Drift Capacity of Lightly Reinforced Concrete Columns

Abstract

A lightly reinforced column is commonly believed to be relatively brittle with a very low drift capacity. A research project has been undertaken to investigate collapse behaviour of such columns. The effect of variation of axial load ratio and longitudinal reinforcement ratio on flexural, yield penetration, and shear displacement as components of the drift capacity were observed. Interesting outcomes showed that lightly confined reinforced concrete was able to sustain gravity axial load considerably greater than the code recommendations. Moreover, the present shear predictions available are deficient for lightly reinforced columns, since they tend to overestimate the nominal shear strength of the column.

Full text

131
© Institution of Engineers Australia, 2014
* Paper S13-002 submitted 11/01/13; accepted for publication
after review and revision 6/03/13.
†
Corresponding author Prof John Wilson can be contacted at
jwilson@swin.edu.au.
technical paper
Drift capacity of lightly reinforced concrete columns
*
A Wibowo and JL Wilson
†
Faculty of Engineering and Industrial Science, Swinburne University of Technology, Hawthorn, Victoria
NTK Lam
Department of Civil & Environmental Engineering, University of Melbourne, Parkville, Victoria
EF Gad
Faculty of Engineering and Industrial Science, Swinburne University of Technology, Hawthorn, Victoria
ABSTRACT: This paper presents the  ndings of a research project investigating the lateral
load drift behaviour of lightly reinforced concrete columns. Such columns of limited ductility are
common in regions of low-moderate seismicity, and although their strength properties are well
de ned, the drift performance is less understood. The paper presents the results of an experimental
study undertaken and the development of a theoretical model for predicting the lateral load-drift
behaviour of lightly reinforced concrete columns together with a simpli ed bi-linear model for
checking purposes. The test results are presented and clearly indicate the dramatic impact that
the axial load ratio has on the drift performance of columns of limited ductility, particularly the
signi cantly lower drift capacities that are available in compression dominated columns.
KEYWORDS: Drift capacity; axial load ratio; reinforced column tests; limited ductility;
columns; seismic performance.
REFERENCE: Wibowo, A., Wilson, J. L., Lam, N. T. K. & Gad, E. F. 2014, “Drift capacity
of lightly reinforced concrete columns”, Australian Journal of Structural Engineering, Vol.
15, No. 2, April, pp. 131-150, http://dx.doi.org/10.7158/S13-002.2014.15.2.
1 INTRODUCTION
Lightly reinforced concrete columns are prevalent
in many old buildings and common in current
detailing practice in the regions of lower seismicity.
This type of structure is believed to have a very low
lateral load and drift capacity from a conventional
design perspective. However, many post-earthquake
investigations have shown that the primary cause
of reinforced concrete building collapse during
earthquakes is the loss of vertical-load-carrying
capacity in critical building components leading to
catastrophic vertical collapse, rather than a reduction
in the lateral-load capacity (Otani, 1997; Wibowo et
al, 2008; Moehle et al, 2002).
The capacity spectrum method (ATC40) (Wilson
& Lam, 2006) provides a very convenient method
for assessing the seismic performance of structural
system by superimposing the structural capacity
curve (push-over curve) with the seismic demand
curve expressed in the form of an acceleration-
displacement response spectrum (ADRS) as shown
in figure 1 (where RSA, RSV and RSD refer to
the response spectral acceleration, velocity and
displacement values, respectively).
The ADRS demand curve can be obtained from
the relevant seismic design code for the region,
eg.Australia, AS1170.4 (Standards Australia, 2007). In
contrast, the push-over curve is structure dependent
and requires knowledge of the relationship between
the lateral force and the associated drift in both the
elastic and inelastic range. The push-over curve for
well detailed ductile columns has been thoroughly
researched and documented (Priestley et al, 1996;
Australian Journal of Structural Engineering, Vol 15 No 2

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Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
2007), with many design guidelines, such as
ATC40 (ATC, 1996) available. The lateral strength
properties of lightly reinforced concrete columns
are well understood and codi ed, but in contrast,
the associated drift estimates beyond peak strength
are less well de ned making it dif cult to construct
a realistic push-over curve. Further, many design
guidelines, such as FEMA273 (FEMA, 1997) and
ATC40, apply very conservative drift limits to lightly
reinforced concrete columns (Wilson et al, 2009;
Elwood & Moehle, 2003).
The overall aim of this paper is to investigate the
load-de ection behaviour and drift capacity of lightly
reinforced concrete columns, which many design
guidelines assume to be brittle in nature with very
low drift capacities, and to develop a simpli ed
push-over curve that can be used to assess the seismic
performance of such structures. An experimental
program undertaken by the authors involving
four column specimens is described in section 2,
while the overall results and speci c displacement
measurements are presented in sections 3 and 4,
respectively. Theoretical displacement estimates are
presented in section 5 together with a simpli ed code
bi-linear model for assessing the drift at maximum
strength presented in section 6. Finally, conclusions
are presented in section 7.
2 EXPERIMENTAL TEST SETUP
Four column specimens were designed to represent
the non-ductile detailed reinforced concrete columns
of old buildings commonly found in low-to-moderate
seismic regions (Wibowo et al, 2010a; 2010b; Wilson
et al, 2009). The two parameters varied were the axial
load ratio (n) and the longitudinal steel reinforcement
ratio (

v
), while both the transverse reinforcement
ratio (

h
) and the aspect ratio (a) remained constant.
(The axial load ratio (n) is de ned as the ratio of
the applied axial stress to the concrete crushing
strength, while the aspect ratio (a) is defined as
the column height to width ratio.) The cantilever
column specimens measured 300×270×1200 mm
high with an aspect ratio of a = 4. Column specimens
S1-S2 were loaded to create an axial load ratio
n = 0.20, while specimens S3-S4 were loaded to
n= 0.40. The longitudinal steel ratio of specimens
S1 and S4 was

v
= 0.56% (4N12 reinforcing bars),
which was below the minimum threshold level of
reinforcing allowed in AS3600 (Standards Australia,
2001) of 1.0%, while specimens S2 and S3 had the
minimum reinforcement ratio of

v
= 1.0% (4N16
reinforcing bars). The transverse steel ratio for all
specimens was

h
= 0.07% (area ratio), consisting
of R6 at 300mm stirrups which was less than the
minimum lateral reinforcement required by AS3600
of 0.09%. All stirrups had 135° hooks but with only
half the hook length of current design codes. The
low reinforcement ratios were deliberately selected
to investigate whether such columns behaved in a
brittle fashion as assumed in many design guidelines
(such as FEMA273 and ATC40) or had some level of
ductility and drift capacity when subjected to lateral
loading. The concrete cover was 20 mm, while the
speci ed concrete compressive strength was 20 MPa
and the ductile steel yield stresses were 536 MPa
for the main reinforcement and 362 MPa for the
stirrups. A summary of the four column specimens
are presented in  gure 2 and table 1.
The drift capacity of concrete columns is made up
of  exural, yield penetration, and shear components
which were all measured using linear variable
displacement transducers (LVDTs) and strain
gauges. The axial displacement was also measured
to detect any loss of axial-load carrying capacity.
Displacements were measured using 18 LVDTs, as
shown in  gure 3(a). The LVDTs were arranged
to measure the axial displacement (no. 18), total
lateral displacement (no. 1-5),  exural displacement
(no.6-11) and shear deformation (no. 12-17), while 16
strain gauges were installed on the reinforcement to
measure the longitudinal and transverse strains as
shown in  gure 3(b). Three strain gauge locations
Fig ure 1: Capacity spectrum method.

133
Australian Journal of Structural Engineering Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
were used; one level for checking yield penetration
length, the second level at the footing-column surface
for measuring the maximum strain and estimating
the yield penetration; and the third level was in the
middle of predicted plastic hinge length.
The axial load was applied and maintained using
a hydraulic jack, while the lateral load was applied
using a hydraulic actuator with a 100 ton loading
capacity as shown in  gure 4. The displacement
controlled loading sequence consisted of drift-
controlled mode at drift increments of 0.25% until
reaching 2% drift, and then followed by drift
increments of 0.5% (where the drift is de ned as the
ratio of the lateral displacement to column height
expressed as a percentage). Two cycles of loading
were applied at each drift ratio to ensure that the
hysteretic behaviour could be maintained. The lateral
loading was held constant at various stages while the
LVDT and strain gauge measurements were taken,
crack patterns recorded, and visual inspections made.
The test ended when the column lost the capacity
to resist and support to the axial load (axial failure)
rather than the more traditional failure de nition
of the peak lateral loading capacity of the specimen
reducing by 20% (lateral load failure).
3 OVERALL EXPERIMENTAL RESULTS
Specimen S1 with

v
= 0.56% rebar ratio and n = 0.20
axial load ratio was able to sustain a maximum drift
of 5.0% prior to axial load collapse with classical
plastic hinge formation at the base of the column and
a rigid body rocking mechanism as shown in  gure
5. Such desirable behaviour is associated with yield
Fig ure 2: Geometry and reinforcement details of column specimens S1-S4.
Table 1: Basic properties of column specimens.
Spec
Dimension
[mm]
L
[mm]
L/D
ρ
v
[%]
Main
rebars
ρ
h
(%)
Stirrups
[@mm]
n
f
c
’
[MPa]
Hook
type
Area Volumetric
S1 270×300×1200 1200 4 0.56 4N12 0.07 0.10 R6@300 0.2 20.3 135°
S2 270×300×1200 1200 4 1.00 4N16 0.07 0.10 R6@300 0.2 21.0 135°
S3 270×300×1200 1200 4 1.00 4N16 0.07 0.10 R6@300 0.4 18.4 135°
S4 270×300×1200 1200 4 0.56 4N12 0.07 0.10 R6@300 0.4 23.7 135°
Notation: L is shear span which is the clear-height of the column; L/D is the aspect ratio de ned as shear span divided by
the column depth; n is the axial load ratio (ratio of the axial load to axial load-carrying capacity A
g
f
c
’);

v
is the longitudinal
reinforcement ratio (

v
= A
s
/A
g
);

h
is the lateral reinforcement (A
sh
/bs); A
sh
= total area of transverse reinforcement; s = tie spacing;
and b = column section width.

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Australian Journal of Structural Engineering
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“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad

Fig ure 3: Instrumentation for column specimens S1-S4 – (a) LVDTs and (b) strain gauges.
(a)
(b)

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Australian Journal of Structural Engineering Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
Fig ure 4: Setup of column specimens S1-S4.
Fig ure 5: Failure damage of column specimens (a) S1, (b) S2, (c) S3 and (d) S4.
(a) (b) (c) (d)
penetration and damage localised at the base rather
than cracking and spalling of the concrete spreading
above the base.
In contrast, specimens S2 and S3 with almost twice
the longitudinal reinforcement

v
= 1.0% tolerated
lower maximum drifts of 2.5% and 1.5% for axial
load ratio of n = 0.20 and n = 0.40, respectively, as
shown in  gure 5. The large tie spacing (300 mm) in
these specimens led to buckling of the longitudinal
reinforcement after the concrete cover had spalled
and an abrupt transfer of axial load from the steel
reinforcement to the damaged concrete. This triggered
lateral load failure due to the deterioration of the
concrete under the cyclic loading. Specimens S4 and
S3, both with an axial load ratio of n = 0.40 responded
in a similar fashion with a maximum drift ratio of
1.5%, despite the different longitudinal rebar ratio.

136
Australian Journal of Structural Engineering
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“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
All specimens exhibitedclassicalreinforced concrete
(RC) column behaviour up to the peak strength,
with lateral load peaks for the same axial load
ratio occurring at a similar drift, but the post peak
deterioration of specimens with

v
= 1.0% rebar
ratio was much faster than that of specimens with

v
= 0.56% rebar ratio. The post peak behaviour of
all specimens except S1 could be predicted using
classical moment-curvature relationships.
The hysteresis curve and backbone moment-drift
curve for each specimen is presented in  gures 6
and 7 respectively (the backbone curve was derived
from the hysteresis curve and is the effective pus-over
curve for the column allowing for cyclic deterioration
effects). A summary of the test results is listed in table
2 including the lateral load and drift values at failure
de ned by (i) 80% of the maximum lateral load-
carrying capacity and (ii) gravity axial load collapse.
The first crack and first yield drift values for
specimens S1 and S2 were less than those of the more
heavily loaded specimens S3 and S4. Conversely, the
peak strength of specimens S1 and S2 occurred at
larger drifts than those of specimens S3 and S4. This
phenomenon could be attributed to the higher axial
load ratio of specimens S3 and S4 that increased the
compressive stress of column cross-sections, and
in turn reduced the curvature ductility capacity
through an increase of yield curvature and a decrease
of ultimate curvature. An increase in the axial load
ratio from n = 0.2 to n = 0.4 resulted in an increase
in the ultimate lateral strength capacity by about
30% for columns with main rebar ratio of

v
=0.56%
(specimens S1 and S4), but had little effect for
columns with

v
= 1.0% main rebar ratio (specimens
S2 and S3). In contrast, the effect of an increase
of main rebar ratio from

v
= 0.56% to

v
= 1.0%
Fig ure 6: Hysteretic curves for column specimens S1-S4.
Fig ure 7: Backbone moment-drift curves for column specimens S1-S4.

137
Australian Journal of Structural Engineering Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
increased the ultimate lateral strength capacity of
columns with n = 0.2 axial load ratio by about 30%
(specimens S1 and S2).
An increase of axial load ratio from n = 0.2 to n=0.4
reduced the ultimate drift capacity for column with

v
= 0.56% rebar ratio (specimens S1 and S4) by
about 70% compared with a 40% drift reduction
for the

v
=1.0% rebar ratio specimens (S2 and S3).
The measured maximum moment strengths M
u,exp
represented an over-strength factor in the range
= 1.4-1.7 compared with the factored design
moment strengths (

M
u
) derived from AS3600
for specimens S1-S4 as shown in figure 7 and
summarised in table 3.
The hook length used in the transverse reinforcement
of all specimens was about half of the required
hook length, but interestingly, an opening hook was
barely found in any specimen. Clearly, the stirrup
spacing has a greater effect rather than hook type and
length in lightly reinforced concrete columns, since
the transverse reinforcement tends to help prevent
longitudinal reinforcement buckling and provide
additional shear strength but has little effect on the
concrete con nement.
4 EXPERIMENTAL DISPLACEMENT
MEASUREMENTS
The lateral displacement of a column (
tot
) consists
of three components,  exural (

), yield penetration
(
yp
) and shear deformation (
sh
) which are illustrated
in figure 8 and explained from an analytical
perspective in this section.

tot
= 

+ 
yp
+ 
sh
(1)
4.1 Flexural displacement
Flexural de ection prediction of the member is well
understood and evaluated by performing curvature
Table 2: Experimental results for specimens S1-S4.
Parameters Unit S1 S2 S3 S4
V
cr
KN 24 28 35 39
V
y
KN 51 67 79 76
V
max
KN 59 79 81 77
V
80%
KN 48 63 67 64
V
collapse
KN 18 28 67 64

cr
% drift 0.13 0.13 0.20 0.20

y
% drift 0.75 0.75 1.00 1.00

Vmax
% drift 1.71 1.73 1.12 1.01

80%
% drift 3.30 2.10 1.50 1.50

collapse
% drift 5.00 2.50 1.50 1.50
Drift ductility – 6.7 3.3 1.5 1.5
Table 3: The over-strength factor as a ratio of
the measured ultimate strength to the
nominal factored moment capacity
(AS3600).
Specimen
ϕ
M
u
ϕM
u
M
u.exp
Ω
S1 0.7 68 48 72 1.45
S2 0.7 92 64 94 1.39
S3 0.6 98 59 99 1.69
S4 0.6 90 54 92 1.71
integration over the column height with the curvature
distribution obtained from a  bre section model. A
plastic hinge analysis is needed to determine the
inelastic deformation from the regions where the
applied moment exceeds the yield moment, resulting
in large curvatures.
The average curvature (

) has been calculated using
equation (2) over the four segments up the height of
the column as shown in  gure 8(a). The three lower
segments which covered the predicted cracked
region were instrumented with LVDTs, while the
average curvature (

) of the upper segment could
be conservatively calculated using elastic properties
since no cracks were observed in this region.
21
1
ff
VhV
LLL





(2)
where L
V
= height per each segment, L
h
= distance
between flexural LVDTs, and

f
= vertical LVDT
measurement.
The  exural displacement component at the column
top for each LVDT segment was obtained using:

.21
0
()
L
Vi
fi i f f
H
LL
x xdx
L


  

(3)

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Australian Journal of Structural Engineering
Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
D
L
H
d
1
d
2
c
s
lip
E
L
V1
G
f 1
G
f 2
T
slip
d
d’
sg
1
sg
2
'
fl
'
sh
'
sh1
L
L
v4
L
v3
L
v2
L
v1
G
f1
G
f2
E
L
h
G
s1
G
s2
]
D
L
L
v3
L
v4
L
v2
L
v1
(b) Shear (a) Flexure
Fig ure 8: Measurements obtained from transducers and strain gauges – (a) flexure, (b) shear,
and (c) yield penetration.
(a) (b)
(c)
While the displacement of the upper segment
without a LVDT transducer was calculated assuming
uncracked section properties:
23
,4
33
ii
fi
c
LVL
EI

 
(4)
where V = lateral load, L
i
= segment length, E
c
=
concrete elastic modulus, and I = uncracked second
moment of area.
The resulting total  exural displacement at the top
of the column could then be obtained as the sum of
the components:
4
,
1
fi fi i
i
 

(5)
The measured average curvatures over the height of
the column are shown in  gure 9, while the  exural
displacement contributions from both within and

139
Australian Journal of Structural Engineering Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
outside the plastic hinge regions are shown in  gure
11 for the four column specimens. Figure 9 shows
that only specimen S1 developed a plastic hinge
mechanism within the predicted plastic hinge length,
while the plastic hinge region of the other three
specimens S2-S4 extended to the second stirrup.
The additional  exural displacement attributed to
deformations outside the plastic hinge region for
specimens S2-S4 are clearly shown in  gure 11.
4.2 Yield penetration displacements
Yield penetration or slip deformation is characterised
by a rigid body rotation of the column associated
with a gap opening at the column-foundation
interface. The reinforcement yields at this location
and the inelastic deformation penetrates into the
foundation due to bond failure. Consequently, the
reinforcement elongates locally, the gap widens and
the column rotates.
The yield penetration effect was obtained from the
strain gauge and LVDT measurements at the column
base interface as shown in  gure 8(c) by assuming a
rocking mechanism within the  rst section of column.
The slip displacement of the tensile steel at the gap
opening can be calculated as follows:
slip =

sg1
f
s
d
b
/4u (6)
while the shortening displacement of the compressive
steel can be obtained via:

sc
=

sg2
L
column
(7)
where

sg1
and

sg2
are strain gauge reading at tensile
and compressive steel respectively, and u
e
is the bond
stress between concrete and steel (u
e
=
c
f

by Sezen
& Moehle, 2003, is used in this study).
Hence, the neutral axis depth at the column base
interface can be estimated via:

sc
sc
c d d' d'
slip


 

(8)
While, the slip rotation

slip
is given by:

slip
= slip/(d – c) (9)
An upper bound of the slip displacement can be
determined from the vertical LVDT measurement
L
L
v4
L
v3
L
v2
L
v1
G
f1
L
h
G
f2
G
f3
G
f4
G
f5
G
f6
2
34
2
1
Vh
ff
LL


G
G
M
1
12
1
1
Vh
ff
LL


G
G
M
3
56
3
1
Vh
ff
LL


G
G
M
M
u
M
y
L
p
Fig ure 9: Average curvature calculations for column specimens S1-S4. (a) Idealised tri-linear and bi-linear
shape of measured curvature distribution, and (b) curvature distribution over column height.
(a)
(b)

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Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
at the  rst level (no. 8 and 11). While the neutral
axis depth at the column base interface can be
estimated via:
2
2
12
f
H
ff
cLd




(10)
The slip rotation of the tensile steel can then be
obtained using:
21ff
slip
H
slip
dc L





(11)
Hence, the related slip displacement can be calculated
using:
slip =

(d + d
2
) –

f2
(12)
The top displacement of the column can then be
calculated from the product of the slip rotation

slip
and the column height assuming rigid body rotation.

yp
=

slip
L
column
(13)
The yield penetration contributions to the total
displacement at the top of the columns for specimens
S1-S4 are plotted in figure 11. Reasonable yield
penetration drifts in the order of 0.5% were measured
in specimen S1 due to the low axial load ratio and
low reinforcement ratio, while much smaller drifts in
the order of 0.2% for specimen S2-S4 were measured.
4.3 Shear displacement
The measured shear deformation 
sh
was estimated
from the diagonal LVDT measurements (refer  gure
8(b)), such that:

22
12 12
sec
22
v
ss ss
sh
v
LD
L
 



 
(14)
where

s
= diagonal LVDT measurement and D= cross-
section depth (parallel to lateral loading direction).
The average shear displacement distribution over the
height of the column was calculated using equation
(14) and is presented in  gure 10 for all specimens.
It was found that the shear deformation of specimen
S1 with the smallest longitudinal reinforcement
ratio and axial load ratio was mostly concentrated
in the plastic hinge region, while specimens S2, S3,
and S4 developed shear deformations up to the
second stirrup region. A prompt increase of shear
deformation was observed in specimens S2, S3 and
S4 that was attributed to rapid broadening and
propagation of the main diagonal cracks. However,
specimens S3 and S4 with a higher axial load ratio
developed larger shear deformations at an earlier
stage of drift compared with specimen S2. The overall
drift due to shear deformation was small and in the
order of 0.1-0.2% for specimens S1-S4 as shown in
 gure 11.
4.4 Total lateral displacement
Figure 11 and table 4 show the various components of
the measured column lateral drifts for all specimens
as a function of lateral load in order to qualitatively
indicate the modes of failure.
5 THEORETICAL DISPLACEMENT
PREDICTIONS
In this section, a detailed theoretical analysis
comprising  exural, yield penetration, and shear
displacement is presented and compared with the
experimental results.
5.1 Flexural displacement
The plastic hinge lengths for all specimens were
estimated using a tri-linear representation of the
Fig ure 10: Shear displacement distributions for column specimens S1-S4.

141
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0
10
20
30
40
50
60
70
80
90
100
00.511.522.533.5
Lateral Load (KN)
Drift (%)
flexural - within Lp flexural - outside Lp shear
yield penetration total displacement
S1 (Uv=0.56% ; n=0.2)
0
10
20
30
40
50
60
70
80
90
100
0 0.5 1 1.5 2 2.5
Lateral Load (KN)
Drift (%)
flexural - within Lp
flexural - outside Lp
shear
yield penetration
total displacement
S2
(Uv=1.0% ; n=0.2)
`
0
10
20
30
40
50
60
70
80
90
100
00.511.522.5
Lateral Load (KN)
Drift (%)
flexural - within Lp
flexural - outside Lp
shear
yield penetration
total displacement
S3
(Uv=1.0% ; n=0.4)
0
10
20
30
40
50
60
70
80
90
100
00.511.522.5
Lateral Load (KN)
Drift (%)
flexural - within Lp
flexural - outside Lp
shear
yield penetration
total displacement
S4
(Uv=0.56% ; n=0.4)
Fig ure 11: Flexure, yield penetration, shear and total drift for column specimens S1-S4.

142
Australian Journal of Structural Engineering
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“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
measured curvature distribution as shown in  gure
9 and summarised in table 5. Numerous empirical
models (Mattock, 1967; Priestley etal, 1996; Sawyer,
1964; Park & Paulay 1975) have been developed to
predict the equivalent plastic hinge length of ductile
columns using the general equation as a function
of shear span length (L), column width (D), and
diameter of main rebars (d
b
), as follows:
L
p
=

L +

D +

f
y
d
b
(15)
where L = shear span length, D = effective depth
of the section, and d
b
= diameter of longitudinal
reinforcement.
Specimen S3 with the highest axial load ratio
(n =0.4) and greatest longitudinal reinforcement
ratio (

v
=1.0%) had the smallest curvature and the
largest plastic hinge length. Further, the longitudinal
steel ratio had a greater effect on spreading the plastic
hinge region compared with the axial force ratio
(compare S1 and S2 when n = 0.2 with S3 and S4
when n = 0.4). The increase of axial load ratio from
n = 0.2 to n = 0.4 increased the plastic hinge length in
the order of 10%, while the increase of longitudinal
reinforcement ratio from

v
= 0.56% to

v
= 1.0%
increased the plastic hinge length by about 30%.
It was observed from the experimental tests that
the concrete spalling was localised and was limited
to the region where the rebar buckling occurred
which was approximately equal to the tie spacing.
Therefore, the spacing of stirrups can be considered
an upper limit of plastic hinge length for lightly
reinforced concrete columns. In contrast, the Park
& Paulay (1975) model provides a conservative
estimate for the lower bound limit of the plastic
hinge length as shown in table 5.
In this study, a computer program based on a
fibre section analysis (Park & Paulay, 1975) has
been developed to calculate moment-curvature
relationship of the column, which was then used
to predict the  exural de ection by idealising the
curvature distribution into elastic and inelastic
regions as follows:


= 
fe
= 

(16)
The elastic displacement can be calculated by
integrating the curvature over the column height
as follows:
2
0
3
L
yy
fe
ML
xdx
EI

 

(17)
The additional inelastic rotation due to plastic
hinge formation at the base of the column can be
expressedas:

p
= (

u
–

y
)L
p
(18)
Hence, the lateral inelastic de ection at the top of the
column is given by:

22
pp
fi p u y p
LL
LLL

 
    
 
 
(19)
The analytical results using the experimental plastic
hinge length to estimate the  exural displacement
showed good agreement with the experimental data
as presented in  gure 12.
Table 4: Drift components for specimens S1-S4.
Specimen
Drift (%)
Max
drift
Total (measured)
drift
Flexure
within L
p
Flexure
outside L
p
Total
 exure
Shear
Yield
penetration
S1 5.0 3.0 2.1 0.3 2.40 0.10 0.50
S2 2.5 2.0 1.2 0.4 1.60 0.10 0.30
S3 1.5 1.5 0.7 0.5 1.20 0.08 0.20
S4 1.5 1.5 1.0 0.3 1.30 0.06 0.17
Note: The total measured drift consists of the component drifts for which the measurements were reliable.
Table 5: Predicted and measured plastic hinge lengths for specimens S1-S4.
Model
αβ ξ
L
p
[mm]
S1 S2 S3 S4
Mattock, 1967 0.050 0.50 0.000 210 210 210 210
Priestley et al, 1996 0.080 0.00 0.022 238 285 285 238
Sawyer, 1964 0.075 0.25 0.000 165 165 165 165
Park & Paulay, 1975 0.000 0.50 0.000 132 133 133 132
Average plastic hinge length (experimental) 170 220 240 190

143
Australian Journal of Structural Engineering Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
5.2 Yield penetration displacement
Yield penetration behaviour has been widely
investigated over the last two decades (Zhao &
Sritharan, 2007). A classical moment-curvature
relationship has commonly been used to calculate
the yield penetration gap opening. The main problem
with this approach is that the steel stress and strain
obtained at the gap opening is based on strain
compatibility between the steel and the concrete,
whereas the presence of a gap opening and yield
penetration at the column base prevents the use of a
closed form solution to predict the neutral axis depth
because of strain incompatibility between the steel
and concrete at the connection interface. A trial-and-
error procedure is usually needed to evaluate the
neutral axis depth through a convergence process
of slip displacement, steel stress-strain, and yield
penetration length. However, this approach is quite
indirect and cumbersome and a closed form model to
predict the yield penetration displacement has been
developed and is presented in this section.
The proposed model and algorithm uses a simpli ed
stress-strain relationship (refer  gure 13) together
with geometrical compatibility principles to solve
the strain incompatibility between the steel and
concrete (refer  gure 14). A closed form algorithm
has been developed by modifying the  bre cross-
section analysis to operate under displacement
control, such that the curvature is directly linked to
the displacement at the top of the column as follows:
1. Fix the increment of global displacement 
top
, and
calculate the related rotation

slip
=

= 
top
/L
(20)
0
10
20
30
40
50
60
70
0 0.5 1 1.5 2 2.5 3
Lateral Load (kN)
Flexural Drift (%)
Experiment Analysis
S1 (Uv=0.56% ; n=0.2)
0
10
20
30
40
50
60
70
80
90
100
0 0.5 1 1.5 2 2.5
Lateral Load (kN)
Flexural Drift (%)
Experiment Analysis
S2 (Uv=1.0% ; n=0.2)
`
0
10
20
30
40
50
60
70
80
90
0 0.5 1 1.5 2
Lateral Load (
kN
)
Flexural Drift (%)
Experiment Analysis
S3 (Uv=1.0% ; n=0.4)
0
10
20
30
40
50
60
70
80
90
00.511.52
Lateral Load (kN)
Flexural Drift (%)
Experiment Analysis
S4
(Uv=0.56% ; n=0.4)
Fig ure 12: Comparison of experimental and analytical  exural drift components for column
specimens S1-S4. Note, drifts are plotted up to the point where the LVDTs were
removed during the experiment.
H
su
H
y
H
s
K=
ysu
ysu
ff
HH


f
su
f
s
f
y
K
1
Fig ure 13: Simplified stress-strain relationships
for yield penetration analysis.
L
L’
y
c
U
(
U
- y)
T
T
s
li
p
'
slip
'
to
p
G
A
B
O
L
d
Fig ure 14: Gap opening mechanism for yield
penetration analysis.
2. Estimate an initial value of concrete strain

c
,
and calculate the neutral axis depth (c) from
geometrical compatibility
• Evaluate curvature, for each case
Strain compatibility

= 3
top
/L
2
(21)
Strain compatibility

= 
top
/L
(22)
• Evaluate neutral axis depth c =

c

=

c
/

(23)

144
Australian Journal of Structural Engineering
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“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
• Evaluate steel deformation at gap slip interface

slip
=

slip
(d – c) (24)
• Evaluate tensile steel strain

s
8
for
slip c
sinitsy
sb
f'
Ed



(25)
2
4
1
2
c
s
s slip y init
b
f'
E
d



   


for

s
<

y
(26)
where

init
= P/BDE
c
= initial strain due to
external axial load and member self-weight.
Fig ure 16: Measured and predicted yield penetration drift for column specimens S1-S4.
'
fl
'
yp
M
Fig ure 15: Moment-deflection relationship for
the yield penetration displacement
calculations for column specimen S1.
The related stress f
s
can then be obtained from
the steel stress-strain relationship.
• Evaluate the section equilibrium, so that the
net axial force (P) results,
C
c
– T
s
+ C
s
= P (27)
where C
c
is determined using moment-
curvature analysis. T
s
and C
s
can be obtained
from steel stress-strain relationship.
3. Iterate Step 2 with a new value of

c
until the
equilibrium equation is satisfied, and then
calculate the moment capacity with the updated
value of c and

c
222
c
sts scs
Cc D D
MTdCdP W



   




(28)
4. Calculate lateral load
F
h
= M/L (29)
5. Repeat the whole process for the next increment
of de ection 
top
.
The solution of this algorithm provides the lateral
load-displacement relationship for the yield
penetration mechanism as shown schematically in
 gure 15 for specimen S1. Good agreement between
the experimental and analytical results for the lateral
load versus yield penetration drift is demonstrated
in  gure 16 for the four specimens.

145
Australian Journal of Structural Engineering Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
5.3 Shear displacement
The displacement contribution from shear
deformation to the total deflection of a limited
ductile column is relatively small and hence the use
of a complicated shear deformation model is not
warranted. Further, since damage to stirrups was
barely found on any specimen post column failure,
the shear deformation model proposed by Park &
Paulay (1975) can be used. The total shear de ection

sh
can be calculated from the summation of the
elastic shear de ection in the uncracked portion

vuncrack
and the shear de ection in the cracked portion

vcrack
as follows:

sh
= 
vuncrack
+ 
vcrack
(30)
A plot of predicted and measured shear de ections
for all specimens is shown in  gure 17. The model
predicted shear deformations with an axial load ratio
of n = 0.4 (specimens S3-S4) is in good agreement with
experimental results and reasonable agreement for
specimens with an axial load ratio of n = 0.2 (S1-S2).
Overall, since the shear displacements are very small
for  exure dominant slender columns (with shear
drifts up to 0.1% for the four specimens or less than
5% of the total drift) as shown in  gure 18 and table
4, the model and predicted results are considered
reasonable and satisfactory.
5.4 Total lateral displacement
The total displacement consisting of the  exural, yield
penetration and shear displacement components is
Fig ure 17: Measured and predicted shear drifts for column specimens S1-S4.
0
1
2
3
4
5
6
00.511.522.533.5
Drift (%)
flexural - within Lp
flexural - outside Lp
shear
yield penetration
total displacement
S1
(
U
v=0.56% ; n=0.2)
Fig ure 18: Shear displacement distribution and drift contributions for column specimen S1.

146
Australian Journal of Structural Engineering
Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
summarised in table 6. The proposed model was used
to construct the backbone force-drift curve which
showed good agreement with the experimental
hysteresis curves as shown in  gure 19. Further,
tables 7 and 8 shows that the proposed model for
estimating the drift at both lateral load failure and
axial load failure showed good agreement with the
experimental results and is an improvement on the
existing models listed (refer to Wibowo et al (2014)
for further details).
6 SIMPLIFIED CODE BI-LINEAR MODEL
The simpli ed code bi-linear model is based on the
assumption underlying most force based seismic
codes of practice, where the inelastic behaviour is
represented by a ductility factor  and over-strength
factor  (ratio of maximum strength to factored
ultimate design strength). The ductility factor (ratio
of ultimate displacement to yield displacement) is
dependent on the level of ductility, and for lightly
Fig ure 19: Experimental hysteretic curves versus the backbone theoretical model curve for column
specimens S1-S4.
Table 6: Total drift for specimens S1-S4.
Results Parameters S1 S2 S3 S4 Stage
Theoretical prediction
Displacement 
top
[mm]
1.90 1.70 2.20 2.20 Crack
12.60 11.90 11.60 11.30 Yield
19.80 20.50 12.50 12.30 Ultimate
Drift

top
[%]
0.16 0.15 0.19 0.19 Crack
0.85 0.89 0.97 0.94 Yield
1.65 1.71 1.04 1.03 Ultimate
Experimental Drift

top
[%]
0.13 0.13 0.20 0.20 Crack
0.75 0.75 1.00 1.0 Yield
1.71 1.73 1.12 1.01 Ultimate
Table 7: Comparison between predicted and measured drift at lateral load failure for column specimens.
Drift [%]
Specimen
S1 S2 S3 S4
Elwood & Moehle, 2003 2.4 2.3 1.7 1.8
Zhu et al, 2007 2.2 2.2 1.6 1.6
Proposed model 2.8 1.9 1.5 1.6
Experimental results 3.2 2.1 1.5 1.5

147
Australian Journal of Structural Engineering Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
The effective stiffness I
eff
can be conservatively
estimated using FEMA356 (FEMA, 2000) to account
for tensioning stiffness effects in RC structures as
follows: I
eff
= 0.7I
g
for axial load ratio n  0.5, or
I
eff
=0.5I
g
for axial load ratio n  0.3. For 0.3  n < 0.5,
the value of I
eff
should be interpolated.
The maximum displacement 
m
is calculated by
multiplying the yield displacement 
yu
by the
ductility and over-strength value

 as shown in
 gure 20. In the Australian context, this results in

m
= 2.6
yu
(

 =2.0×1.3 = 2.6), for limited ductile
columns with standard detailing.
The simplified bi-linear model is presented to
demonstrate the approach implicitly assumed in
force-based seismic codes of practice and to provide a
quick and conservative estimate of the displacement
at peak lateral load that can be used for initial seismic
performance checking using displacement principles.
The bi-linear model is not intended to predict the
drift at lateral load failure or axial load failure, but
provides a quick displacement checking method to
ascertain whether a more detailed study is needed.
The simplified code bi-linear model provides a
conservative estimate of the drift at peak lateral
load for each of the test results as shown in  gure 21
(where it has been assumed that

= 0.8 and =1.3,
hence

 = 1.04). Clearly for the experimental results
presented, each of the columns had significant
additional drift capacity beyond the maximum
displacement capacity (
m
= 


yu
) implied in the
force-based code design approach.
7 CONCLUSIONS
Experimental research on four lightly reinforced
concrete columns has been undertaken with axial
Displacement
'
yu
'
m
=
P
'
yu
I
V
u

I
V
u
Base Shea
r
A
B
I
eff

'
yu
Fig ure 20: Simpli ed code bi-linear lateral
load-drift model.
Fig ure 21: Experimental load-drift curve versus the simpli ed code bi-linear model for column
specimens S1-S4.
Table 8: Column drift limits for specimens S1-S4.
Guidelines and models S1 S2 S3 S4
FEMA, 1997 1.1% 1.2% 0.9% 0.8%
FEMA, 2000 0.9% 1.1% 0.8% 0.7%
Elwood & Moehle, 2003 2.0% 2.0% 1.2% 1.0%
Ousalem et al, 2004 1.7% 1.7% 1.3% 1.2%
Zhu et al, 2007 1.7% 1.7% 1.3% 1.2%
Proposed model 4.8% 2.6% 1.8% 1.3%
Experimental 5.0% 2.5% 1.5% 1.5%
reinforced columns a low ductility factor of

= 2
and an over-strength factor  = 1.3 is assumed in
many seismic codes of practice, such as AS1170.4
(Standards Australia, 2007).
The bi-linear model is constructed by estimating the
yield displacement 
yu
from the factored ultimate
strength

V
u
divided by the effective stiffness I
eff
.

148
Australian Journal of Structural Engineering
Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
load ratios n = 0.2-0.4, longitudinal reinforcement
ratio

v
= 0.56% to 1.0% and a very small transverse
reinforcement area ratio of

h
= 0.07% which was
signi cantly less than minimum code requirement.
The drift at axial load failure for all specimens
was at least 1.5% despite the poor detailing and
signi cantly greater than that predicted by current
design guidelines. The effect of the design parameters
can be summarised as follows:
• Increasing the axial load ratio reduces the
curvature ductility capacity as a result of an
increase of yield curvature and a decrease of
ultimate curvature.
• Increasing the axial load ratio from n = 0.2 to n =0.4
resulted in a reduction of the axial load failure drift
with the larger reduction found on columns with
a lower longitudinal reinforcement ratio.
• Increasing the longitudinal reinforcement ratio
decreased the drift at axial load failure for
specimens S1 and S2 with a lower axial load
ratio of n = 0.2, while the drift was reduced and
similar for both specimens S3 and S4 with an axial
load ratio n = 0.4 close to the balance point of the
interaction diagram.
The flexure, yield penetration and shear drift
components and their effect on the overall behaviour
have been presented in the paper. The flexural
components were the most dominant behaviour
for all specimens at around 75% to 85% of the total
drift due to the large aspect ratio of a = 4. The yield
penetration components for specimens S1, S2, S3
and S4 were quite small and around 10-20% of the
total drift, while the shear component was the least
dominating behaviour observed on all specimens at
around 2% to 5% of total drift.
The experimental tests clearly demonstrates the
reduced drift capacity of columns that are heavily
loaded, particularly as the axial load ratio approaches
or exceeds the balance point on the interaction
diagram. Such columns are considered highly
stressed under gravity loading and hence have
signi cantly reduced drift capacity. This observation
has significant implication for the earthquake
performance of structures that have heavily loaded
columns, since such structures will inherently have
reduced drift capacity under extreme lateral loading.
Designers can readily improve the earthquake
performance of their structures by ensuring the
columns are designed to remain in the tension
controlled region of the interaction diagram.
A theoretical model for predicting the  exural, yield
penetration and shear displacements of a laterally
loaded column was developed and showed very good
correlation with the experimental results. Finally, a
simpli ed code bi-linear model was presented that
provides a quick and conservative estimate of the
displacement at peak lateral load for columns that
can be used for initial seismic performance checking
using displacement principles.
ACKNOWLEDGEMENTS
The  nancial support from the ARC Discovery Grants
titled “Collapse modelling of soft-storey buildings”
(DP0772088) and “Displacement controlled behaviour
of non-ductile structural walls in regions of lower
seismicity” (DP1096753) is gratefully acknowledged.
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Journal of Structural Engineering, Vol. 133, No. 9, pp.
1316-1330.

150
Australian Journal of Structural Engineering
Vol 15 No 2
“Drift capacity of lightly reinforced concrete columns” – Wibowo, Wilson, Lam & Gad
ARI WIBOWO
Ari Wibowo is a Lecturer in Civil Engineering at University of Brawijaya in
Indonesia. He has a Bachelor of Engineering (Civil) from Sepuluh Nopember
Institute of Technology, Indonesia, Masters of Engineering from Bandung
Institute of Technology, Indonesia, and a PhD from Swinburne University of
Technology, Australia. His research interests include earthquake engineering,
structural dynamic, modelling and programming.
JOHN WILSON
John Wilson is Dean of Engineering and Industrial Sciences at Swinburne
University of Technology in Melbourne. Prior to joining Swinburne in 2005, he
was an academic at the University of Melbourne for some 14 years, and as a
consulting engineer for over 10 years with the SECV and Arups in their London
and Melbourne of ces. He has a Bachelor of Engineering degree from Monash
University, a Master of Science degree from University of California (Berkeley),
USA, and a PhD from University of Melbourne. He has a research interest and
expertise in structural systems, earthquake engineering, structural dynamics and
sustainable structures, and has consulted widely in these  elds. Three Chapman
Medals and the Warren Medal awarded by Engineers Australia and the Gupta
Award by the ISET Journal of Earthquake Technology are acknowledgements
of his contributions to the research and practice of earthquake engineering.
NELSON LAM
Nelson Lam, Reader in Civil Engineering at The University of Melbourne, is
an internationally recognised expert in earthquake engineering and structural
dynamics. He has 30 years of experience in the professional practice and
research in structural engineering. In the past 20 years, he has been working
in the specialised  eld of earthquake engineering and impact dynamics. His
achievement in research and knowledge transfer in this  eld was recognised
by the award of the Chapman Medal (1999, 2010) and Warren Medal (2006) by
Engineers Australia, and the Best Paper Award (2004-2007) by the ISET Journal
of Earthquake Technology. He served as member of the committee for developing
the current edition of the Standard for Earthquake Actions in Australia AS1170.4
(2007), and was co-author and co-editor of the Standards Commentary. His early
career as structural engineer was with Scott Wilson International throughout
the 1980s and attained British chartered engineer status during that period.
EMAD GAD
Emad Gad is a Professor in Civil Engineering at Swinburne University of
Technology in Melbourne. Prior to this appointment he worked as a senior
academic at Melbourne University and research scientist at CSIRO. He has
a Bachelor of Engineering (Civil) from Monash University and a PhD from
Melbourne University. Emad has research interest and expertise in structural
dynamics and modelling. In addition to teaching and research he has also been
involved in specialist consulting. He is a Fellow of Engineers Australia and past
Chairman of the Structural Branch, Victoria Division.