EFFECTS OF THE EFFECTIVE WIDTH OF SLABS ON THE SEISMIC

RESPONSE OF CANTILEVER RC WALLS

T. Isaković1 & A. Janevski2

1 University of Ljubljana, Faculty of Civil and Geodetic Engineering, Ljubljana, Slovenia,

tatjana.isakovic@fgg.uni-lj.si
2 University of Ljubljana, Faculty of Civil and Geodetic Engineering, Ljubljana, Slovenia

Abstract: Reinforced concrete walls are one of the most commonly used and one of the most efficient types
of structural systems resisting seismic load. Usually, they are interconnected by a floor system consisting of
slabs and beams. Sometimes, the beams are omitted, and the walls are linked only by slabs. Such walls are
considered cantilever walls. Typically, it is believed that their connection is relatively weak and that their
resistance mainly depends on their flexural resistance. It is generally supposed that the flexural strength of the
slabs is negligible compared to that of the walls and that slabs connect the walls only as rigid diaphragms. It
is further supposed that the coupling level provided by the slabs is small. Most modern codes accept these
assumptions.
Recent experiments on RC walls sometimes call these assumptions into question. For specific wall
configurations, such as elevator shafts, the coupling level provided only by slabs is not negligible, particularly
when the significant effective slab width can be activated. In such cases, the resisting system can differ from
the cantilever walls. Consequently, the effects of the seismic excitations can be considerably different from
that expected in the design, causing unexpected types of damage (shear damage and failure of walls and
buckling of the flexural reinforcement), which were observed in recent earthquakes.
In the paper, the seismic response of walls which are relatively strongly coupled only by slabs is analysed.
Basic large-scale shake table experiments' findings that were used to identify the main parameters causing
notable coupling are presented. The sensitivity study of the tested specimen illustrates the importance of the
main parameters influencing the coupling level, such as the strength and stiffness of walls and slabs and their
ratios, the effective width of slabs, and the rotations of foundations. It is demonstrated that considerable
coupling can activate the considerable frame action, which makes the structure stiffer, increasing the total
base shear. Moreover, owing to the frame action, a considerable increase of compression axial forces can
occur in single piers simultaneously, causing considerable redistribution of shear forces between piers.
To be able to generalise the observations of the shake-table experiment, a parametric study has been
performed, varying the ratio of the strength and stiffness of slabs and walls. The results of this study confirmed
that considerable coupling of slender walls can be provided only by slabs without RC beams. It has been
demonstrated that in strongly coupled piers, shear forces can be considerably larger than the design shear
forces determined based on the elastic analysis of cantilever walls and that in such walls considerable
redistributions of shear forces can occur due to the considerable frame action.
WCEE2024 Isaković & Janevski

1. Introduction
Reinforced concrete walls are one of the most commonly used and one of the most efficient types of structural
systems resisting seismic load. Usually, they are interconnected by a floor system consisting of slabs and
beams. Sometimes, the beams are omitted, and the walls are linked only by slabs. Such walls are considered
cantilever walls. Typically, it is believed that their connection is relatively weak and that their resistance mainly
depends on their flexural resistance. It is generally supposed that the flexural strength of the slabs is negligible
compared to that of the walls and that slabs connect the walls only as rigid diaphragms. It is further supposed
that the wall coupling is weak, and the flexural response of wall piers is the predominant response mechanism
resisting the overturning moment induced by the seismic load (see Fig. 1a). Most modern codes accept these
assumptions.
(a) (b)

Figure 1. The response mechanism of a) cantilever walls and b) coupled walls.

Some recent experiments on RC walls (e.g. Panagiotou et al. 2011, Nagae et al. 2011) call these assumptions
into question for certain wall configurations. When the considerable effective width of slabs connecting a few
slender walls (like in the elevator shafts) is activated, they can provide an important level of wall coupling.
Consequently, the seismic resisting system can differ from the cantilever walls (see Fig. 1b). A considerable
portion of the overturning moment is resisted by the frame action provided by the slabs, which induces the
axial forces NE into the wall piers. The level of the frame action primarily depends on the ratios of the strengths
and stiffnesses of the floor system and wall piers.
Owing to the changed response mechanism, including the frame action, the effects of the seismic excitations
can be considerably different from those expected in the design, and the walls can be damaged in unexpected
ways. This was observed in recent earthquakes (Boroschek et al. 2014, Massone 2013, Elwood 2014), where
unexpected brittle types of failure (shear, confinement and buckling failures) of RC walls were observed,
particularly in taller buildings.
The paper analyses the seismic response of RC walls coupled only by slabs. First, the experimental evidence
of relatively strong wall coupling noted in the half-scale shake table experiment of four three-story RC walls
interconnected only by the slabs (Isakovic et al. 2020, Isakovic et al. 2021) is briefly presented in Section 2.
The sensitivity study of the tested specimen from this experiment is presented in Section 3, and the parameters
influencing the level of wall coupling are discussed.
Based on the previously mentioned studies, the set of buildings was selected, and the parametric study was
performed, primarily analysing the effects of different effective widths of slabs on the coupling of walls and
their basic mechanism of the response. The parametric study and its main results are summarised in Section
4.

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2. Experimental evidence of relatively strong wall coupling provided only by slabs

2.1. Short description of the experiment
A shaking table test of the half-scale three-story specimen, subjected to a series of seismic excitations, was
performed (Isakovic et al. 2020, Isakovic et al. 2021) to evaluate the RC slab-to-wall pier interactions (see Fig.
2). To obtain realistic information about this interaction, the maximum possible size of the specimen was
employed, considering the limitations of the shake table concerning the overturning moment (approximately
500 kNm).

Figure 2. Half-scale three-story specimen consisting of four walls connected by three slabs

The specimen consisted of four rectangular walls coupled with three slabs. The walls' height, lengths, and
thicknesses were 4.50 m, 0.75 m, and 10 cm, respectively (see Fig. 2). The aspect ratio of the walls (the ratio
between the height of the wall and its length) was 6. Thus, conditions typical of slender walls were created.
The 0.5 m-wide openings (simulating door openings) were used between two inplane adjacent walls. The
slabs' lengths, widths, and thicknesses were 3 m, 3 m, and 8 cm, respectively. These dimensions were defined
considering typical tributary areas of RC wall buildings in central Europe.
The total mass of the specimen was 8.8 t. In scaled shaking table experiments, additional masses are often
used to achieve realistic seismic demand in tested specimens. In the presented case, this was not an
appropriate option since the additional masses on the slabs can significantly influence the properties of the
slabs and change their interaction with the wall piers. Thus, the time and acceleration were adequately scaled
to obtain realistic seismic forces (Isakovic et al. 2021). Time and accelerations were modified by factors 0.4
and 2.25, respectively.
The shake table was excited using an artificial accelerogram generated by modifying the Petrovac N-S
accelerogram registered during the 1979 Montenegro earthquake (Isakovic et al. 2021). This accelerogram
was changed to match the EC8 elastic acceleration spectrum corresponding to soil site type A and 2%
damping. A series of uniaxial tests were performed by applying gradually increasing seismic intensity (i.e.,
0.1–1.5 g) in the direction along the axis of the walls (i.e., N-S, see Fig. 3). The peak accelerations for the
various tests are listed in Table 1. More data regarding the experimental specimen and tests are available in
the previous reports (Isakovic et al. 2020, Isakovic et al. 2021).
Table 1. The peak accelerations applied to the shake table during the experimental tests
Test R010 R020 R030 R050 R060(1) R060(2) R080 R090 R120 R150(1) R150(2)
Max.
0.10 0.20 0.30 0.50 0.60 0.60 0.80 0.90 1.20 1.50 1.50
accel.[g]
2.2. The main observations of the experiment
The damage observed in the tested structure was limited until test R120, corresponding to a peak acceleration
of 1.2 g at the shaking table. After this test, the damage in the wall piers was spread approximately 100 cm
from the foundation level (Fig. 3a). Cracks were initially formed at the outer edges of the wall piers. When the

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seismic intensity was increased, they gradually extended toward the inner edges (toward the opening). The
crack pattern differed from the cross-shaped damage pattern typical for cantilever walls (Fig. 3b).

a) b)
Figure 3. a) Cracks, which were observed in the wall b) Crack pattern typical for cantilever walls
piers, (courtesy of Tran and Wallace 2015)

In the last two tests (R150(1) and R150(2)), in specific time steps, the differences in the responses of the two
piers were visible to the naked eye (Fig. 4). Cracking of the wall pier subjected to the seismic tension forces
was observed (see the orange areas circled in red in Fig. 4), whereas the wall pier subjected to compression
cracked only at the foundation level. In the last test, the buckling of the longitudinal reinforcement at the outer
edge of one of the piers was observed, indicating that this pier was subjected to relatively large compression
stresses.
In the last three tests, the cracks in the slabs were spread over their entire width between the two rows of the
wall piers (Fig. 5). The yielding of the reinforcement in the slabs was achieved. The slabs' effective widths
(EW) were equal to their total widths. The frame action generated by the slabs was considerable (see the
discussion in Section 3). More details concerning the observed response can be found in the previous reports
(Isakovic et al. 2020, Isakovic et al. 2021).

Figure 4. The responses of the two piers were Figure 5. The wide cracks were spread over the
evidently different entire width of the slabs

3. Sensitivity study of the response of the tested specimen

The tested specimen was analysed using the UL FGG version of the OpenSees program (Mazzoni et al.,
2006). Since it is symmetric, the analysis was performed using a 2D numerical model representing half of it.
The wall piers were modelled using a nonlinear MVLEM model developed at the University of Ljubljana
(Fischinger et al., 2004). Slabs were modelled using Giberson's lamped plasticity model, where the hysteretic
response was described using Takeda hysteretic rules (Takeda et al., 1970). During the stronger tests, some
rotations of the foundations were observed. They were modelled using the Pinching 4 model (Lowes and
Altoontash, 2003) in OpenSees. More details about the model and its evaluation can be found in (Isakovic and
Janevski, 2023).

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3.1. Level of coupling and its effects

The analysis confirmed a relatively strong coupling level (CL), which was activated primarily because of the
slab's large EW, which increased its strength. The observed CL is discussed below, considering test R150(1),
where the nonlinear response of piers and slabs was observed.
The maximum overturning moment in half of the specimen in test R150(1) was Mover = 246 kNm (492 kNm in
the whole specimen). The maximum axial forces in wall piers caused by the seismic action NE (see Fig. 1)
were NE = ±88.8 kN (compression force in one and the tension force in the other pier). The compression force
due to gravity load was NG = 21.6 kN.
The maximum moment corresponding to the frame action was MFA = NE xT = 88.8 · 1.25 = 111 kNm, where xT
is the horizontal distance of vertical piers' axes, as shown in Figs. 1 and 2. The CL was defined as the ratio of
the moment MFA and overturning moment Mover:
CL = MFA/Mover = 111/246 = 0.45
The CL was not the same in all tests. It gradually increased proportionally to the seismic intensity and drift
demand as long as the yielding of the slab was achieved in the test R120 with a maximum seismic intensity of
1.2 g. In the first three tests, where the drift demand was small (less than 0.15%), the CL was approximately
25% (Fig. 6). This is the CL used in EC8 to distinguish cantilever walls from coupled walls. When the seismic
intensity and the drift demand increased, the CL increased almost linearly as long as the drift demand of 1%
was achieved (Fig. 6). In the last two tests with a seismic intensity of 1.5 g, corresponding to a drift of 1.27%,
the CL was not significantly changed (i.e., from 42% to 45%).

Figure 6. The CL versus drift

Generally, the CL noticeably increased as long as the yielding of the slab was not achieved. The CL increased
because the slabs' bending moments and shear forces increased, simultaneously increasing forces NE in piers
and amplifying the frame actions. After the slabs yielded, the CL level became almost invariant.
The strong CL and frame action influenced the plastic mechanism and the redistribution of bending moments
and shear forces between piers subjected to tensile and compression NE forces. The piers subjected to tensile
NE forces yielded before the slab in test R090 at 0.82% drift. In test R120 at 1% drift, the yielding of the piers
subjected to compression forces NE and the yielding of the slabs were observed. In the last two tests with
1.27% drift, the strengths of the slabs and the strengths of the walls subjected to significant compression
stresses (i.e., piers subjected to compression forces NE) degraded.
The maximum overturning moment of Mover = 263 kNm was reached in test R120. At the time step when it was
achieved, the bending moments were 43.5 and 109.3 kNm in the piers subjected to tensile and compression
forces NE, respectively. The corresponding shear demand was 24.6 and 62.9 kN in the piers subjected to
tensile and compression NE forces, respectively. The bending and shear demand differed significantly from
those in typical cantilever walls, where the values in both piers are the same. Notably, the increase of the
shear forces in the pier subjected to compression forces NE was as large as 72% of the total BS, which is
larger than that observed in standard cantilever walls (i.e., 50% of the entire BS). Further discussion and
analysis regarding the increase of demand in piers subjected to compression forces NE are provided in the
following section.

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3.1. Important parameters influencing CL and the response mechanism

The activated EW of the slab amounted to the total span width and was considerably larger than those typically
considered in the design. The increased EW significantly increased the flexural strength of the slabs.
Consequently, the shear forces in slabs were also increased, simultaneously increasing the axial forces N E in
wall piers. Owing to increased N E, the CL was considerable, and the frame action was exaggerated. Besides
the slab's EW, the foundations' rotations (base rotations) also somewhat increased the CL because they
increased the bending demand in slabs.
A sensitivity study of the tested structure was performed to evaluate the effects of EW and base rotations,
excluding the base rotations and reducing the slabs' EW. First, the EW was decreased from 150 cm to a
standard value of 50 cm (for half of the specimen). Then, the flexural strength of the slab was neglected
entirely, considering that it acts only as a rigid diaphragm. In this way, the analysis of pure cantilever walls was
performed.
The main results of the sensitivity study (maximum overturning moments Mover, corresponding forces NE,
maximum CL, maximum total base shear BS, and maximum shear forces in the piers V) are summarised in
Table 2 and analysed in more detail in the following subsections 3.1.1 – 3.1.2.
Table 2. Main response parameters in the tested structure, considering and excluding the base rotations and
considering different slab EWs
EW =150 cm EW =150 cm EW = 50 cm Cantilever walls
base rotations no base rotations no base rotations no base rotations
Mover [kNm] 263 242 175 145
NE [kN] ±88.8 ±78.4 ±29 0
CL [%] 45 40 21 0
BS [kN] 87.5 79.6 60 50
V [kN] 62.9 59.3 38 25
3.1.1 Base rotations
During the experiment, limited rotations of the foundations were observed. Since they had a certain influence
on the CL, they were considered in the sensitivity study. The global response is shown in Fig. 7, comparing
the total base shear (BS) vs top displacement relationship in the tested structure with and without base
rotations.

Figure 7. The total BS vs. top displacement Figure 8. CL versus drifts in structures with and without
relationship with and without base rotations (all base rotations (all tests)
tests)
The base rotations somewhat increased the top displacements and flexibility of the structure. The maximum
displacement was approximately 35% larger with rotations (5.7 cm) than in the structure without base rotations
(4.2 cm). The piers subjected to tensile forces NE yielded somewhat earlier when the base rotations were
excluded. The yielding was observed in the test R060(1) at the seismic intensity of 0.6 g and 0.3% drift. In the
experiment, their yielding was observed in test R090 at the seismic intensity of 0.9 g and 0.82% drift. When
no base rotations were considered, the degradation of the piers' strength subjected to tensile forces NE started
at 0.5% drift in test R090.

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The yielding of piers subjected to compression forces NE was somewhat postponed when the base rotations
were excluded. Limited yielding was observed in the last test, R150(2), at the seismic intensity of 1.5 g, and
the nonlinearity was minor. It should be noted that the corresponding drift of 0.92% was similar to that observed
in the experiment, where these piers subjected to axial compression forces yielded at 1% drift. Since the
nonlinear response was considerable only when piers were subjected to tensile forces N E, the failure occurred
owing to the rupture of the longitudinal reinforcement rather than their buckling, as observed in the experiment.
Excluding the base rotations, the demand for the slabs was reduced. No yielding and strength degradation
was observed. The bending moments were reduced from 7.4 to 6.5 kNm. The reduction of the bending
moments also caused the reduction of the shear forces in slabs and axial forces in the piers. The maximum
force NE was reduced from ±88.8 to ±78.4 kN. Consequently the CL decreased, from 45% to 40% (Fig. 8).
However, the maximum CL value was still significant, occurring at 0.92% drift in the structure without base
rotations, whereas it occurred at 1.27% drift in the structure with base rotations. The other trends of CL without
base rotations were similar to those observed in the structure with base rotations. The CL increased in the
same manner, directly proportional to the drift, from an initial CL value of 15% to a maximum of 40%. However,
the gradient in the case without base rotations was larger.
3.1.2 The flexural strength and EW of the slabs
One of the main observations of the experiment was that piers yielded before the slabs, primarily because
relatively large EWs of the slabs were activated at relatively large drifts (i.e., 1% or more) significantly
increasing the flexural strength of slabs.
Additional analyses of the tested structure were performed to evaluate the impact of the slab EW and illustrate
its effects. First, the EW of slabs was reduced from 150 cm to 50 cm, which would be typically considered in
the design. In this way, the strength of the slab was reduced by approximately three times. The yielding
moment was reduced from 7.4 to 2.5 kNm. Then, additional studies were performed by completely neglecting
the flexural strength of slabs. In this way, another extreme case was analysed by considering piers as perfect
cantilever walls.
The global responses of all analysed structures with different effective slab widths in terms of the total BS vs.
top displacement relationship are compared in Fig. 9. The response of the structure with a large EW of 150
cm, where base rotations were excluded, differs from the other two cases, exhibiting a larger stiffness and total
BS. The responses of cantilever walls and the structure with a shorter slab EW are similar. This can be
explained by comparing the CL, as shown in Fig. 10.
45%
EW = 50 cm
40%
EW = 150 cm
35%
Cantilever walls
Coupling level - CL

30%
25%
20%
15%
10%
5%
0%
0.00% 0.20% 0.40% 0.60% 0.80% 1.00% 1.20%
Drift

Figure 9. The total BS vs. top displacement Figure 10. CL in structures with different slab EWs
relationship in structures with different slab EWs (all
tests)
In the structure with a larger EW of slabs, CL increased proportionally to the drift level from an initial value of
15% to a maximum of 40%, corresponding to 0.92% drift. On the contrary, the CL was almost invariant when
the EW was reduced. It was in the range of 14%–22%, which is below the level of 25%, the value used in
standard EC8 to distinguish cantilever from coupled walls. This limit appears to be appropriate, at least in the
analysed case, because the response of the structure with a shorter slab EW was similar to the response of
cantilever walls (Fig. 9).

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Along with the CL, the axial forces NE were also reduced. The NE of ±78.4 kN in the structure with a large slab
EW was reduced to ±29 kN when the slab EW was reduced. Consequently, the yielding moments in piers and
their distributions along the structure were changed. When the piers were subjected to compression forces N E,
the bending moments were reduced, whereas they increased when the tensile forces N E were applied,
compared with the structure with a larger EW.
A change in the bending moments also affected the shear forces in the piers. In the structure with a large EW
and large CL, the shear forces were much larger than in the cantilever walls. In the particular time step when
the maximum overturning moment was achieved, the shear forces in the two piers were considerably different
from each other since they were subjected to large forces N E (compression on one side and tension on the
other). The shear force in the pier subjected to compression forces N E was 59.3 kN (74% of the total BS),
whereas the opposite pier exhibited 20.3 kN (26% of the total BS).
In the structure with a smaller slab EW, smaller CL, and reduced forces NE, the difference between shear
forces in two piers at a specific time step was smaller. When the maximum overturning moment was achieved,
the shear forces were 22 and 38 kN (37% and 63% of the total BS) in the piers subjected to tensile and
compression forces NE, respectively. In both cantilever walls, the shear forces were the same, 25 kN (50% of
the total BS).
Overall, a considerable redistribution of the shear forces can be expected between strongly coupled wall piers.
The shear force in a pier subjected to compression forces NE can be considerably larger than that observed in
the cantilever walls. In this particular case, the shear force was more than doubled. It should be noted,
however, that this increase is not only the consequence of the shear redistribution but, to a great extent, also
the increase in the overall stiffness, resulting in larger total BS (i.e., 79.6 and 50 kN in strongly coupled and
cantilever walls, respectively). The increase in the overall stiffness is the consequence of the strong coupling.
In the tested structure, the base rotations further increased the maximum shear force in a single pier to 62.9
kN.

4. Parametric study
4.1 Main properties of analysed structures and the seismic excitations
Considering the main observations of the shake table experiment presented in the previous sections, a
parametric study of RC walls connected only by slabs has been performed. The set of analysed structures has
been selected considering a part of the archetype building presented in Fig. 11. The analysis has been
performed on two walls, considering their tributary mass (see the shaded area in Fig. 11). Rectangular and
flanged walls were analysed. Since the length of this paper is limited and similar results have been obtained
for both types of walls, only the results for rectangular walls are presented.
Several properties of walls and slabs were varied, and the following values were considered: a) two walls'
lengths of Hw = 4m and 6m, b) three different walls' heights, considering N = 5, 10 and 15 stories with the story
height of 3m, c) three different ratios of walls' area and total floor area of Awall/Afloor = 1.5, 2.0 and 2.5%, d)
three EW of slabs - values typically considered in the design, EW equal to the half and to the total span length,
e) two amount of reinforcement in slabs - minimum reinforcement and 1,5 minimum reinforcement.
All analysed walls were designed as cantilever walls according to standard Eurocode 8 (CEN 2005a),
considering the ductility class DCM. Slabs were considered only as rigid diaphragms, and their flexural strength
was neglected in the design. The seismic demand in walls was obtained using elastic modal analysis with the
reduced acceleration design spectrum. The behaviour factor of q = 3.0 was considered. The design was
performed for two ground acceleration intensities of ag = 0.29g and ag = 0.46g (corresponding to soil type C).
The design shear forces Vdesign were obtained, increasing the shear forces from the analysis by factor 1.5
(according to Eurocode 8).
The seismic response assessment of all designed structures has been performed using pushover and
response history analysis. For the response history analysis, a set of registered accelerograms has been
selected using a slightly modified procedure proposed by Jayaram et al. (2011). The source-to-site distance
was limited to 5–50 km, and the magnitude was in a range of 4.5–7.5. The average spectrum of selected
accelerograms matches the elastic acceleration spectrum according to Eurocode 8 (see Fig. 12).

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a) b)

Figure 12. Acceleration spectra

Figure 11. The archetype building: a) the plan view, b) the
corresponding to selected accelerograms and
wall elevation
the target spectrum (ag =0.5g)

For each set of designed structures (ag = 0.29g and 0.46g), the maximum ground acceleration corresponding
to significant damage (SD) and near collapse (NC) limit state were taken into account. The maximum ground
acceleration for NC state was defined according to Eurocode 8/3 (CEN 2005b), considering the return period
of 2475 years. Structures designed considering ag = 0.29g were also assessed using an additional set of
generated accelerograms. Owing to the space limitation, only the results of response history analyses for
structures designed considering ag = 0.29g and using the registered accelerograms corresponding to NC state
(maximum ground acceleration ag = 0.46g) are presented herein. The corresponding acceleration spectra are
presented in Fig. 12.
4.2 Main results of the parametric study
The parametric study confirmed the observations of the experiment. Larger EW of slabs considerably
increased the CL of wall piers. This is illustrated in Fig. 13, where CL is presented considering two different
EW of slabs - EW typically used in the design and EW equal to the total span length, presented in blue and
red, respectively. The CL is presented considering different lengths of walls Hw, different numbers of stories N
(heights of walls), different ratios of wall-to-floor area Aw/Af and different amounts of reinforcement in slabs
(minimum and 1.5 minimum reinforcement).
In all analysed cases, standard EW corresponds to CLs smaller than the value of 25%, used in EC8 to
distinguish coupled form cantilever walls. The CLs were notably larger when the EW was larger (equal to the
total span length). In 10- and 15-story buildings, CLs up to 50% were observed. In five-story buildings, CLs
were smaller and, in most cases, below the 25% level. This confirmed the observations of the experiment that
larger CLs can be expected primarily in slender walls.
The larger slabs' reinforcement increased their flexural strength and maximum shear force demand.
Consequently, the axial forces in wall piers were larger, and the frame action and CL were increased. On the
contrary, the larger flexural capacity of longer walls decreased the importance of the frame action. The CL was
consequently reduced compared to shorter walls. The wall-to-floor area ratio (Aw/Af) did not significantly affect
the CL.
In the specimen tested at the shake table, the maximum shear forces in wall piers were notably larger than in
cantilever walls. Following this observation, within the parametric study, maximum shear forces in wall piers
Vmax calculated using the dynamic response history analysis were compared with the design shear forces
Vdesign. The design shear forces are the shear forces obtained by the elastic modal response spectrum analysis
of cantilever walls multiplied by factor 1.5. This factor is used to consider the shear force magnification in DCM-
type walls owing to the increased importance of the higher mode effects in the nonlinear range. Figure 14a
presents the ratio Vmax/Vdesign for all analysed buildings. Each presented ratio is the average value
corresponding to a complete set of accelerograms. Figures 14b – 14d present this ratio separately for 5, 10
and 15-story buildings.

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Figure 13. Coupling level considering standard (red) and EW of slabs equal to the span length (blue)

a) b)

c) d)

Figure 14. The ratio of maximum shear forces V max and the design forces Vdesign: a) all analysed buildings,
b) 5-story buildings, c) 10-story buildings, d) 15-story buildings

It can be noticed that the ratio Vmax/Vdesign was considerable. It was in the range of 1.5 – 3.2. Larger values
were observed in 10 and 15-story buildings. Although the ratio Vmax/Vdesign was in 5-story buildings smaller, it
was still significant.
There were several reasons that forces Vmax were considerably larger than Vdesign. Two should be primarily
stressed: shear force magnification in the nonlinear range due to higher modes and the magnification due to
the frame action.
In the nonlinear range, the flexural plastic deformations at the base primarily influence the fundamental mode's
vibration period. Owing to the softening of the structural wall in the inelastic range, the first mode acceleration
spectrum value typically diminishes. In contrast, the spectrum values for the higher modes remain on the
plateau of the spectrum. Therefore, the relative influence of the higher modes increases in the inelastic range.
Owing to the first mode forces contributing most of the overall seismic moment at the base of the wall, which
is limited by its flexural resistance, energy dissipation is predominantly limited to the flexural response in the
first mode. Consequently, the first mode shear forces are reduced due to the energy dissipating mechanism,

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whereas the shear forces due to the higher modes are not. This significantly increases the relative contribution
of the higher modes to the shear force which occurs during the inelastic response.
Considering the ratios presented in Fig. 14, it can be concluded that the magnification factor for shear forces
of 1.5, defined in the Eurocode 8 standard for DCM walls, often cannot adequately cover the magnification of
shear forces due to the higher modes.
However, the presented ratios in Fig. 14 are not only the consequence of higher modes. The shear force
magnification due to the higher modes is typically reduced in strongly coupled walls (larger CL). In such
structures, the difference between Vmax and Vdesign was primarily caused by the strong frame action, which
increased the total base shear of the structure and increased the maximum shear forces in a single pier due
to their redistribution between piers, subjected to tensile and compression forces N E (see Fig. 1b). The ratio of
the shear forces in two piers as a function of CL is presented in Fig. 15. The larger is CL, the frame action is
more important, and the shear forces in two piers are much more different from each other.

Figure 15. The ratio of shear forces in two piers as a function of CL (Vc and Vt are shear forces subjected to
compression and tensile forces NE)

5. Conclusions
The shake table experiment, analysed herein, confirmed an observation from the literature that RC slabs
without coupling beams can induce strong coupling CL in RC walls. In the tested specimen, the CL, defined
as the ratio of the moment resisted by the frame action and the overturning moment, was as large as 45%.
Consequently, the response was significantly different from that observed for typical cantilever walls.
The CL and response mechanism of the tested specimen were influenced primarily by two basic parameters:
a) the strength ratio of the walls and slabs and b) the base rotations. The ratio of the strengths crucially
depended on the activated EW of the slabs, which was threefold larger than the standard value considered in
the design according to standard EC2. Larger EWs increased the strength of the slabs, activating more frame
action, which increased the CL. Consequently, the overall stiffness of the structure was increased, and
considerable axial forces were induced in the walls, causing the buckling failure of the longitudinal bars in the
boundary regions of the walls. When the standard EW was considered in the analysis, the response was
similar to that of the cantilever walls.
The total base shear in the tested specimen was increased because of the large CL, and the maximum shear
forces in wall piers were more than doubled compared with those in cantilever walls. This increase was affected
by the larger overall stiffness of the coupled structure and the redistribution of the seismic demand between
piers subjected to tensile and compression axial forces NE owing to the seismic action. Despite the substantial
increase in shear forces, the shear failure of the piers did not occur in the experiment because it was
deliberately prevented by adequate shear reinforcement. The base rotations of the walls also somewhat
influenced the CL, which was increased for 5% for this reason.
To be able to generalise the observations of the shake-table experiment, a parametric study has been
performed, varying the ratio of the strength and stiffness of slabs and walls. The results of this study confirmed
that considerable coupling of slender walls can be provided only by slabs without RC beams. It has been
demonstrated that in strongly coupled piers, shear forces can be considerably larger than the design shear

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forces determined based on the elastic analysis of cantilever walls, and that in such walls considerable
redistributions of shear forces can occur due to the considerable frame action.

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