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Magazine of Concrete Research, 2013, 65(17), 1034–1043
http://dx.doi.org/10.1680/macr.13.00018
Paper 1300018
Received 09/01/2013; revised 25/04/2013; accepted 20/05/2013
Published online ahead of print 11/07/2013
ICE Publishing: All rights reserved
Magazine of Concrete Research
Volume 65 Issue 17
Effect of transverse reinforcement on short
structural wall behaviour
Zygouris, Kotsovos and Kotsovos
Effect of transverse
reinforcement on short
structural wall behaviour
Nick St Zygouris
Civil Engineer/Research Student, Laboratory of Concrete Structures,
National Technical University of Athens, Athens, Greece
Gerasimos M. Kotsovos
Research Associate, Laboratory of Concrete Structures, National Technical
University of Athens, Athens, Greece
Michael D. Kotsovos
Professor, Laboratory of Concrete Structures, National Technical University
of Athens, Athens, Greece
This paper reports on an investigation of the effect of the transverse reinforcement arrangement on the effective
ductility of short structural walls. The work described is based on a comparative study of the behaviour of three
pairs of specimens, with different transverse reinforcement arrangements, tested under cyclic loading. Two of the
reinforcement arrangements investigated are those specified by Eurocode 8 (EC8) for medium and high ductility
levels and the third is that resulting from application of the compressive force path method, with the latter method,
unlike EC8, not specifying confining reinforcement within the critical regions. The results obtained indicate that, in
spite of the significant differences in the reinforcement arrangement, all specimens exhibited similar behaviour as
regards ductility, load-carrying capacity and mode of failure, the latter being characterised by crushing of concrete
and buckling of the flexural bars within the compressive zone at the base of the specimens.
Notation
b wall width
h wall height
l wall length
f
c
uniaxial cylinder compressive strength
f
y
yield stress of steel bar
M
f
flexural capacity of wall
M
y
bending moment of wall corresponding to first yielding
(either of concrete of reinforcing steel)
P
u
experimentally established load-carrying capacity of
wall
P
f
load-carrying capacity of wall corresponding to M
f
P
y
load corresponding to M
y
V
f
shear force corresponding to M
f
ä
fail
displacement at final load cycle (failure)
ä
sust
displacement at last sustained load cycle
ä
y
displacement at nominal yield
ì
fail
ductility ratio corresponding to ä
fail
ì
sust
ductility ratio corresponding to ä
sust
Introduction
Current code provisions (e.g. Eurocode 8 (EC8) (BSI, 2004a)) for
the earthquake-resistant design of reinforced concrete structural
walls specify reinforcement arrangements comprising two parts,
one part forming ‘concealed column’ (CC) elements along the
two vertical edges of the walls and the other consisting of a set of
grids of uniformly distributed vertical and horizontal bars, within
the wall web, arranged in parallel to the wall large side faces.
The CC elements are intended to impart to the walls the code-
specified strength and ductility, whereas the wall web is designed
against the occurrence of ‘shear’ failure, before the wall flexural
capacity is exhausted. The specified ductility is considered to be
achieved by confining concrete within the CC elements through
the use of a dense stirrup arrangement, thus increasing both the
strength and the strain capacity of the material. On the other
hand, shear failure is mainly prevented by providing horizontal
web reinforcement capable of sustaining either the whole shear
force or its portion in excess of that which can be sustained by
concrete alone. It is also important to add that calculation of the
wall flexural capacity allows for the contribution of all vertical
reinforcement within both the CC elements and the web.
The above design procedure, however, has a significant drawback:
the dense spacing of the stirrups often results in reinforcement
congestion within the CC elements and this may cause difficulties
in concreting and, possibly, incomplete compaction of the concrete
(Salonikios et al., 1999). An investigation of the possibility of
preventing reinforcement congestion within the CC elements with-
out lowering the load-carrying capacity and the ductility, which the
current code procedures are considered to safeguard, was the
subject of recently published work (Cotsovos and Kotsovos, 2007;
Kotsovos et al., 2011). This work demonstrated that designing
slender walls (i.e. walls with an aspect ratio (height to length ratio)
greater than 2) in accordance with the compressive force path (CFP)
method results in a considerable reduction of not only the amount of
transverse reinforcement within the CC elements, but also the
1034
length of these elements, without compromising the code perform-
ance requirements. It is important to note that, in contrast with the
code methods, the CFP method specifies reinforcement within the
CC elements not for confining concrete, but for sustaining the
transverse tensile stresses that have been found invariably to
develop within the compressive zone of reinforced concrete
structural elements when their flexural capacity is approached
(Cotsovos and Pavlovic, 2005; Kotsovos and Pavlovic, 1995, 1999).
The work presented here complements the previous work cited
above by investigating the possibility of reducing the amount of
transverse reinforcement within the CC elements of short walls
(i.e. walls with an aspect ratio smaller than 2) without any
significant effect on structural performance. Regarding the work
on slender walls, it was also based on a comparative study of the
results obtained from tests on walls under in-plane loading
mimicking seismic action, with the specimens being designed in
accordance with EC8 specifications for medium (DCM) and high
(DCH) ductility behaviour and in accordance with the CFP
method. In contrast to the code specifications, the CFP method
does not specify any additional transverse reinforcement within the
CC elements, since, unlike slender walls, short walls are not
characterised by the development of transverse tensile stresses
within the compressive zone before flexural capacity is attained
(Kotsovos and Pavlovic, 1999). All structural walls investigated
had an aspect ratio of just over 1
.
35 and, unlike the amount and
arrangement of the transverse reinforcement, their geometric
characteristics and flexural reinforcement are the same. Although
the effect on structural behaviour of placing confining reinforce-
ment within the CC elements of short walls forms the subject of
already published experimental work, none of the specimens tested
were designed in accordance with the CFP method (Kuang and Ho,
2008; Takahashi et al., 2013). Moreover, in some cases, attention
is focused on the study of shear types of failure of walls in which
the rotation of both ends is prevented (Hidalgo et al., 2002).
Structural walls investigated
Design details
The overall dimensions of the structural walls investigated are
shown in Figure 1, which also provides an indication of the
testing arrangement. All specimens (length l ¼ 1060 mm, height
h ¼ 1200 mm, width b ¼ 150 mm) were monolithically connected
to two ‘rigid’ prismatic elements at both their bottom and top end
faces. They were fixed to the laboratory strong floor through the
bottom prismatic element (1720 mm long 3 750 mm high 3
700 mm wide) so as to simulate fixed-end conditions, whereas
load was applied through the top prismatic element (with square
cross-section of 300 mm side and 1420 mm length). Both prisms
were over-sized and over-reinforced so to behave essentially as
rigid bodies.
In total, six walls were tested. The design details of the walls
designed in accordance with the CFP method are shown in Figure
2 and those of the walls designed in accordance with the code
provisions for DCM and DCH are shown in Figures 3 and 4,
respectively. Concrete with a cylinder strength f
c
of 43 MPa at the
time of testing was used for all the specimens. The details of the
reinforcement used are summarised in Table 1, with the steel
properties provided in Table 2.
For all specimens, the longitudinal reinforcement (designated as
A
s,v
in Table 1) comprised 11 pairs of 12 mm dia. (23(11D12))
steel bars at a centre-to-centre spacing of 100 mm, with the bars’
centreline lying at a distance of 15 mm from the closest wall face.
However, specimen DCM-1 (see Figure 3) had three additional
10 mm dia. bars within the CC elements, since these bars form part
of the confining reinforcement cage discussed later. (It should be
noted that the presence of these vertical bars is allowed in the
calculation of the wall’s flexural capacity.)
In contrast to the longitudinal reinforcement, the amount and
arrangement of the horizontal web reinforcement (A
s,h
in Table 1)
depended on the method of design employed. For the specimens
designed either in accordance with the CFP method or in
accordance with the code provisions for DCM, the horizontal web
reinforcement comprised 8 mm dia. stirrups. For the specimens
designed in accordance with the code provisions for DCH,
10 mm dia. stirrups were used. In all cases the centre-to-centre
spacing of the stirrups was 130 mm.
For the specimens designed in accordance with the code provi-
sions either for DCM or DCH, additional reinforcement (A
s,cc
in
Table 1) in the form of 8 mm dia. stirrups at a 65 mm centre-to-
centre spacing was placed along the vertical edges of the walls in
order to provide confinement to the CC elements. Moreover, the
walls designed in accordance with the code provisions for DCH
were also reinforced with eight diagonal 12 mm dia. bars (A
s,d
in
Table 1), as indicated in Figure 3. In the latter case, it is
important to note the difficulties encountered in forming a
reinforcement cage comprising not only vertical and transverse,
but also diagonal, reinforcement.
Loading regimes
The walls were subjected to two types of cyclic loading (type 1
and type 2) applied in the form of statically imposed horizontal
displacements varying between extreme predefined values as
indicated in Figure 5. For type 1 loading, the imposed displace-
ments varied between values corresponding to ductility ratios of
around 4 until failure occurred; failure was considered to occur
when the sustained load was less than 85% of the peak load
value. For type 2 loading, the extreme predefined values of
displacement were initially set to 10 mm, increasing in equal
steps thereafter until specimen failure (as defined above). Three
load cycles were carried out for each of the above predefined
values with a displacement rate of 0
.
25 mm/s.
Design
The walls were designed so that their load-carrying capacity was
reached when their base cross-section attained its flexural capa-
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Magazine of Concrete Research
Volume 65 Issue 17
Effect of transverse reinforcement on
short structural wall behaviour
Zygouris, Kotsovos and Kotsovos
city, the latter condition being referred to as plastic-hinge
formation. Using the cross-sectional and material characteristics
of the walls and the rectangular stress block recommended by
Kotsovos (2011), the flexural capacity M
f
of the elements was
calculated from first principles, allowing for the contribution of
all vertical reinforcement (both within the CC elements and
within the web) and setting all material safety factors equal to 1.
Using M
f
, the wall load-carrying capacity P
f
(and hence the
corresponding shear force V
f
¼ P
f
) can be easily calculated from
static equilibrium. The values of M
f
and V
f
¼ P
f
for each of the
specimens tested are given in Table 3 together with the experi-
mentally established values of the load-carrying capacity P
u
: The
table also includes the values of bending moment M
y
and load
P
y
, which correspond to yielding of the flexural reinforcement
closest to the tensile face of the walls; these values were used to
assess the ductility factors of the specimens tested.
As discussed earlier, the horizontal reinforcement of the walls
was designed either in compliance with the earthquake-resistant
design clauses of EC2 (BSI, 2004b) and EC8 (BSI, 2004a) or in
accordance with the CFP method. From Figures 3 and 4, it is
interesting to note the densely spaced stirrups confining the CC
elements within the ‘critical regions’ (extending throughout the
wall height) specified by the codes. Such spacing, resulting from
expression 5.20 of EC8 (clause 5.4.3.4.2), is considered to
safeguard ductile wall behaviour. In contrast to the reasoning in
the codes for the calculation of stirrups within the CC elements,
the CFP method does not specify such reinforcement for
300
300
150
700
A1–A1
330
A1
1420
1060
330
150
Hold down
bolts
A1
Strong floor
750
1200
2100
HEB300 HEB300 HEB300
HEB450
HEB300
IPE600
MTS actuator
HEA160
HEB300
HEA160
1·25
Figure 1. Loading frame and dimensions of specimens tested
(dimensions in mm)
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Magazine of Concrete Research
Volume 65 Issue 17
Effect of transverse reinforcement on
short structural wall behaviour
Zygouris, Kotsovos and Kotsovos
structural elements such as the walls investigated in this work,
which exhibit type III behaviour (Kotsovos and Pavlovic, 1999).
On the other hand, the horizontal web reinforcement designed in
compliance with the code requirements (clauses 6.2 and 9.6 in
EC2) is considered to improve shear capacity so as to prevent
shear failure of the walls before their flexural capacity is
exhausted. This reasoning is also in conflict with that underlying
the design of the horizontal reinforcement within the wall web in
accordance with the CFP method. In the latter case, horizontal
reinforcement is designed to sustain the horizontal force required
to develop in order to produce additional flexural resistance, in
which, when added to the bending moment corresponding to
structural member’s load-carrying capacity in the absence of
horizontal reinforcement, the resulting bending moment becomes
equal to the flexural capacity M
f
of the cross-section (Kotsovos
and Pavlovic, 1999).
Results
The structural walls investigated are designated with a two-part
label: the first part indicates the method of design (CFP, DCM
and DCH) while the second part (1 or 2) denotes the type of
loading.
Figures 6 and 7 show curves describing the relationship between
applied load and horizontal displacement of the load point for the
case of the CFP specimens under the two types of statically
applied cyclic loading; their counterparts for the DCM and DCH
specimens are shown in Figures 8 and 9 and Figures 10 and 11,
respectively. All curves are shown in a normalised form: the
values of load were divided by the calculated value of the load-
carrying capacity P
f
and the displacements were divided by the
calculated value of the displacement at nominal yield ä
y
:
Figures 12 and 13 show the variation of the energy dissipated
during each load cycle with increasing values of ductility ratio for
the types of cyclic loading adopted for the tests; the numbers
2 (11D12)⫻
2 D8@130⫻
CFP
2 D8@130⫻
2 (11D12)⫻
2 (11D12)⫻
2 D8@130⫻
Figure 2. Reinforcement details of walls CFP-1 and CFP-2
2 (11D12)⫻
D8@65
2 D8@130⫻
2 D10⫻
DCM-1
D8@65
2 (11D12)⫻
2 D8@130⫻
2 D10⫻
2 (11D12)⫻
2 D8@130⫻
D8@65
DCM-2
D8@65
2 (11D12)⫻
2 D8@130⫻
D8@65
3D10/cc
2 (11D12)⫻
3D10/cc
D8@65
2 D8@130⫻
D8@65
2 (11D12)⫻
D8@65
2 D8@130⫻
Figure 3. Reinforcement details of walls DCM-1 and DCM-2
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Magazine of Concrete Research
Volume 65 Issue 17
Effect of transverse reinforcement on
short structural wall behaviour
Zygouris, Kotsovos and Kotsovos
2 (11D12)⫻
D8@65
2 D10@130⫻
2 (2D12)⫻
D8@65
2 (11D12)⫻
2 D10@130⫻
D8@65
DCH
2 (11D12)⫻
D8@65
2 D10@130⫻
2 (2D12)⫻
Figure 4. Reinforcement details of walls DCH-1 and DCH-2
Specimen A
s,v
r
v
:% A
s,h
A
s,cc
A
s,d
CFP-1 2 3 (11D12) 1
.
55 2 3 D8@130 — —
CFP-2 2 3 (11D12) 1
.
55 2 3 D8@130 — —
DCM-1 2 3 (11D12) plus 3D10 within each CC element 1
.
85 2 3 D8@130 D8@65 —
DCM-2 2 3 (11D12) 1
.
55 2 3 D8@130 D8@65 —
DCH-1 2 3 (11D12) 1
.
55 2 3 D10@130 D8@65 2 3 (4D12)
DCH-1 2 3 (11D12) 1
.
55 2 3 D10@130 D8@65 2 3 (4D12)
Table 1. Reinforcement of specimens
Diameter: mm f
y
: MPa f
u
: MPa
8 563 563
f
s
f
u
f
y
(, )f
ss
ε
ε
sy1
ε
sy2
ε
s
ε
ε
sy1 y s
sy2
/
1·5% 3%
⫽
⭐⭐
fE
10 621 697
12 600 726
Table 2. Yield and ultimate strength values for reinforcing bars
and indicative stress–strain diagram
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Magazine of Concrete Research
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Effect of transverse reinforcement on
short structural wall behaviour
Zygouris, Kotsovos and Kotsovos
included in the figures indicate the sequence of the load cycles for
each specimen tested. The dissipated energy during each cycle is
provided in a form normalised with respect to a nominal value of
the elastic energy expressed as E
y
¼ P
y
ä
y
: The backbone envel-
opes of the normalised load–displacement curves in Figures 7, 9
and 11 are shown in Figure 14 and the modes of failure of the
walls are depicted in Figure 15. The calculated values of bending
moment M
y
and corresponding force P
y
at yield, flexural capacity
M
f
and corresponding load-carrying capacity P
f
, and the experi-
mentally established values of load-carrying capacity P
u
are given
in Table 3, whereas Table 4 lists displacements ä
y
, ä
sust
, ä
fail
at
nominal yield, sustained load cycle and load cycle at failure,
respectively, together with the values of the ductility ratio at the
sustained load cycle ( ì
sust
) and the load cycle at failure ( ì
fail
).
Specimen Calculated values P
u
:kN P
u
/P
f
M
y
:kNm P
y
:kN M
f
:kNm P
f
:kN
CFP-1 423 313 697 516 547
.
81
.
06
CFP-2 423 313 697 516 536
.
61
.
04
DCM-1 517 383 809 599 623
.
81
.
04
DCM-2 423 323 697 513 554
.
71
.
07
DCH-1 496 367 861 638 715
.
81
.
12
DCH-2 496 367 861 638 635
.
21
.
00
Table 3. Calculated values of bending moment M
y
and
corresponding force P
y
at yield, flexural capacity M
f
and
corresponding load-carrying capacity P
f
and experimentally
established values of load-carrying capacity P
u
⫺30
⫺20
⫺10
0
10
20
30
0 1000 2000 3000 4000
δ: mm
t: s
CFP-1
⫺40
⫺30
⫺20
⫺10
0
10
20
30
40
0 2000 4000 6000 8000 10 000
δ: mm
t: s
CFP-2
⫺40
⫺30
⫺20
⫺10
0
10
20
30
40
50
0 1000 2000 3000 4000 5000 6000
δ: mm
t: s
DCM-1
⫺40
⫺30
⫺20
⫺10
0
10
20
30
40
0 2000 4000 6000 8000 10 000
δ: mm
t: s
DCM-2
⫺60
⫺40
⫺20
0
20
40
60
0 1000 2000 3000 4000 5000 6000
δ: mm
t: s
DCH-1
⫺30
⫺20
⫺10
0
10
20
30
40
0 1000 2000 3000 4000 5000 6000 7000 8000
δ: mm
t: s
DCH-2
Figure 5. Loading histories adopted for the tests
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Magazine of Concrete Research
Volume 65 Issue 17
Effect of transverse reinforcement on
short structural wall behaviour
Zygouris, Kotsovos and Kotsovos
⫺1·5
⫺1·0
⫺0·5
0
0·5
1·0
1·5
⫺5 ⫺4 ⫺3 ⫺2 ⫺1012345
P P/
f
δδ/
y
CFP-1
Figure 6. Load–deflection curve of CFP-1
⫺1·5
⫺1·0
⫺0·5
0
0·5
1·0
1·5
⫺5 ⫺4 ⫺3 ⫺2 ⫺1012345
P P/
f
δδ/
y
CFP-2
Figure 7. Load–deflection curve of CFP-2
⫺1·5
⫺1·0
⫺0·5
0
0·5
1·0
1·5
⫺3 ⫺2 ⫺1012345
P P/
f
δδ/
y
DCH-2
Figure 11. Load–deflection curve of DCH-2
⫺1·5
⫺1·0
⫺0·5
0
0·5
1·0
1·5
⫺5 ⫺4 ⫺3 ⫺2 ⫺1012345
P P/
f
δδ/
y
DCM-1
Figure 8. Load–deflection curve of DCM-1
0
2
4
6
8
012345
EE
cy
/
μ
1
1
2
2
3
2
1
CFP-1
DCM-1
DCH-1
Figure 12. Variation of energy dissipated within each load cycle of
type 1 cyclic loading
⫺1·5
⫺1·0
⫺0·5
0
0·5
1·0
1·5
⫺5 ⫺4 ⫺3 ⫺2 ⫺1012345
P P/
f
δδ/
y
DCM-2
Figure 9. Load–deflection curve of DCM-2
⫺1·5
⫺1·0
⫺0·5
0
0·5
1·0
1·5
⫺6 ⫺5 ⫺4 ⫺3 ⫺2 ⫺1012345
P P/
f
δδ/
y
DCH-1
Figure 10. Load–deflection curve of DCH-1
0
1
2
3
4
01234
EE
cy
/
μ
CFP-2
DCH-2
DCM-2
Mean
1
1
1
4
2
3
5
6
4
5
5
6
4
7
8
9
11
10
7
8
9
Figure 13. Variation energy dissipated within each load cycle with
increasing ductility for type 2 cyclic loading
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Effect of transverse reinforcement on
short structural wall behaviour
Zygouris, Kotsovos and Kotsovos
Discussion
Figures 2 to 4 show that the walls designed in compliance with
the EC2 and EC8 provisions differ from those designed in
accordance with the CFP method in that the reinforcement of the
former walls includes a dense stirrup arrangement within the CC
elements extending throughout the height of the wall. For all
types of structural walls, current codes specify stirrups within the
CC elements in order to provide confinement to concrete, since
such confinement is considered essential for safeguarding ade-
quate ductility for the walls. On the other hand, the provision of
such reinforcement in accordance with the CFP method is
deemed unnecessary for structural elements exhibiting type III
behaviour (i.e. structural elements with a shear span-to-depth
ratio a
v
/d < 2
.
5) (Kotsovos and Kotsovos, 2008; Kotsovos and
Pavlovic, 1999). Such structural elements include the walls
investigated in the present work since, here, a
v
/d ¼ 1350/627
2
.
15, where d is the distance of the resultant of the forces
⫺1·5
⫺1·0
⫺0·5
0
0·5
1·0
1·5
⫺5 ⫺4 ⫺3 ⫺2 ⫺1012345
P P/
f
δδ/
y
CFP-2
DCH-2
DCM-2
Figure 14. Backbone envelopes of normalised lateral load–
displacement curves in Figures 7, 9 and 11
CFP-1 DCM-1 DCH-1
(a)
CFP-2 DCM-2 DCH-2
(b)
Figure 15. Failure modes of the walls tested
Specimen ä
y
:mm ä
sust
:mm ä
fail
:mm ì
sust
ì
fail
CFP-1 8
.
130
.
130
.
1—3
.
7
CFP-2 8
.
130
.
331
.
23
.
73
.
8
DCM-1 8
.
035
.
535
.
5—4
.
4
DCM-2 8
.
020
.
128
.
02
.
53
.
5
DCH-1 9
.
741
.
044
.
24
.
24
.
5
DCH-2 9
.
720
.
330
.
32
.
13
.
1
Table 4. Displacements at nominal yield (ä
y
), sustained load cycle
(ä
sust
) and load cycle at failure (ä
fail
) and ductility ratios
corresponding to ä
sust
and ä
fail
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Magazine of Concrete Research
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Effect of transverse reinforcement on
short structural wall behaviour
Zygouris, Kotsovos and Kotsovos
developing in the tension reinforcement on account of bending
from the extreme compressive fibre. On the other hand, both the
CFP and code methods specify transverse reinforcement in
amounts sufficient to safeguard against a flexural type of failure.
However, as discussed earlier in the section on design, the
reasoning underlying these methods is different.
Type 1 cyclic loading
As indicated in Figures 6, 8 and 10 and Tables 3 and 4, with the
exception of DCM-1, the walls exhibited similar behaviour under
this type of loading despite differences in their reinforcement
arrangement. Wall DCM-1 exhibited a nearly 20% larger stiffness
and sustained two additional load cycles before loss of load-
carrying capacity, in spite of the larger imposed displacement
corresponding to a ductility ratio of around 4
.
6. Such behaviour
is attributed to the three additional 10 mm bars placed within
each of the CC elements.
All the walls exhibited a similar mode of failure in that the loss
of load-carrying capacity was preceded by failure of the compres-
sive zone at the wall base (see Figure 15(a)). Such behaviour
clearly demonstrates that, under this type of loading, any amount
of reinforcement larger than that specified by the CFP method is
essentially ineffective.
It is interesting to note (Table 3) that deviation of the calculated
values of load-carrying capacity from their experimentally estab-
lished counterparts is of the order of 4–12%. The former values
correspond to values of flexural capacity M
f
calculated by
assuming that, after yielding, the stress of the steel bars remains
constant and equal to the yield stress f
y
: The validity of this
assumption is easily verified through a comparison of the
calculated values of the steel strains corresponding to M
f
with the
maximum strain value of the yield plateau of the experimentally
established stress–strain curves of the steel used; such a compari-
son clearly demonstrates that the former values are smaller than
the latter in all cases investigated. It appears, therefore, that
ignoring the hardening properties of the steel is not, as is usually
suggested (BSI, 2004a), the main cause of the above deviation
and further work is required to clarify this matter.
However, although the calculated values of flexural capacity
slightly underestimate their experimentally established counter-
parts, the walls do exhibit a flexural mode of failure and this is
considered to be indicative of the conservative nature of the
methods used to design the transverse reinforcement.
Figures 6, 8 and 10 and Table 3 also show the values of
displacement at the nominal yield point used for assessing the
specimens’ ductility ratios. The location of the nominal yield
point is determined in the following manner.
j The cross-section’s bending moment at first yield (M
y
)
(assessed by assuming that yielding occurs when either the
concrete strain at the extreme compressive fibre attains a
value of 0
.
002 or the tension reinforcement yields) and the
flexural capacity (M
f
) are first calculated.
j Using the derived values of M
y
and M
f
, the corresponding
values of the transverse load at yield (P
y
) and at flexural
capacity (P
f
) are obtained from the equilibrium equations
P
y
¼ M
y
/a
v
and P
f
¼ M
f
/a
v
, where a
v
¼ 1350 mm is the
distance of the point of application of the applied load from
the wall base.
j Using Figures 6, 8 and 10 (first load cycle to peak load
level), a line is drawn through the points of the load–
displacement curves at P ¼ 0 and P ¼ P
y
: This line is
extended to the load level P
f
: The displacement ä
y
corresponding to P
f
is used to calculate the ductility ratios
ì
sust
¼ ä
sust
/ä
y
and ì
fail
¼ ä
fail
/ ä
y
in Table 3, where ä
sust
and
ä
fail
are the values of displacement at the last sustained and
final load cycles, respectively.
It is evident from the above that all specimens subjected to type 1
cyclic loading exhibited ductile behaviour. In fact, Table 4
indicates that the values of the ductility ratio at the last load cycle
of the specimens (ì
fail
) vary between 3
.
5 and 4
.
5.
Figure 12 indicates that the energy dissipated during the load
cycles leading to failure relates to the specimen’s load-carrying
capacity: the higher a wall’s load-carrying capacity (see Table 3)
the larger the amount of energy dissipated during the first post-
peak load cycle. Such behaviour is considered to indicate that the
horizontal reinforcement arrangement predominantly affects
the post-peak structural characteristics. It may also be noted from
the figure that the energy dissipated reduces with each additional
load cycle.
Type 2 cyclic loading
Figures 7, 9 and 11 show that walls CFP-2 and DCM-2 exhibit
similar load–displacement behaviour despite the presence of a
significant amount of additional stirrup reinforcement within the
CC elements of DCM-2. On the other hand, wall DCH-2 is
characterised by a rather premature failure as a result of signifi-
cant out-of-plane displacements that occurred at the first load
cycle to displacement corresponding to ductility ratio 3
.
1 and
may have been caused by unintended eccentricities of the rein-
forcement due to difficulties encountered in placing the diagonal
bars.
Figure 13 shows the variation of energy dissipated with succes-
sive load cycles corresponding to increasing values of the
ductility ratio. The figure shows that, as for the case of the load–
displacement curves, walls CFP-2 and DCM-2 exhibit similar
trends in behaviour. After an initial slow rate of increase, the
dissipated energy increases at an increasing rate up to the value
of the ductility ratio essentially corresponding to the peak load
level; thereafter, the rate of increase reduces and it appears that
loss of load-carrying capacity occurs when the ability of the
structural element to dissipate energy is diminished. The trend in
behaviour exhibited by DCH-2 deviates sharply from that of
1042
Magazine of Concrete Research
Volume 65 Issue 17
Effect of transverse reinforcement on
short structural wall behaviour
Zygouris, Kotsovos and Kotsovos
CFP-2 and DCM-2 in that the dissipated energy increases at a
significantly higher rate. This trend is considered to reflect the
significant out-of-plane displacements that eventually caused loss
of load-carrying capacity. Moreover, as in the case of type 1
cyclic loading, the dissipated energy appears to reduce with
successive load cycles corresponding to a given ductility ratio,
for all walls investigated.
Figure 14 shows that the backbone envelopes of the normalised
lateral load–displacement curves in Figures 7, 9 and 11 are
identical. This is considered an indication of the insignificant
effect of reinforcement in excess of that specified by the CFP
method on structural behaviour.
The modes of failure are depicted in Figure 15(b), which shows
that, in all cases, failure occurred due to failure of concrete under
the compressive force developing on account of bending in one
of the bottom edges of the specimens. This mode of failure is
similar to that reported elsewhere (Greifenhagen and Lestuzzi,
2005) for the case of lightly reinforced squat walls; however, in
addition to transverse cyclic loading, these walls were also
subjected to axial compression.
Failure of concrete in compression is followed by buckling of the
vertical bars closest to the specimen edge, with the presence of
the additional stirrups within the CC elements of walls DCM-2
and DCH-2 reducing the rate of loss of load-carrying capacity, as
also reported by Kuang and Ho (2008).
Conclusions
Designing in accordance with the CFP method leads to significant
savings in horizontal reinforcement without compromising code
performance requirements. This is because, in contrast to the
code specifications, the CFP method does not specify stirrups for
the formation of CC elements along the edges of a short wall.
With regard to the web horizontal reinforcement, all methods
specify similar amounts for the walls investigated.
Confining reinforcement within CC elements appears to have
only a small effect on the post-peak characteristics of structural
behaviour. Such reinforcement reduces the rate of loss of load-
carrying capacity well beyond the residual load-carrying capacity
of 85% of the peak load level specified by current codes as the
limiting value for load-carrying capacity.
REFERENCES
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BSI (2004b) Eurocode 2: Design of concrete structures. Part 1-1:
General rules and rules of building. BSI, London, UK.
Cotsovos DM and Kotsovos MD (2007) Seismic design of
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Magazine of Concrete Research
Volume 65 Issue 17
Effect of transverse reinforcement on
short structural wall behaviour
Zygouris, Kotsovos and Kotsovos
