The Effect of Steel Jacketing on Strength Capacity and
Ductility of Reinforced Concrete Columns
M. Sheikhi
H. Haji-Kazemi
A. Attari
Department of Civil Engineering, Ferdowsi University of Mashhad,
P.O. Box 91775-1111, Mashhad, Iran
ABSTRACT There are various methods for strengthening reinforced concrete
columns. Among them, covering columns with steel plates is an easy solution due to
the versatility and availability of needed materials. Applying this method will cause
an increase not only in axial and flexural strength, but also in the ductility of the
member. In this research, the moment-curvature curves of strengthened concrete
columns confined by stirrups and steel jackets were studied by investigating the
effective factors in column’s behavior. The results show that, there is not any
noticeable difference between ultimate curvatures of the initially reinforced concrete
column and the strengthened one, but the proportion of final curvature to yielding
curvature, so called curvature ductility, will increase substantially.
Keywords: Reinforced Concrete Column, Strengthening, Confinement, Axial Force,
Moment Curvature Interaction, Ductility.
Introduction
During the last decades, strengthening concrete structures, due to earthquakes,
revising the codes, the process of deterioration of concrete and other related issues,
has become the center of attentions of the construction industry. Among the structural
elements, columns are one of the most crucial members. So in this paper, the method
of covering columns with steel jackets and their confining effects on the behavior of
the section, especially on its moment-curvature relation is chosen for study.
In this strengthening approach, steel plates are usually stuck to the reinforced
concrete columns by the use of resins or screws. Also it is possible to place the steel
box as a cover within a little distance of the concrete column, and to fill the
intervening space with high quality concrete, self consolidating or self expansive
concrete. The resulting element gains more flexural and compressive strength. The
increase in flexural strength is due to the fact that the concrete core does not let the
steel jacket buckle towards inside the section. Also because of the interaction effects
of orthogonal elements, the section will gain extra stiffness at its corners which lead to
a reduction in both buckling length and boundary resistant of the member.
Experiments show that the buckling strength of such columns is about 2.5 times
the strength of steel box sections without a concrete core [1, 2]. On the other hand,
upon further increase of axial load, the stress in concrete reaches beyond the elastic
limit of the concrete strength, and consequently causes the formation of small cracks
in concrete and an increase in the concrete volume [3]. This increase in volume will
be confined by steel jackets, causing the concrete section to experience triaxial
stresses which increases its axial strength. The remarkable point here is the increasing
of ductility due to the improvement of concrete section. This kind of behavior is
important in seismic areas.
Although experimental studies on the effects of stirrups on concrete columns
behavior have been conducted by Saatcioglu et al [4], and also extended researches
have been done by Susantha et al [5], on the behavior of steel box columns filled with
concrete, but there haven’t been done any research on the effects of stirrups and
strengthening steel plates simultaneously on the behavior of reinforced concrete
columns.
Effects of stirrups on reinforced concrete columns
Transverse rebars hold longitudinal reinforcements on their correct positions and
increase shearing strength, besides causing column’s ductility and axial strength to
improve. Equation (1) states the effects of lateral pressure on the axial strength of
concrete columns [6].
f cc  f co  k1 f l
k1 
(1)
1 
(2)

2
Where fcc is confined compressive strength of concrete; f co is unconfined
compressive strength of concrete; f l is lateral pressure. k1 is a coefficient of increase
in strength, which depends on the poisson’s ratio and is defined by equation (2).
k1 is dependent upon the kind of concrete used, and the value of pressure applied.
Researchers also suggested some other equations for the value of k1 . One of the most
credible equations which has been suggested by Richart et al. [6], is:
k1  6.7( f l ) 0.17
(3)
This equation is also verified by other researchers such as Balmer [7] and Sato [8].
The lateral pressure, resulting from axial force applied on the column is resisted by
transverse reinforcements or covering steel jackets. This lateral pressure is not
uniform in the sides of a rectangular section. The equations suggested by Saatcioglu et
al. [4] for equivalent lateral pressure in square sections will be utilized here.
f cc  f co  k1 fle
f le  k 2 f l
fl 
A
s
(4)
(5)
f y sin 
(6)
sb
k1  6.7( f le ) 0.17
(7)
b b 1
k2  0.26 ( )( )( )  1.0
s sl fl
(8)
Where As is area section of transverse reinforcements; α is inclination of stirrups
towards the transverse axis of the section; s is stirrups spacing; b is section width; and
sl is distance between two adjacent longitudinal rebars.
The stress-strain diagram of concrete (Fig. 1), can now be drawn after obtaining
confined compressive strength of concrete (fcc) from above equations, and
corresponding strains using simplified equations (9) to (12). The subscripts of strains
denote the percent of the relative stresses.
 B1   A1 (1  5k )
k  k1
(9)
f le
f co
(10)
 B.85  260  B1   A.85
(11)

(12)
A
s
sb
fc
f cc
Unconfined section (B)
0.85 f cc
f co
3 (A)
Confined section
Fig.1 Stress-strain diagram of concrete
The first nonlinear part of diagram (A) of Fig.1 is obtained by equation (13)
proposed by Saatcioglu et al. [4]. Diagram (B) represents the stress – strain curve of
unconfined concrete section. Since there are not any experimental data on εB1 and εB.85,
for the usual concrete, these two items will be taken 0.002 and 0.0038 respectively.
f c  f cc [2(
1
c

)  ( c ) 2 ] (1 2 k )  f cc
1
1
(13)
Effects of steel jackets on concrete filled steel boxes
Some researchers such as Susantha et al. [4] have studied the behavior of concrete
filled steel box columns without longitudinal and transverse reinforcement. The
following equations are experimental results suggested by Susantha et al. on concrete
specimens with compressive strength of 20 to 50 MPa.
f rp  6.5R
R
( f 'c )1.46
 0.12 ( f 'c )1.03
fy
(14)
2
b 12 (1  ) f y
t
4 2 Es
(15)
f cc  f co  mf rp
(16)
Where frp is the lateral pressure applied to concrete core due to the presence of
cover; fy and Es are yield strength and modulus of elasticity of steel of steel; fc is
concrete compressive strength, and m is a coefficient taken from 4 to 6. m should be
taken as 4 for concrete filled steel box sections.
Suggested equations for the behavior of reinforced concrete columns
strengthened with steel plates
In this section, a concrete column with transverse and longitudinal reinforcement
strengthened with a confining steel box is studied. So far, no research has been
4
reported on the behavior of concrete columns confined with both steel box and
transverse reinforcement. In this research, it is intended to establish new equations
which consider confining effects of both steel box and stirrups simultaneously, by
combining classic formulations and test results.
Lateral pressure applied to the concrete core due to the presence of steel box is
obtained using equations (14) and (15); and lateral pressure resulting from transverse
and longitudinal reinforcements is obtained using equations (5) to (8). Combining
those, results the following equations:
f cc  f co  k1 ( f le  f rp )
k1  6.7( f le  f rp )
(17)
0.17
(18)
(19)
 B1   A1 (1  5k )
k
k1 ( fle  f rp )
(20)
f co
 B.85  260  B1   A.85

A
s
bs

(21)
2t
b
(22)
Which lead to the following useful statements for drawing the stress-strain diagram.
1
c

)  ( c ) 2 ] (1 2 k )
1

0.15 f cc
f c  f cc 
(   )
 B.85   B1 B1 c
f c  f cc [2(
f c  0.2 f cc
0   c   B1
1   c   B.2
 B.2   c
5
(23)
Section analysis and moment-curvature diagram
Regarding the subject of lateral loads and the importance of ductility in structural
members, the moment-curvature relation is been an appropriate criteria to study the
behavior of such sections. In fact, curvature is the rotation per unit length of the
element and as the capability of rotation in joints is one of the most important factors
affecting the issue of ductility, the moment-curvature curve can be a suitable criterion
for evaluating this characteristic.
With respect to the above mentioned methodology, some specimens of ordinary
reinforced concrete columns, and reinforced concrete columns strengthened with steel
plates are analyzed here, using the trial and errors technique; and their momentcurvature curves are presented.
Assuming plane sections remain plane before and after loading, and considering an
assumed value for the extreme compressive fiber’s strain, it is possible to locate
section’s neutral axis by using the equilibrium equations.
Finding internal forces of the section, including forces due to concrete core
resistance, forces due to concrete cover, and forces due to tensile and compressive
rebars, one may utilize the equations of equilibrium, and determine the location of
neutral axis by trial and error method. After verifying the location of neutral axis (c),
resisting moment of the section is calculated.


c
0
fc d ε
(24)
f 'c  c

 1
c
0
 f c d
 f ' c ( c )
(25)
2
cc
C S1
S1
c
cC
C core = f'c.b.c
cC
S2
C S2
Fig.2 Stresses and strains of section
Although the ultimate strain of confined concrete may reaches to about 0.008,
present codes have suggested it to be taken about 0.003 to 0.0035 for design purposes.
In this paper, with respect to the fact that concrete is confined and its ultimate
compressive strain is possibly higher than unconfined section, the ultimate strain of
concrete is assumed to be 0.007. Therefore the maximum resisting moment of the
section is attained. A computer program is prepared for this process.
6
Sections are denoted as bx-py, where x is referred to the width of the square
section and y is referred to the thickness of steel plate. For example, b30-p1.5 is
indicating a concrete section with the dimensions of 30 x 30 cm, strengthened with a
steel plate having thickness of 1.5 cm. Material specifications of the specimens are
shown in Table 1.
Table 1 Materials specification of the specimens
Materials
f’c (MPa)
fy (MPa)
E (MPa)
concrete
25
-
25000
Longitudinal reinforcement
-
300
200000
Transverse reinforcement
-
300
200000
Strengthening steel plates
-
240
200000
The famous Hognestad formula [10] is applied for the stress-strain relationship of
concrete, and steel’s behavior has been modeled using an elastoplastic two-linear
stress – strain diagram.
Results
In order to provide a better knowledge of the column’s behavior, especially within
practical size limits, the moment-curvature curves of some column specimens are
drawn, while changing different parameters.
Besides making a comparison between ordinary reinforced concrete and
strengthened composite sections, it is possible to study the effects of parameters
involved, separately. Some parameters considered here are the dimensions of the
section, length to thickness ratio of the steel plates, and also the value of axial force
applied to the column.
It should be mentioned that when each section reaches its ultimate flexural
strength (balance region), its axial stress is within 0.2 to 0.4 times its ultimate values
corresponding to zero eccentricity. But diagrams here are drawn assuming axial stress
of the section to be 0.3 to 0.7 times its ultimate values to show the behavior of the
column section in the practical region of material failure.
In figures (3 to 14), A is the point when concrete experiences tensile stresses for
the first time. B is the point when steel yields in tension side; C is the point when
compressive stress of the section’s rebars reaches to the yielding value; E and F are
the points corresponding to yielding steel plates at tension and compression sides of
the section respectively. Eventually, D indicates that concrete has reached to its
ultimate strain of 0.007 in compression.
7
In Figure 3, it is shown that final curvature of both plated and unplated sections is
almost the same. On the other hand, the ductility of composite column is more than
the ordinary reinforced concrete column, because of a small difference which exists
between the values of sections’ yielding curvature (point B). It should be mentioned
that diagrams are drawn while the value of axial load for the ordinary concrete
section is within its balance region, causing it to show more flexural strength; but this
value of axial load is not enough for the composite section to arrive at its balance
region.
b30-P1.5
b30-P0
700
D
B
C
M (kN.m)
600
b30-P1.5
E
F
500
400
P=0.3(As.fy+Ac.f’c)=925.2 kN
300
200
A
C
100
b30-P0
B
D
A
0
0
4
8
12
16
20
24
28
32
36
40
44
(1/mm x 106) curvature
Fig 3. Moment-curvature diagrams of b30-p0 and b30-p1.5 sections
In Fig. 4, it is observed that bending resistance of reinforced concrete section has
decreased by increasing the axial load ( C to D is descending ), while bending
resistance of the composite section has not changed evidently. Also diagrams show
that final curvature of both sections has reduced by increasing the axial load.
8
b30-P1.5
b30-P0
700
E
600
B
b30-P1.5
C
D
500
M (KN.m)
P=0.7(As.fy+Ac.f’c) =2158.8 kN
400
F
300
A
200
A
100
C
D
b30-P0
0
0
4
8
12
16
20
24
28
32
(1/mm x 106) curvature
Fig. 4 Moment-curvature diagrams of b30-p0 and b30-p1.5 sections
In figures(5) to (14), the effect of some different parameters on moment-curvature
curve is studied. In figures (5) to (10), the effect of length to thickness ratio (b/t) of
strengthening plates are demonstrated. In figures (11) to (14), the effect of axial load
on moment - curvatures are shown.
9
b30-P0.5
b30-P0.8
b30-P1.5
700
E
M(kN.m)
500
P=0.3(As.fy+Ac.f’c) =925.2 kN
F
400
C
B
D
b30-P0.8
E
300
D
b30-P1.5
B
C
600
F
200
E
A
C
B
D
b30-P0.5
F
100
A
0
0
5
10
15
20
25
30
35
40
45
50
(1/mm x 106) curvature
Fig. 5
Moment-curvature diagrams for sections: b30-p0.5, b30-p0.8 and b30-p1.5
700
D
E
600
C
500
M(kN.m)
B
b30-P1.5
P=0.7(As.fy+Ac.f’c) =2158.8 kN
F
400
b30-P0.8
D
E
300
C
A
A
200
100
A
F
E
F
D
b30-P0.5
C
0
0
5
10
15
20
25
30
35
(1/mm x 106) curvature
Fig. 6 Moment-curvature diagrams for sections: b30-p0.5, b30-p0.8 and b30-p1.5
10
B45-P1.2
B45-P0.6
B45-P0.8
1600
b45-P1.2
1400
D
C
M(kN.m)
1200
E
b45-P0.8
1000
C
F
800
b45-P0.6
E
F
F
400
D
C
E
600
D
P=0.3(As.fy+Ac.f’c) =1790 kN
A
200
A
0
0
5
10
15
20
25
30
35
40
(1/mm x 106) curvature
Fig. 7 Moment-curvature diagrams for sections: b45-p0.6, b45-p0.8 and b45-p1.2
1400
1200
C
b45-P0.8
M(kN.m)
1000
F
A
800
F
A
600
B
C
D
E
E
b45-P0.6
D
B
A F C
400
D
b45-P1.2
B E
P=0.7(As.fy+Ac.f’c) =4170kN
200
0
0
5
10
15
20
25
(1/mm x 106) curvature
Fig. 8 Moment-curvature diagrams for sections: b45-p0.6, b45-p0.8 and b45-p1.2
11
B60-P1.5
B60-P0.8
B60-P1.0
3500
C
2500
M(kN.m)
D
b60-P1.5
3000
C
F
2000
E
b60-P0.8
F
1500
D
C
E
P=0.3(As.fy+Ac.f’c) =3123 kN
F
1000
D
b60-P1.0
E
500
A
0
0
5
10
15
20
25
30
(1/mm x 106) curvature
Fig. 9 Moment-curvature diagrams for sections: b60-p0.8, b60-p1.0 and b60-p1.5
3500
D
b60-P1.5
3000
B
B
M(kN.m)
2500
C
D
b60-P1.0
E
B
2000
F
1500
C
A F
B
FA C
1000
D
b60-P0.8
E
P=0.7(As.fy+Ac.f’c) =7287 kN
500
0
0
5
10
15
20
(1/mm x 106) curvature
Fig. 10 Moment-curvature diagrams for sections: b60-p0.8, b60-p1.0 and b60-p1.5
12
Figures (5) to (10) are categorized in two groups. First group with low axial load is
located under the balance state in moment-axial load interaction diagram. In this
group, final curvature ductility is decreased by increasing b/t ratio due to the reduction
of axial load, which cause the section to exit its balance region. But second group are
applied high axial load, and so are in close proximity to their balance region; in this
group, final curvature will increase by increasing b/t ratio. This phenomenon may
happen because confinement of concrete is more effective in higher axial loads.
Figures (11) and (12) will show only the effect of axial load on moment-curvature
curves while all other parameters are constant.
120
B
100
P=925.2 kN
A
80
M(KN.m)
D
C
C
60
P=2158.8 kN
D
A
40
20
0
0
5
10
15
20
25
30
35
40
45
50
(1/mm x 106) curvature
Fig. 11 Moment-curvature diagram for section b30-p0
450
P=925.2 kN
400
C
350
E
D
P=2158.8 kN
E
300
M(KN.m)
D
B
F
C
250
A
200
F
150
A
100
50
0
0
5
10
15
20
25
30
35
40
45
(1/mm x 106) curvature
Fig. 12
Moment-curvature diagram for section b30-p0.8
13
50
450
P=1790 kN
400
D
B
350
C
M(KN.m)
300
C
250
D
P=4170 kN
A
200
150
A
100
50
0
0
5
10
15
20
25
30
35
40
(1/mm x 106) curvature
Fig. 13 Moment-curvature diagram of b45-p0
1200
E
800
M(KN.m)
D
P=1790 kN
1000
F
600
F
A
C
D
P=4170 kN
B
E
C
400
A
200
0
0
5
10
15
20
25
30
35
40
(1/mm x 106) curvature
Fig. 14 Moment-curvature diagram of b45-p0.8
Figures 11 to 14 are expressing the fact that tensile longitudinal reinforcements are
not yielded when axial load applied to the section is too high or too low, which will
cause a reduction in section's ductility.
Therefore, designers should always try to utilize sections within their balance
region.
14
Conclusion
1. Covering reinforced concrete columns with steel jackets is one of the easiest and
most efficient methods of strengthening them. This method has some advantages
such as ease of performance and availability of materials. Furthermore,
confinement of concrete core will increase the column's strength and will control
its ductility.
2. There is not any noticeable difference between the ultimate curvatures
corresponding to assumed ultimate compressive strains of an ordinary reinforced
concrete column and the strengthened one. But, on the other hand, curvature
ductilities, as explained and demonstrated in result section, will be increased if the
section is strengthened.
3. Upon further, increase of axial load cause the curvature ductility of plated and
unplated sections to decrease, but the rate of decreasing the ductility of plated
sections are noticeably lower than the unplated ones.
4. The flexural strength capacity of the strengthened sections is quite higher than the
unplated sections comparatively. Some records show up to 200 percent increase in
moment capacity
References
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15