Bulletin of Earthquake Engineering
https://doi.org/10.1007/s10518-021-01276-w
ORIGINAL ARTICLE
Displacement‑based seismic design of buildings with thin
reinforced concrete structural walls with a single curtain
of welded wire mesh
Mario E. Rodriguez1
Received: 27 July 2021 / Accepted: 3 November 2021
© Springer Nature B.V. 2021
Abstract
In past decades, multistory housing buildings have been constructed in high-seismic-risk
regions in Latin America using thin reinforced concrete (RC) walls as the primary earthquake-resistant structural system. Typically, these thin walls are built using a light amount
of brittle welded wire mesh placed in a single curtain for longitudinal and transverse reinforcement. This type of construction system is convenient due to the higher speed of construction compared to construction with thicker walls and conventional reinforcement.
However, the seismic design of thin walls in buildings is based mainly on limited experimental research, mainly on squat-thin RC walls. A limitation of thin RC walls is that a
cold-drawn mesh has low ductility and low energy deformation capacity. Furthermore, thin
walls that are subjected to earthquake loading could fail due to out-of-plane instability. A
database of RC thin walls tested under compression-tension cycles or cyclic lateral loading
by several authors is used in this study to review the mechanics of lateral instability of thin
RC walls. This study’s results are used to understand better the potential seismic behavior
of thin RC walls with a single curtain of welded wire mesh fabric. The drift capacities of
typical thin RC walls are estimated in a performance-based seismic design procedure for
buildings with RC thin walls.
Keywords Thin RC walls · Out-of-plane buckling · Drift capacity · Multistory buildings
1 Introduction
In past decades, multistory housing buildings have been constructed in high-seismic-risk
regions in Latin America using thin reinforced concrete (RC) walls as the central earthquake-resistant structural system. Typically, these thin walls are constructed using colddrawn welded wire mesh placed in a single curtain for longitudinal and transverse reinforcement, which is convenient due to the higher speed of installation of this construction
system than construction with conventional reinforcement. However, these buildings’
* Mario E. Rodriguez
mrod@unam.mx
1
Instituto de Ingenieria, National University of Mexico, Mexico City, Mexico
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seismic design is based mainly on limited experimental research on the seismic behavior
of thin RC walls. These thin RC walls are limited because a cold-drawn mesh has low
ductility and energy deformation capacity. Furthermore, these thin walls do not use special
boundary elements, and the drift capacity of a slender thin wall might be governed by wall
out-of-plane instability.
In this study, a database of RC thin walls reinforced with welded wire mesh and tested
by other authors under cyclic lateral loading or tension–compression cycles is evaluated
to define the longitudinal reinforcement tensile strain triggering out-of-plane buckling of
these walls. Based on these results, a parametric study of the stability of RC thin walls
which are subjected to earthquake loading is conducted. A displacement-based approach
(Moehle 1992, 2015; Priestley 1993) is used to determine the possible structural performances of typical buildings with thin walls reinforced with welded wire mesh when subjected to earthquake ground motions that were recorded in the Pacific Coast of Latin America. This study shows the potential response of buildings with thin RC structural walls
reinforced with a single curtain of welded wire mesh when subjected to ground motions
recorded in Latin America. The study does not intend to relate these records to demands
specified by specific codes.
2 Wall database
The study presented in this paper uses two databases: The specimens in the first database
are 16 thin RC walls reinforced with either hot-rolled mesh (8 models) or cold-drawn mesh
(8 models). The wall width in all these test units was typically equal to 150 mm, and they
had two curtains of mesh. These walls were subjected to cyclic lateral loading. Detailed
descriptions of this database and the testing program can be found in Riva and Franchi
(2001). The wall aspect ratio, namely, M/Vlw, where M, V and lw are the moment, the shear
at the wall base induced by the applied lateral forces, and the wall length, respectively, was
approximately 2. It must be noticed that none out of the 16 specimens reached failure due
to lateral instability. In the sixteen tests, failure was due to either mesh failure characterized by tensile failure or premature crushing of concrete in compression (Riva and Franchi
2001). Since these specimens’ failure was not characterized by wall instability, they were
not considered for this study. Later, only two specimens with cold-drawn mesh are studied
to know a possible lower bound of drift capacity of RC thin walls with two curtains of
mesh. Additional databases of thin RC walls with welded wire mesh that other authors
compiled were not considered in this study. In those databases, the wall aspect ratios M/Vlw
were typically smaller than 2, which suggests a predominant shear-dominated behavior.
Furthermore, in residential buildings, which generally are higher than five levels, wall
aspect ratios M/Vlw that are smaller than 2 are not typical.
According to a review of the database that is discussed above, walls with hot-rolled
mesh had higher drift capacity than walls with cold-drawn wire mesh (Riva and Franchi
2001). For this reason, and since most welded wire mesh for walls in buildings in several
countries in Latin America are composed of cold-drawn wire mesh, this study focused on
walls with the latter type of wire mesh.
The specimens in the second database in this study were evaluated by Rosso et al.
(2018). Twelve specimens were tested under tension–compression cycles, and they were
prismatic columns that represented boundary elements in walls. The column height was
2.4 m, and the column depth was 300 mm. The specimens had widths from 80 to 100 mm.
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The longitudinal reinforcement was a single-curtain mesh, and the longitudinal reinforcement content varied from 0.35 to 3.8%. The longitudinal reinforcement content placed in
a single curtain in thin RC walls in several countries in Latin America ranges from 0.25 to
1%. Based on this range of reinforcement, this study selected only four test units from this
database. These selected specimens showed out-of-plane failures.
3 Stability of slender walls that are subjected to earthquake loading
For the study of the stability of slender walls subjected to earthquake loading, it is assumed
that the unbraced height is the clear story height, namely, hu, and the effective height of the
wall is khu. The parameter ξcr is the critical out-of-plane displacement δmax that is normalized to the wall width b (𝜉cr = 𝛿max ∕b). According to Paulay and Priestley (1993), ξcr is
defined as:
�
�
√
𝜉cr = 0.5 1 + 2.35m − 5.53m2 + 4.70m
(1)
where m = 𝜌fy ∕fc� is the mechanical reinforcement ratio, ρ is the wall reinforcement ratio,
fy is the reinforcement yield stress, and fc′ is the specified compressive strength of concrete. Parra and Moehle (2020) proposed that Eq. (1) defining ξcr can be approximated by
Eq. (1a):
(1a)
𝜉cr = 0.3 (1 − 1.5 m)
At the out-of-plane failure, considering the out-of-plane curvature at the instant of crack
closure after the load cycle in which the wall reached its maximum tensile strain εsm, Parra
and Moehle (2017) defined the critical aspect ratio khu/bcr as:
√
khu
𝜅 𝜉cr
=𝜋
(2)
bcr
𝜀sm − 0.005
where κb is the effective depth of the wall, the thin walls considered in this study have a
single curtain of longitudinal reinforcement. For that reason, this study assumes that κ is
equal to 0.5.
3.1 Measured and estimated values of the tensile strain triggering out‑of‑plane
buckling of RC thin walls
The values of the critical tensile strain in the longitudinal reinforcement 𝜀sm,cr computed
via Eqs. (1) and (2) were compared with the measured critical tensile strains 𝜀sm,cr_ exp
obtained by Rosso et al. (2018) for test units with ρ values of up to 1%. In a slender wall
with effectively fixed boundaries, the effective height of the wall equals 0.5hu; however,
considering the out-of-plane cracking of the wall before the out-of-plane failure, this study
assumes that the effective height of the test units equals 0.7hu. Table 1 lists characteristics
of the thin walls tested by Rosso et al. (2018). This table also compares the measured values of the critical tensile strains that trigger out-of-plane buckling, namely, 𝜀sm,cr_ exp, and
the computed values of 𝜀sm,cr via Eqs. (1) and (2). According to Table 1, these equations
yield results in agreement with the results from laboratory tests.
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Table 1 Comparison between the computed values of the critical tensile strains and the experimental results
Test unit
fc′(MPa)
𝜌
𝜉cr
𝜀sm,cr
𝜀sm,cr_exp
𝜀sm,cr_exp ∕𝜀sm,cr
TC01
23.7
0.0035
0.2837
0.0082
0.00813
0.99
TC03
TC04
TC08
25.7
32.3
23.7
0.0085
0.0028
0.0028
0.2169
0.3232
0.3008
0.0088
0.0107
0.0103
0.01063
0.01063
0.01313
1.21
1.00
1.28
Parra and Moehle (2020) have shown the maximum tensile strain (averaged over the
wall out-of-plane unsupported height) required to buckle a wall under cyclic lateral loading
does not depend on the moment variation along with the wall height. Furthermore, these
authors suggest that the wall boundary behaves like an isolated column subjected to axial
force cycles. These findings support the simplified approach in this study based on buckling models of axially loaded prismatic columns.
3.2 Parametric study of the stability of RC thin walls that are subjected
to earthquake loading
A parametric study that utilized Eqs. (1) and (2) was conducted to obtain khu/bcr for typical RC thin walls with a single curtain of reinforcement, representing walls for residential
buildings constructed in several countries in Latin America. Values for fy, fc′, and hu of
540 MPa, 20 MPa, and 2.5 m, respectively, were assumed for this study. Assuming that
there was out-of-plane cracking in the wall before the out-of-plane failure, for the parametric study, the effective height of the wall was considered to be 0.7hu.
The results for hu/bcr obtained in the parametric study are plotted in Fig. 1 as a function of the maximum tensile strain εsm. The lower and upper values of ρ for this parametric study were equal to 0.25 and 1%. Figure 1 also presents the limiting slenderness ratio
of the boundary elements for special structural walls specified by ACI 318-19, equal to
hu/bcr = 16. A typical RC thin wall with hu = 2.5 m and b = 100 mm leads to hu/b = 25. For
this thin wall, Fig. 1 shows that to avoid out-of-plane failure, for the case of ρ = 0.25%, the
maximum tensile strain εsm must be smaller than approximately 0.01, and for ρ = 1%, εsm
must be smaller than 0.008.
Fig. 1 Critical slenderness ratio
as a function of the maximum
tensile strain
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Figure 2 shows computed critical wall thickness values, namely, bcr, as a function of εsm
for ρ values of 0.25 and 1%. The results from Fig. 2 show how the thickness of the wall is
related to the critical tensile strain that triggers an out-of-plane failure. Walls with a thickness of 100 mm are typical in buildings constructed in Latin America using thin walls.
According to Fig. 2, for b = 100 mm and ρ values in the range of 0.25% to 1%, tensile
strains larger than approximately 0.008 trigger out-of-plane failures.
The slenderness limit that is specified by ACI 319-19 (ACI 318, 2019), when applied to
the case of hu = 2.5 m, leads to a critical wall thickness of 2500 mm/16 ≈ 150 mm. Hence,
walls with reinforcement in a single curtain and thickness of up to 150 mm are prone to
out-of-plane failures when subjected to earthquake ground motions. Thus, they are likely to
show low capacities of energy dissipation and displacement ductility.
4 Drift capacity of thin walls reinforced with welded wire mesh
Seismic building codes set limits for story drift ratios. The story drift ratio is the difference
of the lateral displacements at the top and bottom of the story divided by the story height.
The roof drift ratio, defined as the roof displacement divided by the building height, may
be estimated using the equivalent SDOF displacement (Moehle 1992; Sozen 1997). For
multistory buildings, several authors have proposed values for the ratio of the story drift
ratio to the roof drift ratio. For example, for regular RC wall buildings, Panagiotou and
Restrepo (2011) suggested a ratio of 1.4.
A full-scale 7-story RC wall building was subjected to California input ground motions
on a shake-table (Panagiotou and Restrepo 2011). The building responded to the design
basis earthquake with minor damage, even though the building reached a maximum roof
drift ratio of approximately 2%. If we consider that this building satisfied a life-safety
performance objective when using a displacement-based design method, a similar performance would be desirable in RC buildings with thin walls, which poses whether that is
feasible in these buildings. This is studied in the following.
4.1 Cyclic load behavior of RC thin walls with welded wire mesh that were tested
by Riva and Franchi (2001)
Figure 3 shows the typical dimensions and reinforcement details of the two types of wall
sections in RC walls tested by Riva and Franchi (2001). The first type of wall has only
Fig. 2 Critical wall thickness as a
function of the maximum tensile
strain
300
bcr (mm)
250
200
150
100
50
0
0
0.005
0.01
0.015
0.02
0.025
εsm
rho= 0.25%
rho= 1%
bcr= 100 mm
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(a) Wall with only wire mesh
(b) Wall with wire mesh and reinforcing steel
Fig. 3 Reinforcement details of thin RC walls reinforced with welded wire mesh. Test units CD12S and
B14CD8S (Riva and Franchi 2001)
welded wire mesh in two curtains, with no conventional reinforcing bars, as illustrated in
Fig. 3a, and is labeled Test Unit CD12S. The second type of wall combines welded wire
mesh and conventional reinforcement at the wall’s ends, as illustrated in Fig. 3b, and is
labeled as Test Unit B14CD8S. According to a review of the measured drift capacities of
the set of RC walls tested by Riva and Franchi (2001), test units CD12S and B14CD8S can
be regarded as the cases with cold-drawn mesh that had minor measured drift capacities.
Figures 4 and 5 show measured hysteresis loops for test units CD12S and B14CD8S,
respectively. The number of cycles at each applied drift level was small, and typically, only
one cycle was applied at each drift level. This number of cycles might be consistent with
the expected number of cycles in a building wall that responds to a crustal earthquake.
However, it is not compatible with the expected number of cycles in buildings responding
to subduction earthquakes in Latin America, which are typical of much longer duration
than crustal earthquakes.
The failure mode of test units CD12S and B14CD8S is linked to a brittle failure, with
a single crack at the wall base resulting in a tensile failure of bars at the bottom (Riva and
Franchi 2001). In these test units, out-of-plane buckling did not govern the failure mode
CD12S
500
400
LATERAL FORCE (kN)
300
Only CD Mesh 12mm
200
100
0
-100
-200
-300
-400
-500
-0.03
-0.02
-0.01
0.00
DRIFT RATIO
Fig. 4 Hysteresis loop lateral load–drift ratio for test unit CD12S
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0.02
0.03
Bulletin of Earthquake Engineering
B14CD8S
500
400
LATERAL FORCE (kN)
300
Rebars φ14mm
CD Mesh φ8mm
200
100
0
-100
-200
-300
-400
-500
-0.03
-0.02
-0.01
0
DRIFT RATIO
0.01
0.02
0.03
Fig. 5 Hysteresis loop lateral load–drift ratio for test unit B14CD8S
since the test units each had a thickness of 150 mm and two curtains of longitudinal reinforcement. According to Parra and Moehle (2017), walls with two curtains of longitudinal
reinforcement are more stable than walls with a single curtain. Using Eqs. (1) and (2), with
κ = 0.8, it can be shown that for the test units CD12S and B14CD8S, the value of εsm,cr is
near 0.02.
The failure mode observed in the test units CD12S and B14CD8S depend on the applied
strain deformation history, which may not be adequately modeled when using a few lateral load cycles. Therefore, the drift capacity of thin walls represented by these test units
could be smaller than the actual value considering the more significant number of cycles
expected in the subduction earthquakes typical of the Pacific Coast in Central and South
America.
Evaluating the hysteresis loops plotted in Figs. 4 and 5, considering the above discussion on the expected number of cycles in typical subduction earthquakes, leads to the conclusion that the drift ratio capacity of thin RC walls reinforced with welded wire mesh or
with conventional reinforcement might not be larger than 1%. Hence, approximate nonlinear analysis of typical RC thin walls of representative buildings with only a single curtain
of reinforcement is conducted in the following. The values of the tensile strains in the wall
base are computed to assess the wall’s drift capacity and determine whether the mode of
failure is governed by out-of-plane failure or reinforcement fracture. The results of this
analysis are described in the following.
5 Pushover analysis of a typical RC thin wall in residential buildings
A pushover analysis was conducted by subjecting an 8-story RC thin wall to monotonically increasing lateral forces. This wall is considered representative of the construction
practice for residential buildings with thin walls in seismic regions of Peru. Figure 6
shows the elevation and plan views of the thin wall studied in this research. The clearstory height in the building was 2.4 m, and the length and thickness of the wall were
3900 and 100 mm, respectively, with a height of 19.2 m. This study considered two
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WWM Ø6.5mm @150x150
f y (mesh) = 540 MPa
f y (bars) = 420 MPa
f´c = 20 MPa
19.20 m
5Ø12
100 mm
.
3900 mm
5Ø12
WWM Ø6.5mm @150x150
Fig. 6 Wall elevation and plan views of the longitudinal and transverse reinforcements
types of thin walls, each with a single curtain of longitudinal reinforcement. Figure 6
presents the relevant reinforcement details for the first type of wall. In this wall, the longitudinal reinforcement consisted of cold drawn welded wire mesh (WWM) at a spacing
of 150 mm in both directions and 5ϕ12-mm conventional reinforcement at both wall
ends, with yield stresses of 540 and 420 MPa, respectively. The compressive concrete
strength was equal to 20 MPa.
The second selected type of thin wall was similar to the wall that is illustrated in Fig. 6,
except the reinforcement consisted of only WWM at a spacing of 150 mm in both directions, and it had a reinforcement ratio ρ of 0.005, which is typical in residential buildings.
5.1 Pushover analysis for the first type of RC thin wall
The pushover analysis results for the first type of thin wall, with WWM and conventional
longitudinal reinforcement, are presented in Fig. 7, which shows the state corresponding to
the critical tensile strain of the longitudinal reinforcement that triggers out-of-plane buckling, namely, εsm,cr.
According to Fig. 7, the failure due to out-of-plane stability leads to a roof drift ratio
capacity of approximately 0.9%, which may not satisfy a life-safety performance objective
in displacement-based design if that objective corresponds to roof drift ratio values that
exceed 1%.
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Displacement (m)
0.00
120
0.04
0.08
0.12
0.15
100
εsm,cr = 0.009
εc = -0.0016
V (kN)
80
0.19
120
100
80
60
60
40
40
20
20
0
0.0
0.2
0.4
0.6
0
1.0
0.8
Roof Drift Ratio (%)
Fig. 7 Base shear versus the roof drift ratio for a thin wall with WWM and conventional reinforcement
5.2 Pushover analysis for the second type of RC thin wall
Figure 8 shows the pushover analysis results for the thin wall reinforced with only
WWM and a wall reinforcement ratio of 0.005. According to these results, the failure
due to out-of-plane stability leads to a roof drift ratio capacity of approximately 1.0%,
which is slightly higher than the roof drift ratio capacity computed for the thin wall with
WWM and conventional reinforcement.
The drift capacity values of RC thin wall buildings found in this study are substantially smaller than the values for conventional buildings with robust ductile walls
designed according to modern codes.
Displacement (m)
0.00
140
0.04
0.08
0.12
0.15
0.19
120
120
εsm,cr = 0.009
εc = -0.0018
100
V (kN)
0.23
140
100
80
80
60
60
40
40
20
20
0
0
0.2
0.4
0.6
0.8
1
0
1.2
Roof Drift Ratio (%)
Fig. 8 Base shear versus the roof drift ratio for a thin wall that is reinforced with WWM
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6 Drift demands in wall buildings that are computed using typical
ground motions that were recorded in subduction earthquakes
In a building with n stories and a maximum roof displacement of δm that is subjected to
earthquake loading, the roof drift ratio; namely, Drm, can be estimated as:
Drm =
ΓS
ΓS
𝛿m
= d = ( )d
H
H
H
T
T
(3)
where H is the height of the building above ground level, Γ is the modal participation factor, Sd is the spectral displacement, and T is the effective fundamental period of the building, which is typically larger than the period of the building that is computed with gross
sections. As shown later, it is convenient to express the roof drift ratio as a function of the
stiffness index H/T.
The modal participation factor, can be estimated as follows (ASCE, SEI 2016):
)
(
1
Γ = 1 + 0.5zs 1 −
(4)
n
where zs is the modal contribution coefficient modifier, this parameter depends on the seismic-force-resisting system. It is equal to 0.85 for buildings designed with dual systems and
1 for RC wall buildings.
The following expression is commonly used to calculate a preliminary estimate of T:
T=
n
𝜆
(5)
where parameter 𝜆 depends on the type of seismic-force-resisting system.
From Eqs. (4) and (5), we obtain an expression for Γ, which is used in this study to compute Drm:
)
(
1
Γ = 1 + 0.5zs 1 −
(6)
𝜆T
In a regular building with constant interstory height h, H may be expressed as:
H = nh
(7)
H
= 𝜆h
T
(8)
Combining Eqs. (5) and (7) yields:
The spectral displacement Sd in Eq. (3) was computed for various earthquake ground
motions and ductility displacement ratios 𝜇 of 1 and 2 using the RUAUMOKO computer
program (Carr 2011), the Takeda hysteresis rule, and a value of 0.02 for a fraction of critical damping. Roof drift ratios were computed via Eq. (3) for H/T values of 15, 25, 50, and
75 m/s. According to Eq. (8), for buildings with h = 2.5 m, these H/T values correspond to
λ values of 6, 10, 20, and 30 ­s−1, respectively. Based on data of RC wall buildings in Chile,
as reported by Massone et al. (2012) and Lagos et al. (2012), Rodriguez (2018) estimated
that RC wall buildings in Chile had H/T values in the range 28 to 100 m/s, with a mean
value of approximately 50 m/s. These data support the range of H/T values selected for this
study.
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6.1 2007 Pisco earthquake in Peru
Figure 9 shows plots of the roof drift ratio spectra Drm computed via Eq. 3 for a ground
motion recorded in the Ica Station, N–S direction, during the 2007 Pisco earthquake
in Peru, with magnitude Mw equal to 7.9. According to these results, buildings with μ
values of 1 and 2, fundamental periods smaller than 1.5 s, and with H/T values smaller
than 25 m/s, in some cases would reach roof drift ratios exceeding 0.9%. This is a value
that triggers out-of-plane failure in some thin walls with a single curtain of reinforcement, as has been shown in this study. Figure 9 indicates that for seismic demands corresponding to the ground motion recorded in the Ica Station, the roof drift ratio exceeds
0.9% in buildings with the stiffness index H/T equal to 25 m/s and fundamental periods
as low as 0.4 s. For H/T = 25 m/s, h = 2.5 m and T = 0.4 s, Eqs. (5) and (8) leads to n = 4.
This finding suggests limiting the number of stories of buildings with thin RC walls
reinforced with a single curtain of welded wire mesh and with values of the stiffness
index H/T smaller than 25 m/s. For the case of the ground motion recorded in the Ica
Station, this type of buildings should be limited to three stories. However, higher seismic demands in this type of building might be expected; therefore, such a limit should
be reduced to two stories.
This demonstrates the convenience of having RC buildings with a high density of
walls, which would lead to high values of the stiffness index H/T and, therefore, building displacements that could satisfy a life-safety performance objective when using a
displacement-based design method.
Fig. 9 Roof drift ratio Drm spectra for the ICA-NS record, 2007
Peru earthquake
(a) μ = 1
(b) μ= 2
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6.2 2010 Maule earthquake in Chile
Figure 10 shows plots of the Drm spectra computed via Eq. (3) for the Concepcion Centro
ground motion recorded in the NS direction in the city of Concepcion during the 2010
Maule earthquake in Chile, which had a magnitude Mw of 8.8. These spectra were computed for μ values of 1 and 2. According to the results presented in Fig. 10, for this record,
buildings that respond in the elastic range, namely, those that are considered in Fig. 10a,
with fundamental periods that are smaller than 1.5 s and H/T values that are smaller than
50 m/s would reach roof drift ratios that exceed 0.9% in most cases. This value triggers
out-of-plane failure in some thin walls with a single curtain of reinforcement, as shown in
this study. These buildings could not satisfy a life-safety performance objective when using
a displacement-based design method. For the case under investigation, to fulfill this objective, buildings must be tough; namely, they must have μ values of at least 2 and must be
very stiff, with H/T values that exceed 50 m/s; see Fig. 10b. This is feasible only in buildings with a very high density of robust walls, which may not be possible in buildings with
thin walls.
The analysis results obtained in this study should be considered with caution since they
are based on a simple model of the complex behavior of multistory buildings and consider
only out-of-plane failure. Other modes of failure may lead to drift capacities of buildings
that are smaller than the values that were found in this study for the case of out-of-plane
failure. For example, drying shrinkage causes an increase in tensile strains, which may lead
to a drift capacity that is smaller than the values that were computed in this study. Another
limitation of this study is that it ignores the interaction effects caused by the deformation compatibility between the walls and elements framed into them (Bertero et al. 1985;
Fig. 10 Drm spectra for the concepcion CON-1N-S record, 2010
Maule earthquake
(a) μ=1
(b) μ=2
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Panagiotou and Restrepo 2011). These interaction effects may cause a substantial increase
in the shear-force demand and may reduce the drift capacity of RC wall buildings.
7 Conclusions
The following conclusions were obtained from the results of this study:
1. The measured critical tensile strains that trigger the out-of-plane failure of RC thin walls
with a single curtain of reinforcement subjected to tension–compression cycles were
obtained from experimental tests conducted by other authors. These measurements were
compared with the predicted values of the critical tensile strains that trigger out-of-plane
failures of the test units. These predictions were based on results from the literature on
the stability of thin walls, considering the case of walls with a single curtain of reinforcement. The predicted critical tensile strains that trigger the out-of-plane failure of
the selected test units are consistent with the measured values.
2. Based on the above results, a parametric study was conducted to obtain the critical
slenderness ratio; namely, hu/bcr, that triggers out-of-plane failures of typical RC thin
walls with a single curtain of reinforcement. The results were obtained as a function of
the maximum tensile strain, namely, εsm, in the longitudinal reinforcement. The results
demonstrate that RC thin walls with a single curtain of reinforcement and a thickness of
up to 150 mm are prone to out-of-plane failures when subjected to earthquake loading.
3. Base shear and roof drift ratio relationships were obtained for a typical 8-story residential building with RC walls of thickness 100 mm and with a single curtain of reinforcement. According to these relationships, the failure mode in these walls may be governed
by out-of-plane buckling, with a roof drift ratio capacity smaller than approximately 1%.
This value will not satisfy a life-safety performance objective in displacement-based
design if that objective corresponds to values of roof drift ratios that exceed 1%. The
drift capacities of RC thin wall buildings found in this study are significantly smaller
than those of conventional buildings with robust walls designed according to modern
codes.
4. The roof drift ratio demands in the wall buildings were computed using typical ground
motions recorded in subduction earthquakes during the 2007 Peru and 2010 Chile earthquakes. It was found that to avoid out-of-plane failures, RC buildings that have walls of
thickness 100 mm with one curtain of reinforcement must have a high density of walls,
thereby leading to values of the stiffness index H/T that exceed 25 m/s for the 2007
Peru earthquake and 50 m/s for the 2010 Chile earthquake. Buildings with these high
values of the stiffness index H/T must have a very high density of walls, which may not
be possible for buildings with thin walls.
5. Other modes of failure, not considered in this study, may lead to drift capacities of buildings that are smaller than the values found in this study; this observation and the results
obtained in this study guide to the following recommendation. Residential buildings
with more than two stories, walls of thickness 100 mm, and one curtain of welded wire
mesh should not be constructed in high-seismic-risk regions in Latin America.
Acknowledgements Thanks to Dandy Roca, a graduate student at the National University of Mexico, for his
help in the nonlinear analysis conducted in this study, and to Professor José Restrepo, from the University of
California San Diego, for his valuable comments on the manuscript.
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Bulletin of Earthquake Engineering
Funding This research was partly carried out with funding of the Instituto de Ingenieria, National University of Mexico.
Availability of data and material The raw data supporting the conclusions of this article will be made available by the authors upon reasonable requests.
Code availability Closed-source software was employed.
Declarations
Conflicts of interest The authors declare that the research was conducted without any commercial or financial
relationships that could be a potential conflict of interest.
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