-
mna
Buckling behaviorThin-walled structuresDirect strength
method
eigumklindevn e
tures and the Direct Strength Method (DSM) on thin-walled
structures. Following reliability analysis, the
tio, betthrougin str
es of ufter siresidua
buckling behaviors of re exposed aluminum alloy columns,
design of aluminum alloy columns design considering the
stressstrain relationship of aluminum alloys at elevated
temperatures.Manganiello et al. [7] evaluated the inelasticexural
behavior of alu-minum alloy structures through numerical method and
proposed amethod for the ultimate strength of the rotational
capacity of across-section in bending. Maljaars et al. [8] studied
local bucklingof compressed aluminum alloy at elevated temperatures
through
accuracy of the design rules in the current specications.
Theseuckling behaviors
gn codes fminum alloy structural members, such as EN1999-1-2
(ECAmerican Aluminum Design Manual (AA) [15], AustraliaZealand
Standard [16], and Chinese Design SpecicatioAluminum Structures
(GB50429) [17]. To make full use of struc-tural material, the
cross-section of an aluminum alloy member isusually made up of
thin-walled plates. These design codes followthe element approach
to calculate the buckling strength of eachthin-walled element
considering effects of local bucking. In designof thin-walled steel
structures, the effective section is usuallydetermined through the
effective width method [18]. While the
Corresponding author. Fax: +86 531 88392843.E-mail address:
[email protected] (P. Wang).
Engineering Structures 95 (2015) 127137
Contents lists availab
g
lseMaljaars et al. [5] found that EN1999-1-2 [6] didnot give
anaccurateprediction for exural buckling strength of re exposed
aluminumcolumns. A new design method was proposed for the re
resistance
researches greatly advanced the mechanism of bof extruded
aluminum alloy columns.
Many countries have already published
desihttp://dx.doi.org/10.1016/j.engstruct.2015.03.0640141-0296/
2015 Elsevier Ltd. All rights reserved.or alu-9) [6],n/Newns foret
al. [3] quantied the response and failure of 5083-H116 and6082-T6
aluminumplates under compression loadwhile being sub-jected to a
re. Rasmussen and Rondal [4] proposed a column curveto predict the
strengths of the extruded aluminum alloy columnfailed at exural
buckling. Based on the FEM parametric studies on
deformation based continuous method gave more accurate
predic-tion for the ultimate strength. Wang et al. [13] carried out
tests onthe columns of 6082-T6 circular tubes. Zhu and Young [14]
pre-sented tests results of aluminum alloy circular hollow section
col-umns with and without transverse welds and assessed the1.
Introduction
For its high strength-to-weight raand exural manufacture
procedurealloy members are being widely usedSummers et al. [2]
performed a seriAA5083H116 and AA6061T651 aand developed empirical
laws fordesign strength predicted by current design specications
were found to be generally conservative,whereas DSM offered more
accurate results.
2015 Elsevier Ltd. All rights reserved.
ter corrosion resistanceh extrusion, aluminumuctural
applications [1].niaxial tension tests onmulated re exposurel yield
strength. Fogle
tests. Adeoti et al. [9] presented a column curve for extruded
mem-bers made of 6082-T6 aluminum alloy. Yuan et al. [10]
investigatedthe local buckling and postbuckling strengths of
aluminum alloy I-section stub columns under axial compression.
Their researchresults showed that current design codes were
conservative to pre-dict ultimate strength of aluminum alloy
columns. Su et al. [11,12]carriedout a series of stub-columntests
onbox sections and two ser-ies of experiments on aluminum alloy
hollow section beams. TheAluminum alloy columnIrregular shaped
cross section
nd the potential buckling failure mode at a given length. Tested
ultimate strengths were compared withthose predicted by the current
American, European and Chinese specications on aluminum alloy
struc-Buckling behaviors of section aluminucompression
Mei Liu, Lulu Zhang, Peijun Wang , Yicun ChangSchool of Civil
Engineering, Shandong University, Jinan, Shandong Province 250061,
Chi
a r t i c l e i n f o
Article history:Received 30 January 2015Revised 27 March
2015Accepted 28 March 2015Available online 10 April 2015
Keywords:
a b s t r a c t
Thin-walled columns withoffering high strength-to-wpaper,
thin-walled alumincally to investigate the bucelement model (FEM)
wasEffects of plate thickness o
Engineerin
journal homepage: www.ealloy columns under axial
section are used widely as columns in aluminum alloy framed
structures,ht ratios and convenience in connection with maintaining
walls. In thisalloy columns with section were studied
experimentally and numeri-g behavior and to assess the accuracy of
current design methods. A niteeloped and used to perform parametric
studies after being veried by tests.lastic buckling stress was
studied using nite strip method (FSM) and to
le at ScienceDirect
Structures
vier .com/ locate /engstruct
-
aluminum alloy members usually have complex shape cross
sec-tions, the effective width method appears tedious because it
needsiterations for the effective width dependent on stress
distributionacross the section. At this kind of circumstance, the
effective thick-ness method [19] is more feasible.
Schafer and Pekz [20] developed DSM for predicting the ulti-mate
strength of thin-walled steel structural members. The DSMhad been
adopted by AISI [21,22] now. The design equations ofDSM was
proposed by curve tting the test data and FEA resultson open
section thin-walled structural members such as channel,lipped
channel with web stiffeners, Z-section, hat section and rackupright
section. Unlike the traditional design method uses theeffective
section, DSM uses whole section to calculate the ultimatestrength,
which provides rational analysis procedure for irregularshaped
section and allows section optimization. Zhu and Young[23,24] found
that the modied DSM could be used in the designof square hollow
section (SHS) and rectangular hollow section(RHS) aluminum alloy
columns. Aluminum alloy extruded mem-bers usually have complex
sections to include as many functionsas possible. However, the
applicability of DSM in aluminum alloymember with irregular shaped
section has not been investigatedyet.
This paper presented experimental and numerical investigationon
the buckling behaviors of aluminum alloy columns withshape
cross-section under axial compression. The structural com-ponent
with the studied cross section is usually used as columnsin an
aluminum alloy framed structure, as shown in Fig. 1(a). TheFiber
Reinforced Plastic (FRP) wall can be easily xed in the chan-nel of
the section, as shown in Fig. 1(b).The FSM software CUFSM
[25] was used to illustrate effects of plate thickness on the
bucklingstrength and the potential buckling mode at a given length.
TheFEA software ABAQUS [26] was used to obtain the ultimatestrength
of the member considering effects of initial geometricimperfection
and the elasticplastic properties of aluminum alloy.Current design
codes were assessed through the comparison of FEAresults with
predictions by AA [15], EC9 [6], GB50429 [17] andDSM [21,22], as
well as AISI by substituting the material propertiesof steel with
those of aluminum alloy.
aluminum alloy columns. (b) Connection of the aluminum alloy
column with FRP.
f stress)
0.2% proof stressf 0:2 (MPa)
Ultimate strengthf u (MPa)
Ultimatestrain eu (%)
Parametern
Fig. 2. Stressstrain relationships.
128 M. Liu et al. / Engineering Structures 95 (2015) 127137Fig.
1. Application of aluminum alloy column with section. (a) Layout of
the
Table 1Material properties.
Specimens Area A(mm2)
Length L(mm)
Elastic modulusE (GPa)
0.1% proof 0:1 (MPaT01a 113.46 399.6 67.07 187.2T01b 110.25
400.8 70.06 200.5Mean value 111.86 400.2 68.57 193.9193.1 233.2 9.7
22.0207.6 235.4 7.9 19.9200.4 234.3 8.8 20.9
-
2. Experimental studies
2.1. Material properties
Material properties of the specimens were determined by ten-sile
coupon tests. The mean value of the elastic modulus and
yieldstrength of the aluminum alloy were 68.57 GPa and 200.4
MPa,respectively. The stressstrain relationship of aluminum
alloywas described by RambergOsgood expression [27],
e rE 0:002 r
f 0:2
n1
where E and f0.2 were elastic modulus and nominal yield
strength
n ln 2ln f 0:2f 0:1
2
The ultimate tensile strain of the tested aluminum alloy wasonly
about 8.8%, which indicated that the aluminum alloy mem-bers might
encounter ruptures where the tensile strain was rela-tive high. The
stressstrain relationship obtained from coupontests was shown in
Fig. 2.
2.2. Column test
The test specimens were fabricated by extrusion using
6063-T5aluminum alloy. Two column lengths including 350 mm and190
mm were studied. The section dimension was shown in Fig. 3.It had
one symmetric axis and was made up of four cantilever andone
stiffened plates.
7 specimens were tested to investigate the inuence of
columnlength, direction of global buckling and initial geometric
imperfec-tion on buckling behaviors. Since the short tested
specimens allwould fail at local buckling but not interaction of
local and globalbuckling without initial imperfection, two levels
of initial lack ofstraightness, 0.70 mm (l/500) and 5.00 mm (l/70),
were exertedthrough rolling machine before tests. The initial
geometric imper-fection was listed in Table 2.
A servo-controlled hydraulic testing machine was used to
applycompressive force by displacement control at a constant rate
of0.1 mm/ min. The ends of the specimens were milled at and2 kN was
applied before recording in order to ensure full contactwith the
hydraulic machine bearing plates. Two LVDTs were used
Fig. 3. Column section dimension.
agn
.7
.7
.0
.0
.0
.7
s
M. Liu et al. / Engineering Structures 95 (2015) 127137
129(stress at 0.2% plastic strain), respectively. The index n was
usedto describe the shape of the inelastic portion of the
stressstraindiagram, as listed in Table 1. The value of n was
calculated by
Table 2Comparisons of buckling strengths obtained from tests and
FEA.
Specimen Length L (mm) Direction of initial deection M
C01 350 Y 0C02 350 X 0C03 350 Y 5C04 350 X 5C05 350 Y+ 5C06 350
X 0C07 190
Note: X stands for axis of symmetry; Y stands for axis of
non-symmetric axis; + andFig. 4. Test arrto measure the axial
displacement and the horizontal deectionof the specimens, as shown
in Fig. 4. The applied load and LVDTsreadings were recorded at 5
second intervals during tests.
itude of initial deection (mm) Test FEA ComparisonPEXP PFEA
PEXP/PFEA
60.48 60.24 1.0068.78 64.32 1.0742.56 46.24 0.9243.50 47.46
0.9239.54 43.53 0.9065.28 64.32 1.0166.02 61.91 1.07
Mean 0.99COV 0.072
tand for the positive and negative direction of the axis,
respectively.angement.
-
2.3. Test results
2.3.1. Failure modesDeformations of the specimens after tests
were shown in Fig. 5.
Since the section had only one symmetric axis, the
specimensfailed at exuraltorsional buckling when it buckled around
thesymmetric axis; and failed at exural buckling when it
buckledaround the non-symmetric axis. For the 350 mm specimens,
twofailure modes were observed during tests: (1) exural
buckling,
as shown in Fig. 5(a), (c) and (e); and (2) exuraltorsional
buck-ling, as shown in Fig. 5(b) and (d). The 190 mm specimens
failedat local buckling, as shown in Fig. 5(f) and (g).
The initial geometric imperfection would affect the failuremode
of the column. The specimens with initial deection towardx axis
(non-symmetric axis) failed at exuraltorsional bucklingaround the
symmetric axis, as shown in Fig. 5(b) and (d). Whilethe specimens
with initial deection toward y axis (symmetricaxis) failed at
exural buckling around the non-symmetric axis,
130 M. Liu et al. / Engineering Structures 95 (2015) 127137Fig.
5. Deformation of test specimens. (a) Deformation of specimen C01.
(b) DeformatioC04. (e) Deformation of specimen C05. (f) Deformation
of specimen C06. (g) Deformation of specimen C02. (c) Deformation
of specimen C03. (d) Deformation of specimenn of specimen C07.
-
the increase in axial displacement at rst. The axial load
kept
and column end. Hard contact was dened to prevent the
penetra-tion of the column into the rigid plates. The tangential
behaviorwas dened by friction formulation. The friction coefcient
wasset as 0.47 [28]. In order to obtain a stable numerical
solution, apseudo-dynamic was adopted with a default dissipated
energyfraction of 2 104 that are suitable for most applications.
FEMis shown in Fig. 8.
Structures 95 (2015) 127137 131increasing till it reached the
vertex of the loadaxial displacementcurve, where global buckling
occurred, as shown in Fig. 6(ac).
3. Finite element model and verication
3.1. Finite element model
The FEA software ABAQUS [26] was used to predict the
bucklingbehavior and ultimate strength of the aluminum alloy
column. S4R,a 4-node reduced integration shell element, with 5 mm 5
mmmesh size was used after mesh sensitivity analysis
consideringaccuracy, CPU time and memory. The loadaxial
displacementcurves of the FEM with different mesh size were shown
in Fig. 7.Three curves almost coincided with each other indicated
that meshsize with 5 mm 5 mmwas accurate enough to predict the
behav-ior of the studied column. The general purpose shell element
S4Rgave robust and accurate solutions and allowed transverse
sheardeformations. The classical metal plasticity model was
applied. Itused standard Mises yield surfaces with associated
plastic ow.Perfect plasticity and isotropic hardening denitions
were bothavailable. It was simple and adequate for common
applicationsincluding crash analyses, metal forming, and general
collapse stud-ies. The normal stressstrain data obtained through
tensile testswas converted to true stress (Cauchy stress) and true
strain (loga-rithmic strain). Poissons ratio of aluminum alloy was
assumed tobe 0.3.
Meshed by C3D8R, 8-node linear reduced integrated
structuralbrick element, the rigid plates were used to apply axial
load tocolumn through contact interaction between test machine
andcolumn end. The mesh size was selected to be10 mm 10 mm 10 mm.
The rigid plates were made of steelwith Youngs modulus of 2.05 105
MPa and behaved elastically.as shown in Fig. 5(a), (c) and (e).
Because of the smaller ultimatetensile strain of aluminum alloy,
cracks were observed at the ten-sion side of specimen C04 and C05,
as shown in Fig. 5(d) and (e).Specimen C07 failed at local buckling
nally because of its shortlength, as shown in Fig. 5(g).
2.3.2. Ultimate strengthsThe magnitude of the initial
imperfection had signicant effects
on the ultimate strength of the column, as listed in Table 2.
The0.7 mm initial lack of straightness was found appropriate to
triggerglobal buckling. While the initial lack of straightness with
5.00 mmwas too large, thus the buckling strength reduced a lot due
to theP-4 effect.
Length of specimen C03, C04 and C05 was 350 mm and themagnitudes
of initial imperfection was 5.0 mm. Measured ultimatestrengths were
42.56 kN, 43.50 kN and 39.54 kN, respectively. Thedifference from
the average value were very small, which were1.8%, 4.0% and 5.8%,
respectively. However, specimen C03 andC05 failed at exural
buckling and specimen C04 failed at exu-raltorsional buckling,
which showed that the failure mode hadno effects on the exural
buckling strength.
The average ultimate strength of specimen C01, C02 and C06with
0.7 mm initial deection was 64.58 kN, which was muchgreater than
the average value of specimen C03, C04 and C05 as41.80 kN.
2.3.3. Loadaxial displacement curvesLoadaxial displacement
curves obtained from tests were
shown in Fig. 6. The axial compression load increased linearly
with
M. Liu et al. / EngineeringOne rigid plate was xed and the other
could only move axiallytoward the column to apply the axial
compressive load. Contactalgorithm was dened between the surface of
the rigid platesFig. 6. Loadaxial displacement curves obtained from
tests and FEA. (a) Loadaxialdisplacement of specimen C01, C02 and
C06 with 0.7 mm initial imperfection. (b)
Loadaxial displacement of specimen C03, C04 and C05 with 5 mm
initialimperfection. (c) Loadaxial displacement of specimen C07
without initialimperfection.
-
tructures 95 (2015) 127137Fig. 7. Mesh sensitivity analysis.132
M. Liu et al. / Engineering SThe initial imperfection of the column
followed a half-sinecurve with the maximum deection at mid-span
with magnitudeof 0.7 mm. The model was adjusted by modifying the
coordinatesof nodes.
3.2. Effect of residual stress
The residual stress of extruded aluminum alloy members isusually
lower than 20 MPa [29]. The distribution of residual stressacross
the studied section was shown in Fig. 9(a). The maximummagnitude
was 15.7 MPa. Stress distribution across the sectionand deformation
shape of the member with and without residualstress were nearly the
same, as shown in Fig. 9(b) and 9(c). Theaxial loadaxial
displacement curves coincided with each otherbefore reaching the
ultimate strength, as shown in Fig. 9(d). Theultimate strength was
59.06 kN with residual stress and 60.48 kNwithout residual stress.
The difference was only 2.40%, whichshowed very little inuence from
residual stress. Residual stresswas ignored in the following FEM
parametric studies.
3.3. Model verication
The measured material properties in Table 1 were adopted inFEM.
The comparisons of ultimate loads obtained from tests and
Fig. 8. FEM of the aluminum alloy column.
Fig. 9. Effect of residual stress. (a) The distribution of
initial residual stress. (b)Stress distribution of the column
without residual stress. (c) Stress distribution ofthe column with
residual stress. (d) Axial loadaxial displacement curve.
-
FEA were listed in Table 2. The mean value of Test/FEA was
0.99.The associated coefcient of variation was only 0.07.
There existed differences between the loadaxial
displacementcurves obtained from FEA and tests, as shown in Fig. 6.
However,the ultimate loads and the corresponding axial
displacementswhen the columns buckled globally were almost the
same.Furthermore, the loadaxial displacement curves obtained
fromFEA clearly showed the turning points on the ascending
branchwhich reected the reduction of the axial stiffness due to the
localbuckling.
Deformation of specimen C01 and C07 at global buckling
failureobtained from tests and FEA were shown in Fig. 10. The local
buck-ling and global buckling deformation agreed very well with
eachother.
Based on the comparisons in ultimate strengths, loadaxial
dis-placement curves and deformations obtained from FEA and tests,
itwas concluded that the presented FEM could accurately predict
thebehavior of aluminum alloy columns with section subject toaxial
compression. The validated FEM was used thereafter in theparametric
studies to assess current design codes for aluminumalloy
columns.
4. Section optimization
M. Liu et al. / Engineering Structures 95 (2015) 127137 133Fig.
10. Comparison of buckling modes obtained from tests and FEA. (a)
SpecimenC01 failed at the exural buckling. (b) Specimen C07 failed
at local buckling.The section was made up of 6 plates, as shown in
Fig. 11.FSM software CUFSM was used to obtain the elastic buckling
stressof the column with different plate thickness and column
length.
Effects of plate thickness on elastic buckling stress were
shownin Fig. 12. It was seen that the thickness of plate t2, t3 and
t6 had noinuences on global buckling stress, as shown inFig. 12(b),
(c) and (f). With the increase in t1 thickness, the columnglobal
buckling stress increased. However, the increments werevery small,
as shown in Fig. 12(a). Except for small thickness, theincrease in
the thickness of t4 and t5, did not lead to thecorresponding
increase in global buckling stress, as shown inFig. 12(d) and (e).
That was, for the column section studied, itwas not an effective
way to improve the global buckling stressby increasing the plate
thickness.
While for short columns less than 100 mm, t1 thickness
greatlyaffected the buckling stress and bucking modes, as shown
inFig. 12(a). When t1 was 0.2 mm or 0.3 mm, it only occurred
localbucking. When t1 was 0.4 mm or 0.5 mm, it occurred both
localand distortional buckling; however, the local buckling
dominatedthe column failure. When t1 was 0.6 mm or 0.7 mm, it
occurredboth local and distortional buckling and the distortional
bucklingdominated the column failure. Under this circumstance, the
buck-ling capacity of the column could not be improved by
increasing t1thickness. When t1 was 0.7 mm, the local buckling
stress exceededaluminum alloy yield stress. That was, no local
buckling occurredand the whole plate was effective.
Plate t2 was a cantilever plate and was vulnerable to local
buck-ling. When t2 was less than 0.9 mm, short columns with
lengthbeing less than 100 mm failed at local buckling, as shown
inFig. 12(b). When t2 was greater than 1.0 mm, the column failedat
distortional buckling. The increase in t2 thickness did notincrease
the local or distortional buckling stress of the column.
Plate t3 was a stiffened plate in the section. When t3
wasgreater than 0.5 mm, the increase in t3 thickness did not lead
tothe increase of the critical buckling stress accordingly, as
shownin Fig. 12(c).
Plate t4 was a cantilever plate and was vulnerable to
distor-tional buckling. The critical elastic distortional buckling
stresswas signicantly inuenced by t4 thickness. With the increase
int4 thickness, the critical elastic distortional buckling
stressincreased. And the column behavior was controlled by
localFig. 11. Plates division.
-
buckling when t4 was 1.5 mm. Furthermore, it was not efcient
toincrease t4 thickness when it was greater than 1.5 mm since
thecritical elastic distortional buckling stress had exceeded the
yieldstress of aluminum alloy, as shown in Fig. 12(d).
Pate t5 was a stiffened plate and its local buckling stress
keptconstant when t5 increased from 0.5 mm to 2.0 mm. However,the
distortional buckling stress increased along with the increasein t5
thickness, as shown in Fig. 12(e). The elastic local bucklingstress
was less than the elastic distortional buckling stress whent5 was
greater than 1.5 mm. That was, increase in t5 thicknesshad no
signicance under this circumstance.
The existence of plate t6 did not increase the buckling stress
ofthe column, as shown in Fig. 12(f). Plate t6 was not a structural
partin the section. It was to satisfy the leak proof
requirement.
5. Current design codes
5.1. Current design codes for aluminum alloy column
EC9 [6], AA [15] and GB50429 [17] provide design rules for
alu-minum columns with traditional section shapes. AISI [21,22]
for
of t1
134 M. Liu et al. / Engineering Structures 95 (2015) 127137Fig.
12. Effects of plate thickness on elastic buckling stress of the
column. (a) Effects
elastic buckling stress (t1 = 0.6 mm, thickness of other plates
are 1.5 mm). (c) Effects ofEffects of t4 on elastic buckling stress
(t1 = 0.6 mm, thickness of other plates are 1.5 mm)1.5 mm). (f)
Effects of t6 on elastic buckling stress (t1 = 0.6 mm, thickness of
other plateon elastic buckling stress (thickness of other plates
are 1.5 mm). (b) Effects of t2 on
t3 on elastic buckling stress (t1 = 0.6 mm, thickness of other
plates are 1.5 mm). (d). (e) Effects of t5 on elastic buckling
stress (t1 = 0.6 mm, thickness of other plates ares are 1.5
mm).
-
cold-formed steel structures was also used to obtain the
ultimatestrength of thin-walled aluminum alloy column by
substitutingthe material properties of steel with those of aluminum
alloy.
The ultimate strength of the column under axial compressiveload
is the minimum strength of global buckling, local bucklingand
interaction of local and global buckling in AA [15]. Globalbuckling
strength is calculated based on Euler formula. Local buck-ling is
the summation of the local buckling strength of each plate.The
interaction of local and global buckling is calculated when
thestrength of local buckling is lower than that of global
buckling. Thedesign strength is reduced when considering the effect
of localbuckling in AA Specication.
EC9 and GB50429 adopt Perry curve for the design of axial
com-pressive column. The stability factor of global buckling is
Table 3Comparisons of ultimate strengths obtained from design
codes and FEA.
Comparison PFEAPAA
PFEAPAISI
PFEAPEC9
PFEAPGB
PFEAPDSM
Mean 1.21 1.18 1.47 1.62 1.13COV 0.103 0.083 0.101 0.145
0.107
M. Liu et al. / Engineering Structures 95 (2015) 127137 135Fig.
13. Comparisons of results by FEA and design codes. (a) Comparison
of ultimate streand FEA. (c) Comparison of ultimate strength
obtained by EC9 and FEA. (d) Comparisostrength obtained by DSM and
FEA.ngth obtained by AA and FEA. (b) Comparison of ultimate
strength obtained by AISIn of ultimate strength obtained by GB50429
and FEA. (e) Comparison of ultimate
-
calculmetho
minumDS
calculbers.
Pne
5.2. Pa
t4: 2.0 mm;
5.3. Comparison of ultimate strengths
Table 3 gave the mean value and Coefcient of Variation (COV)of
the ratios of FEA results and design codes predictions.Comparisons
of ultimate strengths by FEA and design codes wereshown in Figs.
1316. Results of EC9 were very close to GB50429since they both
considered initial imperfections based on Perrycurve. Ratios of
PFEA/PEC9 and PFEA/PGB were 1.47 and 1.62 withthe corresponding COV
of 0.101 and 0.145, respectively. GB50429considered a bigger
imperfection, which leaded to the ultimatestrength being the most
conservative among these design meth-ods. AA predictions were also
conservative with PFEA/PAA of 1.21and COV of 0.103. Results by AISI
were close to DSM and were rela-tively economic with PFEA/PAISI and
PFEA/PDSM of 1.18 and 1.13 andthe corresponding COV of 0.083 and
0.107, respectively.
Fig. 13 and 14 compared FEA and design codes calculations
foraluminum alloy column with section. From Fig. 13 and 14, itwas
seen that current design codes were all conservative to predictthe
ultimate strength. The column design curves were divided into3
parts in AA. The curves of EC9 and GB50429 agreed well witheach
other. And GB50429 were the most conservative prediction.
DSM exural buckling curve agreed well with that obtainedfrom
FEA, as shown in Fig. 15. Fig. 16 showed the strength ratio
dis-tribution, and the majority of PFEA/PDSM was between 1.05 and
1.15.
Fig. 15. Comparisons of results by FEA and DSM.
136 truc t5: 2.0 mm t6: 1.0 mm.
(2) group II: (30 specimens) t1: 0.8, 1.2, 1.5 mm; t2 and
t3:0.6, 0.8, 1.0, 1.2, 1.4, 1.5, 1.6, 1.8, 2.0, 2.2,
2.4 mm; t4:2.0 mm; t5:2.0 mm; t6:1.0 mm.
(3) group III: (30 specimens) t1:0.8 mm; t2 and t3: 1.5 mm; t4:
1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0 mm; t5: 1.0,
2.0, 3.0 mm; t6: 1.0 mm.
(4) group IV: (30 specimens) t1: 0.8 mm; t2 and t3: 1.0, 1.5,
2.0 mm;The veried FEMwas used to obtain the ultimate strength of
thecolumns with various parameters. The obtained ultimate
strengthswere compared with those calculated by design codes.
The 0.2% proof stress of the aluminum alloy obtained from
testswas adopted in FEM, which was 200.4 MPa. In order to
eliminatethe effects of local buckling at column ends, the
Multi-PointsConstraint (MPC) was used to simulate the xed boundary
condi-tion in FEM. The Beam type MPC was used ensuring a rigid
beamconnection in order to constrain the displacement and rotation
ofeach slave nodes to those of the control point. The
displacementload was applied at the control point.
The parametric studies consisted of 615 specimens including
5lengths and 123 sections with different plate thickness.
Studiedcolumn lengths were 600, 1200, 1800, 2400, 3000 mm,
respec-tively. The section dimension remained unchanged while
platethickness varied. The column lengths and plates thicknesses
werecarefully selected to ensure global buckling occur.
Four groups of sections were studied and plate thicknesses
ineach group were:
(1) group I: (33 specimens) t1: 0.5, 0.6, 0.7, 0.8, 0.9, 1.0,
1.1, 1.2, 1.3, 1.4, 1.5 mm; t2 and t3: 1.0, 1.5, 2.0 mm;Pne is the
global buckling strength of the column; Py is then yielding
strength; kc is dimensionless slenderness ratio.
rameter studieswheresectiorule of DSM for global buckling
strength is
0:658k2c
Py for kc 6 1:5
0:877k2c
Py for kc > 1:5
8>: 3their interactions are all taken into consideration. The
columndesignis also used to predict the ultimate strength of the
alu-alloy column with section in this paper.
M [21,22] assumes that the full section is effective whenating
the ultimate strength of thin-walled structural mem-Global
buckling, local buckling, distortional buckling andsiders the
effect of local buckling using effective width method,whichated
using PerryRoberson formula. Effective thicknessd is applied to
consider the effect of local buckling. AISI con-
M. Liu et al. / Engineering S t4: 2.0 mm; t5: 1.0, 1.2, 1.4,
1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0 mm; t6: 1.0 mm.Fig. 14.
Comparisons of ultimate strengths by FEA and design codes (t1 = 0.9
mm;t2 = 2.0 mm; t3 = 1.0 mm; t4 = 2.0 mm; t5 = 1.0 mm; t6 = 1.0
mm).
tures 95 (2015) 127137Therefore, it was concluded that DSM
exural buckling curve pre-dicted the ultimate strength more
accurately for aluminum alloycolumn with section under axial
compressive load.
-
References
[1] Mazzolani FM. Competing issues for aluminium alloys in
structuralengineering. Progr Struct Eng Mater 2004;6(2):18596.
[2] Summers PT, Case SW, Lattimer BY. Residual mechanical
properties ofaluminum alloys AA5083-H116 and AA6061-T651 after re.
Eng Struct2014;76(1):4961.
[3] Fogle EJ, Lattimer BY, Feih S, Kandare E, Mouritz AP, Case
Scott W. Compressionload failure of aluminum plates due to re. Eng
Struct 2012;34(1):15562.
[4] Rasmussen KJR, Rondal J. Strength curves for aluminum alloy
columns. EngStruct 2000;22(11):150517.
M. Liu et al. / Engineering Structures 95 (2015) 127137 1376.
Conclusions and suggestions
This paper presented experimental and numerical investiga-tions
on the behaviors of section aluminum alloy columnsunder axial
compression. Seven axial compression tests were car-ried out. The
ultimate strengths and failure modes were reported.Columns with
length of 190 mm failed at local buckling; and thosewith length of
350 mm failed at global buckling. A FEMwere devel-oped and veried
by tests in three aspects including ultimate loads,loadaxial
displacement curves and deformations.
Effects of plate thickness and column length on the elastic
buck-ling stress were investigated by FSM. The thickness of plate
t2, t3and t6 had no signicant inuences on global buckling
stress.With the increase in t1 thickness, the column global
buckling stressincreased slightly. Except for small thickness, the
increase in t4 andt5 thickness did not increase the global buckling
stress.
Parametric studies on 615 specimens were presented usingFEM.
Ultimate strengths obtained by FEA were compared withthose
calculated by AA, AISI, EC9, GB50429, as well as DSM.Results of EC9
were close to GB50429 because they both consid-ered initial
imperfections based on Perry curve. GB50429 consid-ered
imperfection greater than EC9, which leaded to the mostconservative
predictions. AA was also a little conservative.
Fig. 16. Strength ratio distribution.Results of AISI were close
to DSM and they both agreed well withFEA results. DSM exural
buckling equation which considered thegross area could predict the
ultimate strength for section col-umn under axial compression more
accurately and conveniently.
Acknowledgements
The supports given to this work by the Independent
InnovationFoundation of Shandong University (No. 2014HW013) are
greatlyacknowledged.[5] Maljaars J, Twilta L, Soetens F. Flexural
buckling of re exposed aluminumcolumns. Fire Saf J
2009;44(5):7117.
[6] EC9. Eurocode 9: design of aluminum structuresPart 11:
General rulesgeneral rules and rules for buildings. DD ENV
1999-1-1:2000. Final draftOctober 2000. European Committee for
Standardization; 2000.
[7] Manganiello M, De Matteis G, Landolfo R. Inelastic exural
strength ofaluminium alloys structures. Eng Struct
2006;28(4):593608.
[8] Maljaars J, Soetens F, Snijder HH. Local buckling of
aluminium structuresexposed to re, Part 1: tests. Thin-Walled
Struct 2009;47(11):140417.
[9] Adeoti GO, Fan F, Wang YJ, Zhai XM. Stability of 6082-T6
aluminium alloycolumns with H-section and rectangular hollow
sections. Thin-Walled Struct2015;89(1):116.
[10] Yuan HX, Wang YQ, Chang T, Du XX, Bu YD, Shi YJ. Local
buckling andpostbuckling strength of extruded aluminium alloy stub
columns with slenderI-sections. Thin-Walled Struct
2015;90(1):1409.
[11] Su MN, Young B, Gardner L. Testing and design of aluminium
alloy crosssections in compression. J Struct Eng
2014;14(9):111.
[12] Su MN, Young B, Gardner L. Deformation-based design of
aluminium alloybeams. Eng Struct 2014;80(1):33949.
[13] Wang YJ, Fan F, Lin SB. Experimental investigation on the
stability ofaluminum alloy 6082 circular tubes in axial
compression. Thin-WalledStruct 2015;89(1):5466.
[14] Zhu JH, Young B. Experimental investigation of aluminum
alloy circular hollowsection columns. Eng Struct
2006;28(2):20715.
[15] AA. American aluminum design manual. Washington, DC: The
AluminumAssociation; 2005.
[16] AS/NZS. Aluminum structures. Part 1: Limit state design.
Australian/NewZealand Standard AS/NZS 1664.1:1997. Sydney,
Australia: Standards Australia;1997.
[17] GB 50429-2007. Code for design of aluminum structures.
Beijing: ChinaArchitecture & Building Press; 2007 [In
Chinese].
[18] Schafer BW. Review: the direct strength method of
cold-formed steel memberdesign. J Constr Steel Res
2008;64(78):76678.
[19] Bulson PS. The treatment of thin-walled aluminum sections
in Eurocode 9.Thin-walled Struct 1997;29(4):312.
[20] Schafer BW, Pekz T. Direct strength prediction of
cold-formed steel membersusing numerical elastic buckling
solutions. In: Proceeding of 14th internationalspecialty conference
on cold-formed steel structures. Rolla, MO: University
ofMissouri-Rolla; 1998. p. 6976.
[21] AISI. North American specication for the design of
cold-formed steelstructural members. Washington, DC: American Iron
and Steel Institute; 2001.
[22] Supplement to the North American Specication for the design
of cold formedsteel structural member. Washington, DC: American
Iron and Steel Institute;2004.
[23] Zhu JH, Young B. Aluminum alloy tubular columnspart I: nite
elementmodeling and test verication. Thin-Walled Struct
2006;44(9):9618.
[24] Zhu JH, Young B. Aluminum alloy tubular columnspart II:
parametric studyand design using direct strength method.
Thin-Walled Struct2006;44(9):96985.
[25] CUFSM: Elastic Buckling Analysis of Thin-Walled Members by
Finite StripAnalysis. CUFSM v4.05. ;2012.
[26] ABAQUS Analysis Users Manual, Version 6.10.1. ABAQUS Inc;
2009.[27] Ramberg W, Osgood WR. Description of stressstrain curves
by three
parameters. National Advisory Committee for Aeronautics; 1943.
p. 902.[28] Minshall H. CRC handbook of chemistry and physics. In:
Lide DR, editor. 73rd
ed. Boca Raton, FL: CRC Press; 1992.[29] Mazzolani FM. Aluminum
alloy structures. 2nd ed. London: E & FN Spon; 1995.
Buckling behaviors of section aluminum alloy columns under axial
compression1 Introduction2 Experimental studies2.1 Material
properties2.2 Column test2.3 Test results2.3.1 Failure modes2.3.2
Ultimate strengths2.3.3 Loadaxial displacement curves
3 Finite element model and verification3.1 Finite element
model3.2 Effect of residual stress3.3 Model verification
4 Section optimization5 Current design codes5.1 Current design
codes for aluminum alloy column5.2 Parameter studies5.3 Comparison
of ultimate strengths
6 Conclusions and suggestionsAcknowledgementsReferences