This document analyzes the stress-strain behavior of reinforced concrete columns through finite element modeling using Calculix and ANSYS software. Eight column specimens were modeled based on experimental specimens. Concrete and steel reinforcements were modeled separately. Static analysis was performed to obtain stress-strain curves, which were validated against experimental data. Results showed Calculix predictions were closer to experiments than ANSYS. The study demonstrated the ability to model confined reinforced concrete columns using finite element analysis to understand stress-strain behavior.

1. Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14)
30 – 31, December 2014, Ernakulam, India
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ANALYTICAL STUDY ON STRESS-STRAIN BEHAVIOUR
OF REINFORCED CONCRETE COLUMN
Ananya John1
, Unni Kartha G.2
, Prof. S.Usha3
1, 3
Civil Engineering, SNGCE Kadayiruppu, India
2
Civil Engineering, FISAT Mookkanoor, India
ABSTRACT
Reinforced concrete columns are main load bearing members in any type of structure, which contribute lateral
stiffness also. There are two types of reinforcements in a column ie. Longitudinal and transverse reinforcements.
Longitudinal reinforcements are provided parallel to the longitudinal axis of column and transverse reinforcements may
be hoop, ties or spirals. Stress-strain behaviour of column is important in order to find out the available ductility from a
column by moment curvature analysis. This paper presents analytical study on stress-strain behaviour of reinforced
concrete column by modelling concrete and steel part separately. A new finite element software Calculix and ANSYS
software are used for the analysis. The results were validated using the available experimental data.
Keywords: ANSYS, Calculix, Column, Strain, Stress.
1. INTRODUCTION
Reinforced concrete columns are main load bearing members of any type of structure. It is necessary to design
and detail the column member adequately since it support beams and slabs and transfer the load to the foundation. There
are two types of reinforcements in a column element. They are; (1)Longitudinal reinforcements: To take care of the
moments and forces in columns. Provided parallel to the longitudinal axis of the column. (2)Transverse reinforcements:
It may be hoops, ties or spirals. It is provided to take care of local buckling, shear resistance and it confines the concrete
also. So transverse reinforcements increases the strength and ductility of column member.
Stress-strain behaviour of column is important in order to find out the available ductility from a column element
by moment curvature analysis. Many studies have been conducted in reinforced concrete columns. In such studies many
of them are experimental studies and others numerical are numerical approaches. In that experimental programes the
maximum load carrying capacity, effect of confinement, ductility etc. were studied. The numerical apporoaches are
proposed a number of mathematical models, from which the stress- strain behaviour can be obtained. The experimental
studies are very costly and time consuming. The use of different finite element softwares overcome such problems. In
this study the finite element softwares Calculix and ANSYS were used. Discrete modelling is adopted in ANSYS. In
both the softwares concrete and steel parts are separately modelled so that its behavior is same as that of experimental
program.
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2. FINITE ELEMENT MODELLING
The finite element analysis softwares give a good approach to reinforced concrete members. In ANSYS
modelling graphic user interface is used while in Calculix, it is based on commands. Table I shows different column
specimens which is used in this analytical studies. To validate the results with experimental data, the same specimens
used in the experimental programs[1-2]were used in this study. These specimens were modelled in both the softwares.
2.1 Calculix Software
Calculix is a open source finite element analysis application that uses a similar input format to Abaqus. It has
an implicit and explicit solver (CCX) written by Guido Dhondt and a pre and post processor (CGX) written by Klaus
Wittig. The solver is able to solve static, dynamic, buckling analysis, heat transfer etc. Material nonlinearities, as well as
geometrical nonlinearities, can be introduced to solve more complex structural and mechanical problems. Calculix
includes a complete element library for volumetric elements, as well as quadratic formulations for plane stress, plane
strain, axi-symmetric, shells, and beam elements.
2.1.1 Calculix Input Deck
An input file is commonly called an “input deck”, the characters from the asterisk to the first comma are called a
“keyword” and the keyword with associated data is called a “card”. An input deck defines the finite element analysis
problem to be solved. In general, it contains a mesh definition, material, analysis type, boundary conditions and output
requests.
2.1.2 Geometry
Columns are modelled in the same way which is used in the experimental program.
2.1.3 Material Properties
Material properties such as Young’s modulus and poisson’s ratios are specified in the calculix inputdeck.
The following concrete and steel properties are defined in Calculix inputdeck and it is assigned in ANSYS.
• Compressive strength of concrete (fc’)
• Modulus of Elasticity of concrete (Ec)
• Concrete density=25 kN/m3
• Poisson’s ratio of concrete(0.2)
• Elastic modulus of steel(Es)
• Poisson’s ratio of steel(0.3)
2.1.4 Elements Used
20 node brick element (he20 or C3D20) was used for the modelling of both concrete and steel. The C3D20
element is a general purpose quadratic brick element. It can be used for linear and nonlinear problems. Fig. 1 shows the
he20 element.
Fig 1: He20 element

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Table 1: Details of the Column Specimens
Sl
No
Size (mm) fc’
(MPa)
Eccentricity
(mm)
Reinforcements Section
1 500 x 500 x 1500
(C1)
24.3 - Long. Reinf. 16mm Φ
Ties 10mmΦ
@ 60mm c/c
2 500 x 500 x 1500
(C2)
24.3 - Long.Reinf. 16mm Φ
Ties 10mmΦ
@ 40mm c/c
3 200 x 200 x 800
(C3)
48.3 - Long. Reinf. 12mm Φ
Ties 8mmΦ
@ 50mm c/c
4 500 Φ (C4) 28.8 - Long. Reinf. 16mm Φ
Transverse Reinf. 10mm Φ
@ 300mm c/c
5 500 Φ (C5) 28.8 - Long.Reinf. 16mm Φ
Transverse Reinf. 10mm Φ
@150mm c/c
6 200 x 200 x 800
(C6)
49 20 Long.Reinf. 12mm Φ
Ties 8mm Φ
@50mm c/c
7 200 x 200 x 800
(C7)
49 40 Long.Reinf. 12mm Φ
Ties 8mm Φ
@50mm c/c
8 200 x 200 x 800
(C8)
49 60 Long.Reinf. 12mm Φ
Ties 8mm Φ
@50mm c/c
2.1.5 Loads and Boundary Conditions
Displacement boundary conditions are applied to all column models. For concentric column models axial
pressure is applied on the top of the specimen. For eccentric column specimen axial pressure on the top plus couple of
forces at extreme edge on both sides of column faces were applied.
Fig.2 shows different column modelled in Calculix.

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Fig 2: 200x200x800 Fig 3: 500x500x1500(s=60mm) Fig 4: 500x500x1500(s=40mm)
Fig 5: 500 Φ(s=300mm) Fig 6: 500 Φ(s=300mm)
Fig 7: mesh of concrete Fig 8: mesh of reinforcements
2.2 ANSYS Software
In ANSYS, there are 3 stages for analysing a structure. They are: (1)Pre-processing, (2)Analysis and (3)Post-
processing. Discrete modeling is adopted for modeling column specimens.
2.2.1 Element Types
The Solid65 element was used to model the concrete. This element has eight nodes with three degree freedom at
each node. A Link8 element was used to model steel reinforcement. This element is a 3D spar element and it has two
nodes with three degrees of freedom.

5. Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14)
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Fig 9: solid65 element
Fig 10: link8 element
2.2.2 Modelling
Modelling of all column specimens using ANSYS were done by creating a three dimensional solid (volume).
Considering symmetry and to avoid complexity only quarter portion of the specimen is modelled. After creating solid
volume meshing is done. Meshing of reinforcement is not needed. Because reinforcements were created in the modeling
through the nodes created by mesh of solid volume.
The following Figs. shows different steps in column modelling and modelled concrete part and reinforcement
part in ANSYS.
Fig 11: solid volume Fig 12: meshed volume

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Fig 13: reinforcements of C1 Fig 14: reinforcements of C2
Fig 15: mesh of C3 Fig 16: reinforcements of C3
Fig 17: reinforcements of C4 Fig 18: reinforcements of C5

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3. STATIC ANALYSIS
Static analysis was performed in Calculix and ANSYS softwares.. The stress and strain diagram obtained from
the softwares were shown in following figures. The peak stress and strain values were notted.
Fig 19: stress diagram of C1 Fig 20: strain diagram of C1
Fig 21: stress diagram of C4 Fig 22: strain diagram of C4

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Fig 23: stress diagram of C1 Fig 24: stress diagram of C1
Fig 25: stress diagram of C4 Fig 26: strain diagram of C4
4. RESULTS AND DISCUSSIONS
The values obtained from the analysis is validated with the available experimental data. The peak stress, peak
strain values were compared. Stress-strain curves were plotted.

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0
5
10
15
20
25
30
35
40
0 0.002 0.004 0.006
Stress(MPa)
Strain
Stress - Strain
Calculix
ANSYS
Fig 27: stress-strain curve of C1 Fig 28: stress-strain curve of C2
0
10
20
30
40
50
60
70
80
0 0.002 0.004
Stress(MPa)
Strain
Stress-Strain
Calculix
ANSYS
0
5
10
15
20
25
30
35
40
0 0.005
Stress(MPa)
Strain
Stress - Strain
Calculix
ANSYS
Fig 29: stress-strain curve of C3 Fig 30: stress-strain curve of C4
0
5
10
15
20
25
30
35
40
45
0 0.002 0.004 0.006
Stress(MPa)
Strain
Stress - Strain
Calculix
ANSYS
0
10
20
30
40
50
60
70
0 0.002 0.004 0.006
Stress(MPa)
Strain
Stress-Strain
Calculix
ANSYS
Fig 31: stress-strain curve of C5 Fig 32: stress-strain curve of C6

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0
10
20
30
40
50
60
70
80
90
0 0.001 0.002 0.003 0.004 0.005
Stress(MPa)
Strain
Stress-strain
Calculix
ANSYS
Fig 33: stress-strain curve of C7 Fig 34: stress-strain curve of C8
Table II shows that comparison of peak stress and peak strain value from experimental and analytical study
(both Calculix and ANSYS). From the table, it is clear that Calculix gives more closer values to the experimental values
than that obtained from ANSYS. So Calculix is an excellent finite element software for the analysis of reinforced
concrete structures.
Table 2: Comparison between Experimental and FEA study
Models
Experimental Calculix ANSYS 10
Peak Stress
MPa
Peak Strain Peak Stress
MPa
Peak
Strain
Peak Stress
MPa
Peak Strain
1 27.44 0.0042 27.9 0.0049 29.25 0.0034
2 32.11 0.0052 33.1 0.0051 35.59 0.0046
3 60.545 0.0027 61 0.0024 66.82 0.0025
4 32.53 0.0032 33.2 0.0035 36.41 0.0023
5 40.76 0.0042 40.9 0.0043 42.85 0.0035
6 68.34 0.0038 68.2 0.00385 71.47 0.0033
7 68.9 0.0037 69 0.00365 69.34 0.0035
8 76.99 0.0039 77 0.00393 74.33 0.0037
4. CONCLUSIONS
The following major conclusions are drawn based on the analytical studies carried out under this investigation.
• Modelling of confined RC column with Calculix and ANSYS is possible.
• Plotted the stress-strain curve of confined RC columns using the results obtained from softwares.
• Analysis results obtained in the present study by creating the model with concrete and reinforcement separately
and assigning the properties is more closer to the experimental value than the results obtained with conventional
model with properties assigning as RCC.

11. Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14)
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For future work,
• Reinforced concrete columns subjected to lateral loads can be studied.
• Different type of structures with different types of reinforcements (fibre reinforced etc.) can be studied.
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