-plane stiffness of the floors. In some models
the rigid diaphragm constraint has been enforced to all
nodes of each floor, to consider the opposite situation of a
very high value of stiffness and resistance to the effects of
horizontal actions.
 The roof configuration was assumed on the basis of the
design drawings and some pictures of the building.
 The foundations have not been modeled.
All of the loads used by the designer have been considered
as stated in the design documents dating back to the time of
the first construction.
 Gravity loads, as well as the horizontal loads, have been
modeled as distributed loads on the beams. The mass of
each floor has thus been modeled locally, coherently with
the assumption for floors listed above.
 For the modal analysis the mass related to the live loads
has been taken as 1/3 of their nominal reference value.
The Young’s modulus for concrete has been determined the
mean concrete strength determined by the cores drilled in situ.
According to the prescriptions of the present Italian Code,
being fcm=14.1 MPa it results Ecm= 24388,7 MPa
5.1
Table 2 - Summary of the different models adopted.
Model
001
002
003
004
005
006
007
008
009
010
011
012
Case studies
It is apparent, from what has been presented in the previous
Sections, that there were many uncertainties on the geometry
of the building and on its boundary conditions. The main
uncertainties concern the in-plane stiffness of floors and the
constraint effect of the ground surrounding the basement.
Furthermore, the mechanical properties of concrete were very
scattered and the extent of cracking at the beginning of
earthquake was not known. For these reasons several
modeling options have been considered:
 Models with or without the rigid diaphragm floor
assumption;
 The ground on the side of the basement walls can either
provide or not provide a constraint to the structure, acting
at this level on the horizontal degree of freedoms directed
perpendicularly to the ground.
 To consider the possible cracking with the seismic
loading of the swarm preceding the main event, the overall
stiffness of the structure can assume different values. The
250
full stiffness (EI) was considered first, and then it was
reduced to 50% and 30% by modifying the Young’s
modulus of concrete;
Table 2 summarizes all the cases taken into consideration.
In addition to these twelve models, a further 3D model was
considered, named Model 000, to simulate as close as possible
the computations carried by the original designer. Coherently,
in this model there are no constraints and no perimeter walls
in the basement. Using the models just described, the
following analyses have been carried out:
1) With the model 000, a static analysis with gravity loads and
horizontal seismic forces, determined using the code
specifications of the time of construction, to verify the
correspondence of the original design to the codes [1] and [2].
The horizontal seismic forces are 5% of the gravity loads,
including dead and permanent loads, and one third of the live
load.
2) With the models from 001 to 012, a modal analysis to
estimate the principal modes and frequencies of the structure
in its original configuration. In this way the range of values
for the first and second modes is determined, depending of
the constraint and stiffness assumptions in the different
models. As it will be shown in the next Section, the natural
modes account for the movement of the building both in the
parallel and orthogonal directions, with respect to via
D’Annunzio.
6
Rigid
diaphragm
X
X
X
X
X
X
Horizontal constraints at
basement level
X
X
X
X
X
X
Stiffness
EI
EI
EI
EI
0.5 EI
0.5 EI
0.5 EI
0.5 EI
0.3 EI
0.3 EI
0.3 EI
0.3 EI
RESULTS OF THE ANALYSIS
From Model 000, the internal actions corresponding to the
seismic design loading have been determined. A few crosssections have been checked with the working stress design
method. The allowable values considered for materials,
according to the design relation and to the 1939 code [2] are,
for flexure and axial load:
Concrete
c=66 kg/cm2
Steel
s=2.000 kg/cm2
The following values were considered for shear:
Concrete:
c=6 kg/cm2 (not reinforced elements)
Concrete:
c=14 kg/cm2 (reinforced elements)
Steel
s=1.400 kg/cm2.
Most of the tension checks were satisfied, when the larger
steel bars actually adopted in construction are considered, if
the concrete would have had the required properties. It must
be noted that while columns have a working stress close to
allowable value, beams show a large overstrength. Of course
the hierarchy of resistance criterion could not be known by the
designer, but, as a result of this overstrength, the building was
prone to a brittle collapse during an earthquake.
The results of the modal analysis of the building, for the
twelve models summarized in Table 2, are listed in Table 3.
rigid diaphragm and horizontal constraints, the first mode has
a torsional component as a main component. Figure 14 and
Figure 15 show, for the first and second mode respectively,
the percentage of the participating mass to the torsional and
translational component. The latter is in the x-direction for the
first mode and in the y-direction for the second mode.
Table 3 - Natural periods of modes 1 and 2, for all the models.
Modal partecipating mass
ratios
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
Torsional Partecipating Mass
60%
38%
51%
33%
48%
43%
39%
41%
52%
38%
51%
33%
48%
43%
39%
41%
52%
38%
51%
33%
48%
43%
39%
20%
41%
52%
40%
1
2
3
4
5
6
7
8
9
10
11
12
0%
Model
Figure 14 - Participating mass associated to the first mode, as
a percentage of the total mass
100%
Transverse Partecipating Mass (y)
Torsional Partecipating Mass
80%
1
2
3
4
6
8
10
62%
11
30%
16%
60%
61%
15%
9
15%
61%
62%
7
30%
16%
60%
61%
5
15%
15%
16%
0%
30%
20%
61%
62%
60%
40%
61%
60%
15%
From the analysis of the results in Table 3 it can be inferred
that the models with the same value of the stiffness EJ present
a limited scatter of the first mode period depending on the
constraint and boundary conditions.
Longitudinal Partecipating Mass (x)
80%
61%
Mode 2 [s]
0.830
0.806
0.734
0.711
1.173
1.140
1.038
1.006
1.515
1.472
1.340
1.299
15%
Mode 1 [s]
0.872
0.855
0.780
0.763
1.233
1.209
1.103
1.079
1.591
1.560
1.424
1.393
Modal partecipating mass
ratios
Model
001
002
003
004
005
006
007
008
009
010
011
012
100%
12
Model
Figure 15 - Participating mass associated to the second mode,
as a percentage of the total mass.
6.1
Figure 13 - Model 005, first and second modal shape.
The modal shapes are similar for all the twelve cases
analyzed; those for the first two modes of Model 005, having
an intermediate value for the structural stiffness, are depicted
in Figure 13. The first mode is always a longitudinal-torsional
coupled mode; the second one is a predominantly transverse
mode, coupled to a torsional component. The latter has a
participating mass that is smaller than the one of the first
mode. In some cases this is so small that cannot be
appreciated by the modal shapes. Longitudinal here refers to
the direction of the 6-bay frame, transverse to that of the
symmetry axis. In all the models, apart from those with the
The structural capacity
During the earthquake a soft-story collapse mechanism
formed at all the stories of the building. To evaluate the
reasons for the collapse, a comparison between the base shear
and the shear capacity is necessary. Since the geometry of
building is not known exactly, the comparison has been
performed only for the first floor, where the geometry of the
columns is well identified and the average values of the
weight of the whole building is sufficiently known. An upper
bound estimate of the seismic shear capacity can be computed
by assuming that the story mechanism developing at the first
floor is governed by the failure of columns in flexure, with
inelastic zones forming at one or both ends, depending on the
shape of the bending moment diagram. The average
experimental values are assumed for the strength of materials
(steel and concrete). The ultimate moment of each column
Mult,i corresponds to the static value of axial force due to dead
load plus 1/3 of the live load, evaluated through influence
areas. The shear capacity has been evaluated separately in
both x and y directions, taking into account that the moment
capacity of each column is different in the two directions. In
fact in each frame the steel reinforcement is placed in the
cross section only to resist in-plane bending moments, and the
frames lack transverse beams to resist out-of-plane actions.
Under the quoted assumptions, the limit values of shear are:
x-direction
Vx,R = 890,2 kN
y-direction
Vy,R = 828,4 kN
251
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014
The inadequacy of the structural configuration can then by
assessed by simple hand computation. In the period range T1 =
0.76-1.59 s for the first mode, the spectral values in Figure 16
are about 0.48g in the most unfavourable direction. In the
April 6th configuration the total weight of the building above
the ground floor was estimated as Wb = 15531.45kN. An estimate of the seismic shear demand at ground floor is obtained
as a product of the mass m = Wb/g by the spectral acceleration:
Vb,d = m∙a = 15531,45 kN/g·0,48 g = 7455,1 kN
(5)
The ratio between the base shear demand and the base shear
capacity provides the q-factor required to resist the actual
seismic actions:
q = Vb,d / Vy,R =7455,1 kN / 828,4 kN ~ 9
(6)
The value obtained is quite higher than the limit allowed by
standard modern Codes
and
too high
for a structure designed
Range
of natural
periods
varyingcodes,
structure
constraints
and stiffness
according obsolete
thus
fully justifying
the collapse.
0.763
1.591
2.00
1.80
1.60
Longitudinal Direction (x)
Se [g]
1.40
Transverse direction (y)
1.20
1.00
0.80
0.60
0.40
0.20
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
T [s]
Figure 16 - Range of natural periods, with reference to the
elastic spectrum in Figure 8.
The question arises whether the values of spectral
acceleration in Figure 16 are compatible with the magnitude
of the static horizontal forces, equal to 5% of gravity loads,
prescribed by the 1937 Code [1] and assumed in a design
process based on a working stress approach. To establish a
meaningful comparison, the latter value must be multiplied by
a safety coefficient to reach the acceleration value consistent
with a limit state design approach. Coherently with the 1939
Italian Code on RC structures [2], this coefficient is assumed
equal to 2.0, the minimum value of the ratio between yielding
and working stress for steel. Thus, the ratio of elastic to design
acceleration is equal to 0.48 / (2 x 0.05) = 4,8. In the modern
seismic design philosophy, this value is representative of the
product of the ductility factor q times an overstrength factor.
The former can be considered to be in the range 2-3, typical of
existing RC framed structures; therefore, the overstrength
factor implicit in the design must be between 1.6 and 2.4. This
value can be assumed as reasonable, also from the observation
that only a very limited number of buildings failed during the
April 6 earthquake, and that all the buildings around the one at
study, some of which even older, survived the earthquake.
7
CONCLUSIONS: THE CAUSES OF THE COLLAPSE
As shown in the previous section, even though at the upper
limit, the ground shaking level of the L’Aquila event of April
6th 2009 was compatible with both the seismic actions
prescribed by the code provisions and a normal seismic design
practice at the time of construction of the building.
252
Therefore the causes of the collapse must be sought in the
design criteria and the construction flaws. The pictures of the
building after the collapse show clearly that the collapse
mechanism resembles the first modal shape, with an xtranslation and a rotation. The torsional effect, arising from
both the C-shape of the plan and the lack of an effective
bidirectional resisting system, has been probably amplified by
an uneven distribution of perimeter walls in the basement
(some of them were weak masonry or stone walls) and by the
presence of jacketed columns, located in unknown positions
during the original construction. Instead, partial jacketing of a
few columns in the basement had practically no effect on the
mode shapes. Furthermore, with a strong beam – weak
column design criterion consistently applied, the hierarchy of
resistance criterion was not enforced in the building, making it
prone to brittle failures at all the stories.
The design for seismic actions based on criteria typical for
vertical forces, as the adoption of influence areas, resulted in a
resisting system of uneven strength and stiffness in the x and y
directions. In this situation, the role of diaphragm played by
the floors was a crucial one, and would have required a
concrete of good quality to resist the in-plane forces. Thus, the
low quality of concrete – with a dispersion of strength values
and the presence of localized defects, as visible in a part of the
structure recovered after the collapse - has further worsened
an already difficult situation, also for the reduction of the
steel-concrete bond, further impairing the available ductility.
As a final remark it must be noted that the torsional modes
appear as a consequence of the geometry of the plan, of the
design assumptions and of the lack of an effective bidirectional resisting system. With a negative feedback, the
presence of the torsional mode has emphasized the effects of
the poor quality of concrete and of the choice of a strong
beam-weak column design. Dynamic behavior and building
capacity are in this case tightly connected and it is almost
impossible to separate the one from the other.
8
DISCLAIMER
The paper content reflects the Authors’ scientific opinions and
does not intend to anticipate any legal opinion or decision.
9
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
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