Buckling and Post Bu ckling of Thin-walle d Composite Columns with Intermediate ...asel.sejong.ac.kr/images/sub04/pdf/33) Buckling and P… · · 2011-01-20Buckling and Post Buckling

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International Journal of Steel Structures

September 2009, Vol 9, No 3, 175-184

Buckling and Post Buckling of Thin-walled Composite Columns

with Intermediate-stiffened Open Cross-sectionUnder Axial Compression

Jaehong Lee1, Huu Thanh Nguyen2, and Seung-Eock Kim2,*

1Department of Architectural Engineering, Sejong University, 98 Kunja-dong, Kwangjin-gu, Seoul, 143-747, Korea2Department of Civil and Environmental Engineering, Sejong University, 98 Kunja-dong, Kwangjin-gu, Seoul, 143-747, Korea

Abstract

The thin-walled composite columns with an open cross-section reinforced by intermediate stiffener under axial compressionhave been considered. The finite element method is employed to study the buckling behaviour of the thin-walled compositecolumn. Eigenvalue analyses are carried out first to predict the buckling load and buckling mode shapes of the column, andthen the geometric nonlinear analyses are performed to investigate the nonlinear buckling properties and post-bucklingbehaviour of the thin-walled structures. The type of angle ply symmetric laminate is used. The investigation is performed overseveral values of ply arrangement angle and various values of stiffener parameter. The numerical results show a significanteffect of the intermediate stiffeners and composite ply angle on loading capacity and buckling behaviour of the thin-walledcomposite column. The research provides insight into the thin-walled structure and composite laminate, which is employed toenhance the loading capacity of thin-walled composite structures.

Keywords: Thin-walled composite column, Intermediate stiffener, Ply angle, Buckling, Finite element method

Introduction

Thin-walled member is one of the structures that

exhibit the most effective employing of material to resist

buckling. Because of being configured from many thin-

walled segments, the thin-walled section can easily be

made to obtain several different forms that have a high

shape factor and less used material. By these factors, the

thin-walled member has been widely used in the

construction industry for many decades. However, besides

the preeminent properties mentioned above, the thin-

walled member has also inherent weakness accompanying

in constituted plates such as local buckling. When a thin-

walled column is under compressive loading, component

plates of the member is usually buckled prior to overall

failure. The majority effect of local buckling is to reduce

the member stiffness against overall bending and/or

torsion. This is the main factor that causes the early

failure of column and considerably decreases the loading

capacity of structures. In order to strengthen the thin-

walled members, several types of stiffener are usually

constructed in thin-walled structures, transverse and

intermediate stiffener. The stiffeners carry a portion of

loads, certainly, but they primarily subdivide the elementary

plates into smaller pieces of higher stiffness, consequently

increasing significantly their loading capacity and of the

member. The size, shape and location of the stiffeners

make changes of the cross section geometric characteristic

that causes a strong influence on the critical load and

post-buckling behaviour of the structure.

Together with the employing of thin-walled structures

in civil engineering, numerous researches on thin-walled

structural members have been extensively investigated. In

the past, most research activities focused on the analysis

of behaviour of thin-walled members, which are made of

isotropic material such as steel, zincalune-metal and

aluminium, and did not take into account the anisotropic

materials (Young and Rasmussen, 1977; Hancock, 1981;

Bradford and Hancock, 1984; Key and Hancock, 1993;

Camotim et al., 2005; Chung et al., 2005; Nadia et al.,

2005; LaBoube and Larson, 2005). Several studies were

performed relying on Vlasov’s thin-walled beam theory

in which several behaviour of thin-walled section, for

instant out-of-plane section deformation, were ignored, thus

they were not applied widely in practical analysis and

design. It is fairly said that the first studies considering

the structural behaviour of thin-walled composite

Note.-Discussion open until February 1, 2010. This manuscript forthis paper was submitted for review and possible publication onOctober 20, 2008; approved on August 28, 2009

*Corresponding authorTel: +82-2-3408-3291; Fax: +82-2-3408-3332E-mail: [email protected]

176 Jaehong Lee et al. / International Journal of Steel Structures, 9(3), 175-184, 2009

members belonged to Bauld and Tzeng (1984), who

expanded Vlasov’s thin-walled beam theory to take

warping deflection into account in analysis of fiber-

reinforced member with open cross-sections. Actually, the

theory developed by these two authors was extended to

incorporate the influence of the coupling effect between

the membrane and bending forces and the effect of cross-

section shear deformation, thus it was enable to analyze

the member formed by asymmetric laminates. However,

since these approaches are just an extension of the

standard Vlasov’s beam theory to account for orthotropic

materials, and the section rigid-body motion assumption

still remained, the analysis is unable to take into account

the occurrence of in-plane cross-section deformations,

which are the primary expressions of local buckling

phenomena.

As the use of composite structures made of Fiber-

Reinforced-Plastic (FRP) increases in the construction

field, more research on composite structural members has

been done. Studies by Raftoyiannis (1994); Godoy et al.

(1995); Babero et al. (2000) have investigated the interaction

of buckling modes in FRP columns. These works, both

analytically (using ABAQUS) and experimentally, showed

that the local deformations of cross-section significantly

affect structural behaviour and capacity of thin-walled

composite members. However, these studies have not

considered the influences of section stiffener to critical

load or the effect of fiber angle on local-buckling modes

and post-buckling behaviour of the examined columns.

Some years ago, Azam and Colin (2006) performed a

numerical study using non-linear finite element analysis

to investigate the response of composite cylindrical shells

subjected to combined load, in which the post buckling

analysis of cylinders with geometric imperfections is

carried out to study the effect of imperfection amplitude

on critical buckling load. It is shown that the effect of

imperfection is more apparent when the composite

cylindrical shell structures are subjected to combined

loading. Ashkan by carrying out linear buckling analysis

has investigated computational models of cracked composite

cylindrical shells, in which the effect of crack size and

orientation as well as the composite ply angle on buckling

behaviour of cylindrical shells under axial compression is

considered (Ashkan, 2006). His study provides some

insight in to composite laminate that enhances the load

capacity of cylindrical shell and minimizes their potential

sensitivity to the present of deflections. Recent research

carried out by Teter and Kolakowski (2004) have dealt

with the interactive buckling of prismatic thin-walled

composite columns with open cross sections with intermediate

stiffeners. These researchers developed an analysis

method relying on Koiter’s asymptotic theory. In their

method, the stiffness of Thin-walled composite members

is derived employing classical composite laminate and

plate theories. The constitutive equations of thin-walled

members is established by applying principal of virtual

work and solved by the asymptotic Byskov-Hutchinson’s

method. This approach of non-linear approximation

allows for the evaluation of effect of imperfection and

interaction of various buckling modes on behaviour of

structures. However, this evaluation can be only the lower

bound estimation of load carrying capacity and the

interaction, in some cases, is not predicted accurately. In

general, the comprehensive study of buckling behaviour

of a thin-walled composite column with open cross-

section reinforced by intermediate stiffener has not been

completely carried out, and the information of the research

considering this problem is rather limited.

The objective of this paper is to deal with the local

buckling and post-buckling behaviour of thin-walled

composite columns under axial compressive loading. The

cross section of the thin-walled members has a channel

shape with intermediate stiffener and inner or outer

reinforced edges as depicted in Figs. 1 and 2. Finite

element method is employed to obtain the numerical

results. Firstly, the linear-buckling analyses (eigenvalue

problem) are carried out to derive critical loads of the

columns and associated buckling mode shapes to

examine the relationships of critical load and mode

shapes with respect to the intermediate stiffener and ply

angle of constitutive thin-walled composite plates. Secondly,

nonlinear buckling analysis is performed to investigate

the interaction of buckling modes and the geometric

deformation on the loading capacity and post buckling

behaviour of the thin-walled composite columns. The

analysis is also carried out for different configuration of

laminate stacking sequence and stiffener parameters.

Whenever possible, the obtained results are compared

with corresponding studies by other researchers to verify

the present study.

2. Finite Element Model for Thin-walled Composite Columns

The thin-walled composite columns with an open cross

section as shown in Figs. 1 and 2 are modeled and

analyzed for buckling behaviour under axial compression

force, applying at centroid of cross section and orientate

along center line of the members. The single supports are

applied to the ends of the columns. Bottom ends are

hinged and top ends are roller. It is described that three

translations of bottom end are fixed, while at the top end

only two transverse translations are prevented and the

longitudinal movement is allowed, all rotations of both

ends are free except that the rotation of bottom end about

the column axis is fixed. To simulate these boundary

conditions, the coupling constrain technique in ABAQUS

(2004) is employed. Using coupling constrain with rigid

category, all nodes on each end cross-section are

constrained to make rigid body section. All movements of

each section are referred to a point, the so-called

reference point, which in this case, is placed at the

centroid of cross-section (Figs. 1, 2). The concentrated

force and boundary conditions are applied at these

Buckling and Post Buckling of Thin-walled Composite Columns with Intermediate-stiffened Open Cross-section 177

reference points. This method of coupling ensures that the

end cross sections of thin-walled column remain planar

after deformation, which is similar to the practical using

condition of thin-walled members where they usually

design very strong stiffeners at the ends of the member to

make the end sections rigid. In addition, the concentrated

load applied at reference points would not cause a very

high local stress concentration in the area of end sections.

Moreover, using this approach of coupling and reference

point, the column buckling problem will be set in the

same boundary and loading condition as other studies in

which the analytical or numerical analysis is carried out

with beam type element employed, thus making it easy

for comparison of investigated results. Two kinds of

cross-section shapes are introduced. Fig. 1b and 1c shows

the cross-section of channel shape with outer reinforced

edge while the inner reinforced edge section is presented

in Figs. 2b, 2c. The existing of intermediate stiffener is

represented by non-dimensional parameter α=bs/b as

depicted in Figs. 1c and 2c, where b and bs is the width

of section and intermediate stiffener, respectively. The

case of α=0 is corresponding to the absence of the

Figure 1. Thin-walled composite column with outer omega section. (a) Thin-walled column, (b) Cross-section withoutstiffener (α=0), (c) Cross-section with stiffener (α=0.08, 0.16, 0.24)

Figure 2. Thin-walled column with inner omega section. (a) Thin-walled column, (b) Cross-section without inter-stiffener(α=0), (c) Cross-section with inter-stiffener (α=0.08, 0.16, 0.24)


stiffener.

The thin-walled columns are modeled by many plane

plates and discretized using shell element S8R, designated

in ABAQUS, which is a single layer eight nodes shear

deformable shell element with reduced integration, allows

large displacements and small strains. Each node of the

element has six degrees of freedom and element deformation

shape functions are quadratic in both in-plane directions.

To model composite laminate, there are two usual

methods of defining laminated section: defining thickness,

material and orientation of each layer or defining equivalent

section properties directly. Throughout this research, the

former method is employed. A multi-layer composite

section as shown in Fig. 3 is defined and assigned to shell

elements. Each layer of the section has specified material

properties, thickness and orientation (Fig. 3). Material

properties consist of six parameters E11, E22, G12=G13,

G23, ν12, where 1-direction is along the fiber, 2-direction

is transverse to the fiber in the surface of lamina and 3-

direction is normal to lamina. The fiber angle θ is defined

to be the angle form element material orientation to fiber

direction (form x-axis to 1-axis in Fig. 3b). The element

material orientation axis (x-axis) is assigned parallel to

column axis.

To analyze the buckling of the thin-walled column, two

analysis methods, Linear eigenvalue analysis and geometric

nonlinear, are employed. The linear eigenvalue analysis is

carried out for the thin-walled columns under compression

to predict its critical loads and associated buckling mode

shapes. This method of analysis is significant commonly

used as an initial stage of buckling studies due to its

simplicity, and in some cases, it is sufficient for design

evaluations. In this study, eigenvalue analysis was carried

out to study the variation of the buckling load and

associated mode shapes versus ply angle (q) and stiffener

parameter (a). However, eigenvalue analysis does not

account for the problems in which the effect of geometric

deformations is significant and post buckling behaviour

of the structure is needed; therefore, an additional

geometric nonlinear analysis was performed. The RIKS

method available in ABAQUS (2004) is a suitable

approach applied for nonlinear buckling and collapse

analysis. This method finds the static equilibrium states

of the structure by moving along the static equilibrium

path in load-displacement space in which the applied

loads are proportional and their magnitudes are controlled

by a single scalar load factor. In present study, the RIKS

method is employed to carry out nonlinear buckling

analyses of the thin-walled composite columns to investigate

the post buckling behaviour of the members and to study

the influences of geometric deformations and local

buckling mode on the loading capacity of the columns.

3. Linear Buckling Analysis of Thin-walled Columns

The thin-walled composite columns in Figs. 1 and 2 are

modeled and analyzed, their sectional dimension are

illustrated in Figs. 1(b,c) and 2(b,c). Typically, b=50 mm,

b1=12.5 mm, h=25 mm, t=8×0.125=1 mm, hs=4 mm

and the length L=650 mm. The stiffener parameter α=bs/

b=0, 0.08, 0.16 and 0.24 corresponding to bs=0, 4, 8 and

12, respectively. The shell section type of Symmetric

Angle Ply Laminate [(θ,-θ)2]s comprised of eight layers

of composite lamina, as shown in Fig. 3c, was studied in

this paper. Each layer is made of Glass-Epoxy composite

material with mechanical properties of E1=140 GPa,

E2=10.3 GPa, G12=G13=5.15 GPa, G23=4.63 GPa, ν12=0.29.

The Glass-Epoxy composite material is comprised of

glass fiber and epoxy matrix. Eight layers of thickness of

0.125 mm are superimposed to make the composite

laminate thickness of t=1 mm. The material orientation

of the lamina with respect to local coordinate system of

shell element is presented in Fig. 3b, and lamina stacking

sequence is in Fig. 3c. Eigenvalue analyses are carried

out to predict the critical load and buckling mode shapes

of the columns with respect to the ply angle variation.

Figure 4 represents the local buckling mode shapes of

the composite columns with outer edge reinforced open

cross-section (outer omega section) under longitudinal

compression, which occurs as the first buckling mode

depending on the composite ply angle (θ) and intermediate

stiffener parameter (α). It is easy to recognize the fact that

the wave length of buckling deformation shape varies

significantly when the ply angle changes; that is illustrated

by number of half wave (n) formed along the column

length. The analysis result indicates that the number of

half wave (n) has significant change with respect to the

existence of the stiffener but is not changed in terms of

size. That variation is depicted in Fig. 4 and the numerical

results are shown in Table 1. The buckling deformation

regularly distributes along column length for θ=0o, while

Figure 3. Laminate arrangement and fiber drection. (a) Lamina configure and local coordinate, (b) Fiber angle relative tothin-walled column axis, (c) Angle ply laminate [(θ,-θ)2]s


it locates mainly at two ends of the column for θ=45o and

at the middle region for θ=90o. The most important

distinction between the columns with un-stiffened section

(Fig. 1b) and the one with stiffened section (Fig. 1c) is the

fact that the local buckling deformation occurs in both

webs and flanges of the section for the former column

(Fig. 4(a,b,c)), while for the latter column it likely

appears only in the flanges of the section (Fig. 4(d,e,f)).

There are not much differences in the buckling shapes

and halfwave lengths for different stiffener parameters

α=0.08, 0.16, 0.24. In Fig. 5, the buckling mode shapes

of the thin-walled column that have inner omega section

are presented. Most of properties of buckling shapes and

critical loads of these columns are similar to those

exhibited by the column with outer omega cross-section.

In Figs. 6 and 7, respectively, the graphs of nominal

critical stress (σcr) and number of buckling halfwave (n)

formed along the length of the column as functions of ply

angle (θ) and stiffener parameter (α) are presented. The

critical stress (σcr) is calculated by dividing the obtained

lowest critical force by cross-section area, and the

corresponding number of buckling halfwave (n) is

directly counted from buckling mode shape. It is seen that

the critical stress (σcr) has the lowest value at θ=0o, and

reaches the maximum value at 45o≤θ≤55o. Together with

the changes of critical stress (σcr), the number of halfwave

(n) also changes with respect to the variation of the ply

angle. The smallest value of n=8 obtained at θ=0o for

α=0 and n=11 for α=0.08, 0.16 and 0.24, and the largest

value of n=25 reached at θ=90o for α=0 and roughly

n=29 for α=0.08, 0.16 and 0.24. The number of halfwave

is summarized in Table 1. The critical stress (σcr) with

respect to ply angle (θ) and stiffener parameter (α) are

shown in Table 2. It is observed that the critical stress

(σcr) and number of buckling halfwave (n) of the columns

with α=0.08, 0.16, 0.24 are close to one another, and

have significant distinction with α=0. The critical stresses

(σcr) with α=0.08, 0.16, 0.24 are significantly greater

than that with α=0, about twice at θ=0o and three times

at θ=45o. It is indicated that the existence of intermediate

stiffener in the cross-section of thin-walled composite

column and the ply angle of composite laminate have

considerable influence on the buckling properties of thin-

walled composite column.

4. Nonlinear Post-buckling Analysis of Thin-walled Composite Columns

In this section, the thin-walled column depicted in the

Fig. 1 is investigated. Two cross-section (un-stiffened and

stiffened section) as shown in Figs. 1(b, c) with dimensions

presented in previous section are taken in to consideration.

The composite laminate that constitutes the thin-walled

column has a stack sequence of [(θ,-θ)2]s and its material

Figure 4. Buckling mode shapes of the thin-walled composite column of outer omega section with variation of fiber angleθ. (a) (b) (c) for unstiffened section, (d) (e) (f) for stiffened section.

Table 1. Variation of number of halfwave with respect to fiber angle and stiffener parameter

Stiffener parameter (α)

Number of halfwave (n) for ply angle θ (degree)

0 30 45 60 90

α=0 8 11 15 21 25

α=0.08, 0.16, 0.24 11 14 19 24 29


is identical to the one in the linear buckling analysis

section. The modified RIKS method has been employed

to carry out the geometric nonlinear analysis with several

values of ply angle (θ) and stiffener parameter (α) to

investigate nonlinear buckling properties and post

buckling behaviour of the thin-walled composite column.

The modified RIKS method is adopted by moving along

the equilibrium path (load-deflection path) with loading

increments, this method can be employed to investigate

geometric nonlinear, material nonlinear, failure and

collapse of structure. However, in present study, only

geometric nonlinearity is employed to study the buckling

of the thin-walled composite column.

In the progress of tracing equilibrium path, when a

significant change in geometric configuration of structure

occurs quickly at a certain load level, buckling appears.

The load-deflection curve bifurcates to another way. That

value of load will be recorded as buckling load and the

corresponding deformation is considered as buckling

shape. An initial small deflection called imperfection is

applied to produce the structure buckle. Because the

sensitivity of the thin-walled columns to imperfection is

not the main objective of investigation in this study, so an

arbitrary imperfection relying on the first eigen buckling

mode shape is imposed on a number of nodes of the thin-

walled column to initiate buckling progress. The

Figure 5. Buckling mode shapes of the thin-walled composite column of inner omega section with variation of fiberangles theta. (a) (b) (c) for unstiffened section, (d) (e) (f) for stiffened section.

Figure 6. Graphs of critical stress σcr (MPa) as a functionof ply arranement angle θ and stiffener parameter α forthe columns in Figs. 1 and 2 obtained by linear bucklinganalysis.

Figure 7. Graphs of number of halfwave (n) as a functionof ply arranement angle θ and stiffener parameter α forthe columns in Figs. 1 and 2 obtained by linear bucklinganalysis.


maximum magnitude of imperfection is taken smaller

than the composite laminate thickness (t).

Figure 8 shows the buckling shapes of the thin-walled

composite column in Fig. 1 with un-stiffened cross-section

obtained by nonlinear buckling analysis. The Figure

indicates that buckling deformation regularly distributes

along the length of the column for all values of ply angle

(θ), the number of buckling halfwave formed along the

column length increases following the increasing of ply

angle (θ). A important detail that can be seen from the

Figure is the interaction of local buckling to global

flexural buckling, which displays clearly for the case of

θ=45o.

In Fig. 9, the deformation shapes at buckling point of

the considering composite column with the stiffened cross-

section under compression are displayed. The nonlinear

buckling analysis was performed with three values of

stiffener parameter α=0.08, 0.16, 0.24 and several values

of composite ply angle 0o

≤θ≤90o; however only the buckling

shapes associated with α=0.16, 0.24 and θ=0, 45, 90 are

presented in this Figure as the most typical cases. It is

recognized that the buckling shapes of the column from

geometry nonlinear analysis are multiform with respect to

the variety values of (α) and (θ). The buckling deformation

occurs in both webs and flanges of the thin-walled section

and regularly distributes along the length of the column.

The interaction of global flexural buckling with local

buckling is more apparent in cases of α=0.16, 0.24 for

θ=45o (Figs. 9(b,e)). Particularly, in the case of α=0.16,

θ=45o, three forms of buckling deformation appear to

occur simultaneously: local buckling, section flat buckling

and global flexural buckling (Fig. 9b). Figs. 10,11,12 and

13 present the load-deflection curves of the composite

columns obtained from geometry nonlinear analysis for

four values of stiffener parameters α=0, 0.08, 0.16, 0.24,

respectively. For each value of a, five curves corresponding

to five values of ply angle (q) from 0o to 90o are displayed.

From these diagrams, it is observed that the post-buckling

equilibrium paths are stable but asymmetric and, as a

result, the thin-walled columns behave stable after

buckling. In all cases of analysis with associated values of

(α) and (θ), a pre-buckling flexural deflection existed in

the column before the local buckling occurs, that magnitude

of the pre-deflection demonstrates the influence of the

imperfection and asymmetry of the section on buckling

behaviour of the column. The pre-buckling deflection for

the case of un-stiffened section (α=0) has a negative value

(Fig. 10), whereas it is positive for the other cases of

stiffened section (α≠0) (Figs. 11, 12, 13). This pre-

deflection showed the effect of the stiffener to the

response of the column under compression (see Figs. 8

and 9 for the opposition of flexural deflection of the

column). The numerical result of nonlinear buckling

analysis shows that the critical load (σcr) and number of

halfwave (n) derived by nonlinear buckling analysis is

roughly same as the result achieved by eigen buckling

analysis, which was previously shown in Table 1 and 2.

It is shown from the nonlinear load-displacement curves

Table 2. The critical stress with respect to fiber angle and stiffener parameter

Stiffener parameter (α)

Critical stress σcr (MPa) for ply angle θ (degree)

0 30 45 60 90

0 52.11 103.96 122.46 109.72 62.48

0.08 110.29 266.21 328.16 294.19 169.19

0.16 112.25 270.47 333.39 298.87 172.09

0.24 115.60 276.72 341.77 308.53 182.15

Figure 8. Buckling mode shapes of the thin-walled composite column in Fig. 1 with un-stiffened section (α=0) obtainedby non-linear buckling analysis.


that the applied load continues to increase after reaching

to the critical value; consequently, it can be concluded

that the loading capacity of the thin-walled composite

column is higher than the critical buckling load.

Next, the results of nonlinear buckling analysis of the

thin-walled composite column in the present study were

compared with the results obtained by Teter and

Kolakowski (2004). These researchers conducted a

buckling analysis of the same composite column as in this

study. Their analysis method relied on Koiter’s asymptotic

theory. The solution of constitutive equations of thin-

walled members was obtained using the asymptotic

Byskov-Hutchinson’s non-linear approximation method.

In their study, the resulting critical stress diagrams was

symmetric at about θ=45o. The comparison in Fig. 14

shows that for the case of α=0, associated with un-

stiffened cross-section, good agreement between two

results is observed, however in the case of α≠0,

corresponding to stiffened cross-section, the results just

nearly meet to each other for ply angle 0o

≤θ≤40o. For

other ply angles 40o

≤θ≤90o, the critical stress (σcr)

obtained by present study is higher. Particularly, different

from the statement in the study of Teter and Kolakowski

(2004) the diagrams of critical stress (σcr) with respect to

Figure 9. Buckling mode shapes of the thin-walled composite column in Fig. 1 with stiffened section (α=0.08, 0.16, 0.24)obtained by nonlinear buckling analysis.

Figure 10. Load-deflection curves obtained by nonlinearanalysis for the column in Fig. 1 with variety of plyarrangement angle (θ) for α=0.

Figure 11. Load-deflection curves obtained by nonlinearanalysis for the column in Fig. 1 with variety of plyarrangement angle (θ) for α=0.08.



the ply angle (θ) obtained by current study is not symmetric

about θ=45o and the maximum value of (σcr) is not at

θ=45o but in a range of 45o

≤θ≤50o. Both this study and

Teter and Kolakowski (2004) agree with the fact that the

number of buckling halfwave increases with the increase

of composite ply angle (θ).

5. Concluding and Remarks

Throughout the eigenvalue and geometry nonlinear

analyses using the finite element method, the thin-walled

composite column constructed by symmetric angle ply

laminates have been studied. The inner and outer omega

sections with intermediate stiffener were analyzed. The

buckling and post-buckling behaviour of the thin-walled

composite columns was investigated for the effects of the

ply angle (θ) and intermediate stiffener width (bs). For the

column adopted in this study, the analysis results show

that the composite ply angle and the intermediate stiffener

have significant effects on the critical load and buckling

behaviour of the composite column. Changing the ply angle

(θ) will lead to significant changes in buckling load and

mode shape. The stiffener can increase the loading

capacity of the columns up to two to three times. The

stiffener width (bs) has a little effect on buckling load and

mode shape. The buckling load of the outer omega and

inner omega sections is almost identical. The present

research has placed the interest in the buckling and post-

buckling behaviour of the thin-walled composite column

of open cross-section with intermediate stiffener. In the

future, research can be extended to investigate the failure,

delaminate and collapse of the composite structures.

Acknowledgments

Support for this research by the Korean Ministry of

Construction and Transportation through Grant C106A1030001-

06A050300220 is gratefully acknowledged.

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Figure 14. Diagrams of critical stress (σcr) with respect toply angle (θ) for comparison between current study andthe analysis result presented by Teter and Kolakowski(2004).


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