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7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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Missouri University of Science and Technology
Scholars' Mine
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Axial capacity of concrete inlled cold-formed steelcolumns
C. Y. Lin
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Ninth International Specialty Conference on Cold-Formed Steel Structures
St. Louis, Missouri, U.S.A., November
8-9,1988
AXIAL CAPACITY
OF CONCRETE INFILLED
COLD FORMED STEEL COLUMNS
by
C.Y. Lin
ABSTRACT
In
this
experiment,
a to ta l
of 18 specimens were
tes ted
to demonstrate
the
behavior
and strength of the concrete in f i l l ed cold-formed s tee l
columns
subjected
to
axial
loads.
The
variables
considered
in
th i s
investigation
included
the concrete strength, the
shape
and
thickness
of
cold-formed s tee l and the length
width
ra t io LID) of the specimen.
Test
resul ts
indicated
that
the
axial
capacity and the res idual post-crushed
strength
of
the
inf i l led concrete
are
functions of
the thickness
of
the
cold-formed
s tee l and
the shape
of
the
sect ion. The ci rcular cold-formed
s tee l sect ion provides be t te r
confinement
on concrete prior and af te r the
crush
of the inf i l led concrete.
Based
on the t es t
resul ts
an equation
with
confining
coeff ic ient C was
proposed for calculating the
axial
capacity
of the concrete in f i l l ed cold-formed s tee l column.
Further
study
has to
be carried out
to evaluate
the confining coeff ic ients
for
rectangular
sect ions
with
different aspects ra t ios .
INTRODUCTION
In
general
pract ice ,
l a te ra l
confining reinforcements such as
t ies or
spi ra ls are
commonly
used in reinforced
concrete
columns to offset the
st rength loss
due
to
spall ing of concrete
cover, to increase the capacity
of the column
and to
sustain
large
deformations without a
s igni f icant
st rength loss . The effect iveness of l a te ra l
confinement depends
upon
the
s ize and spacing of the l a te ra l reinforcement.
Currently,
to carry axial
s tee l section,
sect ion.
2
,3 ,4
cold-formed
s tee l
sect ions are
commonly designed
as
columns
10ads
However, due
to
thinness of
the
cold-formed
the capacity i s generally control led by buckling of the
When a
th in
cold-formed s tee l sect ion i s in f i l l ed with
concrete
to
serve
as
a
column, the
concrete
and the thin cold-formed
s tee l
provide
l a te ra l
confinement to
each other continuously. The
effect
of
confining pressure on
the compressive
st rength of concrete has
been
studied and an
e
5
uation
was
developed to predict the compressive st rength
of
the concrete.
In previous
experiments,
the concrete was tes ted
within
a pressure
chamber, in which the
l a te ra l
pressure
was maintained
constant over the
ent i re loading process.
When concrete
is
confined by
elas t ic material ,
the confining
pressure
varies
with
the
longitudinal
deformation.
In
Professor ,
Department
of Construction Engineering
National
Taiwan
Ins t i tu te of
Technology
Taipei, Taiwan,
R.O.C.
443
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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addit ion, due to the compatibi l i ty, the cold-formed s tee l not
only
provides l a tera l confinement on concrete, but also carr ies longitudinal
load with concrete.
This
paper presents some experimental data on
the axial
capacity of
the concrete inf i l led cold-formed s tee l column. Concrete
materials
with
different strengths were used in the experiment. The effects of thickness
of
the cold-formed s tee l and the shape
of
the
column
on the
axial
capacity
of concrete
in f i l l ed
columns were invest igated.
No
conventional
reinforcements were
used in
ei ther
longitudinal
or transverse direction.
TEST
PROGRAM
In
this
invest igat ion, a to ta l of 18
specimens
were
fabricated and
tested. The concrete
for
a l l 18 specimens was produced with Type I
portland
cement. Local sand
and aggregate with maximum size of 2 mm were
used.
Three mixing proportions were used to
obtain
different concrete
s t rengths .
The shapes of cold-formed s tee l columns, s tee l thicknesses,
and specimen lengths are
given
in Table 1 All specimens
were tes ted in a
MTS
closed-loop
servo
control led hydraulic tes t machine with a
constant
loading
ra te . Displacement
was
measured
by a
dial
gage f i t t ed
paral le l to
the
specimen between the base plate and loading head.
To
evaluate
the
s t ra in in
both
longitudinal and transverse
direct ions ,
s t ra in gages were
placed
on the s tee l surface. The specimen was loaded
with small
increments
over the ent i re loading process.
TEST RESULTS
AND
DISCUSSION
Stress-Strain
Relationship
The
typical
s t ress -s t ra in curve for the
concrete in f i l l ed
cold-formed
s tee l
column is shown
in
Fig. 1 The s t ress -s t ra in curve
can
be
divided
in to
three segments.
Between
point
0 and
point
A is the elas t ic range.
From
point
A
to
point B is the post-cracked range, in which the inf i l led
concrete i s
cracked.
Point
B
i s
the
beginning
of the post-crushed
range,
which indicates
the
res idual
st rength
of the confined
crushed concrete.
The modulus of e las t i c i ty of concrete E
c
the deflect ion and
the
s t ra in
El
corresponding to the maximum concrete st rength f ~ c of the
composite
construct ion
are
shown
in
Table 2.
The
modulus
of
e las t i c i ty
of
the
confined
concrete i s not s igni f icant ly affected by the thickness of
confining s tee l and the shape of the section. The s t ra in El
corresponding
to the maximum s t ress f ~ c
is not
affected
by concrete
strength. For
the
concrete with higher strength,
the
s t ra in
El
was
compensated by
the
higher modulus of e las t i c i ty . When
the
s t ra in
exceeded El the concrete inside the cold-formed s tee l sect ion was
par t ia l ly damaged. The
s t ress
of the composite sect ion i s
graduately
reduced, with increasing s t ra in . The
s t ress
s tabi l ized when the s t ra in
reached E2. The reduction
in s t ress
~ f ~ c
between
El and
E2
i s a
function
of the
thickness
of confining s tee l the shape of column
sect ion
and the inf i l led concrete strength. As shown in Fig.
2,
a smaller
st rength reduction ~ f ~ c i s observed
for the
sect ion confined by thicker
s tee l section. Comparing the section with different geometries as shown
in
Fig.
3, a larger ~ f ~ c was observed in rectangular sections,than
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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5
circular
and
square
sections.
As shown in Fig. 4,
almost equal
post-crushed strength was observed for
specimens with
different concrete
strengths This
indicates
tha t the
specimen
with higher concrete
strength
yielded with
la rger strength
reduction ~ f ~ c
Ultimate Strength
The compressive
strength
of the
confined
concrete f ~ c
is
commonly
expressed
as:
5
f ~ cp
where
specified compressive strength
of
concrete
c confining coeff ic ient
p confining pressure
The confining pressure provided by a circular
cold-formed
s tee l
section,
as shown in Fig. 5,
can
be
calculated
as
where
p
2
f
t
s
D
p confining pressure
fs tensi le s t ress
in confining
s tee l
t
thickness of
cold-formed s tee l
D diameter
of
circular section
1)
2)
For a square
section,
an equivalent circular
section
was proposed for
calculating
the confining pressure provided by cold-formed
s tee l
as shown
in Fig.
6.
Thus,
Eq
2) can
also
be applicable
for
calculating the
confining pressure. When
a rectangular section i s confined by cold-formed
s tee l two different
equivalent
circular sections may
be
proposed as shown
in Fig. 7. In
this
study, a shorter dimension
is
adopted
to
calculate the
diameter
of
the
equivalent circular
section for
the rectangular
section.
The axia l
capacity
of
the
concrete
in f i l led
cold-formed s tee l depends
upon how the s tee l section
i s
considered in calculation. The cold-formed
s tee l can be transformed into concrete by the
modular
ra t io
Es/Ec
or
by
super position, in which s teel and concrete are
considered separately.
I f the
cold-formed s tee l
i s
considered as
the
longitudinal reinforcement
in a reinforced concrete
column, then the
axia l
capacity
of the column
P
n
can
be
calculated
as:
3)
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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446
where
area
of concrete core
compressive strength of confined concrete
area
of cold-formed s tee l
yield strength of
cold-formed
steel
By
knowing
the value of
P
n
from
experiment, the concrete strength
fbc1 can
be
calculated
from
Eq.
(4)
P - A
f 1 = n ty (4)
0.85
A
c
The
calculated
fbc1, as shown
in Table 2,
is
greater
than fb
used
in
this
experiment. This
indicates that the cold-formed
s tee l
not only
carr ies
the
axial load in the
longitudinal
direction, but also provides
l a tera l confinement
on the
concrete
inside
the
steel
section.
From
Eqs.
(1),
(2) and (4), the confining coefficient can
be
calculated
and
denoted
as C1 from Eq. (5);
P - A f - 0.85A f
n s t
y
c C ___
D
__
)
0.85A 2f t
c y
The
confining
coefficient
C1
for
each specimen
was
calculated
and
shown
in Table
3.
(5)
During the tes t ,
large
deformations in the
longitudinal direction
were
observed. The thin, cold-formed s tee l buckled in the
longitudinal
direction and separate from the
concrete
long
before
the rupture
of
steel
was
observed.
Thus
the compatibility
between
concrete
and steel
is not
valid.
Hence,
the transformed area
method is
not applicable in strength
calculation. According to the t es t
resul ts
as shown in Table 2, the
average concrete s t ra in in the
longitudinal
direction reached
0.01
when
the specimen reached i t s axial capacity fbc.
At
this
stage,
with
a
Poisson s rat io of 0.15-0.20
for
concrete, the
s t ra in
in the transverse
direction
could
be
as
high
as 0.002, which exceeds
the
yield s t ra in of the
confining
steel . I f the cold-formed steel is
only
considered as a
confining
material in
the
transverse direction and the
contribution
in the
longitudinal
direction
is ignored, then,
The confined concrete strength, fbc2
can
be
calculated
by Eq. (7)
(7)
In
Eq.
(7) the value
C
can then
be
calculated
by
Eq.
(8) and
denoted
as C2;
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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447
C2
(8)
The
value
of
C2
for
each
specimen was also
calculated and
shown in
Table 3.
Comparing
the values of C and C2 calculated
from
tes t
resul ts for sections with the same
shape,
a larger variat ion in
C
was
observed. In calculating C1 i t
was
assumed
that
the
confining
s tee l
carried
the
axia l
load in the
longitudinal direc t ion and
provided
confinement
on
concrete in the t ransverse direc t ion simultaneously.
Hence, the thickness
of s tee l plays
a
very important role
in
the
calculation of C1.
Smaller
C was observed
for
the
thicker section.
On
the
other hand, when
the
confining
s tee l only
provided
confinement on
concrete
in
the t ransverse direc t ion,
a re la t ively
uniform C2
was
observed. Thus, the ult imate axia l
capacity
of the concrete
in f i l l ed
cold-formed
s tee l column can be predicted more accurately by
using
Eqs.
(6)
and
(7), with
C
3.2 for
circular
sections,
C
1.9
for square
sections,
and
C 1.5 for rectangular sections
In this
experiment,
different C values were obtained for square
and
rectangular
sections.
This indicates that the
C
value i s
a
function of
the aspect
rat io of the rectangular section.
Thus,
further investigation
has to be conducted
to
study the C value for sections with different
aspect
rat ios .
Failure
Modes
The s tee l
section
used in this experiment was
cold-formed
from th in
s tee l plate and then welded
along
the longitudinal direc t ion. The weld
was
designed
to develop the fu l l
strength
of the s tee l
section.
The
weld
l ine for
square
and rectangular sections
was located
very
close to the
corner of the section. According
to
t es t results 14 out of 18 specimens
fai led
by
rupture of confining
s tee l
in
the longitudinal direc t ion
as
shown in Fig.
8. For of those
14
specimens, the ruputure occurred
ei ther
a t top
or bottom
of the
specimen,
and for
10
of
them
the
rupture
occurred along
the weld l ine . The rupture zone is
l imited to
1 to 1-1/2 D
of the section regardless the length of the member. Reviewing the C
values for those
specimens
ruptured along the weld l ines no s ignif icant
difference was observed for circular sections
and
square
sections.
However,
lower C values were
observed for rectangular sections
D 14
and
D-18.
This difference
may be contributed by poor
welds.
For
those
3
specimens which did not fa i l in rupture of
s tee l section,
the
tes ts
were
stopped
when the
tes t machine reached i t s
maximum
stroke.
CONCLUSIONS
This exploratory tes t
program
demonstrated
the axial capacity
and
behavior
of
the
concrete
in f i l l ed cold-formed
concrete.
Based
on the
resul ts
discussed
in
th is
paper, the
following
conclusions
may
be
drawn:
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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448
1. For
the
concrete infi l led
steel
columns with the same length,
the
longitudinal st rain
E
corresponding
to the maximum stress f tc
remains constant
regardless
the concrete strength, the shape of the
section,
and
the thickness
of confining
steel .
The
st rain E
varies
with
the length
of
the
element.
A
shorter element
yielded with a
higher value of E1'
2. The post-crushing strength of the
confined
concrete is a function of
the thickness of confining material and the shape of the
section.
Larger strength
reductions,
bftc
in square
and
rectangular sections
were observed.
No
s ignif icant difference
in residual , post-crushed
strength of the in f i l l ed
concrete
was observed for concrete with
different
in i t ia l
strengths f t .
3. The rupture of confining steel in square and rectangular sections
occurred
at
the corner
of
the
section
in
the t ransverse
direction,
while
the
rupture
mostly
occurred
a t ei ther
top or bottom of the
column in the
longitudinal direction.
The rupture zone
is
l imited
to
1 to 1-1/2 D of the section regardless the length of the member.
4.
The axial capacity
of
the column
can
be more
accurately predicted
by
Eq. (6), in which the
cold-formed
steel
only provides l a te ra l
confinement on concrete, and the axial capacity provided by the
cold-formed
steel
in the
vert ical
direction i s ignored in
strength
calculation. The circular section has a higher confining coefficient
than the square and
rectangular sections.
The
confining
coefficient C
for the rectangular section is a function of i t s aspect
rat io . Thus,
further
study
has
to
be
carried
out
to evaluate the
confining
coefficient for rectangular
sections
with different
aspect
rat ios.
APPENDIX I - REFERENCES
1.
Yu W.W. Cold-Formed
Steel Design,
John Wiley and Sons, Inc. , New
York, 1985, 545pp.
2.
Shil l ing,
C.G., Buckling
Strength
of Circular Tubes,
Journal
of the
Structura l
Division, ASCE Proceedings, Vol. 91, Oct. 1968.
3.
Miller, C.D., Buckling of
Axially
Compressed
Cylinder, Journal
of
the Structural Division,
ASCE Proceedings, Vol. 103,
Mar. 1977.
4. Sherman, D.R.,
Structura l
Behavior of
Tubular Sections,
Proceedings
of the Third
Internat ional
Specialty Conference on Cold-Formed
Steel
Structures,
University
of
Missouri-Rolla,
Nov. 1975
5. Park, R. and Pauley, T., Reinforced Concrete Structures, John Wiley
and Sons,
Inc.,
New York, 1975,
769pp.
APPENDIX I I - NOTATIONS
The
following
symbols
are
used
in
this
paper:
Ac = area of
concrete
core
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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C
z
D
f
c
H
t
9
area of
cold formed
steel
width of square
and
rectangular cold formed
steel
sections
confining coeff ic ient
confining
coeff ic ient
confining
coeff ic ient
diameter
of
circular cold formed
steel
section
specified compressive strength of concrete
maximum
compressive stress of confined concrete
reduction
in s t ress between
El and Z
tensi le
stress
in
cold formed
steel
yield
stress of
cold formed
steel
depth of rectangular section
confining pressure
axial
capacity
of column
thickness
of cold formed steel
st r in corresponding to
maximum
stress
s tabi l ized st r in corresponding to post crushed concrete
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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450
Table 1
Proper t ies
of Specimens
specimen specimen
steel
specimen A A
no.
dimension thickness
length
c
s t y
c
cm
2
2
cmxcm)
cm)
cm)
ton)
kg/cm
D l
5< > 0 07
48
177
8 3
230
D2
5< >
0 07
80 177
8 3
230
D4
5< > 0 14
80 177 16.5 230
D6
5< >
0 21
80
177
24.7 230
D7 15x15
0 07
48 225 10 5
230
D8
15x15
0 07
80 225
10 5
230
Dl0
15x15
0 14
80 225 21.0
230
D12
15x15
0 21
80
22.5
31.5
230
D
13
15x20
0 07
48 300 12 3
230
D14
15x20
0 07
80
300 12 3
230
D
16
15x20
0 14
80
300
24.5
230
D18
15x20
0 21
80
300
36.8
230
E l
5< >
0 07
48 177 8 3
344
E6
5< >
0 21
80 177
24 7
360
E7
15x15
0 07
48
225
10 5
344
E 10 15x15
0 14 80
225
21.0
360
E
15 15x20 0 14 48
300 24.5
344
E 18
15x20
0 21
80
300 36 8
360
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451
Table 2. Mechanical
Proper t ies of
Test Specimens
specimen
\
El E2
( , f l
e 2
-2
(10
-2
ern/
ern
ee
2
no.
(kg/ern )
ern
(10
ern/em)
(kg/em)
D1
22300
0.65 1.354 2.922
124
D2 34320
0.725
0.906 1.656
74
D4 37250
0.70
0.875
3.312
59
D6
35850
1.10 1.375
3.063
38
D7
22280 0.60 1.250 2.135
90
D8
41180
0.575 0.719
1.875
135
D10 29890
0.70
0.875 1.750
72
D12 30110
0.65
0.813
2.219 74
D13
20976
0.70
1.302
3.542
142
D14 35960 0.60
0.750 1.438
88
D16 39600 0.50
0.625 1.250
107
D18
44290 0.525
0.656
1
781
56
E1
40400
0.45
0.938
5.730
148
E6
56600 0.70 0.875 6.250
113
E7 31500
0.43
0.896 2.500
179
E10
41411
0.65
0.813
2.000
154
E15
42240
0.50
1.04
4.170
170
E18 44370
0.55 0.688 2.188
156
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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452
Table
3 es t
Resul t s
specimen
P
f
f
Failure
Mode
n
eel
C
1
cc2 C
2
(kg/ cm
2
(kg/
no. (ton)
cm
2
Longitudinal
Transverse
D1
54.9 310
3.43
310
3.43
Middle
Non-Weld
D2 52.4 293
2.70
296
2.83 Bottom
Weld
D
71.1
363
2.85
402 3.68
Bottom
Non-Weld
D6
80.3
370 2.00 454
3.20
Middle
Weld
ave:2.75
ave:3.285
0:0.59 0:0.36
D7
56.9 243
0.56
253 0.99 Top
Non-Rupture
D8
62.4 271 1.
76
277
2.02 Top
Non-Weld
D1
72.6
270 0.86
322 1.97
Bottom
Non-Rupture
D12
80.9
258 0.40
358 1.83
Middle
Weld
ave:0.90
ave:1.70
0:0.61
0: 0.48
D13
81.1
273
1.84
273 1.
71
Middle
Non-Rupture
D14
71.9
234
0.17
240
0.43
Top Weld
D16
89.9
257
0.58
300
1.50
Bottom
Weld
D18 86.1
194
-0.51
287
0.81
Bottom
Weld
ave:0.52
ave :1.113
0:0.99
0:0.59
E1
75.9 450
4.55
429 3.60 Top
Weld
E6
109.5 443
1.67
620
3.71
Top
Weld
ave:3.11
ave:3.66
0:2.03
0:0.08
E7
76.2 344 0
339 0
Middle
Non-Rupture
E1 99.3
409
1. 78
441 1.74 Top
Weld
ave:0.87 ave:0.87
0: 1. 23
0: 1. 23
E15 119.6
373 0.62 399 1.15
Bottom
Weld
E18
129.3
263
0.53
431
1.13
Bottom
Non-Weld
ave:0.58
ave:
1.14
0:0.06 0:0
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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3
A
2
'
0
o
.
U
l
U
l
Q
J
I
1
o
O
1
2
3
S
t
a
i
n
c
m
/
c
m
x
1
F
g
1
T
c
s
t
e
s
s
t
a
i
n
c
v
3
'
E
2
b
.
U
l
U
l
Q
J
I
1
0
D
6
=
2
m
)
A
_
D
4
=
O
.
1
m
)
D
2
=
O
.
0
m
)
0
2
4
6
S
t
a
i
n
c
m
/
c
m
x
F
g
2
S
t
e
s
s
t
a
i
n
c
v
f
o
s
p
m
e
w
i
h
d
i
e
r
e
n
t
s
t
e
e
l
t
h
i
c
k
n
e
s
s
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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3
2
C
E
0
-
b
O
O
J
;
+
r
n
1
0
D
(
e
i
c
u
l
a
r
D
1
q
e
D
1
r
e
e
t
a
a
0
2
4
6
S
t
a
i
n
-
2
c
m
/
c
m
x
O
)
F
i
g
.
3
S
t
e
s
a
i
n
c
v
f
o
r
s
p
m
e
w
i
h
d
i
e
r
e
n
t
s
h
3 2
C
E
0
b
O
O
J
;
+
r
n
1
0
D
7
(
=
2
3
0
c
j
{
c
m
2
)
E
(
=
3
4
4
k
c
m
2
)
c
0
2
4
6
S
t
a
i
n
c
m
/c
m
x
1
)
F
i
g
.
4
S
t
e
s
a
i
n
c
v
f
o
r
s
p
m
e
w
i
1
d
i
e
r
e
n
t
f
c
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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455
-
_
1/---'- _. . . -1 1-_
t
Y
D
Fig. 5 Confinement on c i rcu la r sec t ion .
B
i
.. //---
'...:-
1
.
-
b ~
/ _.
0
-
\
..
.
B
\
.
\ ~ .
.
~ h
,-
. .
./.;/
t
Y
Fig. 6 Equivalent confinement on square sec t ion .
t f
Y
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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56
Fig Equ iva len t con: ine nent on r ec t angu l a r s e c t i o n
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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57
Fig
ai lure
modes
7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns
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