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HKIE Transactions
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Ductility design of reinforced concrete shear wallswith the consideration of axial compression ratio
J S Kuang & Y P Yuen
To cite this article: J S Kuang & Y P Yuen (2015) Ductility design of reinforced concrete shear
walls with the consideration of axial compression ratio, HKIE Transactions, 22:3, 123-133, DOI:10.1080/1023697X.2015.1071027
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HKIE Transactions, 2015
Vol. 22, No. 3, 123–133, http://dx.doi.org/10.1080/1023697X.2015.1071027
Ductility design of reinforced concrete shear walls with the consideration of axial compression
ratio
J S Kuanga∗ and Y P Yuen b
a Department of Civil and Environmental Engineering, the Hong Kong University of Science and Technology, Hong Kong, People’s Republic of China; b Department of Civil Engineering, Bursa Orhangazi University, Turkey
( Received 1 November 2013; accepted 9 December 2014 )
To evaluate and quantify the effect of the axial compression ratio on the seismic performance of reinforced concretewalls, a comprehensive statistical analysis with 474 sets of experimental data was conducted. Stipulated limits on theaxial compression ratio and their evaluation methods in various design codes were analysed and compared. Based on
the results of these analyses, methods for calculating the effective axial compression and the limiting value of the axialcompression ratio for reinforced concrete (RC) structural walls stipulated in the Code of Practice for Structural Useof Concrete 2013 may be amended and improved on a more scientific basis. Recommendations are made for possibleamendments to the provision of design or detailing for ductility of structural walls in Clause 9.9.3 of the Hong Kongstructural concrete code 2013.
Keywords: shear wall; axial compression ratio; ductility; reinforced concrete; seismic design
Introduction
It has been demonstrated repeatedly by many disastrous
earthquakes [1 – 4] that well-designed structural walls can
render excellent lateral stability and drift ductility to
medium-to-high-rise reinforced concrete (RC) buildings
under seismic actions. Under reversed cyclic loading,well-detailed and confined RC shear walls display very
good and stable flexural deformability and energy dissi-
pation capacity, which are attributed to the high curvature
ductility and extended plastic hinge length.[5] Mean-
while, as compared with the frame systems, the structural
behaviour of shear-wall systems is less influenced by
random non-structural component effects such as infill
panels, which often trigger soft-storey phenomena in the
frame structures.[6] Shear walls are thus recognised as the
very important structural members with relatively high
ultimate lateral load-carrying capacity in seismic resistant
design.[2,7]
With credit given to the efforts made in experimen-
tal and analytical studies undertaken by researchers in the
past decades, the design and analysis methods for typical
RC walls have been well-established and standardised.
RC shear walls in high-rise buildings are often charac-
terised by high compression forces and aspect ratios, as
a consequence of architectural designs which maximise
clear floor heights and usable floor areas. Recent stud-
ies [8,9] indicated that structural wall elements in tall
buildings can sustain axial compression ratios as high
*Corresponding author. Email: cejkuang@ust.hk
as 0.4 f
c Ac or above, which is already beyond the typi-
cal range of 0 to 0.2 investigated experimentally.[10 – 12]
A few studies on RC walls under an axial force ratio
above 0.3 can be found in the literatures,[12 – 15] and
these experimental studies revealed that high axial force
ratios severely deprive drift ductility and stability of RC walls. Shear walls suddenly fail in a brittle manner
when subjected to lateral reversed-cyclic loading under
a high axial compression ratio, thus losing their vertical
load-carrying capacity.
The 2010 Chile earthquake is a good example where
lessons were learned on the effect of high axial forces on
the seismic performance of RC structural walls. It has
been indicated from post-earthquake field investigations
that thin walls, with thicknesses ranging from 150 mm to
200 mm, in newly built high-rise buildings are normally
subjected to a higher axial compression and suffered sev-
erer damage than thicker walls in old buildings during
the earthquake.[16,17] Out-of-plane insatiability of walls,
buckling or fracturing of the boundary reinforcement, and
compression failure over the entire wall lengths are typi-
cal significant damage modes observed in thin RC walls,
as shown in Figure 1. The design of new buildings in
Chile mainly follows the American Concrete Institute’s
1995 building code for structural concrete, but the provi-
sions on the detailing of transverse reinforcement at wall
boundaries are not included, which can be a major cause
of the significant wall damage.
© 2015 The Hong Kong Institution of Engineers
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124 J.S. Kuang and Y.P. Yuen
Figure 1. Compression failure of a shear wall during the 2010Chile earthquake. (Courtesy of M Francisco; acquired from NISEE e-Library, EERC, University of California, Berkeley, theUSA).
To prevent undesirable brittle failures of RC walls,
many design codes of practice for RC structures,
including the Hong Kong structural concrete code
2013 (HKConcrete2013),[18] Chinese seismic code GB
50011–2010,[19] and Eurocode 8,[20] stipulated upper
limits for axial compression ratios and boundary-element
detailing requirements for various ranges of axial com-
pression ratios. Nonetheless, later it can be seen that the
provisions in different codes of practice have dissimilari-
ties, including the definitions and limiting values. In view
of this issue, this paper presented a comprehensive survey
and study on the suitability of various code provisions
on axial compression ratios. The detailed effect of axial
compression ratios on the seismic performance of RC
walls was firstly studied, followed by a comprehensive
comparison and discussion on the corresponding code
provisions. Based on an analysis of the results, methods
for calculating the effective axial compression and the
limiting value of axial compression ratio for RC structural
walls stipulated in the Code of Practice for Structural Use
of Concrete 2013 [18] may be amended and improved on
a more scientific basis. Recommendations were made for
possible amendments to the provision of design or detail-
ing for ductility of structural walls in Clause 9.9.3 of the
HKConcrete2013.
Definitions and effects of axial compression ratios
Effect on ductility of RC walls
Axial force has a crucial role in governing the drift
ductility of RC walls. An apparent and instant effect
with a higher axial compression is the reduction of the
curvature ductility µφ of walls,[5,21] which is directly
and inversely proportional to the natural axis depth c
and in turn is a monotonic increasing function of axial
compression, given as follows:
µφ =φu
φ y
=εcul w
2.00ε y c, (1)
where l w is the wall length. Hence, the curvature ductil-
ity, as well as the drift ductility µ, decreases with an
increase in axial compression. On the other hand, when
the strain penetration effect is deemed negligible and the
plastic hinge length is assumed to be l p ≈ 0.08l w, the
drift ductility of flexural-controlled wall segments can be
estimated as follows:
µ =u
y
≈φ y H 2/3 + (φu − φ y )l p H
φ y H 2/3
= 1 +1
αV
0.12εcu
ε y cαV
− 0.24
, (2)
where αV is the vertical aspect ratio ( H /l w) and H is the
wall height.
Equation (2) further indicates that the aspect ratio αV ,
concrete crushing strain εcu and steel yielding strain ε y arealso effective parameters of the drift ductility of a wall
segment, as well as the natural axis depth c as an influ-
ential parameter. This explains why confining boundary
elements for wall segments subjected to high axial forces
are required by various design codes to compensate for
the reduced ductility due to axial compression. The con-
fined concrete in the confining boundary elements can
attain a much higher ultimate crushing strain, εcu, than the
unconfined concrete; hence, the higher curvature ductil-
ity can be achieved in RC walls with confining boundary
elements.
In addition, strength and stiffness degradation of RC
members under cyclic loading is much more pronounced
under high axial compression, which is attributed to the
low cyclic fatigue effect.[22] High axial compression can
prompt pre-emptive buckling of thin RC walls, thus lead-
ing to a sudden and complete loss of axial force carrying
capacity in a brittle manner. Although on some occasions,
axial compression may be beneficial to the shear strength
of squat RC walls with potential shear failure modes such
as diagonal tension and sliding shear,[23] this benefit gen-
erally cannot compensate for the overall adverse effect.
It is thus widely recognised that RC walls subjected to
the high axial compression are more vulnerable to seismic
effects.
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HKIE Transactions 125
To parametricise the axial compression effect on
the structural performances of RC walls, the axial
compression ratio is usually used, defined as follows:
η = N
f c A. (3)
Indeed, in addition to the confinement detailing,
aspect ratios, lap and splices etc., the axial compres-
sion ratio is a very important indicator for evaluating
the expected ductility and fragility of RC walls during
earthquakes. However, it should not be confused with the
load and resistance design or limit state design concepts,
since the axial compression ratio alone cannot represent
or be used to assess the actual seismic performance of
RC walls. Furthermore, this axial compression ratio is
particularly effective for RC structures with high ductil-
ity demands such as under seismic or other exceptionalloading cases. Therefore, the axial force in the numer-
ator is often evaluated based on the realistic situation,
when the rare loading cases take place and no criti-
cal load combination procedure is generally required by
design codes.
Effect on displacement and load capacity
A comprehensive statistical analysis was conducted
for evaluating and quantifying the effect of the axial
force ratio on the seismic performance of RC struc-
tural walls. A total of 474 sets of data, composed of experimental results of small to full-scale RC walls of
various shapes and detailing methods, were collected
from the literatures.[10 – 15,22,24 – 54] The gathered load-
displacement data were analysed, wherein the defini-
tions of yield displacement, ultimate displacement and
displacement ductility of the loading curves are based
on Park.[55]
In the collected database, more than 60% of the tests
were conducted with a relatively low axial force ratio of
below 0.05; in contrast, only about 15% and 7% were
tested with an axial force ratio of above 0.15 and 0.30,
respectively. Nonetheless, these high axial force testsdemonstrated that RC walls fail in very different manners
such as out-of-plane buckling, resembling the observed
damage modes of walls in the 2010 Chile earthquake
(Figure 1). RC walls that fail in out-of-plane buckling
are generally the very brittle members, which exhibit
(a) (b)
(c)
Figure 2. Relationship between displacement ductility and axial compression ratio for different types of RC (a) all walls; (b) slender
walls; and (c) squat walls.
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126 J.S. Kuang and Y.P. Yuen
relatively low ductility, and hence the classical ductility
evaluation methods that assumed in-plane flexural failure
are no longer applicable to these walls.
Figure 2(a) shows the relationship between drift duc-
tility and axial force ratio of different kinds of RC shear walls. It is shown that RC walls can easily achieve
high ductility (µ ≥ 6) at a low axial force ratio (η ≤
10%) as long as the boundary elements are well detailed
and designed. However, when the axial compression
ratio increases to above 20%, RC walls can only barely
maintain moderate ductility (4 < µ ≤ 6) and special
detailing methods like composite-reinforced boundary
elements are necessary in order to acquire high ductility.
When the axial compression ratio is above 35%, pre-
emptive out-of-plane buckling can be the dominating
failure mode as reported in the literatures,[13 – 15] thus
RC walls are not suitable for providing lateral and vertical
resistances in seismic design.
It is recognised that squat shear walls with an aspect
ratio ( H / L) lower than 1.5 are prone to shear failure, in
particular sliding shear failure rather than flexural failure,
and the displacement ductility is not necessarily reduced
by an increase in axial compression. In contrast to theductility of slender shear walls (Figure 2( b)), the ductil-
ity of squat walls (Figure 2(c)) is less influenced by the
axial compression ratio such that the inherent ductility
generally remains in the range of 2 < µ ≤ 5.
The relationship between the ultimate displacement
capacity and axial compression ratio of various types of
RC shear walls is also plotted in Figure 3(a). Again, as
shown in Figure 3( b), there is a trend of diminishing the
ultimate displacement capacity of slender walls with an
increase in axial compression ratio, owing to the reduc-
tion in neutral axial depth, low cycle fatigue effect and
potential out-of-plane buckling. In contrast, the ultimate
displacement capacity of squat walls tends to increase
(a) (b)
(c)
Figure 3. Relationship between ultimate displacement ratio and axial compression ratio for different types of RC (a) all walls; (b)
slender walls; and (c) squat walls.
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HKIE Transactions 127
with the axial compression ratio, as shown in Figure 3(c).
This reversed trend is actually due to the fact that the
shear strength and sliding resistance of cracks in squat
walls are enhanced by axial compression, which increases
the interfacial friction between crack faces.Another important structural property of RC walls
related to axial compression is the shear strength. For
comparison purposes, the peak base shears reported by
the tests in the database are further normalised by the
following equation:
vn =V p
f 0.5c Aw
, (4)
where Aw is the web area of the wall.
Figure 4 shows the relationship between the nor-
malised shear strength and the axial compression ratio.
It shows that a higher axial compression tends to increasethe shear strength of all types of RC walls, in particu-
lar the squat RC walls, as shown in Figure 4(c). This is
because axial compression not only can enhance the shear
strength of walls, but also the moment resistance in some
cases.[9,23] Nevertheless, the enhanced shear strength
attributed to axial compression cannot generally compen-
sate for the adverse effect of reduced drift capacity, and
after all, the system ductility is far more important than
the strength in seismic design.
Code provisions on axial compression ratio
In view of the adverse effect of axial compression on the
seismic performance of RC structural walls, most of the
modern design codes of practice for RC structures stipu-
late upper limits for the axial compression ratio. RC walls
with an axial compression ratio beyond the limits are gen-
erally deemed to be ineffective in resisting seismic action,
even with confinement detailing in the critical regions of
the members (such as expected plastic hinges). These pro-visions, in addition to confinement detailing, intend to
ensure that sufficient drift ductility and axial force car-
rying capacity can be retained in RC structures during
earthquakes or other exceptional load cases.
(a) (b)
(c)
Figure 4. Relationship between the normalised shear strength and axial compression ratio for different types of RC (a) all walls; (b)
slender walls; and (c) squat walls.
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128 J.S. Kuang and Y.P. Yuen
The HKConcrete2013
In Clause 9.9.3.3 of the HKConcrete2013,[18] the upper
limit of axial compression ratios of RC structural walls is
specified as follows:
N W , HK
0.45 f cu Ac
≤ 0.75, (5)
where N W , HK is the design axial force, which is 1.4G k +
1.6Qk (wherein G k is the total permanent or dead load and
Qk is the total live load for the wall due to gravity load);
f cu is the characteristic cube strength of concrete under
uniaxial compression at 28 days; and Ac is the gross area
of the concrete section.
It was noted that the safety factor for concrete com-
pressive strength used in the Hong Kong code is 1.5,
which is divided by the characteristic concrete strength
giving the design strength. The constant 0.45 = 0.67/1.5in the denominator converts the characteristic concrete
strength into the equivalent design compressive strength
for the sections subjected to the dominant flexural bend-
ing action, wherefore another multiplying factor 0.67 is
used. Meanwhile, the axial force in the numerator takes
the ultimate load value due to the sole gravity action,
without considering possible non-permanent imposed-
load reductions or representative gravity action during
rare events with exceptional loading actions, such as
earthquakes and explosions.
Chinese seismic design code (GB50011–2010)In the Chinese seismic design code GB50011–2010,[19]
the upper limits of the axial compression ratio for RC
shear walls (sectional aspect ratio L/t > 8) take differ-
ent values under different seismic fortification intensities
and structural grades. There are four classes of structural
grades: Grade I structures have high drift ductility, Grade
II and III structures have moderate-to-high drift ductility,
and Grade IV structures have relatively low drift ductil-
ity. The upper limits for structures with different grades
are given as follows:
N W ,C
f c Ac
≤
0.4 Grade I, Intensity 9
0.5 Grade I, Intensity 7 or 8
0.6 Grade II or III
− Grade IV
, (6)
where N W ,C is the factored axial force for the wall, which
is 1.2(G k +
i r diQki) (wherein r di is the combination
coefficient (≤ 1) for variable action i [19] due to repre-
sentative gravity load); and f c is the design axial compres-
sive strength of concrete under uniaxial compression at 28
days, which is equal to the characteristic axial strength of
concrete f ck divided by the safety factor 1.4.
The characteristic axial strength f ck is determined by
150 mm × 150 mm × 300 mm prism compression tests.
In the Chinese code, it can conservatively be taken as
0.67 of the characteristic cube strength f cu,k , which resem-
bles the value of f cu adopted in the Hong Kong code.
The average value of the ratio f ck / f cu,k or so-called effec-
tiveness factor is about 0.76 based on the experimentalstudies.[56,57]
More stringent provisions are set for short pier RC
shear walls (4 < L/t ≤ 8) such that the axial compres-
sion ratios for Grades I, II and III short pier walls should
not exceed 0.45, 0.50 and 0.55, respectively in the critical
regions (JGJ3-2010).[58] The axial force in Equation (6)
is first calculated from the representative gravity action
(G k +
i r diQki), instead of the ultimate gravity action,
and expected to be taken by structures during earth-
quakes; then a multiplying factor of 1.2 is used to account
for the additional axial force incurred by unforeseen and
excluded actions on the walls. In the calculation of the
representative gravity action, the combination coefficient
r di is used to consider the reduced likelihood that full
variable actions are considered during earthquakes and,
for instance, the combination coefficient for residential
floor live load is 0.5. The reduction factors for floor
live loads (GB50009-2012) [59] in multi-storey buildings
are already absorbed in the combination coefficients; in
other words, variable actions Qki should not be reduced
before multiplying by combination coefficients. Further-
more, it was noted that the design axial compressive
strength f c used in Equation (6) can be rewritten in the
form of characteristic compressive cube strength as f c =
0.67 f cu/γ c = 0.67 f cu/1.4 = 0.48 f cu, which is close to thevalue (0.45 f cu) used in the Hong Kong code calculation,
which is presented in Equation (5).
Eurocode 8 (EC8) (EN 1998-1:2004)
EC8 [20] stipulates the upper limits for axial compression
ratio (calculated from the normalised axial force) for duc-
tile walls and columns designed for moderate (DCM) and
high (DCH) ductility classes, but there is no restriction
for low (DCL) ductility classes as follows:
N ED, EC
f cd Ac
≤
0.35 DCH
0.4 DCM
− DCL
, (7)
where N ED, EC is the design axial force from the
analysis for the seismic design situation (i.e. G k +i ψ E ,iQki + E , wherein E is seismic action and ψ E ,i
is the combination coefficient (≤ 1) for variable action
Qki); and f cd is the design (with a safety factor of 1.5)
cylinder strength of concrete under uniaxial compression
at 28 days, which approximately equals 0.8 times the
corresponding cube strength.
The definitions of axial compression ratio for RC
walls and columns are identical in EC8. The denominator
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HKIE Transactions 129
in Equation (7) has a similar form to that of Equation (6),
but the cylinder strength is used in RC designs with EC8.
If the design cylinder strength f cd in EC8 is converted to
the characteristic cube strength f cu, it can beshown below:
f cd = 0.8 f cu/γ c = 0.8 f cu/1.5 = 0.53 f cu.
The design axial force in Equation (7) consists of two
major components: (i) axial force induced by representa-
tive gravity action and (ii) axial force induced by seismic
action. Similar to the Chinese seismic code, the limits for
columns are less restrictive than walls and the representa-
tive gravity load is used by EC8 in calculation of the axial
force, in which the effect of seismic action for RC walls is
also included. Although axial forces incurred in cantilever
walls by seismic loads are relatively minor as compared
with permanent gravity action in general, coupled shear
walls have to bear significantly extra axial forces incurred by seismic action due to the coupling action aggregated
from the shear forces of coupling beams, which obviously
has a non-negligible effect on the seismic performance of
the walls. Therefore, amongst the three aforementioned
design codes, the definition of the axial compression ratio
used in EC8 can be considered as the most appropri-
ate description of realistic stress states experienced by
RC structures during earthquakes. Actually, limits of the
axial compression ratio stipulated in EC8 can readily
be compared with experimental studies to see whether
the provisions can ensure sufficient ductility of the RC
members.
New Zealand concrete code (NZS 3101:2006) and
other design codes
New Zealand concrete code NZS 3101:2006 [60] does not
have similar provisions on the axial force ratios as those
in the Hong Kong, GB and EC codes, but does specify
limiting sectional curvatures or strains in potential plastic
hinge regions for different RC members (Clause 2.6.1.3.4,
Part 1:2006). Limiting material strains is apparently the
most direct method to control curvature ductility of RC
members; however, whether it is sufficient to prevent thelow cyclic fatigue phenomenon or rapid strength and stiff-
ness degradation of RC members under cyclic loading is
uncertain.
It is also worth mentioning that the United States (US)
ACI 318-11 [61] also does not introduce similar lim-
its on the axial compression ratio for RC columns and
walls. Nevertheless, a standard for the seismic rehabili-
tation of buildings ASCE/SEI 41-06 [62] stated that RC
walls with axial loads greater than 35% of nominal axial
load strength P 0 shall not be considered effective in resist-
ing seismic forces. The Canadian concrete code CSA
A23.3-04 (R2010) [63] also stated that flexural members
with factored axial loads in excess of 0.35 P 0 shall have
a nominal resistance greater than the induced member
force, i.e. not be designed to form potential plastic hinges
and dissipate energy in any circumstances under seismic
effects.
Comparisons of code provisions
Although the definitions of axial force ratio in the Hong
Kong, GB and EC codes are not the same, particularly the
axial forces in the numerators, the compressive strength
term in the denominators can conveniently be con-
verted to the characteristic equivalent axial strength with f ck = 0.67 f cu for comparison. Table 1 summarises the key
comparisons of the provisions on the axial compression
ratios defined in the three codes.
At first sight, looking at the last row in Table 1, the
Hong Kong code has the least stringent limit on the axial
compression ratio for RC walls as compared with the
other two codes. In addition, it was noticed that the axial
Table 1. Comparisons of code provisions on axial compression ratios for RC walls.
HKConcrete2013 GB50011-2010 EC8
Original definition of axialcompression ratio
N W , HK 0.45 f cu Ac
N W ,C f c Ac
N ED, EC f cd Ac
Limit ≤ 0.75 ≤
0.4 Grade I, Intensity 9
0.5 Grade I, Intensity 7 or 8∗
0.6 Grade II or III
− Grade IV
≤
0.35 DCH
0.4 DCM
− DCL
Seismic/lateral force effects × ×
Variable load reduction ×
Re-normalised axialcompression ratio limit vs f ck
N W , HK
f ck Ac≤ 0.50
N W ,C
f ck Ac≤
0.29 Grade I, Intensity 9
0.36 Grade I, Intensity 7 or 8
0.43 Grade II or III
− Grade IV
N ED, EC
f ck Ac≤
0.28 DCH
0.32 DCM
− DCL
*Limits for Grades I, II and III short pier RC shear walls (4 < H / B ≤ 8) are 0.45, 0.50 and 0.55, respectively.
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130 J.S. Kuang and Y.P. Yuen
Figure 5. Code-specified axial compression ratio limits and expected achievable ductility.
force in the numerator is generally much larger than those
of the GB and EC codes, where the full ultimate gravity
action is considered instead of the representative grav-
ity action. For instance, if both sides of the inequality
are divided by 1.4 (a safety factor for dead loads in the
HKConcrete2013), the limit is immediately toughened to
0.36 and the possible reduction in variable or live loads
is not even considered yet. The limits of axial compres-
sion ratio stipulated in the Chinese code resemble thosein EC8, but again, the combinations of actions for cal-
culating the axial forces are different in the two codes
as mentioned before. For cantilever walls, the Chinese
code is virtually more stringent because the safety factor
1.2 is used to amplify the action. But for coupled shear
walls, it is not conclusive in which one of the two codes
is more conservative, since the factor of 1.2 may not be
sufficient to cover the exceeding axial forces induced by
the coupling action. Nevertheless, EC8 provides a more
realistic assessment for these cases by taking into the
consideration of seismic action or generally lateral force
effects.
If the relationship between the displacement ductility
and the axial compression ratio shown in Figure 2 is intro-
duced again and plotted together with the code-specified
limits of the axial compression ratio, the expected achiev-
able ductility of RC walls can clearly be evaluated
as shown in Figure 5. In general, the required dis-
placement ductility for fully ductile structures under
moderate-to-high seismic effect should not be less than
3.5 [5] and EC8 provisions undoubtedly satisfy this tar-
get level of ductility. The Grade I structures designed
according to the Chinese code can also satisfy this
target, but the Grade II and III structures may only
have restricted inherent ductility and are susceptible to
out-of-plane buckling. It can be shown, however, that
the limit of the HKConcrete2013 is somehow unjusti-
fiable in the sense of targeting to control the ductility
and is far beyond the other limits stipulated in GB and
EC8, if it is accepted that the ultimate design gravity1.4G k + 1.6Qk is effective in evaluating the axial com-
pression ratio during exceptional loading cases. There-
fore, the provision in the HKConcrete2013 on the axial
compression ratio for RC walls has some improv-
able aspects, including the definition, load combination
method and specified limit.
Recommendations for possible amendments to
Clause 9.9.3, the HKConcrete2013
Based on the results of a comprehensive statistical analy-
sis using 474 sets of experimental data and comparisons
with other design codes, the methods for calculating
the effective axial compression and the limiting value
of the axial compression ratio for RC structural walls
stipulated in the HKConcrete2013 may be amended and
improved on a more scientific basis. Recommendations
are made for possible amendments to Clause 9.9.3, the
HKConcrete2013 as follows:
(1) In Clause 9.9.3.3, the value of axial compression
should be calculated based on the realistic rep-
resentative or the effective gravity action rather
than the ultimate gravity action; hence it should
be determined as follows:
N W , HK = 1.2
G k +
i
ψriQki
, (8)
where ψri is the combination coefficient (≤ 1)
reducing the imposed action Qki to the cor-
responding effective gravity action during rare
loading cases. Values of ψri for various actions
in different usage can be taken from Table 2. The
factor of 1.2 is used to account for incurred axial
force due to excluded actions.
(2) As Hong Kong is a region of moderate
seismicity,[19] for the design of building struc-
tures, it would be appropriate to design for dis-
placement ductility values µ corresponding to
the structures of limited ductility [64] and the
ductility factor may be taken as 2 < µ ≤ 4.
Referring to the results of the comprehensive
statistical analysis presented in Figure 5, a reason-
able limit on the axial compression ratio of RC
structural walls is found and given as follows:
ncr = N W , HK
f ck Ac
≤ 0.4. (9)
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HKIE Transactions 131
Table 2. Values of ψri for various imposed actions.
Specific use Storey Examples ψri
Areas for domestic and residential
activities, offices and places where people may congregate.
Roof 1.0
Storeys with correlated occupancies.
School, theatre, etc. 0.8
Independently occupied storeys. Dwelling area, restaurant, etc. 0.5
Areas in retail shops, departmentstores, storage, industrial use and accumulation of goods may occur.
Warehouse, library, mechanicalroom, etc.
1.0
By rewriting Equation (9) and taking f ck = 0.67 f cu,
then the axial compression ratio of RC structural walls
is given as follows:
ncr = N W , HK
f cu Ac
≤ 0.27. (10)
To preserve the clear physical meaning of the axial
compression ratio, it is not necessary for the factor of 0.45
to be included in the denominator (Equation (5)).
Conclusions
Excellent lateral stability and drift ductility of reinforced
concrete shear walls are important in the design of
medium-to-high-rise buildings to resist seismic actions
and other exceptional loads. However, shear walls in
modern buildings are often subjected to very high axial
compression, which has been pushing the limits of the
conventional design and analysis theories.
A comprehensive statistical analysis using 474 sets
of experimental data was conducted to investigate the
effect of the axial compression ratio on the structural per-
formance of various types of RC structural wall. It was
shown that the ductility of shear walls generally dimin-
ished with an increase in axial compression ratio, and
this trend was particularly noticeable for slender walls
with an aspect ratio greater than 1.5. Provisions on the
limits of the axial compression ratio stipulated in vari-
ous design codes of practice were then compared. The
expected attainable ductility of RC walls designed to
different codes was evaluated and compared with thestatistical analysis results.
Based on the analysis results, recommendations were
made for possible amendments to Clause 9.9.3 detail-
ing for ductility of walls in the HKConcrete2013 [18]
for calculation of the effective axial compression and
determination of the limiting value of the axial compres-
sion ratio. The suggested amendments include: (1) the
calculation of the effective axial compression in RC struc-
tural walls should be based on a realistic, representative
gravity action; and (2) the limiting value for the axial
compression ratio should guarantee that well-detailed RC
structural walls can attain moderate or at least restricted
ductility.
Funding
This work was supported by the Hong Kong Research GrantsCouncil [grant number 614011].
Notes on contributors
Ir Prof J S Kuang is a Professor of Civil and Environmental Engineering,the Hong Kong University of Scienceand Technology. His areas of exper-tise span seismic engineering, with anemphasis on seismic design and the behaviour of concrete structures, seis-mic vulnerability assessment of tall buildings, large-scale testing of struc-
tural concrete, and computational mechanics and simulationin structural engineering. Ir Prof Kuang’s awards include theTelford Premium and the TK Hsieh Award from the Institu-tion of Civil Engineers UK in 2014 and 2006, respectively, and
the HKIE Transactions Prize from the Hong Kong Institution of Engineers in 2007.
Dr Y P Yuen is currently an AssistantProfessor of the Department of CivilEngineering at the Bursa OrhangaziUniversity, Turkey. His research inter-ests include seismic analysis and engi-neering of building and bridge struc-tures, theoretical and computationalmechanics of materials, reinforced concrete and masonry structures, and
tall building structures. Dr Yuen is the recipient of the 2014Telford Premium from the Institution of Civil Engineers in theUK, presented for the best paper on engineering and computa-tional mechanics.
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