1-s2.0-S0263823106001418-main
Transcript of 1-s2.0-S0263823106001418-main
-
8/10/2019 1-s2.0-S0263823106001418-main
1/8
Thin-Walled Structures 44 (2006) 961968
Aluminum alloy tubular columnsPart I:
Finite element modeling and test verification
Ji-Hua Zhu, Ben Young
Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China
Received 23 February 2006; received in revised form 11 August 2006; accepted 18 August 2006
Available online 12 October 2006
Abstract
A numerical investigation on fixed-ended aluminum alloy tubular columns of square and rectangular hollow sections is described in
this paper. The fixed-ended column tests were conducted that included columns with both ends transversely welded to aluminum end
plates using the tungsten inert gas welding method, and columns without welding of end plates. The specimens were extruded from
aluminum alloy of 6061-T6 and 6063-T5. The failure modes included local buckling, flexural buckling, interaction of local and flexural
buckling, as well as failure in the heat-affected zone (HAZ). An accurate finite element model (FEM) was developed. The initial local and
overall geometric imperfections were incorporated in the model. The non-welded and welded material nonlinearities were considered in
the analysis. The welded columns were modeled having different HAZ extension at the ends of the column of 25 and 30 mm. The
nonlinear FEM was verified against experimental results. It is shown that the calibrated model provides accurate predictions of the
experimental loads and failure modes of the tested columns. The load-shortening curves predicted by the finite element analysis are also
compared with the test results.
r 2006 Elsevier Ltd. All rights reserved.
Keywords: Aluminum alloys; Buckling; Column; Experimental investigation; Finite element analysis; Heat-affected zone; Transverse welds
1. Introduction
Finite element analysis (FEA) is a powerful tool that can
be employed to a wide range of applications, such as
aluminium structures. The finite element approach pro-
vides many advantages over conducting physical experi-
ments, especially when a parametric study of cross-section
geometry is involved. FEA is capable to predict the
ultimate loads and failure modes of aluminum structural
members, provided that the finite element model (FEM) is
reliable. Therefore, it is necessary to verify the modelagainst experimental results.
Aluminum tubular members are used in curtain walls,
space structures and other structural applications, and
these members can be joined by welding. The aluminum
tubular members are normally manufactured by heat-
treated aluminum alloys. This is because the heat-treated
alloys have notably higher yield stress than non-heat-
treated alloys. The advantages of using aluminum alloys as
a structural material are the high strength-to-weight ratio,
lightness, corrosion resistance and ease of production.
However, when heat-treated aluminum alloys are welded,
the heat generated from the welding reduces the material
strength significantly in a localized region, and this is
known as the heat-affected zone (HAZ) softening. It is
assumed that the HAZ extends 1 in (25.4 mm) to each side
of the center of a weld [1]. In the case of the 6000 Series
aluminum alloys, the heat generated from the welding can
locally reduce the parent metal strength by nearly half[2].The effects of welding on the strength and behavior of
aluminum structural members depend on the direction,
location and number of welds. In aluminum structures,
welds are mainly divided into two types, namely (1)
transverse welds; and (2) longitudinal welds. Generally,
transverse welds are often used in connections, whereas
longitudinal welds are used for the fabrication of built-up
members [3]. Structural members such as columns may
easily connect to other structural members or parts by
welding at the ends of the columns. Hence, it is important
ARTICLE IN PRESS
www.elsevier.com/locate/tws
0263-8231/$ - see front matterr 2006 Elsevier Ltd. All rights reserved.
doi:10.1016/j.tws.2006.08.011
Corresponding author. Tel.: +852 2859 2674; fax: +852 2559 5337.
E-mail address: [email protected] (B. Young).
http://www.elsevier.com/locate/twshttp://localhost/var/www/apps/conversion/tmp/scratch_2/dx.doi.org/10.1016/j.tws.2006.08.011mailto:[email protected]:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_2/dx.doi.org/10.1016/j.tws.2006.08.011http://www.elsevier.com/locate/tws -
8/10/2019 1-s2.0-S0263823106001418-main
2/8
to investigate the behavior of aluminum columns with
transverse welds at the ends of the columns.
A series of fixed-ended compression tests on aluminumsquare and rectangular hollow section (RHS) columns has
been conducted by Zhu and Young [4]. The test program
included columns with both ends transversely welded to
aluminum end plates using tungsten inert gas (TIG)
welding method, and columns without welding of end
plates. Following the experimental investigation, a numer-
ical investigation using FEA is performed and presented in
this paper. The objective of the numerical investigation
presented in this paper is to develop an advanced non-
linear FEM for the investigation on the strengths and
behavior of fixed-ended aluminum columns with
and without transverse welds. Finite element programABAQUS [5]was used to perform the numerical analysis.
Initial geometric imperfections and material non-linearity
were included in the model. The FEM was verified against
the column test results conducted by Zhu and Young[4].
2. Summary of test program
The test program presented in Zhu and Young [4]
provided experimental ultimate loads and failure modes of
aluminum alloy square and RHSs compressed between
fixed ends. The test specimens were fabricated by extrusion
using 6063-T5 and 6061-T6 heat-treated aluminum alloys.
The test program included 25 fixed-ended columns with
both ends welded to aluminum end plates, and 11 fixed-
ended columns without the welding of end plates. In this
paper, the term welded column refers to a specimen with
transverse welds at the ends of the column, whereas the
term non-welded column refers to a specimen without
transverse welds. The testing conditions of the welded and
non-welded columns are identical, other than the absence
of welding in the non-welded columns.
The experimental program consisted of five test series
with different cross-section geometry and type of alumi-
num alloy, as shown in Table 1 using the symbols
illustrated in Fig. 1. The series N-S1, N-R1 and N-R2
refer to the specimens of normal strength aluminum alloy
6063-T5 in nominal cross-section dimension of
44 44 1.1, 100 44 1.2 and 10044 3.0 mm3, re-spectively. The series H-R1 and H-R2 refer to the
specimens of high strength aluminum alloy 6061-T6 in
nominal cross-section dimension of 10044 1.2 and
100 44 3.0 mm3, respectively. The measured cross-sec-
tion dimensions of each specimen are detailed in Zhu and
Young[4]. The specimens were tested between fixed ends at
various column lengths ranging from 300 to 3000 mm. The
test rig and operation are also detailed in Zhu and Young
[4]. The experimental ultimate loads (PExp) and failure
modes observed at ultimate loads obtained from the non-
welded and welded column tests are shown in Tables 27.
ARTICLE IN PRESS
Nomenclature
B overall width of SHS and RHS
COV coefficient of variation
E initial Youngs modulus
e axial shorteningFEA finite element analysis
FEM finite element model
H overall depth of SHS and RHS
L length of specimen
P axial load
PExp experimental ultimate load of column (test
strength)
PFEA ultimate load predicted by FEA
PFEA25 ultimate load predicted by FEA using 25 mm
heat-affected zone extension for welded column
PFEA30 ultimate load predicted by FEA using 30 mm
heat-affected zone extension for welded column
t thickness of section
e
engineering strainef elongation (tensile strain) at fracture
pltrue true plastic straineu elongation (tensile strain) at ultimate tensile
stress
s engineering stress
strue true stress
s0.2 static 0.2% proof stress
su static ultimate tensile strength.
Table 1
Nominal specimen dimensions
Test series Type of material Dimension HB t (mm)
N-S1 6063-T5 44 44 1.1
N-R1 6063-T5 100 44 1.2
N-R2 6063-T5 100 44 3.0
H-R1 6061-T6 100 44 1.2
H-R2 6061-T6 100 44 3.0
Note: 1in 25.4mm.
t
B
B
B
tH
SHS (b) RHS(a)
Fig. 1. Definition of symbols.
J.-H. Zhu, B. Young / Thin-Walled Structures 44 (2006) 961968962
-
8/10/2019 1-s2.0-S0263823106001418-main
3/8
-
8/10/2019 1-s2.0-S0263823106001418-main
4/8
same approach as detailed in Yan and Young [6] for cold-
formed steel columns.
3.2. Type of element and finite element mesh
Shell element is one of the most appropriate types of
elements for modeling thin-walled metal structures. The
4-noded doubly curved shell elements with reduced
integration S4R were used in the model. The S4R element
has six degrees of freedom per node and proved to give
accurate solutions from previous research as described in
Yan and Young[6], and Ellobody and Young[7].
The size of the finite element mesh of 1010mm2
(length by width) was used in the modeling of the non-
welded columns. The 1010mm2 element size has been
used to simulate axially loaded fixed-ended columns and
shown to provide good simulation results [6].
As mentioned in Section 1 of the paper, the heat-treated
aluminum alloys suffer loss of strength in a localized region
when welding is involved, and this is known as HAZ
softening. The welded columns were modeled by dividing
ARTICLE IN PRESS
Table 3
Comparison of test and FEA results for welded columns of Series N-S1
Specimen Experimental FEA Comparison
PExp (kN) Failure mode PFEA30 (kN) PFEA25 (kN) Failure mode PExp
PFEA30
PExp
PFEA25
N-S1-W-L300 18.8 HAZ 16.5 17.0 HAZ 1.14 1.11N-S1-W-L1000 19.2 HAZ 17.1 17.6 HAZ 1.13 1.09
N-S1-W-L1650 19.8 HAZ 17.7 18.5 HAZ 1.12 1.07
N-S1-W-L2350 18.4 F 15.6 16.2 F 1.18 1.14
N-S1-W-L3000 15.2 F 12.8 13.2 F 1.19 1.15
Mean 1.15 1.11
COV 0.028 0.029
Note: 1 kip 4.45kN.
Table 4
Comparison of test and FEA results for welded columns of Series N-R1
Specimen Experimental FEA Comparison
PExp (kN) Failure mode PFEA30 (kN) PFEA25 (kN) Failure mode PExp
PFEA30
PExp
PFEA25
N-R1-W-L300 26.4 HAZ 28.8 28.8 HAZ 0.92 0.92
N-R1-W-L1000 27.7 HAZ 27.4 27.9 HAZ 1.01 0.99
N-R1-W-L1650 28.5 F+L 26.1 26.8 HAZ 1.09 1.06
N-R1-W-L2350 25.1 F+L 24.2 24.9 F+L 1.04 1.01
N-R1-W-L3000 23.2 F+L 21.8 22.2 F+L 1.07 1.05
Mean 1.02 1.01
COV 0.066 0.057
Note: 1 kip 4.45kN.
Table 5
Comparison of test and FEA results for welded columns of Series N-R2
Specimen Experimental FEA Comparison
PExp (kN) Failure mode PFEA30 (kN) PFEA25 (kN) Failure mode PExp
PFEA30
PExp
PFEA25
N-R2-W-L300 101.0 HAZ 91.1 96.4 HAZ 1.07 1.01
N-R2-W-L1000 89.7 HAZ 89.0 94.0 HAZ 1.01 0.95
N-R2-W-L1650 85.4 F 81.5 84.1 HAZ 1.05 1.02
N-R2-W-L2350 74.3 F 66.8 69.2 F 1.11 1.07
N-R2-W-L3000 60.4 F 55.1 56.4 F 1.10 1.07
Mean 1.07 1.02
COV 0.038 0.048
Note: 1 kip 4.45kN.
J.-H. Zhu, B. Young / Thin-Walled Structures 44 (2006) 961968964
-
8/10/2019 1-s2.0-S0263823106001418-main
5/8
-
8/10/2019 1-s2.0-S0263823106001418-main
6/8
3.3. Boundary condition and loading method
The fixed-ended boundary condition was simulated by
restraining all the degrees of freedom of the nodes at both
ends, except for the translational degree of freedom in the
axial direction at one end of the column. The nodes other
than the two ends were free to translate and rotate in anydirections. The displacement control loading method,
which is identical to that used in the column tests, was
used in the FEM. Compressive axial load was applied to
the column by specifying an axial displacement to the
nodes at one end of the column.
3.4. Material properties
In the modeling of non-welded columns, the material
properties obtained from the non-welded tensile coupon
tests were used. In the modeling of welded columns, the
material properties obtained from the non-welded tensile
coupon tests were used for the main body of the
columns, whereas the material properties obtained from
the welded tensile coupon tests were used for the HAZ
regions at both ends of the columns. The material
properties of the respective test series were used in the
FEM.
In the linear analysis stage of the simulation, the material
properties of the columns were only defined by density,
initial Youngs modulus and Poissons ratio. In the
non-linear analysis stage, material non-linearity or plas-
ticity was included in the FEM using a mathematical
model known as the incremental plasticity model [5], in
which true stresses (strue) and true plastic strains pltrue were
specified. The true stresses and true plastic strains were
obtained from the static engineering stresses (s) and strains
(e) using strue s1 , andpltrue ln1 strue=E, as
specified in ABAQUS [5], where E is the initial Youngs
modulus of the static engineering stressstrain curve.
The incremental plasticity model required only a
range of the true stressstrain curve from the point
corresponding to the last value of the linear range of the
static engineering stressstrain curve to the ultimate point
of the true stressstrain curve. Fig. 2 shows the stress
strain curve of the non-welded material plasticity for Series
H-R1.
3.5. Initial geometric imperfections
Both initial local and overall geometric imperfections
were incorporated in the model. Superposition of local
buckling mode and overall buckling mode with the
measured magnitudes was carried out. These buckling
modes were obtained by eigenvalue analysis of the columns
with very high value of width-to-thickness ratio and very
low value of width-to-thickness ratio to ensure
local and overall buckling occurs, respectively. Only the
lowest buckling mode (eigenmode 1) is used in the
eigenvalue analysis. All buckling modes predicted by
ABAQUS eigenvalue analysis are generalized to 1.0;
therefore, the buckling modes are factored by the measured
magnitudes of the initial local and overall geometric
imperfections.
4. Test verification
The developed FEM was verified against the experi-
mental results. For the non-welded columns, the ultimate
loads and failure modes predicted by the FEA are
compared with the experimental results as shown in Table
2. It is shown that the ultimate loads (PFEA) obtained from
the FEA are in good agreement with the experimental
ultimate loads (PExp). Generally, the ultimate loads
predicted by the FEA are slightly lower than the
experimental ultimate loads, except for the specimens
H-R1-NW-L300 and H-R1-NW-L1000. The experimen-tal-to-FEA ultimate load ratio (PExp/PFEA) for these
two specimens are 0.94 and 0.95, respectively. The mean
value of the experimental-to-FEA ultimate load ratio is
1.02 with the corresponding coefficient of variation
(COV) of 0.045 for the non-welded columns, as shown in
Table 2.
For the welded columns, both the ultimate loads
predicted by the FEA using the HAZ extension of 25 mm
(PFEA25) and 30 m m (PFEA30) are compared with the
experimental results as shown in Tables 37 for Series
N-S1, N-R1, N-R2, H-R1 and H-R2, respectively. It is
shown that the PFEA25
are in better agreement with the
experimental ultimate loads compared with the PFEA30.
The mean values of the experimental-to-FEA ultimate load
ratio (PExp/PFEA25) are 1.11, 1.01, 1.02, 0.99 and 1.11 with
the corresponding COV of 0.029, 0.057, 0.048, 0.046
and 0.056 for Series N-S1, N-R1, N-R2, H-R1 and H-
R2, respectively. The mean values of the load ratio PExp/
PFEA30 are 1.15, 1.02, 1.07, 1.04 and 1.14 with the
corresponding COV of 0.028, 0.066, 0.038, 0.043 and
0.056 for Series N-S1, N-R1, N-R2, H-R1 and H-R2,
respectively.
The failure modes at ultimate load obtained from the
tests and FEA for each specimen are also shown inTables
27. The observed failure modes included local buckling
ARTICLE IN PRESS
0
50
100
150
200
250
300
350
7 8
Strain, (%)
Stress,
(
MPa)
Engineeringcurve
True curve
Plasticity
6543210
Fig. 2. Modeling of non-welded material plasticity for Series H-R1.
J.-H. Zhu, B. Young / Thin-Walled Structures 44 (2006) 961968966
-
8/10/2019 1-s2.0-S0263823106001418-main
7/8
(L), flexural buckling (F), interaction of local and flexural
buckling (L+F), and failure in the HAZ. The failure
modes predicted by the FEA are in good agreement
with those observed in the tests, except for the specimens
N-R2-NW-L1000, N-R1-W-L1650 and N-R2-W-L1650.
Fig. 3 shows the comparison of the load-shortening
curves obtained from the test and predicted by the FEA
for the non-welded specimen H-R1-NW-L1000. It is
shown that the FEA curve follows the experimental curve
closely, except that the ultimate load predicted by the
FEA is slightly higher than the experimental value.
Fig. 4 also shows the load-shortening curves for the
welded specimen H-R1-W-L2350. The load-shortening
curves predicted by the FEA using the HAZ extension of
25 and 30 mm are shown in Fig. 4. Besides, Fig. 5(a)
shows the photograph of specimen H-R2-NW-L1000
immediately after the ultimate load has reached. The
specimen failed in flexural buckling. Fig. 5(b) shows the
deformed shape of the specimen predicted by the
FEA right after the ultimate load. The resemblance of
Fig. 5(a) and (b) demonstrates the reliability of the FEA
predictions.
5. Conclusions
This paper presents a numerical investigation on fixed-
ended aluminum alloy square and RHSs non-welded and
welded columns using FEA. An advanced non-linear FEM
incorporating geometric imperfections and material non-
linearity was developed. Heat-treated aluminum alloys of
6063-T5 and 6061-T6 material were investigated. The
welded columns were modeled by dividing the column intodifferent portions along the column length, so that the
HAZ softening at both ends of the welded columns was
included in the simulation. Two different dimensions of the
HAZ extension were considered in the study that equal to
25 and 30 mm. The FEM was verified against the
previously reported test results that included five test series
with column length varied from 300 to 3000 mm. It is
shown that the FEM provides accurate predictions of the
experimental ultimate loads and failure modes for both the
non-welded and welded columns. It is also shown that
ultimate loads predicted by the FEA using the HAZ
extension of 25 mm are in closer agreement with
the experimental results compared to the ultimate
loads predicted by the FEA using the HAZ extension of
30 mm.
References
[1] AA. Aluminum design manual. Washington, DC: The Aluminum
Association; 2005.
[2] Mazzolani FM. Aluminum alloy structures. 2nd ed. London: E & FN
Spon; 1995.
[3] Kissell JR, Ferry RL. Aluminum structuresa guide to their
specifications and design. 2nd ed. New York: Wiley; 2002.
[4] Zhu JH, Young B. Test and design of aluminum alloys compression
members. J Struct Eng 2006;132(7):1095107.
ARTICLE IN PRESS
0
10
20
30
40
50
60
5
Axial shortening, e (mm)
Axial
load,
P(
kN)
Test
FEA
43210
Fig. 3. Comparison of experimental and FEA axial load-shortening
curves for specimen H-R1-NW-L1000.
0
5
10
15
20
25
30
35
0 1 5
Axial shortening, e (mm)
Axialload,
P(
kN)
FEA30Test
FEA25
432
Fig. 4. Comparison of experimental and FEA axial load-shortening
curves for specimen H-R1-W-L2350.
Fig. 5. Comparison of experimental and FEA deformed shapes for
specimen H-R2-NW-L1000.
J.-H. Zhu, B. Young / Thin-Walled Structures 44 (2006) 961968 967
-
8/10/2019 1-s2.0-S0263823106001418-main
8/8
[5] ABAQUS analysis users manual, Version 6.5. ABAQUS, Inc., 2004.
[6] Yan J, Young B. Numerical investigation of channel columns with
complex stiffenersPart I: Tests verification. Thin-Walled Struct
2004;42(6):88393.
[7] Ellobody E, Young B. Structural performance of cold-formed high
strength stainless steel columns. J Construct Steel Res 2005;61(12):
163149.
[8] AS/ NZS. Aluminum structures Part 1: Limit state design, Australian/
New Zealand Standard AS/NZS 1664.1:1997. Sydney, Australia:
Standards Australia; 1997.
[9] EC9. Eurocode 9: Design of aluminum structuresPart 1-1: General
rulesGeneral rules and rules for buildings, DD ENV 1999-1-1:2000,
Final Draft October 2000. European Committee for Standardization,
2000.
ARTICLE IN PRESS
J.-H. Zhu, B. Young / Thin-Walled Structures 44 (2006) 961968968