numerical analysis of concrete-filled steel tubes

7/30/2019 Numerical Analysis of Concrete-filled Steel Tubes

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NUMERICAL ANALYSIS OF CONCRETE-FILLED STEEL TUBES

SUBJECTED TO AXIAL FORCE

Hsuan-Teh HU1, Chiung-Shiann HUANG2, Ming-Hsien WU3 and Yih-Min WU3

SUMMARY

Proper material constitutive models for concrete-filled steel tube (CFST) are proposed andverified by the nonlinear finite element program ABAQUS against experimental data. The crosssections of the CFST in the numerical analysis are categorized into three groups, i.e., circularsection, square section, and square section strengthened by reinforcing ties. Via the numerical

analyses, it has been show that for circular CFST, the tubes can provide good confining effect to

concrete especially when the diameter-to-tube thickness ratio is small. For square CFST, the tubesdo not provide too much confining effect to concrete especially when the diameter-to-tubethickness ratio is large. The confining effect of square CFST with reinforcing ties is enhanced bythe use of reinforcing ties especially when the tie spacing is small and the tie number (or tiediameter) is large.

Keywords: concrete-filled steel tube, diameter-to-tube thickness ratio, lateral confining pressure,material degradation parameter.

INTRODUCTION

The concrete-filled steel tube (CFST) can provide excellent earthquake resistant properties such as high strength,high ductility and large energy absorption capacity. In addition, a considerable amount of time can be saved

during the construction stage due to the no need of formwork. As the result, the applications of CFST in

engineering structures have been increased rapidly in recent year (Furlong, 1967; Knowles and Park, 1969;

Furlong, 1974; Ge and Usami, 1992; Ge and Usami, 1994; Boyd, Cofer and McLean, 1995; Bradford, 1996;

Hajjar and Gourley, 1996; Shams and Saadeghvaziri, 1997; Uy, 1998; Morino, 1998; Schneider, 1998; Zhang

and Shahrooz, 1999; Liang and Uy, 2000; Huang et al., 2002).

The enhancement of CFST in structural properties is due to the composite action between the constituent

elements. The steel shell acts as longitudinal and transverse reinforcement. The shell also provides confining

pressure on concrete, which puts the concrete under a triaxial state of stress. On the other hand, the steel tube is

stiffened by the concrete core. This can prevent the inward buckling of the steel tube and increase the stability

and strength of the column as a system. It is known that the ultimate strengths of CFST are influenced by its

constituent material properties such as the compressive strength of the concrete and the yielding strength of the

steel. In addition, the ultimate strengths of CFST are also influenced by the concrete confining pressure and the

geometric properties of the tubes such as the shape of cross section, the diameter-to-tube thickness ratio, and the

spacing and the diameter of the reinforcing tie.

The aim of this investigation is to employ the nonlinear finite element program ABAQUS (Hibbitt, Karlsson and

Sorensen, 2000) to perform numerical simulations of CFST subjected to axial loads. To achieve this goal, proper

material constitutive models for steel reinforcing tie, steel tube and concrete are proposed. Then the proposed

material constitutive models are verified against the experimental data from Schneider (1998) and Huang et al.

(2002). Finally, the influence of the concrete confining pressure and the geometric properties of the columns on

the uniaxial behavior of CFST are studied.

1 Professor, Department of Civil Engineering, National Cheng Kung University, Taiwan, e-mail: [email protected] Professor, Department of Civil Engineering, National Chiao Tung University, Taiwan, e-mail: [email protected] Research Assistants, Department of Civil Engineering, National Cheng Kung University, Taiwan


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MATERIAL PROPERTIES AND CONSTITUTIVE MODELS

The cross sections of the CFST in this investigation can be categorized into three groups (Fig. 1), i.e., circular

section (denoted by CU), square section (denoted by SU), and square section strengthened with steel reinforcing

ties forming an octagonal shape (denoted by SS). The materials used in the numerical analysis involve steel

reinforcing tie (for SS section only), steel tube and concrete. Their proposed constitutive models are discussed in

the following sections.

Fig. 1 Cross sections of CFST

Steel Reinforcing Tie

When the stress in the reinforcing tie exceeds the yield stress, the tie will exhibit plastic deformation. The

stress-strain curve of the reinforcing tie is assumed to be elastic-perfectly plastic with y being the yield stress

and Es the elastic modulus (Fig. 2).

Fig. 2 Elastic-perfectly plastic model for steel reinforcing tie

Steel Tube

In the analysis, the Poisson's ratio s of the steel tube is assumed to be s = 0.3.

Fig. 3 von Mises yield criterion in three-dimensional principal stress space for steel tube

The uniaxial behavior of the steel tube is similar to reinforcing tie and thus can be simulated by anelastic-perfectly plastic model (Fig. 2). When the steel tube is subjected to multiple stresses, a von Mises yieldcriterion F is employed to define the elastic limit, which is written as

y)()()(2

1J3F 2132

322

212 =++== (1)


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where J2 is the second stress invariant of the stress deviator tensor and 1, 2, and 3 are principal stresses.Figure 3 shows the von Mises yield surface in the three-dimensional principal stress space. The response of the

steel tube is modeled by an elastic-perfectly-plastic theory with associated flow rule. When the stress points fall

inside the yield surface, the behavior of the steel tube is linearly elastic. If the stresses of the steel tube reach the

yield surface, the behavior of the steel tube becomes perfectly plastic. Consequently, the steel tube is assumed to

fail and can not resist any further loading.

Concrete

The Poisson's ratio cof concrete under uniaxial compressive stress ranges from 0.15 to 0.22, with arepresentative value of 0.19 or 0.20 (ASCE 1982). In this study, the Poisson's ratio of concrete is assumed to be

c = 0.2. Let the uniaxial compressive strength and the corresponding strain of the unconfined concrete be f'cand 'c (Fig. 4). The value of'c is usually around the range of 0.002 to 0.003. A representative value suggestedby ACI Committee 318 (1999) and used in the analysis is 'c = 0.003.

Fig. 4 Equivalent uniaxial stress-strain curve for concrete

When concrete is subjected to laterally confining pressure, the uniaxial compressive strength f'cc and the

corresponding strain 'cc (Fig. 4) are much higher than those of unconfined concrete. The relations between f'cc,

f'c and between

'cc,

'c suggested by Mander, Priestley and Park (1988) and used in this investigation which are

lfk'cf

'ccf 1+= (2)

'cf/fk1

'c

'cc 2 l+= (3)

where lf is the laterally confining pressure. The k1 and k2 are constants and can be obtained from experimental

data. Typical values for k1 and k2 suggested by Richart, Brandtzaeg and Brown (1928) and used in this

investigation are 1.41k = , 1k52k = .

Fig. 5 Linear Drucker-Prager yield criterion for concrete

Because the concrete in the CFST is usually subjected to triaxial compressive stresses, the failure of concrete is

dominated by the compressive failure surface expanding with increasing hydrostatic pressure. Hence, a linear

Drucker-Prager yield criterion G (Fig. 5) is used to model the yield surface of concrete, which is expressed as

0dtanptG == (4)

where

3/)(p 321 ++= , 'ccf]3/)(tan1[d =


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+=

3

2

2

J3

r)

K

11(

K

11

2

J3t ,

3/133

32

31 )SSS(2

9r

++=

and S1, S2, and S3 are principal stress deviators. The constants K and are material parameters determined fromexperimental data. In the analysis, K = 0.8 and = 20o are used (Wu, 2000).

The response of the concrete is modeled by an elastic-plastic theory with associated flow and isotropic hardening

rule. When plastic deformation occurs, there should be a certain parameter to guide the expansion of the yield

surface. A commonly used approach is to relate the multidimensional stress and strain conditions to a pair of

quantities, namely, the effective stress fc and effective strain c, such that results obtained following differentloading paths can all be correlated by means of the equivalent uniaxial stress-strain curve. The stress-strain

relationship proposed by Saenz (1964) has been widely adopted as the uniaxial stress-strain curve for concrete

and it has the following form

32 )'cc

c(R)'cc

c)(1R2()'cc

c)(2ERR(1

ccEcf

+

++

= (5)

=R

1

)1R(

)1R(RR

2

E ,'ccf

'cccEER

=

and R = 4, R = 4 may be used (Hu and Schnobrich, 1989). The initial modulus of elasticity of concrete Ec ishighly correlated to its compressive strength and can be calculated with reasonable accuracy from the empirical

equation (ACI 1999)

MPa'ccf4700cE = (6)

In the analysis, Eq. (5) is taken as the equivalent uniaxial stress-strain curve for concrete when the concrete

strain c is less than'cc (Fig. 4). When

'ccc > , a linear descending line is used to model the softening

behavior of concrete. If k3 is defined as the material degradation parameter, the descending line is assumed to be

terminated at the point where 'ccfkcf 3= and'cc11c = .

Generally, the parameters fland k3 have to be provided to completely define the equivalent uniaxial stress-strain

relation. These two parameters apparently depend on the diameter-to-tube thickness ratio (D/t or B/t),

cross-sectional shape, and stiffening mean. Consequently, their appropriate values are determined by matching

the numerical results with experimental results by trial and error.

Fig. 6 Finite element mesh for CFST

FINITE ELEMENT MODEL FOR CFST

Due to symmetry, only one eighth of the CFST is analyzed (Fig. 6) and symmetric boundary conditions are

enforced on the symmetric planes, which are u = 0 on the plane normal to x axis, w = 0 on the plane normal to zaxis and v = 0 on the bottom surface normal to y axis. The top surface of the column is fixed with u = w = 0 but

allows displacement to take place in y direction. The uniform compressive loading in y direction is applied to the


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top surface of the column directly. In the finite element mesh, both the concrete core and the steel tube are

modeled by 27-node solid elements (three degrees of freedom per node). For the SS section, the steel reinforcing

tie is modeled by 3-node truss elements. The interface between the concrete and the steel tube is modeled by

special 9-node interface elements. The interface elements allow the contact surfaces between the concrete and

the steel tube to remain closed or open but not to penetrate each other. In addition, the interface elements allow

friction to be developed on the contact surfaces. Based on the results of convergent studies (Wu, 2000), mesh

refinement has very little influence on the numerical results. Hence, the meshes shown in Fig. 6 are used throughout the analyses.

NUMERICAL ANALYSIS

In this section, the experimental data from Schneider (1998) and Huang et al. (2002) are used to verify andcalibrate the proposed material model for CFST. For convenience, each specimen in the analysis has anindividual designation, involving two English letters followed by a series of numbers (Table 1). The first letter,C or S, represents the cross-sectional shape of the column being circular or square. The second letter, S or U,denotes a column with or without stiffening ties, respectively. The three digital numbers following the Englishletters denote the diameter-to-tube thickness ratio (D/t or B/t). For stiffened CFST, the last three digital numbersbefore the parentheses represent the center-to-center spacing between the steel reinforcing ties in terms of mm.

Finally, the number in the parentheses is the reinforcing bar number of the steel tie.

Table 1 Geometry and material properties of CFST

Column No.B or D(mm)

t(mm)

B/t orD/t

Length(mm)

Tubefy(MPa)

Concrete'cf (MPa)

Tiefy(MPa)

Note

CU-022 140 6.5 22 602 313.0 23.80 - S

CU-040 200 5.0 40 840 265.8 27.15 - H

CU-047 140 3.0 47 602 285.0 28.18 - S

CU-070 280 4.0 70 840 272.6 31.15 - H

CU-100 300 3.0 100 900 232.0 27.23 - S

CU-150 300 2.0 150 840 341.7 27.23 - H

SU-017 127 7.47 17 609.6 347.0 23.80 - S

SU-022 127 5.67 22 609.6 312.0 23.80 - S

SU-029 127 4.34 29 609.6 357 26.00 - S

SU-040 200 5.0 40 840 265.8 27.15 - H

SU-070 280 4.0 70 840 272.6 31.15 - H

SU-150 300 2.0 150 840 341.7 27.27 - H

SS-040-050(3) 200 5.0 40 840 265.8 27.15 410.9 H

SS-040-050(4) 200 5.0 40 840 265.8 27.15 386.0 H

SS-040-100(4) 200 5.0 40 840 265.8 27.15 386.0 H

SS-070-093(2) 280 4.0 70 840 272.6 30.49 588.6 H

SS-070-093(3) 280 4.0 70 840 272.6 30.49 615.3 H

SS-070-093(4) 280 4.0 70 840 272.6 29.18 511.1 H

SS-070-140(3) 280 4.0 70 840 272.6 29.84 615.3 H

SS-070-140(4) 280 4.0 70 840 272.6 28.52 511.1 H

SS-070-187(3) 280 4.0 70 840 272.6 29.18 615.3 H

SS-070-187(4) 280 4.0 70 840 272.6 29.84 511.1 H

SS-150-050(2) 300 2.0 150 840 341.7 24.00 735.8 H

SS-150-100(2) 300 2.0 150 840 341.7 25.21 735.8 H

S CFST tested by Schneider; H CFST tested by Huang et al.

Simulations of CFST with CU Section

The results of numerical simulations for CFST with CU section are given in Table 2 and the curves of axial force

versus axial strain for these columns are plotted against the experiment data in Fig. 7. Generally, the numerical

results show very good agreement with the experimental data. It can be observed that both the lateral confiningpressure fland the material degradation parameter k3 decrease with the increasing of diameter-to-tube thickness


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ratio D/t. When the D/t ratio is small (i.e., the tube thickness is relatively thick comparing with the diameter of

concrete), the steel tubes provide strong lateral support to the concrete core. As the result, the lateral confining

pressure flusually has a very large value (say 8 MPa for CU-022 column). In addition, the material degradation

parameter k3 may be equal to 1 (e.g. CU-022 and CU-040), which means the concrete strength does not degrade

beyond the ultimate point. On the other hand, when the D/t ratio is large (i.e., the tube thickness is relatively thin

comparing with the diameter of concrete), the steel tubes provide weak lateral support to the concrete core. As

the result, the lateral confining pressure flusually has a very small value (say 0.3 MPa for CU-150 column). Inaddition, the material degradation parameter k3 may also have a lower value (say 0.6 for CU-150 column). The

behaviors of CFST with CU section are highly influenced by the k3 parameter of concrete. When k3 = 1 (e.g.

CU-022 and CU-040), the axial force-axial strain curves of the CFST do not show the degrading effect. However,

when 1k3 < , the axial force-axial strain curves of the CFST do show the degrading effect. This degradingphenomenon is more prominent with smaller value of k3.

Table 2 Results of numerical analyses

Failure Strength (kN)Column No.

Experiment Analysis

Error

(%)

fl

(MPa)fl/fy k3

CU-022 1666.0 1628.0 2.30 8.00 0.0256 1.00

CU-040 2016.9 2024.0 0.35 2.85 0.0107 1.00

CU-047 893.0 860.0 3.70 1.30 0.0046 0.90

CU-070 3025.2 3029.0 0.13 1.00 0.0037 0.70

CU-100 2810.0 2835.0 2.80 0.97 0.0042 0.68

CU-150 2607.6 2618.0 0.40 0.30 0.0009 0.60

SU-017 2090.0 2083.0 0.30 8.00 0.0231 0.90

SU-022 1242.0 1239.0 0.30 0.90 0.0029 0.70

SU-029 1106.0 1130.0 2.10 0.00 0.0000 0.60

SU-040 2311.5 2337.0 1.10 1.95 0.0073 0.50

SU-070 3401.1 3518.0 3.44 0.00 0.0000 0.40

SU-150 3061.5 3100.0 1.26 0.00 0.0000 0.40

SS-040-050(3) 2727.6 2741.0 0.49 3.00 0.0113 1.00

SS-040-050(4) 2902.6 2885.0 0.61 3.50 0.0132 1.00

SS-040-100(4) 2463.1 2476.0 0.52 2.50 0.0094 0.55SS-070-093(2) 3744.5 3745.0 0.01 0.70 0.0026 0.40

SS-070-093(3) 3855.3 3862.0 0.17 1.00 0.0037 0.45

SS-070-093(4) 3807.3 3812.0 0.12 1.10 0.0040 0.45

SS-070-140(3) 3610.1 3609.0 0.03 0.45 0.0017 0.55

SS-070-140(4) 3596.3 3568.0 0.78 0.60 0.0022 0.50

SS-070-187(3) 3457.0 3465.0 0.23 0.46 0.0017 0.45

SS-070-187(4) 3507.1 3541.0 0.97 0.43 0.0016 0.55

SS-150-050(2) 3184.2 3213.0 0.90 0.45 0.0013 0.60

SS-150-100(2) 3104.7 3092.0 0.41 0.10 0.0003 0.30

0.0

0.5

1.0

1.5

2.0

0 0.01 0.02 0.03 0.04 0.05

Experiment

SimulationAxialforce(M

N)

Axial strain

CU-022

fl=8MPa, k

3=1

(a)

0.0

0.5

1.0

1.5

2.0

2.5

0 0.005 0.01 0.015 0.02 0.025

Experiment


N)

Axial strain

CU-040

fl=2.85MPa, k

3=1

(b)

0.0

0.2

0.4

0.6

0.8

1.0

0 0.01 0.02 0.03 0.04 0.05

Experiment


N)

Axial strain

CU-047

fl=1.3MPa, k

3=0.9

(c)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 0.005 0.01 0.015 0.02 0.025

Experiment

SimulationAxialforce(MN)

Axial strain

CU-070

fl=1MPa, k

3=0.7

(d)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

CU-100

fl=0.97MPa, k

3=0.68

(e)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

CU-150

fl=0.3MPa, k

3=0.6

(f)

Fig. 7 Axial force vs. axial strain for CFST with CU section


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0.00

0.01

0.02

0.03

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

Simulation

Suggestionf l/fy

D/t

(a)

CU

0.2

0.4

0.6

0.8

1.0

1.2

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

Simulation

Suggestion

k3

D/t

CU

(b)

Fig. 8 fl/fy and k3 vs. D/t for CFST with CU section

Figures 8a and 8b shows the values of fl/fy and k3 versus D/t ratio for CFST with CU section, respectively. From

the results of numerical simulations, two empirical equations calibrated from the experimental data may be

suggested for fl/fy as follow:

)t/D(000832.0043646.0yf/f =l )47D/t7.21( (7a)

(D/t)0000357.0006241.0y/ff =l )150D/t47( (7b)

In addition, another two empirical equations calibrated from the experimental data may be suggested for k3

as follow:

1k3 = )40D/t7.21( (8a)

3491.1(D/t)010085.0(D/t)0000339.0k 23 += )150D/t40( (8b)

These suggested equations are also plotted in Figs. 8a and 8b for comparisons.

Fig. 9 Deformation shapes of CFST

Figures 9a and 9d show the deformation shapes of CU-040 and CU-150 columns at the values of axial

compressive strains very close to 0.025. It can be observed that these columns deform laterally in the radial

direction. This lateral deformation for column with larger D/t ratio is larger than that with smaller D/t ratio,especially in the middle section of the column (bottom of the finite element mesh). Because the confining

pressure is uniformly applied to the concrete in all the radial directions, concrete core and steel tube contact


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entirely to each other and no local buckling of tube takes place.

Simulations of CFST with SU Section

The results of numerical simulations for CFST with SU section are again given in Table 2 and the curves of axial

force versus axial strain for these columns are plotted against the experiment data in Fig. 10. Generally, the

numerical results show good agreement with the experimental data. Similar to the columns with CU section,both the lateral confining pressure fland the material degradation parameter k3 decrease with the increasing of

diameter-to-tube thickness ratio B/t. When the B/t ratio is small, fl and k3 tend to be large due to the lateral

confinement from the steel tube. When the B/t ratio is large, fland k3 tend to be small due to the lake of lateral

support from the tube. Again, the behaviors of CFST with SU section are highly influenced by the k3 parameter

of concrete. When k3 is large (say 1k7.0 3


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Figures 11a and 11b show the values of fl/fy and k3 versus B/t ratio for CFST with SU section, respectively.

From the results of numerical simulations, two empirical equations calibrated from the experimental data may be

suggested for fl/fy as follow:

(B/t)001885.0055048.0y/ff =l )2.29B/t17( (9a)

0y/ff =l )150B/t2.29( (9b)

In addition, another two empirical equations calibrated from the experimental data may be suggested for k3 as follow:

2722.1(B/t)02492.0(B/t)000178.0k 23 += )70B/t17( (10a)

4.03k = )150B/t70( (10b)

These suggested equations are also plotted in Figs. 11a and 11b for comparisons.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

SS-040-050(3)

fl=3MPa, k

3=1

(a)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

(b)

SS-040-050(4)

fl=3.5MPa, k

3=1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

SS-040-100(4)

(c)

fl=2.5MPa, k

3=0.55

0.0

1.0

2.0

3.0

4.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

(d)

SS-070-093(2)

fl=0.7MPa, k

3=0.4

0.0

1.0

2.0

3.0

4.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

(e)

SS-070-093(3)

fl=1MPa, k

3=0.45

0.0

1.0

2.0

3.0

4.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

(f)

SS-070-093(4)

fl=1.1MPa, k

3=0.45

0.0

1.0

2.0

3.0

4.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

SS-070-140(3)

fl

=0.45MPa, k3

=0.55

(g)

0.0

1.0

2.0

3.0

4.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

SS-070-140(4)

(h)

fl

=0.6MPa, k3

=0.5

0.0

1.0

2.0

3.0

4.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

(i)

SS-070-187(3)

fl=0.46MPa, k

3=0.45

0.0

1.0

2.0

3.0

4.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

(j)

SS-070-187(4)

fl=0.43Mpa, k

3=0.55

0.0

1.0

2.0

3.0

4.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

(k)

SS-150-050(2)

fl=0.45MPa, k

3=0.6

0.0

1.0

2.0

3.0

4.0

0 0.005 0.01 0.015 0.02 0.025

Experiment


Axial strain

(l)

SS-150-100(2)

fl=0.1MPa, k

3=0.3

Fig. 12 Axial force vs. axial strain for CFST with SS section

Simulations of CFST with SS Section

The results of numerical simulations for CFST with SS section are given in Table 2 and the curves of axial force

versus axial strain for these columns are plotted against the experiment data in Fig. 12. Generally, the numerical

results show good agreement with the experimental data. Similar to the columns with CU and SU sections, both

the lateral confining pressure fl and the material degradation parameter k3 decrease with the increasing of

diameter-to-tube thickness ratio B/t. Comparing Fig. 12e with Fig. 10e and Fig. 7d, we can observe that the

value of fl for SS-070-093(3) column is higher than that for SU-070 column. This is because the use of

reinforcing ties prevents the local buckling of steel tube and enhances the lateral confining pressure of the square

tubes. However, the lateral confining pressure of the strengthened square column is still less than the circular one.

As the result, the material degradation parameter k3 for columns with SS section would be higher than that forcolumns with SU section but lower than that for columns with CU section.


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0.4

0.6

0.8

1.0

1.2

80 100 120 140 160 180 200

#3 Bar

#4 Bar

f l(MPa)

Space of tie (mm)

(a)

0.20

0.40

0.60

0.80

1.00

1.20

80 100 120 140 160 180 200

#3 Bar

#4 Bar

k3

Space of tie (mm)

(b)

Fig. 13 Influence of tie space and tie number on fland k3 for SS-070 CFST

Figures 9c and 9f show the deformation shapes of the SS-040-050(3) and SS-150-050(2) columns at the values

of axial compressive strains very close to 0.025. It can be observed that the local buckling of tube is totally

prevented by the reinforcing ties not only for columns with small B/t ratio but also for columns with large B/t

ratio. Figure 13a plots fl versus tie spacing and tie number for SS-070 columns. From the figure, it can be

concluded that the lateral confining pressure decreases with the increasing of tie space. In addition, with the

same tie spacing, the column having larger reinforcing tie number (larger diameter) would have larger lateral

confining pressure. Figure 13b plots k3 versus tie spacing and tie number for SS-070 columns. From the figure, it

can be concluded that as long as the reinforcing ties are used, the influences of tie space and bar number on k3are not significant.

CONCLUSIONS

In this paper, nonlinear finite element analyses of CFST with CU, SU and SS sections are analyzed. Based on the

numerical results, the following conclusions may be drawn:

(1) For CFST with CU section, the tubes can provide good confining effect to concrete especially when the

diameter-thickness ratio is small. Local buckling of steel tube is not likely to occur.

(2) For CFST with SU section, the tubes do not provide too much confining effect to concrete especially whenthe diameter-thickness ratio is large. Local buckling of steel tube is very likely to take place.

(3) The confining effect of CFST with SS section is enhanced by the use of reinforcing ties especially when the

tie spacing is small and the tie number (or tie diameter) is large. Local buckling of steel tube is prevented by

the reinforcing tie and is not likely to occur.

(4) Both the lateral confining pressure fland the material degradation parameter k3 decrease with the increasing

of diameter-to-tube thickness ratio (D/t or B/t). When the diameter-to-tube thickness ratio is small, fland k3

tend to be large due to the lateral confinement from the steel tube. When the diameter-to-tube thickness ratio

is large, fland k3 tend to be small due to the lake of lateral support from the tube.

ACKNOWLEDGMENT

This research work was financially supported by the National Science Council, Republic of China under Grant

NSC 89-2711-3-319-200-37.

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