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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

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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

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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.

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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.

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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

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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



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



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.


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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

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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.


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(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

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[5] ABAQUS analysis users manual, Version 6.5. ABAQUS, Inc., 2004.

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