Engineering Structures 207 (2020) 110238
Contents lists available at ScienceDirect
Engineering Structures
journal homepage: www.elsevier.com/locate/engstruct
Role of punching shear reinforcement in the seismic performance of flat slab
frames
T
⁎
Brisid Isufia, , Ildi Cismasiua,b, Rui Marreirosa, António Pinho Ramosa,c, Válter Lúcioa,c
a
NOVA School of Science and Technology, Universidade NOVA de Lisboa, Caparica, Portugal
UNIC Research Center in Structures and Construction of UNL, Caparica, Portugal
c
CERIS, Lisbon, Portugal
b
A R T I C LE I N FO
A B S T R A C T
Keywords:
Punching
Cyclic loading
Flat slab
Flat plate
Seismic loading
Headed studs
Fragility
Performance-based engineering
Horizontal cyclic loading tests of flat slab–column specimens indicate that a considerable enhancement of the
drift capacity can be achieved by introducing punching shear reinforcement. However, seismic design codes
either do not recommend or do not cover buildings in which flat slabs are part of the primary lateral load
resisting system. Nonetheless, flat slabs are popular, even in earthquake-prone areas. The purpose of this paper is
to contribute towards a better understanding of the benefits and limitations of using punching shear reinforcement in the seismic performance of such structures. To this end, nonlinear static analyses and a set of
fragility functions are derived for two reinforced concrete three story frame models. To minimize modelling
uncertainties, the numerical models are calibrated based on two laboratory specimens (one without punching
shear reinforcement and the other with headed studs) tested under reversed horizontal cyclic loading. The
results show that the performance of the frames can be improved by introducing punching shear reinforcement.
However, it is shown that the inherent flexibility of slab–column connections under lateral loading remains a
limiting factor even when punching shear reinforcement is provided.
1. Introduction
Horizontal cyclic loading tests of flat slab specimens have shown
that a significant increase in the drift capacity of slab–column connections can be achieved by introducing punching shear reinforcement
in the slab’s region around the column. Headed studs are among the
most effective and practical solutions and their efficiency has been investigated through several horizontal cyclic loading tests [1–9]. Considerably high drift ratios at failure have been reported in the aforementioned publications (refer to [9] for a summary of results on tests
under uniaxial lateral loading and square columns). In a real building,
however, it is often not possible to attain such high drifts without
failure of other structural elements (for example, columns, shear walls
and nonstructural elements).
Although tests indicate that the drift capacity can be large when
punching shear reinforcement is added, the use of flat slabs as primary
seismic elements in highly seismic areas is currently discouraged due to
insufficient code regulations (for example, Eurocode 8 [10] does not
fully cover such structures). Furthermore, flat slab structures have behaved poorly during some of the past earthquakes (notably the Mexico
City earthquakes of 1985 [11] and 2017 [12]). A better understanding
of the seismic behavior of such structures would therefore contribute to
the risk mitigation of existing buildings and safer design of new ones.
Currently, one of the most comprehensive approaches to study the
seismic performance of structures or groups thereof is to analytically
derive a set of fragility functions that represent the probability of exceeding a Damage State (DS) for a given ground motion Intensity
Measure (IM). However, Silva et al. [13] pointed out that many challenges still exist in the nonlinear numerical modeling of components of
reinforced concrete structures, with the main issue being the interaction
between different failure modes. Flat slab–column connections represent a complicated case in which different failure modes ranging
from pure flexure to pure punching can occur. Often, the failure is a
combination of flexural yielding with punching shear failure. As a
consequence, fragility analyses specific for flat slab buildings are scarce
in the literature (a brief literature review is provided in Section 2).
In this context, this paper aims to quantify the benefits and limitations of punching shear reinforcement in the seismic design of flat slab
structures. To this end, two flat slab specimens tested under constant
gravity loads and reversed horizontal cyclic drifts are used to reliably
⁎
Corresponding author at: Department of Civil Engineering, NOVA School of Science and Technology, Universidade NOVA de Lisboa, Quinta da Torre, Campus
Universitário, 2829-516 Caparica, Portugal.
E-mail address: b.isufi@campus.fct.unl.pt (B. Isufi).
https://doi.org/10.1016/j.engstruct.2020.110238
Received 2 September 2019; Received in revised form 13 January 2020; Accepted 13 January 2020
Available online 28 January 2020
0141-0296/ © 2020 Elsevier Ltd. All rights reserved.
Engineering Structures 207 (2020) 110238
B. Isufi, et al.
was 2.0 m, with the slab in the middle (Fig. 1). The HE120M steel
column was designed to remain elastic throughout the test. The connection between the steel column and the slab was made using rigid
plates with a thickness of 50 mm and a square plan dimension equal to
250 mm. The longitudinal reinforcement ratio of the slab was approximately 1.0%.
The concrete properties determined from tests are summarized in
Table 1 along with the applied gravity load in the critical shear perimeter, Vg. The measured yield stress for steel reinforcement was
541.9 MPa for Φ12 mm bars (top bars), 549.5 MPa for Φ10 mm bars
(bottom bars) and 488.8 MPa for the studs (Φ8 mm).
The test setup is described in detail in [22]. This setup allows
modelling of specimens with both negative and positive bending moment regions, i.e. the specimens represent the region from mid-span to
mid-span in the longitudinal direction. For the transversal direction, the
specimens are limited to points of zero moment under gravity loading,
that is approximately a width equal to 22% of the span on each side of
the column. This feature of the test setup makes it very suitable for the
purposes of this study, because it allows for the direct calibration of the
entire flat slab in the numerical models.
The first step of each test was to apply the full gravity load with the
values given in Table 1. Afterwards, reversed horizontal cyclic displacements were applied at the top end of the column while maintaining the gravity load constant, until failure of the specimen. A brittle
punching shear failure occurred in the third cycle with target drift 1.0%
in specimen C-Ref. The specimen with shear reinforcement, C-SSR5b,
continued to carry the gravity load even after significant flexural
yielding of the top reinforcement, until a 5.5% drift, when a punching
shear failure outside the shear-reinforced zone marked the failure of the
specimen. The horizontal force – displacement relationships for the two
specimens are given in Section 6, along with the numerical results.
calibrate numerical models of two reinforced concrete equivalent
frames with similar geometry, material characteristics and loading but
with different slab–column connection characteristics. In one of the
frame models, no shear reinforcement is used in the flat slab around the
columns. In the other frame model, the connections are reinforced with
headed shear studs in a cruciform layout, leading to a significant enhancement of the ultimate drift capacity. The frames are compared in
the framework of Performance Based Engineering.
2. Fragility analysis of structures containing flat slabs in the
literature
The fragility analysis of a 5-story flat slab building was presented in
Erberik and Elnashai [14]. The authors used simplified two-dimensional models of a regular building for nonlinear static analyses and
dynamic Time History Analyses (THA). The slabs were designed such
that punching failures and progressive collapse would not occur. The
effect of infill walls was taken into account.
Hueste and Bai [15,16] included the possibility for a punching shear
failure in their model of a 5-story reinforced concrete building with flat
slabs, by adding a drift limit for which punching was deemed to occur
based on the model proposed earlier in [17]. The lateral load resisting
system of the building analyzed in [15,16] consisted of moment resisting frames in the perimeter of the building.
Han et al. [18] performed a performance evaluation of two flat slab
frame models with 3 and 7 stories with two levels of imposed loads, for
different seismic hazard levels. The slabs contained no punching shear
reinforcement. Han et al. [18] did not derive fragility functions, but
they conducted pushover and nonlinear dynamic analyses and they
concluded that the performance of the frames deteriorates with the
increase of the ratio between the applied gravity load and the concentric punching shear resistance of the slab–column connections.
Studies on the fragility analysis focused on slab–column connections
as isolated components rather than the entire building were performed
by Aslani and Miranda [19] and Gogus and Wallace [20]. These studies
rely on experimental test results from the literature to propose component fragility functions which represent relationships between the
probabilities associated with each damage limit state and the drift ratio
and gravity shear ratio (GSR, defined as the ratio between the applied
gravity load and concentric punching resistance).
To the best of the authors’ knowledge, no previous study deals with
the fragility analysis of flat slab frames without an accompanying lateral load resisting system, with flat slab–column connections susceptible to punching. The necessity for further research towards numerical
modelling and derivation of fragility functions for structures with flat
slabs was also highlighted in Silva et al. [13], in which a review of the
current challenges and future trends in analytical fragility modelling
was presented.
4. Overview of the frame models
Two two-dimensional equivalent frame models of the prototype
building were modelled and analyzed in the OpenSees [23] platform,
one with flat slabs without shear reinforcement and another using studs
as shear reinforcement. The frame models consist of an array of basic
sub-assembly units such as those tested experimentally (Section 3), as
illustrated in Fig. 2. The models are given names based on the following
convention: number of stories followed by the type of slab–column
connections. The types of slab–column connections are: NoSr for connections calibrated based on specimen C-Ref and SSR for connections
calibrated based on specimen C-SSR5b, resulting in frames 3-NoSr and
3-SSR, respectively.
It is assumed that punching failure can occur in the interior connections, and the connections are modelled with rotational springs as
described in Section 6. It is assumed that punching failures cannot occur
in the exterior connections due to the presence of a continuous support
(a beam) for the slab.
The columns represent a reinforced concrete square 250 × 250
column reinforced with 12Ø12 longitudinal bars. The cross-section dimensions of the columns are the same as the dimensions of the steel
base plate used in the laboratory tests. Modelling of the columns is
discussed in Section 5. Both frames have 5 bays and the same overall
geometry (Fig. 2).
Gravity load is applied in locations distributed along the slab-beam
elements, resulting in a shear force in the slab–column connections
equal to Vg = 215 kN. This is close to the value applied in the experiments (Table 1) and it is kept the same for both frame models to
facilitate comparison. For nonlinear THA (Section 8), it was assumed
that the mass is consistent with the gravity load and it is lumped at the
points of application of the gravity load.
3. Experimental program
Two specimens tested under constant gravity loads and reversed
horizontal cyclic displacements in one direction are used as the basis of
calibration of the structural models for which the fragility curves are
derived in this paper. Fig. 1 shows a general view of a specimen installed in the test setup. For a detailed description of the entire experimental campaign and the results, the reader is referred to [9,21].
Nonetheless, a brief description of the main details relevant to this
paper is given in this Section.
The two specimens were similar in terms of geometry and longitudinal reinforcement. However, one of the specimens (C-Ref) had no
shear reinforcement whereas the other (C-SSR5b) was reinforced with
five rows of twelve 8 mm diameter studs spaced at 70 mm in a cruciform layout near the column. The slab specimens had a thickness equal
to 150 mm and plan dimensions of 4.15 m × 1.85 m. A steel column
was used and the total distance from the pinned base to the pinned top
2
Engineering Structures 207 (2020) 110238
B. Isufi, et al.
Fig. 1. Test setup.
Table 1
Main characteristics of the specimens.
Specimen
fc (MPa)
Ec (GPa)
fct,sp (MPa)
Vg (kN)
Shear reinforcement
C-Ref
C-SSR5b
62.3
57.6
41.4
38.8
4.4
4.1
224.8
213.9
None
Studs, 5 perimeters × 12 studs
5. Modelling of the columns
concrete. With the input parameters as described above, the confined
concrete strain–stress relationship is obtained following the procedure
described in [24], resulting in εcu,c equal to 5.6% for a compressive
stress of 41 MPa and confined compressive concrete strength equal to
75 MPa.
The reinforcement was modelled using a Giuffré-Menegotto-Pinto
model with isotropic strain hardening (named Steel02 in OpenSees).
The yield stress was taken equal to 550 MPa for both longitudinal and
transverse steel.
A fiber modelling approach was adopted for the columns. Two
concrete materials were defined: an unconfined concrete material that
is used for the fibers outside the confined core and a confined concrete
model. For the unconfined concrete model, a Kent-Scott-Park concrete
material model with no tensile strength was used. To minimize the
variables, the unconfined concrete strength was assumed equal to
60 MPa for all the columns (in both frames). This value is close to the
concrete strength used for the slabs in the experimental campaign
(Table 1). Confined concrete was modelled based on the work of [24].
The model for the confined concrete requires the following inputs:
unconfined concrete strength, initial modulus of elasticity of unconfined concrete, the ultimate strain of confined concrete, geometry of
the hoops (diameter, configuration and spacing), steel characteristics of
the hoops and the diameter of the longitudinal bars. For the unconfined
concrete strength, the same value used for the concrete cover (60 MPa)
was used. The modulus of elasticity was calculated in accordance with
Eurocode 2 [25], resulting in a value equal to 37.7 GPa.
For the ultimate strain of confined concrete, εcu,c, the formulation
proposed by [26] was used. The geometry of the assumed confining
steel is shown in Fig. 3, along with the cross section of the columns and
the shape of the stress–strain curves for confined and unconfined
6. Modelling and calibration of the slab–column connections
6.1. Description of the adopted model for the slab–column connections
Nonlinear finite element models with 3D solid elements such as
those described in [27] and [28] have been shown to provide good
estimates of the response of flat slab–column systems under monotonic
loads. However, dynamic analyses of large structural models under
horizontal loading can be extremely time consuming and challenging
for finite element models with solid elements. Alternatively, shell elements can be used to model the behavior of flat slabs. However, modelling of punching shear failure in this case is rather complex and it
involves special formulations. An example of an efficient numerical
nonlinear
fiber elements
II-1
III-3
III-4
II-2
II-3
II-4
I-3
I-4
nonlinear
fiber elements
Lx = 3.84m
I-2
2.00m
I-1
2.00m
Lx /2
nonlinear
fiber elements
full
restraint
III-2
2.00m
rotational springs
III-1
specimen
Lx
Lx
Fig. 2. Model of the equivalent frames.
3
Lx
Lx
Engineering Structures 207 (2020) 110238
B. Isufi, et al.
unconfined concrete
ı
confined concrete
confined concrete
250 mm
250 mm
Ec
fc
unconfined concrete
ε cu,u =0.35%
12Ø12mm bars
ε cu,c
İ
ε c1 =2 f c / E c
Fig. 3. Cross section of the columns and confining reinforcement.
model involving shell elements and nonlinear joint elements is proposed by Setiawan et al. [29]. For the purposes of this paper, however,
simplified approaches using one-dimensional finite elements and nonlinear spring elements are considered, because the experimental results
from Section 3 are directly used to calibrate the numerical models.
The model used herein is partially based on the model proposed by
Kang et al. [30]. However, some simplifications and modifications are
proposed to better fit to the purposes of this study. A nonlinear fiber
element modelling approach is adopted here (Fig. 4) to model the beam
(“slab-beam”) elements instead of the elastic elements and slab plastic
hinges of the original model.
The behavior of the connection spring is shown in Fig. 5. This spring
controls the unbalanced moment transfer from the column to the flat
slab. Since the slab–column connections herein are calibrated based on
experimental tests, simplifications are also made on the nonlinear behavior characteristics of this spring. A linear transition zone is added
between the rigid branch and the perfectly plastic branch in the connection spring (Fig. 5-b) as it was found to produce results that better
match the experimental data. Regarding the loss of unbalanced moment
transfer due to punching shear failure, two representative scenarios are
considered:
drift induced punching is based on the connection rotation, which is
estimated by taking out the contribution of the elastic deformation of
the steel column in the laboratory.
The reinforcement is modelled using a Giuffré-Menegotto-Pinto
model with isotropic strain hardening (named Steel02 in OpenSees). A
concrete material with linear tension softening (named Concrete02 in
OpenSees) is used to model the slab-beams. It was found that neglecting
the tensile strength leads to an initial stiffness that is closer to the experimental results. Therefore, tensile strength was set equal to zero for
the subsequent analyses.
The mechanical properties of the materials determined from tests
were used (refer to Section 3). Assumptions were made for properties
required by the material models that were not directly determined from
tests. For instance, the strain hardening ratio of steel was assumed close
to zero. The modulus of elasticity was taken equal to 200 GPa for reinforcement steel. Unconfined concrete ultimate strain was assumed
equal to 0.35%. Concrete strain at strength fc was taken as described in
Fig. 3 for unconfined concrete.
- Punching shear failure before global yielding (i.e. before reaching
the horizontal plateau in the unbalanced moment - drift relationship). This is the case of specimen C–Ref (Fig. 5-a).
- Punching shear failure at a certain connection rotation (drift-induced punching), after global flexural yielding. This is the case of
specimen C-SSR5b (Fig. 5-b).
The connection spring characteristics were calibrated using the
numerical model illustrated in Fig. 4. This model replicates the
boundary conditions of the test setup. Equal deflections and rotations
are enforced at the opposite slab borders (i.e. at mid-spans) through
constraints. The column is made of two force-based elements with an
elastic HE120M steel cross section with modulus of elasticity equal to
210 GPa. Four integration points are used along each column element.
The slab is modelled by 6 force-based elements with fiber cross section.
The division into six elements was made in order to apply the gravity
load in the correct position (Fig. 4). The cross section was made of five
stacked layers of concrete fibers and two layers of steel representing the
6.2. Calibration of the flat slab–column connections
The rotational spring is modelled using the LimitState [31,32]
uniaxial material in OpenSees [23], which has a trilinear backbone
curve and a hysteretic behavior. The limit state model for the case of
horizontal loading
fibre element (column)
constrained rotation
and deflection
gravity loads
fibre element (slab)
joint region
coinciding points
fibre column
rigid elements
connection spring
fibre slab
fibre element
Fig. 4. Adopted model for the specimens and the flat slab–column connections.
4
Engineering Structures 207 (2020) 110238
B. Isufi, et al.
Fig. 5. Connection spring moment-rotation relationship for specimen: (a) C-Ref, (b) C-SSR5b.
top and bottom reinforcement respectively. Three integration points
were used along each slab element. The rigid elements in the slab–column connection region were modelled using elastic elements with
large axial, shear and bending stiffness.
To fully describe the hysteretic behavior, the pinching factors for
deformation and force (pX and pY) and a factor (β) need to be determined. The latter is used to calculate the unloading stiffness, Kunload,
based on ductility, μ, and the initial loading stiffness, K0. A parametric
study was conducted to estimate the parameters pX, pY and β based on
two criteria: (a) the minimization of the difference between the energy
dissipated during the test and in the numerical model and (b) numerical
stability. The pinching factors were varied from 0.20 to 0.80 in steps of
0.05 while keeping β equal to 0.90, which was found suitable for numerical stability reasons. The minimum absolute difference in dissipated energy between the experiment and the numerical model was
obtained for pinching factors pX = 0.8 (for displacement) and pY = 0.3
(for force).
The comparison of the numerical results with the experiments is
given in Fig. 6. A reasonably good match between the experiment and
the numerical model was achieved.
Fig. 7. Comparison of pushover curves for the two equivalent frame models.
same figure in the primary axis. Using this graphical representation, it is
possible to directly observe the influence of punching failures in the
global response of the frames. For instance, it is noticed from Fig. 8-a
that punching failures (starting from the lowest story) are associated
with a change of the slope of the pushover curve. When punching
failures occurred in the roof level, the base shear could not further
increase significantly. In Fig. 8-b, the influence of slab–column connections in the global response is noticeable, but to a lesser extent. The
maximum base shear force corresponds roughly to the point where the
slab–column connections in the two lower stories reached their yielding
plateau. The changes of slope due to punching failures are subtler to
notice in the pushover curve of this frame. This is related to the fact that
plastic mechanisms are formed in the columns for lower roof displacements, before the occurrence of punching failures.
For both frames the connections in the first story failed first. The
two upper level connections did not fail at all in frame 3-SSR, but failed
soon after the first floor connections in frame 3-NoSr.
To compare the pushover curves of frames 3-NoSr and 3-SSR and to
7. Static pushover analysis
A pushover analysis was performed to assess the global behavior of
the equivalent frame models. A lateral load pattern compatible with the
first mode of vibration of the structure was applied. P-Δ effects were
included. The resulting pushover curves for the two frame models are
given in Fig. 7, where it can be noticed that the initial stiffness of the
two frames is almost the same. However, the frame with no shear reinforcement in the flat slabs (3-NoSR) possesses a considerably lower
base shear capacity. The post peak behavior of the two frames is similar
(with comparable slope of the pushover curves).
The unbalanced moments in one slab–column connection for each
story are plotted in the secondary axis in Fig. 8. The names of the
connections are defined in Fig. 2. Due to the regularity of the frame, the
unbalanced moments in all the connections within the same story were
approximately the same. The global pushover curve is plotted in the
Fig. 6. Comparison of the specimen numerical models with the experimental results for specimen: (a) C-Ref, (b) C-SSR5b.
5
Engineering Structures 207 (2020) 110238
B. Isufi, et al.
Fig. 8. Influence of punching failures in frame: (a) 3-NoSr, (b) 3-SSR.
0.5
Spectral acceleration (g)
0.28g
8. Seismic fragility analysis
0.30g
0.25g
0.4
8.1. Definition of damage states
0.20g
0.15g
0.3
0.2
Three damage states are defined: two global damage states and a
damage state that corresponds to the occurrence of the first punching
shear failure in the model. The occurrence of a punching failure is a
major, potentially unrepairable, event. The flat slab-specific damage
state is therefore introduced to understand the role of punching shear
reinforcement in the seismic behavior of the frames from a performance-based perspective.
The global damage states are based on the current version of EC8
[10], according to which two performance levels are defined for the
design of new buildings: “no-collapse” and “damage limitation”. The
no-collapse requirement is fulfilled if the structure withstands the design seismic action without local or global failures. In the design of
conventional buildings with moment resisting frames, local failures are
normally not a concern when capacity design rules are strictly followed.
In case of the buildings with flat slabs, however, punching failures can
occur, thus violating the no-collapse requirement. The three considered
damage states are:
0.10g
0.05g
0.1
0.0
0.00
3-NoSr
3-SSR
0.02
0.04 0.06 0.08 0.10 0.12
Spectral displacement (m)
0.14
0.16
Fig. 9. Comparison of the capacity curves of the two frame models.
evaluate the performance of each frame, the curves are transformed
into idealized elasto–perfectly plastic curves for an equivalent Single
Degree of Freedom (SDOF) system following the N2 procedure [33], as
recommended in Annex B of EC8 [10]. The formation of the plastic
mechanism is assumed to correspond to the point in the curve with
maximum base shear force. The resulting capacity curves are plotted in
Fig. 9 in Acceleration Displacement Response Spectrum (ADRS) format.
Response spectra for different values of the reference ground acceleration, agR, are shown in Fig. 9. These spectra are constructed in
accordance with EC8 [10], for ground type C and spectrum type 1. The
values of agR that correspond to a complete exhaustion of the capacity
of the structure are 0.25 g and 0.28 g for the frame 3-NoSr and 3-SSR
respectively. These values are not far from each other. Furthermore, the
two capacity curves demonstrate comparable ductility of the two
frames, although one of them had shear reinforcement. There is some
difference between the two frames in the reference ground acceleration
for which the behavior becomes plastic (both are around 0.10 g, but
global yielding is reached for a lower agR in 3-NoSr).
Due to the high flexibility, the frames under consideration are
subjected to lower seismic forces compared to stiffer structures. The
intersection of the constant period line (elastic branch of the capacity
curve and its extension in Fig. 9) with the response spectra occurs in the
constant spectral velocity region of the spectra, i.e. the fundamental
period of the frames is between TC and TD (EC8 [10]). On the other
hand, this means that the displacements of the structure are larger
compared to stiffer structures. This issue is addressed in the following
sections.
- DLS (damage limitation state). This DS corresponds to the damage
limitation requirement of EC8 [10]. It is assumed that the building
has ductile non-structural elements that do not interact significantly
with the main structure. The criterion for DLS is set in terms of interstory drift ratios. A limiting value of 0.75% is considered for the drift
ratio, in accordance with EC8 [10] for the described type of nonstructural elements.
- NCS (no-collapse state). This DS corresponds to the fulfilment of the
no-collapse requirement as defined in EC8. It is assumed that this
state is reached when the maximum base shear of the frame is
reached or when a punching failure occurs anywhere in the frame.
For convenience, it is assumed that the maximum base shear is
reached when the roof displacement exceeds the corresponding
displacement from the pushover curve of Fig. 7 (namely, 156.7 mm
for 3-NoSr and 186.1 mm for frame 3-SSR).
- FPDS (first punching shear failure). This DS is reached when at least
one punching failure occurs in the structure, regardless of whether
any global damage state is reached. This is not to be confused with
NCS described earlier, because FPDS can be reached with NCS or
after it. In other words, when punching shear failures occur after the
attainment of the maximum base shear capacity, NCS is reached
before FPDS. On the contrary, punching shear failures occurring
before the frame has reached its maximum base shear capacity result in the simultaneous attainment of NCS and FPDS.
6
Engineering Structures 207 (2020) 110238
1.2
EC8, 0.2g
1.1
0.9
0.8
0.7
0.5
0.4
0.3
0.1
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Period (s)
(a)
Acceleration (g)
1.2
EC8, 0.1g
1.1
0.9
0.8
0.7
0.5
0.4
0.3
0.1
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Period (s)
Acceleration (g)
Acceleration (g)
B. Isufi, et al.
1.2
EC8, 0.3g
1.1
0.9
0.8
0.7
0.5
0.4
0.3
0.1
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Period (s)
(b)
(c)
Fig. 10. Five percent damped spectra for the horizontal component for the three sets of ground motion records: (a) Set I, agR = 0.10 g. (b). Set II, agR = 0.20 g. (c) Set
III, agR = 0.30 g.
the frames under consideration. For nonlinear dynamic analyses, Rayleigh damping with a damping ratio of 5% at the first two modes of
vibration was considered.
A lognormal cumulative distribution function in the form given in
Eq. (1) was fitted to the results obtained from the analysis by means of
the Maximum Likelihood approach. According to [39], this approach is
appropriate for fitting data from MSA.
8.2. Ground motion selection and scaling
The selection and scaling of ground motion records for nonlinear
dynamic analysis is an important task as it can influence the results
[34]. Direct scaling of ground motion records should be done with
caution. To minimize the scaling factors applied to the accelerograms,
therefore maintaining the accelerograms realistic, the following approach is followed in this paper. Three sets containing 30 unscaled
records each are chosen from the PEER NGA-West2 database [35,36] to
three Eurocode 8 [10] target spectra, based on the mean squared errors.
The chosen target spectra correspond to Ground Type C, Type 1 spectrum and reference ground accelerations 0.10 g, 0.20 g and 0.30 g for
Set I, II and III respectively. The unscaled ground motions in the PEER
NGA database were chosen from all fault types, with magnitudes from
6.5 to 8.5, velocity vs30 from 180 m/s to 360 m/s as recommended in
EC8 for Ground Type C and distance from rupture surface limited from
10 km to 80 km. The unscaled records and the target spectra for each
set are shown in Fig. 10 for the horizontal component and 5% damping.
Basic information for each record is provided in Appendix C of [37].
The mean squared errors of the chosen records in relation to the
target spectrum were less than 0.15 g2 for Set I, less than 0.28 g2 for Set
II and less than 0.57 g2 for Set III. The larger error in Set III is due to the
reduced number of records in the database that match the corresponding target spectrum. For the same reason, some records belong to
both Set II and Set III.
The ground motion records were scaled to spectral acceleration
values for the fundamental period of vibrations of the structure Sa(T1)
in steps of 0.1 g. The scaling scheme consisted in direct scaling of the
accelerograms of Set I to Sa(T1) values from 0.1 g to 0.4 g, of Set II
records from 0.5 g to 0.8 g and of Set III records from 0.9 g to 1.2 g. The
fundamental periods of the two frames were approximately the same.
The fundamental period of vibrations T1 = 0.95 s, that resulted after
the application of the gravity load was used as a reference for scaling.
For comparison, the Eigenvalue was T1,el = 0.52 s for linear elastic
analysis. It is acknowledged that flat slab buildings are generally more
flexible than common moment resisting frame buildings.
P (DS|Sa (T1) = x ) = Φ ⎜⎛
⎝
ln(x / θ) ⎞
⎟
β ⎠
(1)
In Eq. (1), the left-hand side represents the probability of reaching
the damage state DS given the spectral acceleration x. This probability
is shown in the right-hand side of the equation, where Φ is the standard
Normal cumulative distribution function, θ is the median of the fragility
function and β is the dispersion (logarithmic standard deviation) of the
spectral acceleration. Further details are provided in Section 8.4.1.
8.4. Results and discussion
8.4.1. No-collapse state
Fig. 11 shows the maximum roof displacements during the MSA
performed on each frame model. During the nonlinear dynamic analyses, the Set I of ground motion records was scaled into additional
levels of 0.010 g, 0.025 g, 0.050 g, 0.075 g, 0.125 g and 0.150 g for
frame 3–NoSr. Scaling into these additional levels was necessary because it was found that failures occur for considerably low spectral
accelerations in this frame model. Especially for high spectral acceleration values, some of the time history analyses were interrupted before the end of the time history. It was found that this always occurred
after local or global failures that caused dynamic instability. A different
marker is used for these analyses to clarify the fact that although they
cross the threshold for the NCS, the roof displacement value is not valid.
These analysis results are stacked around roof displacement value of
400 mm and some random scatter is added to get a sense of the quantity
of analyses.
In Fig. 11, the threshold roof displacement for the NCS is shown
with a vertical dashed line for each frame model. Counting the analyses
that exceed the threshold and adding the ones in which localized
punching failures occurred, the total number of analyses that exceed
NCS is determined for each spectral acceleration value. Knowing the
total number of analyses for each IM (spectral acceleration), the percentage of analyses that exceed NCS is calculated. In Fig. 12, these
calculated values are represented by markers. The fragility functions
are obtained by fitting lognormal distribution functions to these markers, as described in Section 8.3, resulting in the curves shown in
Fig. 12.
Fig. 12 demonstrates that the performance of the two frames is very
different. It is almost impossible to fulfil the no-collapse requirement in
frame 3-NoSr for spectral acceleration values higher than 0.2 g. On the
other hand, the no-collapse requirement is easily fulfilled in frame 3SSR for similar spectral acceleration values. The ability of the frame 3NoSr to resist seismic actions without local or global failures is very
8.3. Derivation methodology of the fragility functions
For the derivation of fragility functions, the frame models described
in Section 4 were subjected to a Multiple Stripes Analysis (MSA)
[38,39]. This type of analysis consists in multiple nonlinear dynamic
time-history analyses for several IM levels. MSA is similar to Incremental Dynamic Analysis (IDA), but in contrast to IDA, different ground
motion inputs can be used in MSA for different IM levels. Considering
the purpose of this paper (Section 1), only aleatory uncertainties related
to the ground motion were considered. A total of 360 analyses per
frame were run, corresponding to three sets of thirty ground motion
records each scaled in four levels (see Section 8.2). The spectral acceleration at the fundamental period of vibration was chosen as IM.
This choice is often made in the derivation of fragility functions for
first-mode dominated structures [13] and it is deemed appropriate for
7
Engineering Structures 207 (2020) 110238
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
50 100 150 200 250 300 350 400
Roof displacement (mm)
Spectral acceleration Sa(T1) (g)
Spectral acceleration Sa(T1) (g)
B. Isufi, et al.
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
50 100 150 200 250 300 350 400
Roof displacement (mm)
THA completed
THA interrupted after dynamic instability
max. base shear threshold
(a)
(b)
Fig. 11. Results of the MSA - maximum roof displacements for each spectral acceleration level at frame: (a) 3-NoSr and (b) 3-SSR.
Probability of exceeding NCS
1.0
even after punching failures (Fig. 8-a), because the columns had sufficient strength and ductility. Since punching failures are major events
for a structure (potentially leading to progressive collapse), they should
be carefully considered in the structural model and in the post-processing of the results.
0.9
0.8
0.7
0.6
8.4.2. Damage limitation
As mentioned earlier, the DLS is deemed to be reached when the
limiting drift ratio is reached. The technique followed to derive the
fragility functions for DLS was similar to that adopted for NCS, but the
threshold here was the limiting drift ratio. For the two frame models,
the corresponding fragility functions are plotted in Fig. 13.
It is noticed that the fragility curves corresponding to DLS are basically the same for both frame models. The minor differences in the
figure are not of significant importance, because they are caused by the
additional scaling levels of spectral accelerations that were used in
frame 3-NoSr.
Although it was shown that the performance of the two frames was
very different for the ultimate limit state (NCS in Section 8.4.1), Fig. 13
proves that there is no difference towards the fulfillment of the damage
limitation requirement of EC8 [10]. In general, this holds true as long as
the ultimate drift capacity of the slab–column connections is higher
than the limiting drift of the damage limitation state. As it was discussed in Section 3, the ultimate drift of the specimen C-Ref (without
shear reinforcement) was 1.00%, which is higher than the considered
limiting drift of 0.75%.
0.5
0.4
0.3
MSA results, 3-NoSr
NCS curve for 3-NoSr
MSA results, 3-SSR
NCS curve for 3-SSR
0.2
0.1
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Spectral acceleration Sa(T1) (g)
Fig. 12. Fragility functions for NCS.
limited. A major improvement of the performance was achieved by
adding shear reinforcement in the flat slabs around the columns.
The mean value of the lognormal fragility function corresponding to
the NCS curve for 3–SSR is 0.45 g (Table 2). For the target spectrum
shape considered (see Section 8.2), this spectral acceleration value at
period T1 corresponds to a reference ground acceleration of 0.25 g. This
value is only slightly lower than the value determined using the pushover analysis method described in EC8 [10], as shown in Fig. 9. This
indicates that when enough drift capacity is provided for the slab–column connections (for example, through sufficient punching shear
reinforcement), the rather convenient pushover analysis method can be
used to estimate the performance of the structure.
On the other hand, the mean value of the lognormal curve corresponding to 3-NoSr is very far from the prediction of Fig. 9. The reason
for this is that the occurrence of local failures is not clearly visible in the
pushover analysis. The base shear in the frame continued to increase
Probability of exceeding NCS
1.0
Table 2
Lognormal parameters of the fragility functions.
Damage state
DLS
NCS
FPDS
3-NoSr
3-SSR
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
θ
β
θ
β
0.07
0.07
0.07
0.34
0.34
0.34
0.08
0.45
0.69
0.18
0.35
0.45
MSA results, 3-NoSr
DLS curve for 3-NoSr
MSA results, 3-SSR
DLS curve for 3-SSR
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
Spectral acceleration Sa(T1) (g)
Fig. 13. Fragility functions for DLS.
8
Engineering Structures 207 (2020) 110238
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
Probability of exceeding DS
Probability of exceeding DS
B. Isufi, et al.
DLS
NCS
FPDS
0.2
0.4
0.6
0.8
1.0
Spectral acceleration Sa(T1) (g)
1.2
(a)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
DLS
NCS
FPDS
0.2
0.4
0.6
0.8
1.0
Spectral acceleration Sa(T1) (g)
1.2
(b)
Fig. 14. Fragility functions for all damage states considered for frame: (a) 3-NoSr and (b) 3-SSR.
8.4.3. Damage state of the flat slabs
The fragility functions corresponding to the global damage states
are plotted in Fig. 14 along with the flat slab specific damage state,
FPDS. The lognormal parameters describing each fragility function are
summarized in Table 2.
The figure shows that FPDS is reached when NCS is reached in
frame 3-NoSr, whereas it is reached after the NCS in frame 3-SSR. This
demonstrates that the limiting factor in the frame without shear reinforcement was punching shear in slab–column connections. On the
contrary, in the frame with studs, punching failures occurred only after
the structure had reached its maximum resistance (i.e., FPDS was
reached after NCS).
In EC8 [10], damage limitation should be ensured for frequent
earthquakes (with a shorter return period compared to the design
earthquake, and normally, with a lower ground acceleration). In
Fig. 14-a and Table 2 it is noticed that the curves for NCS and DLS
perfectly match for the frame 3-NoSr. This means that the frame is not
properly designed from a performance-based point of view. The
earthquakes that cause exceedance of the DLS also cause exceedance of
NCS. In frame 3-SSR, on the other hand, the two performance levels are
clearly distinguished. This major improvement of the seismic performance was achieved by just introducing shear reinforcement in the flat
slabs.
Under these conditions, it was shown that the capacity of the frame
can be assessed reasonably well through a conventional pushover
analysis.
- It was shown that the ultimate capacity can be substantially improved by introducing punching shear reinforcement if it is designed
such that it enables the flat slab–column connection to exhaust the
full unbalanced moment transfer capacity, as it occurred in specimen C-SSR5b and the corresponding frame model.
- The damage limitation requirement was violated for relatively low
spectral accelerations (median 0.07 g to 0.08 g) for both frames.
This indicates that even with shear reinforcement installed, the
damage in the non-structural elements remains a limiting factor for
the use of flat slab frames without bracing elements in highly
seismic regions.
CRediT authorship contribution statement
Brisid Isufi: Conceptualization, Methodology, Formal analysis,
Investigation, Resources, Data curation, Writing - original draft, Writing
- review & editing, Visualization. Ildi Cismasiu: Conceptualization,
Resources, Writing - review & editing, Supervision. Rui Marreiros:
Conceptualization, Writing - review & editing, Supervision. António
Pinho Ramos: Conceptualization, Writing - review & editing,
Resources, Supervision. Válter Lúcio: Conceptualization, Writing - review & editing, Resources, Supervision.
9. Conclusions
Declaration of Competing Interest
The role of punching shear reinforcement in the enhancement of the
global behavior of two regular three-story flat slab structures towards
seismic actions was investigated through pushover analyses and a set of
fragility functions developed specifically for this purpose. Given the
complexity of punching shear failure under seismic loading, the results
cannot be considered to cover the entire range of scenarios that are
encountered in practice. However, the following conclusions on the role
of punching shear reinforcement in the global seismic behavior of flat
slab frames are derived:
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The first author wishes to acknowledge the support received by an
individual scholarship under the Grant Agreement 2014-0848/001001-Erasmus Mundus Action 2-Partnerships.
- It was shown that punching failures in the frame without shear reinforcement were the governing factor in the global structural behavior. Since a punching failure is a major event for a structure,
possibly unrepairable and with a high risk of being followed by
progressive damage, such failures are considered to violate the nocollapse requirement of EC8 [10]. Punching failures occurred for
very low spectral accelerations (median equal to 0.07 g) in the case
of the frame without punching shear reinforcement.
- In the frame with shear-reinforced flat slabs, yielding of the bending
reinforcement of the slab–column connections was found to be related to the maximum frame base shear. Punching failures occurred
for very large drifts, in the post-peak region of the pushover curve
and their influence was not significant in the capacity of the frame.
References
[1] Dilger W, Cao H. Strength of slab-column interior connections under reversed cyclic
loading. Proc. Fifth Int. Colloq. Concr. Dev. Ctries., Cairo. 1994. p. 595–608.
[2] Robertson IN, Kawai T, Lee J, Enomoto B. Cyclic testing of slab-column connections
with shear reinforcement. ACI Struct J 2002;99:605–13.
[3] Brown SJ. Seismic response of slab column connections. University of Calgary;
2003.
[4] Broms CE. Flat plates in seismic areas: comparison of shear reinforcement systems.
ACI Struct J 2007;104:712–21.
[5] Tan Y, Teng S. Interior slab-rectangular column connections under biaxial lateral
loadings. ACI Spec Publ 2005;SP 232:147–74.
[6] Kang TH-K, Wallace JW. Seismic performance of reinforced concrete slab-column
9
Engineering Structures 207 (2020) 110238
B. Isufi, et al.
slabs under reversed horizontal cyclic loading. Eng Struct 2016;117:204–19.
https://doi.org/10.1016/j.engstruct.2016.03.007.
[23] McKenna F, Scott MH, Fenves GL. Nonlinear finite-element analysis software architecture using object composition. J Comput Civ Eng 2010;24:95–107. https://
doi.org/10.1061/(ASCE)CP.1943-5487.0000002.
[24] Braga F, Gigliotti R, Laterza M. Analytical stress-strain relationship for concrete
confined by steel stirrups and/or FRP jackets. J Struct Eng 2006;132:1402–16.
https://doi.org/10.1061/(ASCE)0733-9445(2006) 132:9(1402).
[25] CEN. EN 1992-1-1. Eurocode 2 — Design of concrete structures. Part 1–1: General
rules and rules for buildings 2004.
[26] Scott BD, Park R, Priestley MJN. Stress-strain behavior of concrete confined by
overlapping hoops at low and high strain rates. ACI J Proc 1982;79:13–27. https://
doi.org/10.14359/10875.
[27] Silva Mamede NF, Pinho Ramos A, Faria DMV. Experimental and parametric 3D
nonlinear finite element analysis on punching of flat slabs with orthogonal reinforcement. Eng Struct 2013;48:442–57. https://doi.org/10.1016/j.engstruct.
2012.09.035.
[28] Genikomsou AS, Polak MA. Finite element analysis of punching shear of concrete
slabs using damaged plasticity model in ABAQUS. Eng Struct 2015;98:38–48.
https://doi.org/10.1016/j.engstruct.2015.04.016.
[29] Setiawan A, Vollum RL, Macorini L, Izzuddin B. Efficient 3-D modelling of punching
shear failure at slab-column connections by means of nonlinear joint elements.
109372 Eng Struct 2019;197. https://doi.org/10.1016/j.engstruct.2019.109372.
[30] Kang TH-K, Wallace JW, Elwood KJ. Nonlinear modeling of flat-plate systems. J
Struct Eng 2009;135:147–58. doi:10.1061/(ASCE)0733-9445(2009)135:2(147).
[31] Elwood K, Moehle JP. PEER Report 2003/01: Shake table tests and analytical studies on the gravity load collapse of reinforced concrete frames; 2003.
[32] Elwood KJ. Modelling failures in existing reinforced concrete columns. Can J Civ
Eng 2004;31:846–59. https://doi.org/10.1139/l04-040.
[33] Fajfar P. A nonlinear analysis method for performance-based seismic design. Earthq
Spectra 2000;16:573–92. https://doi.org/10.1193/1.1586128.
[34] Vamvatsikos D, Cornell CA. Incremental dynamic analysis. Earthq Eng Struct Dyn
2002;31:491–514. https://doi.org/10.1002/eqe.141.
[35] Pacific Earthquake Engineering Research Center. PEER Ground Motion Database n.
d. http://ngawest2.berkeley.edu/ (accessed September 20, 2017).
[36] Ancheta TD, Darragh RB, Stewart JP, Silva W, Chiou B, Wooddell K, et al. PEER
NGA-West2 Database 2013.
[37] Isufi B. Seismic behaviour of flat slabs with punching shear reinforcement (PhD
Thesis). Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa; 2018.
[38] Jalayer F, Cornell CA. Alternative non-linear demand estimation methods for
probability-based seismic assessments. Earthq Eng Struct Dyn 2009;38:951–72.
https://doi.org/10.1002/eqe.876.
[39] Baker JW. Efficient analytical fragility function fitting using dynamic structural
analysis. Earthq Spectra 2015;31:579–99. https://doi.org/10.1193/
021113EQS025M.
connections with thin plate stirrups. ACI Struct J 2008;105:617–25.
[7] Park H-G, Kim Y-N, Song J-G, Kang S-M. Lattice shear reinforcement for slabcolumn connections. ACI Struct J 2007;104:425–37. https://doi.org/10.14359/
18619.
[8] Matzke EM, Lequesne RD, Parra-Montesinos GJ, Shield CK. Behavior of biaxially
loaded slab-column connections with shear studs. ACI Struct J 2015;112:335–46.
https://doi.org/10.14359/51687408.
[9] Isufi B, Pinho Ramos A, Lúcio V. Reversed horizontal cyclic loading tests of flat slab
specimens with studs as shear reinforcement. Struct Concr 2019;20:330–47.
https://doi.org/10.1002/suco.201800128.
[10] CEN. EN 1998-1. Eurocode 8: Design of structures for earthquake resistance - Part 1:
General rules, seismic actions and rules for buildings; 2004.
[11] Butcher G, Hopkins D, Jury R, Massey W, McKay G, McVerry G. The September
1985 Mexico earthquakes: final report of the New Zealand reconnaissance team.
Bull New Zeal Natl Soc Earthq Eng 1988;21:3–96.
[12] Galvis F, Miranda E, Heresi P, Dávalos H, Silos JR. Preliminary statistics of collapsed buildings in Mexico City in the September 19, 2017 Puebla-Morelos
Earthquake 2018:17. http://www.learningfromearthquakes.org/2017-09-19puebla-mexico/images/2017_09_19_Puebla_Mexico/pdfs/Preliminary_Report_
Mexico2017_v7.pdf (accessed October 20, 2018).
[13] Silva V, Akkar S, Baker J, Bazzurro P, Castro JM, Crowley H, et al. Challenges and
future trends in analytical fragility and vulnerability modelling. Earthq Spectra
2019;042418EQS101O. https://doi.org/10.1193/042418EQS101O.
[14] Erberik MA, Elnashai AS. Fragility analysis of flat-slab structures. Eng Struct
2004;26:937–48. https://doi.org/10.1016/j.engstruct.2004.02.012.
[15] Hueste MBD, Bai J-W. Seismic retrofit of a reinforced concrete flat-slab structure:
Part I — seismic performance evaluation. Eng Struct 2007;29:1165–77. https://doi.
org/10.1016/j.engstruct.2006.07.023.
[16] Hueste MBD, Bai J-W. Seismic retrofit of a reinforced concrete flat-slab structure:
Part II — seismic fragility analysis. Eng Struct 2007;29:1178–88. https://doi.org/
10.1016/j.engstruct.2006.07.022.
[17] Hueste MBD, Wight JK. Nonlinear punching shear failure model for interior slabcolumn connections. ASCE J Struct Eng 1999;125:997–1008.
[18] Han SW, Lee CS, Kwon HW. Seismic performance evaluation for gravity-designed
flat plate frames. Mag Concr Res 2013;65:1110–27. https://doi.org/10.1680/macr.
13.00110.
[19] Aslani H, Miranda E. Fragility assessment of slab-column connections in existing
non-ductile reinforced concrete buildings. J Earthq Eng 2005;9:777–804. https://
doi.org/10.1080/13632460509350566.
[20] Gogus A, Wallace JW. Fragility assessment of slab-column connections. Earthq
Spectra 2015;31:159–77. https://doi.org/10.1193/061812EQS220M.
[21] Isufi B, Ramos AP, Lúcio V. Post-earthquake performance of a slab-column connection with punching shear reinforcement. (in Press). J Earthq Eng2020. https://
doi.org/10.1080/13632469.2020.1713924.
[22] Almeida AFO, Inácio MMG, Lúcio VJG, Ramos AP. Punching behaviour of RC flat
10