This report summarizes finite element modeling of a concrete filled steel column conducted in ABAQUS. The objectives were to determine the elastic critical buckling load and ultimate load through nonlinear analysis, and compare results to analytical solutions. The concrete and steel materials were modeled using damaged plasticity and multi-linear stress-strain curves. A linear buckling analysis found the critical buckling load, which was then used as an imperfection in the nonlinear analysis to obtain the ultimate load. Results showed good agreement with analytical solutions from design codes.

1. KU
KASETSART UNIVERSITY
REPORT
ON
FINITE ELEMENT MODELING OF CONCRETE FILLED STEEL
COLUMN USING ABAQUS/CAE 2017
Submitted to
Asst. Prof. Dr. Kitjapat Phuvoravan
Submitted By:
Gokarna Sijwal
Department of Civil Engineering
November

2. List of figures
Figure 1: Typical sections of CFT ...............................................................................................2
Figure 2: Buckling of column......................................................................................................3
Figure 3: Stress strain curve for concrete in compression.............................................................6
Figure 4: Stress-Strain curve for Concrete in tension ...................................................................7
Figure 5: stress-strain curve of steel ............................................................................................8
Figure 6: Concrete model..........................................................................................................10
Figure 7: Steel model ................................................................................................................11
Figure 8: Assembling two model...............................................................................................11
Figure 9: Meshing of CFT.........................................................................................................16
Figure 10: Meshing of Cross-section.........................................................................................17
Figure 11: Load vs Axial Displacement of the model ................................................................18
Figure 12: Load vs Mid span lateral displacement of the model.................................................19

3. Table of Contents
1) INTRODUCTION...............................................................................................................2
2) OBJECTIVES.....................................................................................................................2
3) MODELING .......................................................................................................................3
3.1 LITERATURE REVIEW ..................................................................................................3
ELASTIC BUCKLING ANALYSIS ...................................................................................3
PROCESS IN ABAQUS FOR LINEAR BUCKLING ANALYSIS.....................................4
LIMITATION:....................................................................................................................4
NONLINEAR BUCKLING ANALYSIS.............................................................................4
PROCESS IN ABAQUS FOR NON-LINEAR BUCKLING ANALYSIS ...........................4
MATERIAL PROPERTY ...................................................................................................5
MATERIAL MODELING IN ABAQUS FOR CONCRETE...............................................9
MODELING OF INITIAL IMPERFECTION .....................................................................9
3.2 MODEL DESCRIPTION ................................................................................................10
UNITS ..............................................................................................................................10
GEOMETRY ....................................................................................................................10
MATERIAL......................................................................................................................11
STEPS...............................................................................................................................14
MESHING ........................................................................................................................16
4) RESULTS.........................................................................................................................17
LINEAR ELASTIC BUCKLING ANALYSIS......................................................................17
NONLINEAR BUCKLING ANALYSIS ..............................................................................18
5) COMPARISION TO ANALYTICAL SOLUTION (ANSI/AISC 360-16).........................20
CLASSIFICATION OF FILLED COMPOSITE SECTIONS FOR LOCAL BUCKLING .....20
COMPRESSIVE STRENGTH OF FILLED COMPOSITE SECTION..................................20
6) CONCLUSION AND DISCUSSION ................................................................................23
7) REFERENCES..................................................................................................................23

4. FEM MODELING OF CFT COLUMN BY ABAQUS
2
1) INTRODUCTION
Concrete-Filled Steel Tubes (CFST) are composite members consisting of a steel tube infilled
with concrete, possessing the favorable attributes of both concrete and steel. The continuous
confinement provided to the concrete core by the steel tube enhances the core strength and
ductility. The concrete core restrains inward buckling of the steel tube, while the steel tube
serves as tensile reinforcement for the concrete.
The steel lies at the outer perimeter where it performs most effectively in tension and in resisting
bending moment. The concrete forms an ideal core to withstand the compressive loading in
typical applications, and it delays and often prevents local buckling of the steel.
Figure 1: Typical sections of CFT
2) OBJECTIVES
1) To find out the elastic critical buckling load of the model.
2) To find out the ultimate load by non-linear analysis.
3) To compare the FEM solutions with analytical solution.

5. FEM MODELING OF CFT COLUMN BY ABAQUS
3
3) MODELING
3.1 LITERATURE REVIEW
ELASTIC BUCKLING ANALYSIS
Many structures require an evaluation of their structural stability. Thin columns, compression
members, and vacuum tanks are all examples of structures where stability considerations are
important. At the onset of instability (buckling) a structure will have a very large change in
displacement {x} under essentially no change in the load (beyond a small load perturbation).
Figure 2: Buckling of column
Eigenvalue or linear buckling analysis predicts the theoretical buckling strength of an ideal linear
elastic structure. The Eigenvalue buckling solution of an Euler column will match the classical
Euler solution. For a linear buckling analysis, the Eigenvalue problem below is solved to get the
buckling load multiplier λi and buckling modes φi .
(Ke+ λi*Ks)*( φi)= 0
Ke= Elastic stiffness matrix (constant)
Ks= stress stiffness matrix (constant)
λi = Eigen values
φi= Eigen vectors representing the buckled mode shapes
Linear elastic material behavior is assumed. Small deflection theory is used, and no nonlinearities
are included.
Imperfections and nonlinear behavior prevent most real world structures from achieving their
theoretical elastic buckling strength. So, nonlinear buckling analysis has to be done to get the
desired ultimate load.

6. FEM MODELING OF CFT COLUMN BY ABAQUS
4
PROCESS IN ABAQUS FOR LINEAR BUCKLING ANALYSIS:
 First reference load Funit with corresponding boundary condition was applied.
 Eigen value problem was solved.
It can be solved by two ways in ABAQUS: subspace and lanczos. Lanczos is used for large
number of Eigen modes. Whereas subspace is used for few number of Eigen modes.
 The lowest value of Eigen value is associated with critical buckling load.
 The critical load or buckling load is
Fcri= λcri*Funit
LIMITATION:
 Only linear elastic material properties can be used.
NONLINEAR BUCKLING ANALYSIS
Arch length method or Riks method is mainly used for post buckling analysis or nonlinear buckling
analysis. The Arc-Length method [Riks E., 1979] is a very efficient method in solving non-linear
systems of equations when the problem under consideration exhibits one or more critical points.
In terms of a simple mechanical loading-unloading problem, a critical point could be interpreted
as the point at which the loaded body cannot support an increase of the external forces and an
instability occurs. It can also include geometrical as well as materials nonlinearities.
PROCESS IN ABAQUS FOR NON-LINEAR BUCKLING ANALYSIS:
 Material nonlinearities and geometric nonlinearities should be considered.
 Load as of same magnitude and direction as critical buckling load from the linear buckling
analysis should be considered.
 Load proportionality factor obtained from the analysis should be used to obtain ultimate
buckling load.

7. FEM MODELING OF CFT COLUMN BY ABAQUS
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MATERIAL PROPERTY
Concrete
Uni-axial stress strain relationship in Compression
The strain corresponding to compressive strength of the concrete fc ‘was taken εc’ as 0.003.
The value of the proportional limit stress was taken as 0.5fc ‘ and the initial modulus of
elasticity of the concrete Ec is calculated by :
𝐸𝑐 = 4700√ 𝑓𝑐′(𝑀𝑝𝑎)
as recommended in ACI 318-08.
The stress-strain relationship of the concrete for compression after proportional limit was
determined from the relation given by Eq.
𝑓𝑐 =
𝐸𝑐 𝜀𝑐
1 + (𝑅 + 𝑅𝐸 − 2)(
𝜀𝑐
𝜀𝑐′) − (2𝑅 − 1) (
𝜀𝑐
𝜀𝑐′)
2
Where,
𝑅 =
𝑅𝐸(𝑅𝜎 − 1)
(𝑅𝜖 − 1)2
−
1
𝑅𝜖
𝑅𝐸 =
𝐸𝑐 𝜀𝑐′
𝑓𝑐′
Rε and Rσ were equal to 4, as recommended by Hu and Schnobrich.
εc= strain after proportional limit in stress-strain curve

8. FEM MODELING OF CFT COLUMN BY ABAQUS
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fc ‘= 25 Mpa
Ec = 23500 Mpa
Ѵc = 0.16
Density= 2400 kg/m3
Figure 3: Stress strain curve for concrete in compression
0
5
10
15
20
25
30
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
Stress(Mpa)
Strain
Concrete in compression

9. FEM MODELING OF CFT COLUMN BY ABAQUS
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Uni-axial relationship in tension
The stress-strain relationship of concrete in tension is was assumed to be linear to the uni-axial
tensile strength and determined using the equations provided by Belarbi and Hsu (Belarbi and
Hsu, 1994; pang and Hsu,1995) as:
𝑓 = 𝐸𝑐 𝜀, 𝜀 ≤ 𝜀𝑡
𝑓 = 𝑓𝑡(
𝜀𝑡
𝜀
)0.4
, 𝜀 > 𝜀𝑡
Where,
𝑓𝑡 = 0.33√𝑓𝑐′(𝑀𝑝𝑎) is the tensile strength of concrete.
𝜀𝑡 = 𝑓𝑡/𝐸𝑐 is corresponding strain.
Figure 4: Stress-Strain curve for Concrete in tension
Steel
The tri-linear stress-strain relationship for steel is illustrated in Fig. . An isotropic hardening
plasticity rule was used. Young s modulus Es was approximated as 200,000MPa; Poisson’s ratio
ѵs was set to be 0.3; and the ultimate strain of the steel εsu was approximated as 0.1. The plastic
plateau terminates when strain of the steel εs is equal to 10 times of yield strain of the steel (10εsy
), as shown in Fig.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 0.0005 0.001 0.0015 0.002
Stress(Mpa)
Strain
Concrete in tension

10. FEM MODELING OF CFT COLUMN BY ABAQUS
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fy = 375 Mpa
fu= 410 Mpa
Density= 7800 kg/m3
Figure 5: stress-strain curve of steel
0
50
100
150
200
250
300
350
400
450
0 0.02 0.04 0.06 0.08 0.1 0.12
Stress(Mpa)
Strain
Steel

11. FEM MODELING OF CFT COLUMN BY ABAQUS
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MATERIAL MODELING IN ABAQUS FOR CONCRETE
Two types of modeling are available in ABAQUS for concrete modeling; CDP (Concrete
Damaged Plasticity) and Smeared Crack Model. Smeared crack model can be used for the case of
monotonic straining and CDP can be used in monotonic as well as cyclic loading, according to
ABAQUS manual. So, CDP is used for modeling concrete.
CDP modeling technique used various parameters. The five main parameters of concrete that
define the failure or damage criteria are dilation angle, flow potential eccentricity, ratio of initial
equibiaxial compressive yield stress to initial uniaxial compressive yield stress(fbo/fco), ratio of
the second stress invariant on tensile meridian to that on the compressive meridian(K), and
viscosity parameter. The dilation angle is a ratio of vertical shear strain increment and strain
increment. Flow potential eccentricity is a small positive number that defines the rate at which
flow potential approaches its asymptote. The viscosity parameter is visco-plastic regularization of
the concrete constitutive equations in ABAQUS.
Dilation angle Eccentricity fbo/fco K Viscosity parameter
31 0.1 1.16 0.67 0
MODELING OF INITIAL IMPERFECTION
For non-linear analysis, Initial imperfections is considered by multiplying the deformation in
linear eigenvalue analysis with some scale factor. And the scale factor is generally few
percentage of column section dimension. And scaled factor of 1% of breadth of column
section was used.

12. FEM MODELING OF CFT COLUMN BY ABAQUS
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3.2 MODEL DESCRIPTION
UNITS
Newton, millimetre, second
GEOMETRY
Concrete dimension:
b =56 mm
d =56 mm
Steel dimension:
t= 2mm
Length of column= 900 mm
Figure 6: Concrete model

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Figure 7: Steel model
Figure 8: Assembling two model

14. FEM MODELING OF CFT COLUMN BY ABAQUS
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MATERIAL
In Abaqus, the relevant stress-strain data must be input as true stress and true strain data
(correlating the current deformed state of the material). The analytical equations for converting
engineering stress-strain to true stress-strain are given below:
In order to include plasticity within Abaqus, the stress-strain points past yield, must be input in
the form of true stress and logarithmic plastic strain. The logarithmic plastic strain required
by Abaqus can be calculated with the equation given below:

15. FEM MODELING OF CFT COLUMN BY ABAQUS
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Concrete
Compressive Behavior
Stress
Inelastic
strain
12.507 0.00000
15.285 0.00030
15.823 0.00033
20.216 0.00064
23.060 0.00102
24.604 0.00145
25.075 0.00193
24.711 0.00244
23.753 0.00298
22.416 0.00354
20.880 0.00410
19.273 0.00466
17.686 0.00523
16.173 0.00579
14.764 0.00635
13.471 0.00690
12.299 0.00744
11.240 0.00799
10.290 0.00852
9.437 0.00905
8.673 0.00958
4.194 0.01471
Tensile Behavior
Yield
Stress
Cracking
strain
1.650 0.00000
0.753 0.00047
0.700 0.00057
0.658 0.00067
0.624 0.00077
0.239 0.00895
0.229 0.00994

16. FEM MODELING OF CFT COLUMN BY ABAQUS
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Steel
Yield
Stress
plastic
strain
375.703 0.0000
382.031 0.0167
451.000 0.0931
STEPS
1) Initial steps
 Boundary Conditions
One end is fixed and other is pinned.
 Interactions between steel and concrete
Surface-to-surface contact is generally preferred for the interaction simulation of the
steel tube and concrete. A contact surface pair consists of the inner surface of the
steel tube and the outer surface of concrete core . For the properties in the normal
direction “Hard contact” can be specified for the interface, which allows the separation of
the interface in tension and no penetration of that in compression. For tangential behaviour,
there is little slip or no slip as the CFST is loaded simultaneously. In current model, a
friction coefficient of 0.25 was used because results was observed to be same for different
friction coefficient 0.6, 0.45, 0.35, 0.25 and 0.15. Steel inner surface and concrete outer
surface were used as master surface and slave surface in the model, respectively.
2) Step 1
 Eigen value analysis is used for linear buckling analysis. And Arch length method or
Riks method is used for nonlinear analysis.

17. FEM MODELING OF CFT COLUMN BY ABAQUS
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 Pressure of 1 N/mm2 was used as load for elastic buckling analysis and 484.04
N/mm2 was used for non-linear buckling analysis.

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MESHING
An 8-node linear brick elements with reduced integration and hourglass control were used for
meshing the concrete core and steel tube. Different iterations were done for mesh size of 20, 15,
10, 5 and 3mm, respectively. And it was found that the results were almost same for 10, 5 and 3
mm mesh size. So, approximate global size of 10mm was used for meshing the both model.
Sweep technique with hexahedral element shape is used to model concrete core whereas
structured technique with hexahedral element shape is used to model steel tube.
Figure 9: Meshing of CFT

19. FEM MODELING OF CFT COLUMN BY ABAQUS
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Figure 10: Meshing of Cross-section
4) RESULTS
LINEAR ELASTIC BUCKLING ANALYSIS
Minimum eigenvalue= 480.04
Elastic critical buckling load= min. eigenvalue* gross area= 1728.144 KN

20. FEM MODELING OF CFT COLUMN BY ABAQUS
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NONLINEAR BUCKLING ANALYSIS
Figure 11: Load vs Axial Displacement of the model
0
15
30
45
60
75
90
105
120
135
150
165
180
195
210
225
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25
Load(KN)
Axial Displacement(mm)
Load vs Top Axial Displacement

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Figure 12: Load vs Mid span lateral displacement of the model
Ultimate load from the graph= 212.42 KN
0
15
30
45
60
75
90
105
120
135
150
165
180
195
210
225
0 1 2 3 4 5 6
Load(KN)
Lateral Deflection(mm)
Load vs Mid span lateral deflection

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5) COMPARISION TO ANALYTICAL SOLUTION (ANSI/AISC 360-16)
 CLASSIFICATION OF FILLED COMPOSITE SECTIONS FOR LOCAL
BUCKLING
For compression, filled composite sections are classified as compact, noncompact or
Slender. For a section to qualify as compact, the maximum width-to-thickness ratio
of its compression steel elements shall not exceed the limiting width-to-thickness
ratio, λp, from Table I1.1a. If the maximum width-to-thickness ratio of one or more
steel compression elements exceeds λp, but does not exceed λr from Table I1.1a, the
filled composite section is noncompact. If the maximum width-to-thickness ratio of
any compression steel element exceeds λr, the section is slender. The maximum
permitted
Width-to-thickness ratio shall be as specified in the table.
 COMPRESSIVE STRENGTH OF FILLED COMPOSITE SECTION
The axial capacity of doubly symmetric axially loaded filled composite members shall be
determined for the limit state of flexural buckling based on member slenderness as follows:

23. FEM MODELING OF CFT COLUMN BY ABAQUS
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(a) For compact sections
Pno = Pp
C2 = 0.85 for rectangular sections and 0.95 for round sections
(b) For noncompact sections
c) For slender column
Pe= Elastic critical buckling load

24. FEM MODELING OF CFT COLUMN BY ABAQUS
22
C3
Where,
Ac= Area of concrete
As= Cross-section area of steel
Asr= Area of reinforcing bars
Es= Modulus of Elasticity of steel
Ec= Modulus of Elasticity of concrete
Lc = Effective length of member
fy= minimum yield stress of steel section
fc’= compressive strength of concrete
Is= moment of inertia of the steel section about the elastic neutral axis of the composite section
Ic= moment of inertia of the concrete section about the elastic neutral axis of the composite
section
Isr= moment of inertia of the concrete reinforcing bars about the elastic neutral axis of the
composite section
FEM(KN) CODE(KN) % difference
Elastic analysis 1728.144 1696.042 1.89
Non-linear analysis 212.420 226.766 6.3

25. FEM MODELING OF CFT COLUMN BY ABAQUS
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6) CONCLUSION AND DISCUSSION
1) The elastic critical buckling load for the model was 1728.144 KN from Eigenvalue
linear analysis.
2) The ultimate load from non-linear analysis was 212.420 KN from Non-linear Riks
method.
3) Percentage error for linear buckling analysis and non-linear analysis was about 1.9%
and 6.3%, respectively.
4) Error for linear buckling load was observed less than ultimate load while compared to
analytical formula. The reason of obtaining less ultimate load to that of analytical one
was that stress-strain curve for unconfined concrete was used in the model. In real
behavior, concrete in CFT is confined by the steel tube and this confinement can increase
the strength and ductility of concrete. And also, the error may be due to not able to
consider all material nonlinearities.
5) Initial Imperfection also plays important role in non-linear analysis. The results;
considering imperfection, were observed to be better than the results; not considering the
imperfection.
6) It was observed that the results were not affected by the change of Friction coefficient
(from 0.15-0.6).
7) REFERENCES
Bambang Piscesa, M. M. (January 2018). Evaluation of Codes of Practice and Modelling of High
Strength Circular Concrete Filled Tube. 13th International Conference on Steel, Space
and Composite Structures.
Bhushan H. Patil, P. M. (August 2014). Parametric Study of Square Concrete Filled Steel Tube
Columns Subjected To Concentric Loading. Int. Journal of Engineering Research and
Applications ISSN : 2248-9622.
Professor Zhong Tao, Z.-B. W. (October 2013). Finite element modelling of concrete-filled steel
stub columns under axial. Journal of Constructional Steel Research .
Specification For Structural Buildings. (2016). The American Institute of Steel Construction
(AISC).
Tusshar Goel, A. K. (May 2018). Finite Element Analysis of Circular Concrete Filled Steel
Tube: A review. International Research Journal of Engineering and Technology (IRJET).