An Estimate of the Yield Displacement of Coupled Walls for Seismic Design
International Journal of Concrete Structures and Materials
An Estimate of the Yield Displacement of Coupled Walls for Seismic Design
Enrique Herna´ ndez-Montes
A formula to estimate the yield displacement observed in the pushover analysis of coupled wall lateral force-resisting systems is presented. The estimate is based on the results of an analytical study of coupled walls ranging from 8 to 20 stories in height, with varied amounts of reinforcement in the reinforced concrete coupling beams and walls, subjected to first-mode pushover analysis. An example illustrates the application of these estimates to the performance-based seismic design of coupled walls.
coupled walls; shear walls; earthquake engineering
Some displacement-based methods for seismic design
(Aschheim and Black 2000; Aschheim 2000; Paulay 2002)
use an estimate of the yield displacement as a basis for
establishing values of critical design parameters such as base
shear strength. In contrast to the lateral stiffness or
fundamental period of vibration, whose values are unknown at the
beginning of the design process and vary with the lateral
strength provided to the structure, the yield displacement is a
kinematic quantity and varies little with changes in lateral
strength. Figure 1 illustrates the base shear resistance
developed by two building models under a constant
(increasing) lateral force profile, as a function of the
displacement of the roof. The only difference between the two
models is the amount of reinforcement. While the strength
and stiffness differ, the yield displacement is nearly
invariant, and can be estimated based on kinematic relationships
associated with strains, member dimensions, and structural
geometry, for the usual distributions of mass and stiffness in
a structural system (Aschheim and Black 2000). In contrast,
conventional seismic design approaches are based on the
fundamental period of vibration. The period is a function of
the stiffness of the structure (assuming the mass of the
building is kept constant) which in turn depends on the
amount of reinforcing steel and concrete in the member cross
sections and hence changes as member strengths are adjusted
to achieve the intended seismic performance goals. This
dependence of period on lateral strength, if represented
accurately in the model, causes period-based seismic design
approaches to require a larger number of iterations than are
needed with approaches that are based on the yield
displacement. If the variation of stiffness with strength is not
represented in the model, the analytical results are likely to
be of poor fidelity and may lead to an imprecise
characterization of the suitability of the design relative to the seismic
Because changes in lateral strength are achieved by
changing the amount of material used, rather than the
inherent strengths of the steel and concrete materials, the
changes in lateral strength are associated with changes in
lateral stiffness. The yield displacement observed in a
nonlinear static (pushover) analysis is nearly invariant with
changes in lateral strength. This is easily explained for
individual structural elements (Priestley et al. 1995;
Herna´ndez-Montes and Aschheim 2003), and is also observed in
a more generalized way for entire buildings (Paulay 2002;
Tjhin et al. 2007).
Recognition of the stability of the yield displacement has
led to work in recent years to provide formulas to estimate
the yield displacement and yield curvature of various
structural elements (e.g., columns and beams of various
cross-sectional shapes) as well as structural systems
comprised of walls or frames and dual systems. As an
illustration, relatively current approximations for the effective yield
curvature of reinforced concrete (RC) members and steel
members are (Priestley et al. 2007) given in Table 1.
Priestley et al. (2007) provide a method to estimate the
yield displacement of coupled walls which relies on the
degree of coupling of the beams, bCB, quantified as:
where MCB,b is the base moment resistance associated with a
couple resulting from the shears carried by the coupling
beams and MOTM is the overturning moment at the base
Fig. 1 Results of pushover analysis, for models that differ
only in component reinforcement quantity.
induced by the applied lateral loads. The yield displacement
of the wall is then estimated by considering curvatures over
the height of a wall, recognizing that the influence of
coupling beam resistance on the bending moments within the
walls. The degree of coupling beam, bCB, affects the location
of zero moment within the wall, and is determined from
2. Behavioral Assumptions for Coupled Walls
Coupled walls can be considered to be an extension of the
strong-column weak-beam philosophy of seismic design,
applied to shear walls. This philosophy seeks to ensure that
primary elements critical to structural integrity maintain
gravity load resistance throughout the seismic action, while
yielding develops within the beams. Yielding at the base of
the columns or walls is accepted as an unavoidable part of
the mechanism that develops during inelastic response,
although yielding of the beams is the preferred way to confer
ductility to the lateral force-resisting system.
The lateral response of coupled walls is complex because
the coupling beams generally yield first, in a sequence that
emerges as the lateral displacements increase, and prior to
flexural yielding at the base of each wall pier. Coupling
beams within a coupled wall system can be chosen to be
identical, having the same dimensions and reinforcement
over the height of the coupled wall system. The amount of
shear resisted by the coupling beams over the height of the
system at one instant during the linear elastic portion of
response in a first-mode pushover analysis of a 12-story
coupled wall is shown in Fig. 2. The results obtained are
similar to those described in Naeim (2001). The deformed
shape was obtained using a commercial software package
SeismoStruct (2016), in which inelastic fiber elements
were used to represent the flexural and axial response of
the wall and coupling beams, while linear elastic resistance
to shear was modeled. One may observe the wall profile is
nearly linear above the location of peak coupling beam
An estimate of the yield displacement observed in a
firstmode nonlinear static (pushover) analysis is useful for
seismic design. In such an analysis, lateral forces are applied
over the height of the building in proportion to the amplitude
of the first mode, /1,i and mass, mi, at each floor (i).
Recognizing that the first mode shape may vary with bCB, thus
Height above base
Shear in coupling beams
affecting the lateral force distribution and moments (and
curvatures) over the heights of the walls, analytical studies
were conducted to calibrate a simple expression for the yield
displacement of a cantilever wall.
Consider first that a cantilever wall, loaded by a single
force at the roof, has a linear distribution of bending moment
that reaches a peak at its base. Assuming that all sections
have the same stiffness, the curvature distribution varies
linearly from the roof to the base. When the maximum
curvature (at the base of the wall) is the yield curvature, Øy,
the displacement at the top of the wall is given (by
integrating the curvature twice) as:
Table 1 Estimates of yield curvature provided in Priestley et al. (2007).
where ey is the yield strain of the reinforcing steel, and D, hc, lw, hs and hb are the depths of the circular column, rectangular column,
rectangular wall, steel section and flanged concrete beam sections, respectively. One may notice a distinction in that expressions of the yield
curvature initially were functions of the overall height of the member section (Priestley et al. 1995), while later studies (Herna´ndez-Montes and
Aschheim 2003) introduced the effective depth (to the centroid of the tension reinforcement) as a more physically meaningful term in yield
curvature expressions for RC members.
where H is the height of the wall.
Now, consider that based on common approximations of
the yield curvature for other structural elements (Table 1 and
Herna´ndez-Montes and Aschheim 2003; Priestley et al.
2007), the yield curvature (Øy) may be represented
where ey is the yield strain of the reinforcing steel and j is a
coefficient to be deduced for coupled walls that accounts for
the complicated mechanical behavior of coupled walls
undergoing response in a first-mode pushover analysis. The
depth of the wall, Dcw, in Eq. 3 is the distance between the
center of gravity of the primary longitudinal reinforcement at
one boundary of the coupled wall and the extreme concrete
fiber of the remote edge (i.e., the overall section height of the
cross section of the entire coupled wall less the cover to the
centroid of the boundary longitudinal reinforcement), as
illustrated in Fig. 3.
3. Numerical Study of Coupled Walls
To calibrate the value of j in Eq. 3, and to evaluate the
applicability of this approach for a relevant range of coupled
walls, three sets of coupled walls were studied, having 8, 12,
and 20 stories above the base. The cross section and
Circular concrete column
Rectangular concrete column
Rectangular concrete wall
Symmetrical steel section
Flanged concrete beam
Fig. 3 Nomenclature.
coupling beam dimensions are shown in Fig. 4, which
illustrates the 12-story coupled wall. A plan view applicable
to the three sets is also shown, which shows the floor plan
that is common to all stories. Ordinary steel and concrete
materials are used—using Eurocode designations, the
reinforcing steel is B500 (having characteristic strength
fyk = 500 MPa and expected yield strength of 575 MPa)
and the concrete is C-30 (having characteristic strength
fck = 30 MPa and expected compressive strength of
39 MPa) for all the walls.
The design of coupling beams is normally governed by
shear strength limits. Thus, the analytical study considered
two design shear levels, 500 and 1000 kN, representing unit
shear stresses on the gross sectpionffiffiffiffiof 0.33 and 0.65 Hfck
(MPa units) and 3.95 and 7.91 f 0c (psi units), and
corresponding bending moment strengths at the wall face of 250
and 500 kN m (184 and 369 k-ft), respectively, following
Figure 5 illustrates the reinforcement of each wall pier
with 22Ø25 (corresponding to 0.006Ac, between the limits
of 0.002Ac and 0.04Ac). An additional case was considered,
in which the longitudinal reinforcement within the end zone
is increased by 50%. Thus, two levels of longitudinal
4.5 m 4.5m
6@5 m= 30 m
Fig. 4 Elevation of 12-story building, and floor plan applicable to 8, 12, and 20-story buildings.
Fig. 5 Cross-section of one wall pier.
reinforcement at the base of the wall were considered, for the
8-, 12-, and 20-story buildings.
In the uniform coupled wall cases considered herein,
where cross sectional dimensions of all components and
reinforcement within the coupling beams is held uniform,
the proportion of overturning moment resisted at the base of
the wall system resisted by the coupling action (represented
by bCB) increases as the number of stories increase. As will
be shown later in the paper, yielding at the base of the wall
may be postponed to much later in the lateral (pushover)
analysis. As the number of stories increases, the
reinforcement provided at the base of the wall has less influence on
the lateral strength of the coupled wall because the resistance
provided by the coupled beams may be substantial.
The walls were modeled using fiber elements, with steel
and concrete materials represented at their expected
strengths of fye = 575 MPa and fce = 39 MPa rather than at
the nominal characteristic strengths. The models of each
coupled wall were subjected to nonlinear static (pushover)
analysis using lateral forces applied to the coupled wall in
proportional to the first mode forces. The applied force to
story i is Fi, defined by EC-8 (§ 126.96.36.199.3) (2004).
where Fb is the shear at the base of the wall, and si and sj are
the displacements of masses mi, mj, respectively, in the
fundamental mode. The pushover curve is obtained using a
displacement-controlled analysis, in which the roof
displacement is gradually increased with Fb adjusted to provide
equilibrium at the nodes. The results are typically displayed
as a ‘‘capacity curve,’’ which plots Fb on the ordinate and
roof displacement on the abscissa.
Figure 6 shows the capacity curves determined for the
four coupled walls of the 8-story set. The solid lines
66.000000 Base Shear (kN)
Yield at the base of the wall
Yield at coupling beam
Top displacement (m)
Fig. 6 Capacity curves for the set of 8-story coupled walls.
12-Story Coupled Walls
Fig. 7 Capacity curves for the set of 12-story coupled walls.
correspond to the reinforcement of the wall shown in Fig. 5,
and the dashed lines represent the response of walls having
50% greater area of longitudinal reinforcement. The lower
two curves correspond to a coupling beam shear resistance
of V = 500 kN, while the upper two curves correspond to a
coupling beam shear resistance of V = 1000 kN. The series
of numbers in the boxes identify the sequence of yielding of
the coupling beams. The yield displacement is defined as the
intersection of the horizontal line that marks the maximum
value of the base shear and the inclined line defined by the
slope in the linear range, representing cracked section
behavior (Fig. 6). It can be seen that the yield displacement
Yield at the base of the wall
Yield at coupling beam
Top displacement (m)
stays in a narrow segment whose mean value is 0.039 m for
the 8-story coupled walls (or 0.14% of the height of 28.3 m).
Similarly, Figs. 7 and 8 show that the mean yield
displacement for the 12-story coupled walls and for the 20-story
coupled walls is 0.0785 and 0.198 m, respectively. This
corresponds to 0.19% of the height of the 12-story coupled
walls (41.9 m) and 0.29% of the height of the 20-story
coupled walls (69.1 m).
It can be observed that solid lines and dashed lines get
closer as the number of stories of the coupled walls
increases, as shown in Figs. 6, 7, and 8. For the case of 20-story
wall and Vcb = 500 kN, both lines coincide. This is
Yield at the base of the wall
Yield at coupling beam
Top displacement (m)
Fig. 8 Capacity curves for the set of 20-story coupled walls.
Yield displacement, Dy (m)
congruent with the fact already commented that as the
number of stories increases, the reinforcement provided at
the base of the wall has less influence on the lateral strength
of the coupled wall.
Introducing Eq. 3 into Eq. 2:
Figure 9 plots mean values of Dy as a function of eyH2/
3Dcw for the three sets of coupled walls. The empirical
results are approximately linear; the slope of the curve
provides an estimate of j equal to 0.52 for the coupled walls.
Therefore, an estimate of the displacement at the top of a
coupled wall at yield in a first mode pushover analysis is
where ‘‘yield’’ is defined as the intersection of the bilinear
curves that were fitted to the analytical results of Figs. 6, 7,
4. Example of Seismic Design Based
on an Estimated Yield Displacement
In this section the preliminary design of a coupled wall is
developed to illustrate how the estimated yield displacement
can be used in seismic design. First, the design is based on
application of the equal displacement rule to an elastic
design spectrum. Then, to illustrate an alternative approach,
Yield Point Spectra are used.
The coupled wall is part of the perimeter of a 12-story RC
frame structure (Fig. 4). The height of the first story is 4.5 m
while the overlying stories are 3.4 m high, resulting in a total
height of 41.9 m. The coupled wall consists of two
rectangular section walls having a plan length of 4.5 m and
thickness of 0.4 m. B500 steel reinforcement
(fyk = 500 MPa) and C-30 concrete (fck = 30 MPa) are
used. The material safety factors used in the design are
cs = 1.0 and cc = 1.0.
The seismic design performance objectives are: first to
limit the interstory drift (Du,drift) given by EC-8 (§188.8.131.52) to
where m = 0.5 for buildings of importance classes I and II,
and second to limit the ductility demand to the value given
by the EC-8 behavior factor (q = 3.6) for coupled walls of
medium ductility (§184.108.40.206).
The seismic action is calculated based on EC-8 (2004).
The horizontal seismic action is represented by the elastic
response spectrum Type 1 (Ms [5.5, EC-8 §220.127.116.11 where
Fig. 10 Elastic spectra
Ms is the surface-wave magnitude). The type of soil is B
(EC-8 Table 3.1), and according EC-8 Table 3.2:
TB = 0.15 s, TC = 0.5 s, TD = 2.0 s, and S = 1.2. TB and
TC are the lower and the upper limit of the period of the
constant spectral acceleration branch, respectively. TD is the
value defining the beginning of the constant displacement
response range of the spectrum and S is the soil factor.
The reference peak ground acceleration is agR = 0.3 g,
where g is the acceleration of the gravity. The building is
classified as importance class II, meaning cI = 1.0 [EC-8
Table 4.3 and §4.2.5(5), where cI is the importance
factor]. Thus the peak ground acceleration ag =
cIagR = 0.3 g. Damping of 5% is considered by imposing
g = 1.0.
4.1 Design Based on an Elastic Spectrum
The elastic pseudo-acceleration response spectrum
(q = 1) given in EC-8 §18.104.22.168 and corresponding
displacement spectrum [Sd,displ = Sd(T/2p)2] are shown in
Application of the drift limit corresponds to a peak roof
Du; drift ¼ 0:0075 m ¼ 0:0075 0:5 ¼ 0:62 m
The roof displacement at yield is estimated using Eq. 6,
Thus, application of the ductility limit of q = 3.6 for a
wall of medium ductility class results in a roof displacement
Equal displacement rule
Fig. 11 Equal displacement rule.
qDy ¼ 3:6 0:078 m ¼ 0:281 m
Since we wish to exceed neither the drift nor the ductility
limits, the more restrictive roof displacement limit of
0.281 m applies. Noting that the first mode participation
factor, C1, should be approximately 1.46 for a coupled wall
building 12 stories in height (NEHRP 2009), the associated
peak displacement of an ‘‘equivalent’’ SDOF system
(NEHRP 2009) is
Since we expect the equal displacement rule (Fig. 11) to
apply to structures with periods greater than TC, we can use
the spectral displacement plot of Fig. 10 to determine the
period of a long-period system whose spectral displacement
is 0.192 m. This period is 1.72 s; the corresponding
pseudospectral acceleration (Sd) value (Fig. 10) is 2.57 m/s2.
Considering similar triangles, the required Sd value for the
yielding SDOF oscillator is given by (2.57 m/s2)(0.078/1.46/
0.192) = 0.72 m/s2.
The tributary mass per story is 234,000 kg; the total
reactive weight is (234,000 kg)(12)(9.81 m/s2)(1 kN/
1000 N) = 27,546 kN. The first-mode effective mass
coefficient a1 is approximately 0.79 for a coupled wall building
of this height (NEHRP 2009). Therefore, the required base
shear strength at yield is estimated to be 0.79(0.72 m/
s2)(27,546 kN)/(9.81 m/s2) = 1597 kN.
4.2 Design Using Yield Point Spectra
Yield Point Spectra were generated considering the elastic
response spectrum reduced by assumed values of the
behavior factor q, representing different ductilities (EC-8,
§22.214.171.124). The design spectrum is plotted with ordinate Sd
and abscissa yield displacement Dy, determined
parametrically as a function of T. The spectral design acceleration
Sd(T) is given by EC-8 (§126.96.36.199), while Dy(T) is given by:
Figure 12 shows the EC-8 Design Spectra in a Yield Point
Spectra representation, for q = 1, 3.6 and 8.0.
The following flowchart shows the steps taken to obtain
the initial design of the structure (Fig. 13).
Fig. 12 Yield Point Spectra representation of EC-8 Design
Duc lity limit (Du, duc lty)
Dri limit (Du, dri )
= Min(Du, duc lty, Du, dri )/Dy dri
Code lateral forces
Ini al design
Fig. 13 Design method.
As before, the roof displacement at yield is estimated
according to Eq. 6 as
Application of the drift limit is associated with a peak roof
Du; drift ¼ 0:0075 m ¼ 0:0075 0:5 ¼ 0:62 m
Because we have estimated Dy be 0.078, the q factor for
this limit is q & l = Du,drift/Dy = 7.95.
Similarly, the roof displacement associated with the
ductility limit of q = 3.6 is determined as
0:078 m ¼ 0:281 m
The corresponding design spectra for both values of q in a
yield point representation are shown in Fig. 12. As in
previous section, we use an estimate of the first modal
participation factor of C1 = 1.46. Therefore, we enter the Yield
Point Spectra with an estimated yield displacement of
The required yield strength coefficient to meet both
performance objectives is associated with the smaller value of q.
Therefore, in this case, the system design is controlled by
ductility limits and not by interstory drift limits. The ductility
limit for design is 3.6. According to Fig. 12 the required
spectral acceleration is Sd = 0.72 m/s2. The associated
period of vibration, applicable to both the SDOF system and
the first mode of the MDOF system, is
T ¼ 2p DSdy ¼ 1:72 s ð17Þ
The result is identical to that obtained in Sect. 4.1.
However, the Yield Point Spectra format may be appreciated as
more direct, and applies more generally, including portions
of the spectrum where short period displacement
amplification is present.
As previously calculated, the required base shear strength
at yield is Vb = 1597 kN. The horizontal seismic forces can
then be calculated according to EC-8 §188.8.131.52.3(3).
Table 2 Horizontal forces.
Moment distribu on
Fig. 14 Mechanism analysis.
The overturning moment, MOTM, at the base of the
coupled wall, due to the horizontal seismic forces indicated in
Table 2 is
Fihi ¼ 46; 539 kN m
In order to calculate the reinforcement in the members,
the value of bCB (Priestley et al. 2007) is chosen. bCB
should be established for design between 0.25 and 0.75
(Priestley et al. 2007). In this example, we chose bCB to be
equal to 0.4.
where MCB,b is the total moment of the coupling beams at
the base. Assuming that the shear carried by all coupling
beams is identical (Vi), with the coupling beams having
dimensions Lw = 4.5 m and LCB = 1.0 m, then Vi is equal
to 564.1 kN
ViðLw=2 þ Lcb=2Þ !
Fig. 16 Reinforcement of the coupling beams.
At the same time, assuming that the ultimate behavior of
the wall is described by the mechanism shown in Fig. 14, the
required flexural strength of each of the two walls at the
base, MCW,b, is
MCB;b ¼ 4654:2 kN m
The moment at the base, MCW,b, acts with an axial force in
tension of 3150 kN. The cross section of Fig. 15, designed
following EC-2 prescriptions, contains 10/25 bars within
Each coupling beam is designed to resist a shear
Vi = 564.1 kN, along with a flexural moment of 282.1
kN m at the face of the wall. The resulting reinforcement is
indicated in Fig. 16.
The coupled wall was modeled using SeismoStruct
(2016), with concrete modeled assuming
fce = 1.3 fck = 39 MPa (per Priestley et al. 2007) and steel
modeled assuming fye = 1.15 fyk = 575 MPa. The resulting
period is 1.7 s. Because this period is slightly less than
1.72 s, we are confident the spectral displacement will be
acceptable. An eigenvalue analysis of the preliminary design
determined C1 = 1.47, which is very close to the value of
1.46 assumed at the start of the design process. The
eigenvalue analysis determined a1 = 0.62, which is less than the
value of 0.79 assumed when establishing the design base
shear. Relative to the values assumed in preliminary design,
the reduction in period will cause the spectral displacement
to be slightly smaller, while the increase in C1 will cause a
slight increase in the roof displacement relative to the
spectral displacement, representing a minor combined effect.
Design for the higher value of a1 confers greater lateral
strength than is needed (which is also reflected in greater
stiffness that results in a slightly lower period). While the
Fig. 15 Longitudinal reinforcement of the wall.
ductility and interstory drift demands should be acceptable, a
minor refinement using the values of C1 and a1 determined
for the initial design can be done, if such precision is needed.
In comparison, the EC-8 estimate of period for a coupled
wall of this height is given by 0.05H3/4 = 0.823 s. Similarly,
the ASCE-7 (§184.108.40.206) estimate is 0.804 s. These two
estimates of period, relied upon in conventional code-based
seismic design approaches, are suggested without regard to
lateral strength, stiffness, or mass, and thus are seen to be
less precise than that determined based on seismic
performance objectives and an estimate of the yield displacement.
Because the code period estimates are less than half of the
computed first mode period, peak displacements would be
substantially underestimated using the code period
estimates; any updating to recognize the eigenvalues would
necessitate a series of iterative design refinements. The
approaches herein (Sects. 4.1 and 4.2) led to an excellent
preliminary design in a single step. Past behaviors of walls
under earthquake motions (Wallace 2012; Kim et al. 2016)
force us to consider improvements in the design.
In the case of walls with non-uniform coupling beams,
walls having different geometry, or non-uniform mass
distributions or story heights, the yield displacement will
deviate from the estimates developed herein. However, the
stability of the yield displacement will apply to these
systems as well, i.e., the yield displacement observed in a first
mode pushover analysis will remain approximately constant
for proportional changes in strength. Thus, the estimate of
yield displacement and modal parameters used in the initial
design can be updated using values computed in the analysis
of the first design.
New expressions to estimate the yield displacement of
coupled wall systems in a nonlinear static (pushover)
analysis are presented herein. The expressions were calibrated to
uniform coupled walls having a range 8–20 stories, for wall
cross-sections of 10 9 0.4 m, with coupling beams of
1 9 0.7 9 0.4 m and story heights of 3.4 m. The
expressions are stated in terms of parameters that are known or may
be estimated early in the design process. A design example
using an ‘‘equivalent’’ single-degree-of freedom system in
conjunction with Yield Point Spectra was provided to
illustrate the application of these estimates to the design of a
RC coupled wall. The design example and method more
generally demonstrates that the fundamental period of
vibration is a consequence of the lateral strength (and
stiffness) provided to satisfy the seismic performance objectives,
and is estimated with poor fidelity by current code formulae
for the so-termed ‘‘approximate period,’’ Ta. The accuracy of
the yield displacement estimate allowed the preliminary
design to be achieved in a single step, whereas the use of
conventional code estimates of fundamental period of
vibration is likely to require a series of design iterations in
order to obtain a preliminary design that achieves the desired
seismic performance objectives.
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Aschheim , M. A. ( 2000 ). The primacy of the yield displacement in seismic design . In Second US-Japan workshop on performance based design of reinforced concrete buildings , Sapporo, Japan, September 10 - 12 , 2000 .
Aschheim , M. A. , & Black , E. F. ( 2000 ). Yield Point Spectra for seismic design and rehabilitation . Earthquake Spectra , EERI, 16 ( 2 ), 317 - 335 .
Eurocode 2 ( 2002 , July). Design of concrete structures-Part 1: General rules and rules for buildings . prEN 1992 - 1 -1. Brussels: European Committee for Standardization.
Eurocode 8 ( 2004 , April). Design of structures for earthquake resistance-Part 1: General rules, seismic actions and rules for buildings . EN1998-1 . Brussels: European Committee for Standardization.
Herna´ndez-Montes , E. , & Aschheim , M. ( 2003 ). Estimates of the yield curvature for design of reinforced concrete columns . Magazine of Concrete Research , 55 ( 4 ), 373 - 383 .
Kim , J. , Jun , Y. , & Kang , H. ( 2016 ). Seismic behavior factors of RC staggered wall buildings . International Journal of Concrete Structures and Materials , 10 ( 3 ), 355 - 371 .
Naeim , F. ( 2001 ). The seismic design handbook (2nd ed.). Boston: Kluwer Academic Publishers.
NEHRP recommended seismic provisions for new buildings and other structures, 2009 edition. Resource Paper 9 : Seismic design using target drift, ductility, and plastic mechanisms as performance criteria .
Paulay , T. ( 2002a ). A displacement-focused seismic design of mixed building systems . Earthquake Spectra , 18 ( 4 ), 689 - 718 .
Paulay , T. ( 2002b ). An estimation of displacement limits for ductile systems . Earthquake Engineering and Structural Dynamics , 31 , 583 - 599 .
Priestley , M. J. N. , Calvi , G. M. , & Kowalsky , M. J. ( 2007 ). Displacement-based seismic design of structures . Pavia: IUSS Press.
Priestley , M. J. N. , Seible , F. , & Calvi , M. ( 1995 ). Seismic design and retrofit of bridges . New York : Wiley.
SeismoStruct ( 2016 ). www.seismosoft.com.
Tjhin , T. N. , Aschheim , M. A. , & Wallace , J. W. ( 2007 ). Yield displacement-based seismic design of RC wall buildings . Engineering Structures , 29 ( 11 ), 2946 - 2959 .
Wallace , J. W. ( 2012 ). Behavior, design, and modeling of structural walls and coupling beams-Lessons from recent laboratory tests and earthquakes . International Journal of Concrete Structures and Materials , 6 ( 1 ), 3 - 18 .