finite element modeling of cold formed steel columns ...sreedhar kalavagunta, sivakumar naganathan,...

Jordan Journal of Civil Engineering, Volume 11, No. 1, 2017

- 1 - © 2017 JUST. All Rights Reserved.

Finite Element Modeling of Cold Formed Steel Columns Strengthened with

CFRP

Sreedhar Kalavagunta1)*, Sivakumar Naganathan2), Kamal Nasharuddin Bin Mustapha2) and

Goh Kay Yun2)

1) Structural Engineering, Bentley Systems Singapore Pvt. Ltd. * Corresponding Author. E-Mail: [email protected]

2) Civil Engineering, Universiti Tenaga Nasional, Selangor, Malaysia.

ABSTRACT

Advances in the field of finite element analysis software in the past 50 years have been quite extensive and

have led to considerable benefits in research industry, mainly for composite structures. In this paper, finite

element analysis was carried out to investigate the failure modes and axial capacity of CFRP strengthened

cold formed steel lipped channel sections. A total of 27 test cases were analyzed using FEA software and

results were compared with capacities recorded from the experimental tests. The results indicate that the

proposed FEA modeling with material properties can be used to calculate the axial capacity of CFRP

strengthened cold formed lipped channel sections.

KEYWORDS: Finite element analysis, Cold formed steel columns, CFRP strengthening.

INTRODUCTION

Carbon Fiber Reinforced Polymer (CFRP)

materials are being increasingly used in engineering

structures due to their high strength-to-weight ratios,

high durability and corrosion resistance (Shaat and

Farm, 2009; Mohamed and Masmoudi, 2010; Telue

and Mahendran, 2003; Karimi et al., 2013). These

methods have been widely used to retrofit industrial

structures in the past few decades (Youssef et al.,

2014). The major advantages of CFRP materials are

high tensile strength, low thickness and weight, ease of

transport and corrosion resistance (Hu and Barbato,

2014). CFRP strengthening in cold formed steel

sections attracted researchers, as cold-formed steel

structural members are usually thin and with large

width–to-thickness ratios. Therefore, these thin

members may have locally buckled at a stress lower

than the yield stress of steel when they are subjected to

compression in flexural bending, axial compression,

shear or bearing. So, local buckling can be controlled

by strengthening CFS using high tensile CFRP sheets.

Extensive experimental studies that have been

conducted by many researchers are available on

bonding, surface preparation and strength (Bambach et

al., 2009; Kalavagunta et al., 2013; Kalavagunta et al.,

2013; Kalavagunta et al., 2014; Kalavagunta et al.,

2013; Silvestre et al., 2009).

Finite Element Model is an inexpensive method of

investigating complex research models. There are

numerous investigations carried out by various

researchers in this area (Abdelkarim and El-Gawady,

2014; Kalfat and Al-Mahaidi, 2015; Siromani et al.,

2014; Al-Zubaidy et al., 2013). The major

disadvantages of experimental analysis over FEA are

Received on 28/1/2015. Accepted for Publication on 20/5/2015.

Finite Element… Sreedhar Kalavagunta, Sivakumar Naganathan, Kamal Nasharuddin Bin Mustapha and Goh Kay Yun

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time consumption and expensive laboratory testing,

thus hindering progress in composite research areas.

The research organizations often decided on

conservative modeling in either analytical or FE

modeling to simulate the problems. The advances in

the field of computer aided engineering during the past

two decades have changed, thereby offering different

modeling techniques. Many researchers proved that

increase in strength is due to CFRP strengthened

structural elements like concrete and steel (Feraboli

and Masini, 2004; Siromani et al., 2014; McGregor et

al., 2010; Joosten et al., 2010; Mamalis et al., 2006;

Kalavagunta et al., 2014).

While CFRP strengthened cold formed steel

sections have been investigated over two decades, the

application of CFRP strengthened cold formed steel in

field has been limited. The first field application of

ultra-high modulus CFRP strengthened steel bridges

was in the United States (Kwon et al., 2007; Nozaka et

al., 2005b).

This paper presents the load carrying capacity and

different mode shapes of CFRP strengthened CFS

sections. The study focuses on the buckling behavior of

the CFRP strengthened channel section under axial

compression load. The investigation also includes

viability of the use of external CFRP strengthening of

cold formed steel in delaying local buckling such that

buckling strength can be increased.

EXPERIMENTAL ANALYSIS

A total of 2 sets of 27 specimens were prepared for

the test program according to the details shown in

Table 1. The specimens named C7510

(C75x33x7x1.0mm), C7512 (C75x33x7x1.2 mm) and

C10010 (C100x49x12x1.0 mm) of lengths of 300 mm,

500 mm and 700 mm were tested. The sectional

properties are followed as per manufacturers'

guidelines and are tabulated in Table 1. Cold-formed

steel lipped channel sections with yield stress of 550

Mpa and modulus of elasticity of 205 GPa were used in

all steel sections. The technical characteristics of Mape

Wrape C UNI-AX were mono-directional carbon fiber

fabrics characterized by high tensile strength of

230,000 N/mm2. The steel plates were glued to the

CFRP by using MC-DUR1280 adhesive. The test

specimen was placed under 500 kN capacity hydraulic

testing machine at 0.25 mm/min displacement

controlled rate. Two LVDTs were placed to record the

deflection corresponding to the load. The vertical

clamps were placed to allow vertical displacement and

free rotation about the edges.

The values were recorded and graphs were

generated for deflection corresponding to the load

applied. The experimental results are tabulated in Table

2 and Table 3. The results of ultimate load were

recorded using the calibrated Lab Tech computer data

acquisition system. The experimental setup is

illustrated in Figure 1.

Table 1. Sectional properties from manufactures

Section Designation

Thickness (mm)

Yield Stress (MPa)

Area (mm2)

Ixx (x104

mm4)

Iyy (x104 mm4)

Section Modulus,

Zx (x103mm3)

Section Modulus,

Zy (x103mm3)

Radius of

Gyration Rx (mm)

Radius of

Gyration Ry (mm)

C7510 1 550 137 12.2 2.85 3.25 1.02 29.84 12.67

C7512 1.2 550 204 18.9 5.2 5.14 1.84 30.43 15.96

C10010 1 550 216 36.4 7.55 7.13 2.19 41.1 18.7


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Figure (1): Experimental setup

Figure (2): CFRP strengthened 7510X300 mm length specimen deflection vs. compression capacity for LVDT 1

0

5

10

15

20

25

30

35

40

45

0 1 2 3 4 5 6 7

Load

(

kN)

Deflection (mm)

Load Vs. Deflection

Load


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Table 2. Experimental results of 7510X300 section

Time (s) Load Deflection (kN) LVDT 1 LVDT 2

0 0 0 0 2 1.955 0.299 0.319 4 2.81 0.459 0.469 7 4.24 0.649 0.659 9 5.75 0.879 0.899

11 7.32 1.119 1.129 14 9.15 1.399 1.399 17 10.46 1.699 1.699 19 12.75 1.949 1.949 22 14.45 2.209 2.219 24 16.54 2.529 2.559 26 18.44 2.819 2.859 29 21.7 3.139 3.209 31 22.1 3.379 3.459 34 23.6 3.609 3.679 36 25.04 3.859 3.929 38 27.2 4.159 4.239 50 28.97 4.429 4.519 53 30.47 4.689 4.779 55 33.87 5.179 5.289 58 36.62 5.899 5.999

1:00 40.14 6.139 6.249 1:10 41.86 6.409 6.509

Figure (3): CFRP Strengthened 7510X300 mm length specimen deflection vs. compression capacity for LVDT 2

051015202530354045

0 1 2 3 4 5 6 7

Load

(

kN)

Deflection (mm)

Load Vs. Deflection

Load


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Table 3. Experimental results

The experimental results are presented in the form

of load-displacement relationships. The experimental

parametric investigation covers (1) width, (2) length

and (3) thickness. Table 2 represents load versus

deflection under LVDT 1 and LVDT 2. Figure 2 and

Figure 3 represent load against deflection. The failure

loads are tabulated in Table 4 for all the test specimens.

The test results show some variations in load carrying

capacity due to displacement at the top of the column.

The recorded ultimate tensile strains are slightly higher

than the actual values due to strain gauges damaged

prior to failure of the test specimens. All the

experimental test cases show delamination prior to

ultimate load.

FEA Analysis

The finite element software ABAQUS is used in

various investigations in science and technology. It is

suitable for the analysis of composite structures like

CFRP strengthened cold formed steel structures (Kwon

et al., 2007; Nozaka et al., 2005b; Teng and Hu, 2007;

Lama et al., 2011; Al-Mayah et al., 2006). The finite

element model was developed using the commercially

available software package ABAQUS. The ABAQUS

Version 6.12 was used in this investigation. According

to the test setup, the boundary conditions were fixed at

the bottom of the specimen and allowed rotations and

transversal translations on the top of the specimen. The

general purpose of shell element S4R is used to

develop the model as shown in Figure 4. A total of

seven mode shapes are analyzed and compared with

test results. The material properties are used as per

manufactures’ data. The tensile strength of CFRP is

4830 MPa, with a tensile modulus of 230 GPa, a

weight of 300 g/m2, an ultimate elongation of 2% and a

fiber thickness of 0.166 mm. The unidirectional carbon

fiber is used in this study. Fibers are placed in

transverse direction to that of the application of load.

The MC-Dur 1280 epoxy resin (adhesive for CFRP-

strips and flat-bar steel for structural strengthening) is

used to bond the carbon fabrics over the cold formed

channel columns. The density of MC-DUR 1280 is

1.65 kg/dm3, the modulus of elasticity is 8600 MPa and

the tensile strength is 20 MPa (Seleem et al., 2010).

In this investigation, S4R shell elements were

employed in the models based on the existing research

(Obaidat, 2013; Kalavagunta, 2014; Haddad et al.,

2011). S4R element is a conventional shell element and

has unique features like converging to classical theory

for thin shells. The element is a robust and general

purpose element that is suitable for a wide range of

applications. This is a very efficient shell element and

has proved to give effective results for CFRP

strengthened thin walled steel elements (Nozaka et al.,

2005b; Lim et al., 2008; Shen et al., 2001; Fernando et

al., 2009; Koller et al., 2012; Alam and Fawzia, 2015;

Artero-Guerrero et al., 2013).

The proposed FEA model approach for CFRP

strengthened cold-formed lipped channel sections

subjected to axial compression is given as follows:

The thickness of composite section (tt ) is

considered as CFRP thickness (tcf ) + steel plate

thickness (ts ) neglecting adhesive layer thickness (as

this is weak in strength and buckling) and is given by

Eq. (1). The elastic modulus of the CFRP with steel is

determined from the modular ratio concept, Ecfrp, given

by Eq. (2). tt = (tcf ) + ts; (1)

. (2)

Section Capacity(kN)

7510x300 41.86

7510x500 45.93

7510x700 42.43

7512x300 67.04

7512x500 69.5

7512x700 56.88

10010x300 63.2

10010x500 49.95

10010x700 56.75


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Mesh and boundary conditions are shown in Figure

2. The elements are modeled in order to satisfy the

displacement and boundary conditions, including the

fiber orientation. The auto mesh option is used in order

to achieve the best solution. The bottom end of the

column is fixed with no degree of freedom and uniform

compressive loading is applied. FEA model is shown in

Figure 4. First mode shape and buckling load of section

10010x300 and second mode shape and buckling load

of section 10010x300 are shown in Figure 5 and Figure

6, respectively.

Figure (4): Analytical model of section 10010x300

Figure (5): First mode shape and buckling load of section 10010x300


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Figure (6): Second mode shape and buckling load of section 10010x300

Figure 5 and Figure 6 show that initial local

bucking exists from flange buckling and rotation at

flange and web junction exists due to continuously

applied load. For short column considered, short

wavelength buckling of individual plate elements is

genially called local buckling. The cross-section

deformation is expected due to inner walls undergoing

bending and is shown in Figure 5 and Figure 6. Third

mode shape and buckling load of section 10010x300

and fourth mode shape and buckling load of section

10010x300 are shown in Figure 7 and Figure 8,

respectively.

Figure (7): Third mode shape and buckling load of section 10010x300


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Figure (8): Fourth mode shape and buckling load of section 10010x300

With further increase in load, Figure 7 and Figure 8

show rotation and translation of each flange and lip.

The above third and fourth mode shapes are due to

rotation of the member's flange and junction of flange

to web. These rotations of the members clearly show

that the length of the column influences the distortional

buckling stress. These modes are also called interaction

modes between local and global buckling. Fifth, sixth

and seventh mode shapes and buckling load of section

10010x300 are shown in Figures 9, 10 and 11,

respectively.

Figure (9): Fifth mode shape and buckling load of section 10010x300


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Figure (10): Sixth mode shape and buckling load of section 10010x300

Figure (11): Seventh mode shape and buckling load of section 10010x300

Mode shapes five, six and seven show the global

buckling where the member deflects with no

deformation in a section. Global buckling FEA models

are shown in Figure 9, Figure 10 and Figure 11. FE

load displacement curves and buckling mode shares are

extracted and shown in Figure 5 through Figure 11. A


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uniform pressure is applied at the top of the shell

elements. Buckling analysis was undertaken by

including geometry and material effects. The results

from finite element models are validated by comparing

their results with the corresponding experimental

results of buckling loads. The validated finite element

model is then used to determine the buckling loads for

other sections. The FEA analysis is performed and the

results are tabulated in Table 4. Table 5 shows

buckling loads for CFRP strengthened sections,

comparing experimental results with FEA results.

Table 4. Buckling loads for CFRP strengthened section from FEA analysis

Section Mode 1-Px

(kN)

Mode 2-Px

(kN)

Mode 3-Px

(kN)

Mode 4-Px

(kN)

Mode 5-Px

(kN)

Mode 6-Px

(kN)

Mode 7-Px

(kN)

C7510x300mm 35.476 38.067 40.285 43.846 48.267 49.787 57.184

C7510x500mm 35.537 36.991 37.541 39.215 40.799 42.904 45.437

C7510x700mm 35.593 36.704 36.908 37.875 38.512 39.789 41.016

C7512x300mm 59.304 63.207 66.66 71.727 73.053 79.785 91.681

C7512x500mm 59.367 61.564 62.468 64.898 67.169 68.325 70.443

C7512x700mm 59.442 61.121 61.468 62.874 63.909 65.753 -

C10010x300mm 17.942 32.978 35.306 43.563 49.663 58.921 67.431

C10010x500mm 26.585 27.88 29.023 30.965 33.055 36.844 39.914

C10010x700mm 26.553 27.427 27.858 29.095 29.902 31.854 33.389

RESULTS AND DISCUSSION

The experimental results of load-deflection

behavior of CFRP strengthened beams with different

cross sections and lengths are shown in Figure 2 and

Figure 3. Table 3 represents the experimental results of

ultimate loads. It is observed from experimental

investigation that initially all the CFRP strengthened

cold formed steel columns control the overall strength.

When the local buckling yields, the additional tensile

force is carried by the CFRP system and an increase in

the load carrying capacity of the composite section is

obtained. The failure modes which are observed on the

CFRP strengthened cold formed steel channel sections

are similar to those observed on plain cold formed steel

channel sections. These failure modes or buckling

modes are classified as:

Local buckling;

Distortional buckling;

Lateral torsional buckling.

The load deflection plots of CFRP strengthened

cold formed steel channel sections are similar to those

of plain sections, but there are sudden decreases in load

due to peeling of CFRP. This is generally called

debonding failure.


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Table 5. Buckling loads for CFRP strengthened section: experimental vs. FE analysis

Section Experimental-

Px (kN)

Mode 1-Px

(kN)

Mode 2-Px

(kN)

Mode 3-

Px (kN)

Mode 4-Px

(kN)

Mode 5-

Px (kN)

Mode 6-Px

(kN)

Mode 7-Px

(kN)

C7510x300mm 41.86 35.476 38.067 40.285 43.846 48.267 49.787 57.184

C7510x500mm 45.938 35.537 36.991 37.541 39.215 40.799 42.904 45.437

C7510x700mm 42.43 35.593 36.704 36.908 37.875 38.512 39.789 41.016

C7512x300mm 67.04 59.304 63.207 66.66 71.727 73.053 79.785 91.681

C7512x500mm 69.5 59.367 61.564 62.468 64.898 67.169 68.325 70.443

C7512x700mm 56.88 59.442 61.121 61.468 62.874 63.909 65.753 -

C10010x300mm 63.2 17.942 32.978 35.306 43.563 49.663 58.921 67.431

C10010x500mm 49.957 26.585 27.88 29.023 30.965 33.055 36.844 39.914

C10010x700mm 56.758 26.553 27.427 27.858 29.095 29.902 31.854 33.389

The results of the buckling analysis from

experimental investigation and FEA software

ABAQUS for the CFRP strengthened cold formed steel

channel sections are compared.

The experimental results are represented in the 2nd

column of Table 4.

The results of buckling analysis are eigenvalues and

buckling mode shapes are tabulated for 7 mode

shapes in columns 3 to 9.

In C7512x700mm column, failure load at the 6th

mode is identified, so no further mode shape is

obtained.

Theoretical failure loads are approximately the

same as in one of the mode shapes of FEA results.

This is due to premature failures due to peeling of

CFRP from steel sections.

Debonding failures are also noticed in experimental

issues due to non-uniform surface preparation.

The shorter columns are getting higher values of

critical loads due to slenderness effect. This has

been noticed in mode 7.

The failure modes from the FE analysis are plotted

and it is observed that the test results are slightly

varying and that the first mode of failure is not always

the ultimate failure of the section. Experimental test

results also show that the debonding failure from the

section is due to issues associated with surface

preparation and with peeling of CFRP from the steel

section.

However, the test results are comparable to those of

any of the modes of failure shown in the FE analysis.

This could have been controlled by providing proper

surface preparation.

CONCLUSIONS

This study presents a method to predict the ultimate

strength of CFRP strengthened cold formed steel

sections. The FE results obtained from the proposed

model are compared and they are found to be in good

agreement. Compared to experimental results, the

proposed model is more accurate to calculate the

ultimate load for CFRP strengthened cold formed steel

column sections under axial compression loads. FEA

results also demonstrated how the use of finite element

tools for composite sections develops accurate design

methods.

While the studies conducted at Universiti Tenaga


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Nasional are presented in this paper, it represents a

significant advancement in understanding the behavior

of CFRP strengthened cold formed steel structures. The

following issues need to be further addressed in the

future:

Different types of surface preparation to address

debonding failure.

Different epoxy types can be used as adhesive

materials, which may result in a stronger bond

between CFRP and cold formed steel.

Parametric FEA models need to be developed with

composite section CFRP-adhesive-cold formed

steel.

Different experimental and analytical investigations

should be carried out in order to develop design

standards for CFRP steel composite sections:

o Material strength under elevated temperatures,

cold temperatures,... etc.

o Flexural strength.

o Axial strength.

o Shear.

o Detailing.

o Design guidelines with detailed construction

specifications.

Acknowledgment

The authors would like to acknowledge BlueScope

Lysaght, Malaysia, SDN BHD, for giving support to

this research by providing cold formed steel sections.

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