ANALYTICAL STUDY ON STRESS-STRAIN BEHAVIOUR OF ...

Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14)

30 – 31, December 2014, Ernakulam, India

45

ANALYTICAL STUDY ON STRESS-STRAIN BEHAVIOUR

OF REINFORCED CONCRETE COLUMN

Ananya John1, Prof. S.Usha

2

1, 2

Civil Engineering, SNGCE Kadayiruppu, 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.

INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND

TECHNOLOGY (IJCIET)

ISSN 0976 – 6308 (Print)

ISSN 0976 – 6316(Online)

Volume 5, Issue 12, December (2014), pp. 45-55

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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)


Ties 8mm Φ

@50mm c/c

8 200 x 200 x 800

(C8)


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.



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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



50

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




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Fig 23: stress diagram of C1 Fig 24: stress diagram of C1


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.



53

0

5

10

15

20

25

30

35

40

0 0.002 0.004 0.006

Str

ess

(M

Pa

)

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

Str

ess

(MP

a)

Strain

Stress-Strain

Calculix

ANSYS

0

5

10

15

20

25

30

35

40

0 0.005

Str

ess

(M

Pa

)

Strain

Stress - Strain

Calculix

ANSYS


0

5

10

15

20

25

30

35

40

45

0 0.002 0.004 0.006

Str

ess

(M

Pa

)

Strain

Stress - Strain

Calculix

ANSYS

0

10

20

30

40

50

60

70

0 0.002 0.004 0.006

Str

ess

(M

Pa

)

Strain

Stress-Strain

Calculix

ANSYS




54

0

10

20

30

40

50

60

70

80

90

0 0.001 0.002 0.003 0.004 0.005

Str

ess

(M

Pa

)

Strain

Stress-strain

Calculix

ANSYS


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.



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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.

REFERENCES

[1] J. Hoshikuma, K. Kawashima, and A. W. Taylor, Stress-Strain Model for confined Reinforced concrete in

Bridge Piers, ASCE Journal, 1997, 624-632.

[2] Teng-Hooi Tan, and Ngoc-Ba Ngugen, Flexural Behaviour of High Strength Concrete Columns, ACI Structural

Journal, 2005, 19-26.

[3] Shamim A. Sheikh and Ching-Chung Yeh, Tied concrete column under axial load and flexure, Journal of

Structural Engineering 2009, 2780-2800.

[4] Rami EID, 1999. Compressive behaviour of steel confined square and circular reinforced concrete columns

[5] Dr. Khaled S. Ragab and Dr. S. I. Zaki, Stress-strain behavior of concrete column with different types of

rectangular hoops, 2009.

[6] Ibrahim H. H. H, Mac Grogor J.G, Test of Eccentrically loaded High Strength Concrete Column, ACI Structural

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[7] J. B. Mander, M. J. N. Priestley and R. Park, Theoretical stress strain model for confined concrete, Journal of

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[8] Metin Husem & Selim Pul, 2007, Investigation of stress – strain model for high strength concrete.

[9] S. Lavanya Prabha, J.K.Dattatreya and M.Neelamegam, “Stress Strain Behaviour of Ultra High Performance

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