International Journal of Steel Structures
September 2009, Vol 9, No 3, 175-184
www.ijoss.org
Buckling and Post Buckling of Thin-walled Composite Columns
with Intermediate-stiffened Open Cross-section
Under Axial Compression
Jaehong Lee , Huu Thanh Nguyen , and Seung-Eock Kim *
1
2
2,
Department of Architectural Engineering, Sejong University, 98 Kunja-dong, Kwangjin-gu, Seoul, 143-747, Korea
Department of Civil and Environmental Engineering, Sejong University, 98 Kunja-dong, Kwangjin-gu, Seoul, 143-747, Korea
1
2
Abstract
The thin-walled composite columns with an open cross-section reinforced by intermediate stiffener under axial compression
have been considered. The finite element method is employed to study the buckling behaviour of the thin-walled composite
column. Eigenvalue analyses are carried out first to predict the buckling load and buckling mode shapes of the column, and
then the geometric nonlinear analyses are performed to investigate the nonlinear buckling properties and post-buckling
behaviour of the thin-walled structures. The type of angle ply symmetric laminate is used. The investigation is performed over
several values of ply arrangement angle and various values of stiffener parameter. The numerical results show a significant
effect of the intermediate stiffeners and composite ply angle on loading capacity and buckling behaviour of the thin-walled
composite column. The research provides insight into the thin-walled structure and composite laminate, which is employed to
enhance 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 thinwalled 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 thinwalled member has also inherent weakness accompanying
in constituted plates such as local buckling. When a thinwalled 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 thinNote.-Discussion open until February 1, 2010. This manuscript for
this paper was submitted for review and possible publication on
October 20, 2008; approved on August 28, 2009
*Corresponding author
Tel: +82-2-3408-3291; Fax: +82-2-3408-3332
E-mail: sekim@sejong.ac.kr
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
., 2005; Chung
., 2005; Nadia
.,
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
et al
et al
et al
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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 fiberreinforced 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 crosssection 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 FiberReinforced-Plastic (FRP) increases in the construction
field, more research on composite structural members has
been done. Studies by Raftoyiannis (1994); Godoy
.
(1995); Babero . (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
et al
et al
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 crosssection 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
Thin-walled composite column with outer omega section. (a) Thin-walled column, (b) Cross-section without
stiffener (α=0), (c) Cross-section with stiffener (α=0.08, 0.16, 0.24)
Figure 1.
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)
Figure 2.
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 =b /b as
depicted in Figs. 1c and 2c, where b and b is the width
of section and intermediate stiffener, respectively. The
case of α =0 is corresponding to the absence of the
s
s
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Jaehong Lee et al. / International Journal of Steel Structures, 9(3), 175-184, 2009
Laminate arrangement and fiber drection. (a) Lamina configure and local coordinate, (b) Fiber angle relative to
thin-walled column axis, (c) Angle ply laminate [(θ,-θ)2]s
Figure 3.
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 3direction 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
Buckling and Post Buckling of Thin-walled Composite Columns with Intermediate-stiffened Open Cross-section
179
Buckling mode shapes of the thin-walled composite column of outer omega section with variation of fiber angle
(a) (b) (c) for unstiffened section, (d) (e) (f) for stiffened section.
Figure 4.
θ.
Table 1.
Stiffener parameter
(α)
α=0
α=0.08, 0.16, 0.24
Variation of number of halfwave with respect to fiber angle and stiffener parameter
Number of halfwave (n) for ply angle θ (degree)
0
30
45
60
90
8
11
15
21
25
11
14
19
24
29
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 thinwalled composite column.
4. Nonlinear Post-buckling Analysis of Thinwalled 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
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Jaehong Lee et al. / International Journal of Steel Structures, 9(3), 175-184, 2009
Buckling mode shapes of the thin-walled composite column of inner omega section with variation of fiber
angles theta. (a) (b) (c) for unstiffened section, (d) (e) (f) for stiffened section.
Figure
5.
Graphs of critical stress σcr (MPa) as a function
of ply arranement angle θ and stiffener parameter α for
the columns in Figs. 1 and 2 obtained by linear buckling
analysis.
Graphs of number of halfwave (n) as a function
of ply arranement angle θ and stiffener parameter α for
the columns in Figs. 1 and 2 obtained by linear buckling
analysis.
Figure 6.
Figure 7.
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 thinwalled column to initiate buckling progress. The
Buckling and Post Buckling of Thin-walled Composite Columns with Intermediate-stiffened Open Cross-section
The critical stress with respect to fiber angle and stiffener parameter
Critical stress σcr (MPa) for ply angle θ (degree)
0
30
45
60
52.11
103.96
122.46
109.72
110.29
266.21
328.16
294.19
112.25
270.47
333.39
298.87
115.60
276.72
341.77
308.53
181
Table 2.
Stiffener parameter
(α)
0
0.08
0.16
0.24
90
62.48
169.19
172.09
182.15
Buckling mode shapes of the thin-walled composite column in Fig. 1 with un-stiffened section (α=0) obtained
by non-linear buckling analysis.
Figure 8.
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 crosssection 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 predeflection 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
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Jaehong Lee et al. / International Journal of Steel Structures, 9(3), 175-184, 2009
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 9.
Load-deflection curves obtained by nonlinear
analysis for the column in Fig. 1 with variety of ply
arrangement angle (θ) for α=0.
Figure 10.
Load-deflection curves obtained by nonlinear
analysis for the column in Fig. 1 with variety of ply
arrangement angle (θ) for α=0.08.
Figure
11.
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
Load-deflection curves obtained by nonlinear
analysis for the column in Fig. 1 with variety of ply
arrangement angle (θ) for α=0.16.
Figure 12.
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 thinwalled 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 unstiffened 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
Buckling and Post Buckling of Thin-walled Composite Columns with Intermediate-stiffened Open Cross-section
183
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 postbuckling 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.
Load-deflection curves obtained by nonlinear
analysis for the column in Fig. 1 with variety of ply
arrangement angle (θ) for α=0.24.
Figure 13.
Acknowledgments
Support for this research by the Korean Ministry of
Construction and Transportation through Grant C106A103000106A050300220 is gratefully acknowledged.
References
Diagrams of critical stress (σcr) with respect to
ply angle (θ) for comparison between current study and
the analysis result presented by Teter and Kolakowski
(2004).
Figure 14.
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
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