Ductility Design of Reinforced Concrete Shear Walls

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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: [email protected]

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

http://-/?-

mailto:[email protected]

mailto:[email protected]

http://-/?-



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.



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.




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.




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.




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




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 ≤


0.5 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≤


0.36 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.




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)




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.

References

[1] Fintel M. Need for shear walls in concrete buildings for seismic resistance: observations on the performance of buildings with shear walls in earthquakes of the last thirtyyears. In: Hsu and Mau, editors. Concrete shear in earth-quake. London-New York: Elsevier Science Publishers,Inc.; 1992; p. 34–42.

[2] Holden T, Restrepo J, Mander JB. Seismic performance of precast reinforced and prestressed concrete walls. J StructEng-ASCE. 2003;129(3):286–296.

[3] Sezen H, Whittaker AS, Elwood KJ, Mosalam KM. Per-formance of reinforced concrete buildings during the




August 17, 1999 Kocaeli, Turkey earthquake, and seismicdesign and construction practise in Turkey. Eng Struct.2003;25:103–114.

[4] Wyllie LA Jr, Filson JR. Armenia earthquake recon-naissance report. Earthq Spectra Publication No. 89.01,

Special Supplement; 1989.[5] Paulay T, Priestley MJN. Seismic design of reinforced

concrete and masonry buildings. New York: John Wiley& Sons; 1992.

[6] Yuen YP, Kuang JS. Nonlinear responses and failure of infilled RC frame structures under biaxial seismic exci-tation. 15th World Conf Earthq Eng. Lisbon, Portugal;2012.

[7] Kuramoto H. Seismic design codes for buildings in Japan.J Disaster Res. 2006;1(3):341–356.

[8] Su RKL, Wong SM. A survey on axial load ratios of medium-rise residential buildings in Hong Kong. HKIETransactions. 2006;14(3):40–46.

[9] Wallace JW, Massone LM, Bonelli P, et al. Damage and implications for seismic design of RC structural wall

buildings. Earthq Spectra. 2012;28(S1):S281–S299.[10] Adebar P, Ibrahim AMM, Bryson M. Test of high-rise core

wall: effective stiffness for seismic analysis. ACI Struct J.2007;104(5):549–559.

[11] Bohl A, Adebar P. Plastic hinge lengths in high-rise con-crete shear walls. ACI Struct J. 2011;108(S15):148–157.

[12] Kazaz I, Gülkan P, Yakut A. Deformation limits for structural walls with confined boundaries. Earthq Spectra.2012;28(3):1019–1046.

[13] Qian J, Chen Q. A macro model of shear walls for push-over analysis. P I Civil Eng-Str B. 2005;158(2):119–132.

[14] Su RKL, Wong SM. Seismic behaviour of slender rein-forced concrete shear walls under high axial load ratio.Eng Struct. 2007;29:1957–1965.

[15] Zhang Y, Wang Z. Seismic behaviour of reinforced con-

crete shear walls subjected to high axial loading. ACIStruct J. 2000;97(5):739–750.

[16] Adebar P. Compression failure of thin concrete walls dur-ing 2010 Chile earthquake: lessons for Canadian design practice. Can J Civil Eng. 2013;40:711–721.

[17] EERI. The Mw 8.8 Chile earthquake of 27 February 2010.EERI Special Earthquake Report. Newsletter. EarthquakeEngineering Research Institute, California; 2010.

[18] Buildings Department. Code of practice for structural useof concrete 2013. Hong Kong: The HKSAR Government;2013.

[19] National Standard of the People’s Republic of China. Codefor seismic design of buildings (GB 50011–2010). Beijing:China Architecture & Building Press; 2010. Chinese.

[20] CEN. Eurocode 8: design of structures for earthquake

resistance. Part 1: general rules, seismic actions and rulesfor buildings (EN 1998–1:2004). European Committee for Standardization, Brussels; 2004.

[21] Priestley MJN, Calvi GM, Kowalsky MJ. Displacement- based seismic design of structures. Pavia, Italy: IUSSPress; 2007.

[22] Borg RC, Rossetto T, Varum H. The effect of the number of response cycles on the behaviour of reinforced concreteelements subject to cyclic loading. 15th World Conf onEarthq Eng. Lisbon, Portugal; 2012.

[23] Kappos A, Penelis GG. Earthquake resistant concretestructures. Boca Raton: CRC Press; 1996.

[24] Ali A, Wight JK. RC structural walls with staggered door openings. J Struct Eng-ASCE. 1991;117:1514–1531.

[25] Barda F, Hanson J, Corley W. Shear strength of low-rise walls with boundary elements. Reinf Concrete StructSeism Zones, SP-53, American Concrete Institute, Detroit,1977;149–202.

[26] Birely AC. Seismic performance of slender reinforced

concrete structural walls [Ph.D. thesis]. Washington (DC):University of Washington; 2011.

[27] Cardenas AE, Magura DD. Strength of high-rise shear walls – rectangular cross sections. Response MultistoryConcrete Struct Lateral Forces, SP-36, American ConcreteInstitute, Detroit, 1973;119–150.

[28] Carrillo J, Alcocer SM. Backbone model for performance- based seismic design of RC walls for low-rise housing.Earthq Spectra. 2012;28(3):943–964.

[29] Carrillo J, AlcocerSM. Acceptance limits for performance- based seismic design of RC walls for low-rise housing.Earthq Eng Struct D. 2012;41:2273–2288.

[30] Dazio A, Beyer K, Bachmann H. Quasi-static cyclic testsand plastic hinge analysis of RC structural walls. EngStruct. 2009;31:1556–1571.

[31] Devi GN, Subramanian K, Santakumar AR. Experi-mental investigations on reinforced concrete lateral load resisting systems under lateral loads. Exp Techniques.2011;35(4):59–73.

[32] Ghorbani-Renani I, Velev N, Tremblay R, Palermo D,Massicotte B, Lége P. Modeling and testing influence of scaling effects on inelastic response of shear walls. ACIStruct J. 2009;106(3):358–367.

[33] Han SW, Oh YH, Lee LH. Seismic behaviour of struc-tural walls with specific details. Mag Concrete Res.2002;54:333–345.

[34] Kuang JS, Ho YB. Seismic behavior and ductility of squatreinforced concrete shear walls with nonseismic detailing.ACI Struct J. 2008;105(2):225–231.

[35] Kuang JS, Ho YB. Enhancing the ductility of non-

seismically designed reinforced concrete shear walls. P ICivil Eng-Str B. 2007;160(3):139–149.

[36] Hirosawa M. Past experimental results on reinforced con-crete shear walls and analysis on them. Ministry of Con-struction, Tokyo; 1975. Japanese.

[37] Hidalgo PA, Ledezma CA, Jordan RM. Seismic behavior of squat reinforced concrete shear walls. Earthq Spectra.2002;18(2):287–308.

[38] Lefas ID, Kotsovos MD, Ambrasseys NN. Behaviour of RC structural walls: strength, deformation character-istics and failure mechanism. ACI Struct J. 1990;87(1):23–31.

[39] Lefas ID, Kotsovos MD. Strength and deformation charac-teristics of reinforced concrete walls under load reversals.ACI Struct J. 1990;87(6):716–726.

[40] Liao FY, Han LH, Tao Z. Seismic behaviour of cir-cular CFST columns and RC shear wall mixed struc-tures: experiments. J Constr Steel Res. 2009;65(8–9):1582–1596.

[41] Morgan BJ, Hiraishi H, Corley WG. US-Japan quasi statictest of isolated wall planar reinforced concrete structure.PCA Report, Construction Technology Division, Skokie,Illinois; 1986.

[42] Oesterle RG. Inelastic analysis for in-plane strengthof reinforced concrete shear walls [Ph.D. dissertation].Evanston (IL): North-western University; 1986.

[43] Pilakoutas K, Elnashai AS. Cyclic behaviour of RC can-tilever walls, part I: experimental results. ACI Struct J.1995;92:271–281.




[44] Qian J, Jiang Z, Ji X. Behavior of steel tube-reinforced concrete composite walls subjected to high axial force and cyclic loading. Eng Struct. 2012;36:173–184.

[45] Riva P, Franchi A. Behavior of reinforced concrete wallswith welded wire mesh subjected to cyclic loading. ACI

Struct J. 2001;98(3):324–334.[46] Salonikios T, Kappos A, Tegos I, Penelis G. Cyclic

load behavior of low-slenderness reinforced concretewalls: design basis and test results. ACI Struct J.1999;96(4):649–660.

[47] Shiu KN, Daniel JI, Aristizabal JD, Fiorato AE, CorleyWG. Earthquake resistant structural walls – tests of wallswith and without openings. Report to the National Sci-ence Foundation. Portland Cement Association, Skokie,Illinois; 1981.

[48] Takahashi S, Yoshida K, Ichinose T. Flexural drift capacityof reinforced concrete wall with limited confinement. ACIStruct J. 2013;110(S10):95–104.

[49] Thomsen JH, Wallace JW. Displacement-based designof reinforced concrete structural walls: an experimental

investigation of walls with rectangular and t-shaped cross-sections. Report No. CU/CEE-95/06, Potsdam, N.Y.:Department of Civil and Environmental Engineering,Clarkson University; 1995.

[50] Vallenas MV, Bertero VV, Popov EP. Hysteretic behaviour of reinforced concrete structural walls. UCB/EERC Report79/20, Berkeley: Earthquake Engineering Research Cen-ter, University of California; 1979.

[51] Wallace JW, Moehle JP. Ductility and detailing require-ments of bearing wall buildings. J Struct Eng-ASCE.1991;118(6):1625–1644.

[52] Wang TY, Bertero VV, Popov EP. Hysteretic behavior of reinforced concrete framed walls. UCB/EERC Report75/23, Berkeley: Earthquake Engineering Research Cen-ter, University of California; 1975.

[53] Yuen H, Choi C, Lee L. Earthquake performance of high-strength concrete structural walls with boundary ele-ments. 13th World Conf on Earthq Eng. Vancouver, B.C.,Canada; 2004.

[54] Zhou Y, Lu X. SLDRCE database on static tests of struc-tural members and joint assemblies. State key laboratoryof disaster reduction in civil engineering. Shanghai, China:Tongji University; 2008. Chinese.

[55] Park R. Evaluation of ductility of structures and structural

assemblages from laboratory testing. B New Zeal Natl SocEarthq Eng. 1989;22(3):155–166.

[56] Zhang Q. Concrete structure design: Basic theory, methodsand examples. Jiangsu: Jiangsu Science and TechnologyPublishing House; 1993. Chinese.

[57] Nielsen MP. Limit analysis and concrete plasticity. 2nd ed.Boca Raton: CRC Press; 1999.

[58] National Standard of the People’s Republic of China.Technical specification for concrete structures of tall building (JGJ 3–2010). Beijing: China Architecture &Building Press; 2010. Chinese.

[59] National Standard of the People’s Republic of China. Load code for the design of building structures (GB 50009– 2012). Beijing: China Architecture & Building Press;2012. Chinese.

[60] Standards New Zealand. Concrete structure standard-thedesign of concrete structures (NZS 3101:Part 1:2006).Wellington, New Zealand: SNZ; 2006.

[61] American Concrete Institute. Building code requirementsfor structural concrete (ACI 318–11) and Commentary.Farmington Hills, MI: ACI; 2011.

[62] American Society of Civil Engineers (ASCE). Seis-mic rehabilitation of existing buildings (ASCE/SEI 41).Reston, Virginia: ASCE; 2006.

[63] Canadian Standard Association. Design of concrete struc-tures (CSA:A23.3–04 (R2010)). Ontario, Canada: CSA;2010.

[64] Park R. Design procedures for achieving ductile behaviour of reinforced concrete buildings. In: Lam ESS, Ko JM,editors. International workshop on earthquake engineer-

ing for regions of moderate seismicity. Hong Kong: theHong Kong University of Science and Technology; 1998. p. 45–50.

Ductility Design of Reinforced Concrete Shear Walls

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