aluminum tubular sections subjected to web crippling—part i:: tests and finite element analysis

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Thin-Walled Structures 46 (2008) 339–351

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Aluminum tubular sections subjected to web crippling—Part I:Tests and finite element analysis

Feng Zhou, Ben Young�

Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China

Received 20 April 2007; accepted 8 October 2007

Available online 26 November 2007

Abstract

A series of tests on aluminum square and rectangular hollow sections subjected to web crippling is presented. A total of 150 web

crippling tests were conducted. The web crippling tests were conducted under two loading conditions of end-two-flange (ETF) and

interior-two-flange (ITF). The concentrated load was applied by means of bearing plates, which act across the full flange width of the

specimen sections. Different bearing lengths were investigated. The test specimens were fabricated by extrusion using 6063-T5 and 6061-

T6 heat-treated aluminum alloys. The test specimens consisted of normal strength material (T5) with the 0.2% tensile proof stress

(yield stress) ranging from 185 to 196MPa, and high-strength material (T6) with the 0.2% tensile proof stress ranging from

226 to 317MPa. The measured web slenderness value of the tubular sections ranged from comparatively stocky webs of 6.3 to

relatively more slender webs of 74.5. The effect of the 0.2% proof stress and bearing length on the web crippling strength (capacity)

of aluminum tubular sections was investigated. In the literature, little test data are available on aluminum members subjected to

web crippling. The web crippling test results obtained from this study are valuable for the development of design rules. A non-

linear finite element model (FEM) is developed and verified against the test results. The geometric and material non-linearities

were considered in the FEM. It is shown that the FEM closely predicted the web crippling strengths and failure modes of the tested

specimens.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Aluminum; Experimental investigation; Metal structures; Square and rectangular hollow sections; Tubular sections; Web crippling

1. Introduction

The use of aluminum alloys as structural members hasincreased in recent years. New products based on therelatively high strength and good corrosion resistance arebeing developed. The webs of aluminum beam may buckledue to high localized bearing force. Therefore, webcrippling needs to be considered in designing aluminumbeams.

In the literature, little test results are available onaluminum members subjected to web crippling. Trylandet al. [1] performed 52 tests on aluminum beams subjectedto concentrated load. Three different sections (an I-sectionand two square hollow sections with different plate

e front matter r 2007 Elsevier Ltd. All rights reserved.

s.2007.10.003

ing author. Tel.: +852 2859 2674; fax: +852 2559 5337.

ess: [email protected] (B. Young).

thicknesses) fabricated by extrusion using aluminum alloyAA6082-T6 were investigated. The specimens were testedas simply supported beams loaded either at the midspan orat the end supports. Most of the specimens were loadedthrough a circular bar, which is a curved surface. It shouldbe noted that the web crippling failure load for concen-trated load applied by means of circular bars is quitedifferent from those loaded using flat bearing plates.In all structural design, an accurate prediction of the

load carrying capacity is required for an efficient and safedesign. The web crippling design rules can be found in theAluminum Design Manual [2], Australian/New ZealandStandard [3] for aluminum structures, and European Code[4] Design of Aluminum Structures. Two loading condi-tions are considered in these specifications and they areinterior loading and end loading. The two loadingconditions are not clearly defined in these specifications.

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Nomenclature

b overall width of flanged overall depth of webE0 Young’s modulus of elasticityfy yield stressh depth of flat portion of web measured along the

plane of webL actual length of test specimenN length of bearing

PExp experimental ultimate web crippling load perweb

PFEA web crippling strength predicted from finiteelement analysis

t web thicknessef elongation after fracture based on gauge length

of 50mmsu static ultimate tensile strengths0.2 static 0.2% tensile proof stress

Table 1

Nominal section dimensions

Section Section

geometry

d� b� t

Type Shape (d�2t)/t (b�2t)/t

S1 32� 32� 2 T6 SHS 14.0 14.0

S2 40� 40� 2 T5 and T6 SHS 18.0 18.0

S3 40� 40� 5 T6 SHS 6.0 6.0

S4 44� 44� 1.1 T5 and T6 SHS 38.0 38.0

S5 50� 50� 2 T6 SHS 23.0 23.0

S6 50� 50� 3 T6 SHS 14.7 14.7

S7 64� 64� 3 T6 SHS 19.3 19.3

S8 76� 76� 3 T6 SHS 23.3 23.3

S9 88� 88� 1.7 T6 SHS 49.8 49.8

S10 102� 102� 2.3 T6 SHS 42.3 42.3

S11 112� 112� 3.2 T6 SHS 33.0 33.0

S12 152� 152� 3.2 T6 SHS 45.5 45.5

R1 100� 44� 1.3 T5 and T6 RHS 81.3 34.7

R2 100� 44� 3 T5 and T6 RHS 31.3 12.7

F. Zhou, B. Young / Thin-Walled Structures 46 (2008) 339–351340

There are four loading conditions specified in the NorthAmerican Specification [5] and the Australian/New ZealandStandard [6] for cold-formed steel structures, namely, end-one-flange (EOF), interior-one-flange (IOF), end-two-flange (ETF), and interior-two-flange (ITF) loading con-ditions. The loading conditions are classified based on theconcentrated load acting on one flange only or both flangesas well as the location of the applied load.

In this paper, aluminum tubular sections of square andrectangular hollow sections were tested under two loadingconditions of ETF and ITF in accordance with the loadingconditions specified in the NAS Specification [5] and AS/NZS Standard [6]. The concentrated load was applied bymeans of bearing plates, and different bearing lengths wereused. The test specimens consisted of normal strength(6063-T5) and high-strength (6061-T6) materials. The testresults of aluminum square and rectangular hollow sectionssubjected to web crippling can be used for the developmentof design rules for aluminum structures. Furthermore, anaccurate finite element model (FEM) was developed foraluminum square and rectangular hollow sections sub-jected to web crippling. The finite element analysis (FEA)program ABAQUS [7] was used for the numericalsimulation. The FEM included geometric and materialnon-linearities. The interfaces between the bearing platesand the specimen were carefully modeled. The FEM wasverified against the web crippling tests conducted in thisstudy.

2. Experimental investigation

2.1. Test specimens and bearing plates

A series of tests was performed on aluminum square andrectangular hollow sections subjected to web crippling.Fourteen different section sizes were tested as shown inTable 1, having the nominal thicknesses ranging from 1.1to 5mm, the nominal depth of the webs ranged from 32 to152mm, and the nominal flange widths ranged from 32 to152mm. A total of 14 sections were fabricated by extrusionusing 6061-T6 heat-treated aluminum alloy. In addition,sections S2, S4, R1, and R2 were also fabricated byextrusion using 6063-T5 heat-treated aluminum alloy. Themeasured web slenderness values of the tubular sections

ranged from comparatively stocky webs of 6.3 to relativelymore slender webs of 74.5. The specimen lengths (L) weredetermined according to the NAS Specification [5] and theAS/NZS Standard [6]. Generally, the distance from theedge of the bearing plate to the end of the member was setto be 1.5 times the overall depth of the web (d) rather than1.5 times the depth of the flat portion of the web (h), thelatter being the minimum specified in the specifications.Tables 2–5 show the measured test specimen dimensionsusing the nomenclature defined in Fig. 1.The load or reaction force was applied by means of

bearing plates. The bearing plates were fabricated usinghigh-strength steel having a nominal yield stress of800MPa. All bearing plates were machined to specifieddimensions, and the thickness was 50mm. The bearingplates were designed to act across the full flange widths ofthe hollow sections. Various bearing lengths were used inorder to investigate the effects of the bearing length on theweb crippling strength. Six different bearing lengths wereused for sections S2, S4, R1, and R2 and three differentbearing lengths were used for the rest of the sections duringtesting. The flanges of the hollow section specimens werenot fastened (unrestrained) to the bearing plates duringtesting.

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Table 2

Measured specimen dimensions and experimental ultimate loads for normal strength specimens under ETF loading condition

Specimen Web d (mm) Flange b (mm) Thickness t (mm) Length L (mm) Web slenderness h/t Exp. load per web PExp (kN)

ETF-S2T5-N25 40.0 40.0 1.98 83 18.2 10.1

ETF-S2T5-N50(1) 40.0 40.0 2.00 109 18.0 17.4

ETF-S2T5-N50(2) 40.0 40.0 2.01 110 17.9 17.2

ETF-S2T5-N75 40.0 40.0 2.00 134 18.0 26.2

ETF-S2T5-N100(1) 40.0 40.0 1.99 159 18.1 35.5

ETF-S2T5-N100(2) 40.0 40.0 2.01 161 17.9 34.9

ETF-S2T5-N150 40.0 40.0 2.00 208 18.0 54.2

ETF-S2T5-N200 40.0 40.0 2.00 259 18.0 71.7

ETF-S4T5-N25 44.6 44.6 1.15 91 36.8 2.4

ETF-S4T5-N50 44.6 44.6 1.15 117 36.8 5.2

ETF-S4T5-N75 44.6 44.6 1.15 143 36.8 6.1

ETF-S4T5-N100 44.6 44.6 1.14 164 37.1 8.0

ETF-S4T5-N150 44.6 44.6 1.15 215 36.8 13.6

ETF-S4T5-N200 44.6 44.6 1.16 266 36.4 16.5

ETF-R1T5-N25(1) 100.1 44.1 1.31 178 74.4 1.7

ETF-R1T5-N25(2) 100.1 44.2 1.31 176 74.4 1.7

ETF-R1T5-N50 100.1 44.2 1.31 202 74.4 2.1

ETF-R1T5-N75 100.1 44.1 1.31 222 74.4 2.9

ETF-R1T5-N100 100.1 44.2 1.32 248 73.8 3.4

ETF-R1T5-N150 100.1 44.1 1.32 299 73.8 4.8

ETF-R1T5-N200 100.1 44.1 1.31 350 74.4 5.9

ETF-R2T5-N25 99.9 43.9 2.94 175 32.0 14.0

ETF-R2T5-N50 100.1 44.0 2.93 200 32.2 18.8

ETF-R2T5-N75 100.0 44.0 2.96 223 31.8 29.6

ETF-R2T5-N100 100.0 44.0 2.96 248 31.8 36.2

ETF-R2T5-N150 100.0 44.0 2.94 300 32.0 59.0

ETF-R2T5-N200 99.9 44.0 2.94 350 32.0 76.3

Table 3

Measured specimen dimensions and experimental ultimate loads for high-strength specimens under ETF loading condition


ETF-S1T6-N30 31.9 31.9 1.95 78 14.4 14.4

ETF-S1T6-N60 31.9 31.9 1.95 108 14.4 27.5

ETF-S1T6-N90 31.8 31.9 1.95 138 14.3 40.8

ETF-S2T6-N25 39.9 39.9 1.98 84 18.2 13.6

ETF-S2T6-N50 40.0 40.0 1.96 111 18.4 25.3

ETF-S2T6-N75 39.9 39.9 1.98 133 18.2 39.0

ETF-S2T6-N100 39.9 40.0 1.95 170 18.5 54.3

ETF-S2T6-N150 40.0 40.0 2.00 209 18.0 77.9

ETF-S2T6-N200 40.0 40.0 2.00 260 18.0 90.0

ETF-S3T6-N30 39.8 39.8 4.82 90 6.3 41.3

ETF-S3T6-N60 39.8 39.8 4.82 120 6.3 77.5

ETF-S3T6-N90 39.8 39.8 4.82 149 6.3 112.8

ETF-S4T6-N25 44.6 44.5 1.13 91 37.5 3.0

ETF-S4T6-N50 44.5 44.5 1.14 116 37.0 4.6

ETF-S4T6-N75 44.5 44.5 1.12 139 37.7 7.1

ETF-S4T6-N100 44.6 44.5 1.13 164 37.5 8.9

ETF-S4T6-N150 44.5 44.6 1.14 210 37.0 15.1

ETF-S4T6-N200 44.6 44.5 1.15 267 36.8 17.7

ETF-S5T6-N30 50.7 50.7 1.96 105 23.9 7.5

ETF-S5T6-N60 50.7 50.7 1.96 135 23.9 12.2

ETF-S5T6-N90 50.6 50.7 1.97 167 23.7 17.4

ETF-S6T6-N30 50.8 50.4 3.04 105 14.7 17.1

ETF-S6T6-N60 50.7 50.4 3.04 137 14.7 30.3

ETF-S6T6-N90 50.8 50.4 3.05 167 14.7 43.9

ETF-S7T6-N30 63.9 63.9 3.00 126 19.3 20.9

ETF-S7T6-N60 63.9 63.9 3.01 156 19.2 32.9

ETF-S7T6-N90 63.9 63.9 3.00 186 19.3 50.9

F. Zhou, B. Young / Thin-Walled Structures 46 (2008) 339–351 341

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Table 3 (continued )


ETF-S8T6-N60 76.0 76.0 3.05 174 22.9 30.8

ETF-S8T6-N90 75.9 76.0 3.07 205 22.7 50.3

ETF-S8T6-N120 76.0 76.0 3.08 234 22.7 70.4

ETF-S9T6-N60 88.0 88.0 1.76 192 48.0 6.3

ETF-S9T6-N90 88.0 88.0 1.72 223 49.2 8.6

ETF-S9T6-N120 88.0 87.9 1.75 252 48.3 10.4

ETF-S10T6-N90 101.6 101.8 2.31 243 42.0 17.3

ETF-S10T6-N120 101.6 101.8 2.31 272 42.0 22.2

ETF-S10T6-N150 101.6 101.8 2.31 302 42.0 27.5

ETF-S11T6-N90 112.0 111.5 3.16 257 33.4 49.3

ETF-S11T6-N120 111.8 112.0 3.14 288 33.6 53.9

ETF-S11T6-N150 111.8 112.2 3.16 318 33.4 63.7

ETF-S12T6-N90 153.1 153.4 3.30 319 44.4 27.0

ETF-S12T6-N120 153.1 153.3 3.31 350 44.3 39.3

ETF-S12T6-N150 153.2 153.0 3.29 379 44.6 51.3

ETF-R1T6-N25 100.1 44.1 1.31 175 74.4 1.9

ETF-R1T6-N50 100.2 44.2 1.31 201 74.5 2.5

ETF-R1T6-N75 100.2 44.1 1.32 223 73.9 3.2

ETF-R1T6-N100 100.2 44.1 1.32 248 73.9 3.9

ETF-R1T6-N150 100.1 44.1 1.34 298 72.7 5.4

ETF-R1T6-N200 100.2 44.1 1.33 353 73.3 6.7

ETF-R2T6-N50 99.8 44.1 2.91 201 32.3 22.7

Table 4

Measured specimen dimensions and experimental ultimate loads for normal strength specimens under ITF loading condition


ITF-S2T5-N25 40.0 40.0 2.00 144 18.0 12.9

ITF-S2T5-N50 40.0 40.0 2.00 170 18.0 21.6

ITF-S2T5-N75 40.0 40.0 2.01 194 17.9 30.0

ITF-S2T5-N100 40.0 40.0 2.01 221 17.9 39.1

ITF-S2T5-N150 40.0 40.0 2.01 269 17.9 55.7

ITF-S2T5-N200 40.0 40.0 2.01 320 17.9 72.7

ITF-S4T5-N25 44.6 44.6 1.15 148 36.8 5.4

ITF-S4T5-N50 44.6 44.6 1.16 192 36.4 6.6

ITF-S4T5-N75(1) 44.7 44.6 1.15 205 36.9 8.8

ITF-S4T5-N75(2) 44.6 44.6 1.15 208 36.8 8.7

ITF-S4T5-N100 44.6 44.6 1.15 228 36.8 10.4

ITF-S4T5-N150 44.6 44.6 1.16 282 36.4 16.1

ITF-S4T5-N200 44.6 44.6 1.16 330 36.4 19.5

ITF-R1T5-N25 100.0 44.1 1.35 326 72.1 6.2

ITF-R1T5-N50 100.0 44.2 1.34 348 72.6 6.7

ITF-R1T5-N75 100.1 44.2 1.35 374 72.1 7.2

ITF-R1T5-N100 100.0 44.1 1.35 399 72.1 7.6

ITF-R1T5-N150 100.0 44.1 1.35 450 72.1 8.8

ITF-R1T5-N200 100.0 44.1 1.35 501 72.1 9.8

ITF-R2T5-N25 100.0 44.0 2.96 325 31.8 21.2

ITF-R2T5-N50 100.0 44.0 2.96 348 31.8 33.3

ITF-R2T5-N75 100.0 44.0 2.99 376 31.4 41.5

ITF-R2T5-N100 99.9 44.0 2.96 400 31.8 47.3

ITF-R2T5-N150 99.9 44.0 2.97 449 31.6 62.7

ITF-R2T5-N200 99.9 44.0 2.96 499 31.8 81.4


2.2. Specimen labeling

In Tables 2–5, the specimens were labeled such that theloading condition, section geometry, and material type of thespecimens as well as length of the bearing could be identified

from the label. For example, the labels ‘‘ETF-S2T5-N50(1)’’and ‘‘ITF-S2T5-N50’’ define the following specimens:

�
The first three letters indicate that the loading condi-tions of ETF and ITF were used in the tests.

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Table 5

Measured specimen dimensions and experimental ultimate loads for high-strength specimens under ITF loading condition


ITF-S1T6-N30 31.9 31.9 1.95 126 14.4 17.6

ITF-S1T6-N60 31.9 31.9 1.95 155 14.4 32.7

ITF-S1T6-N90 32.0 31.9 1.95 185 14.4 43.3

ITF-S2T6-N25 39.9 39.9 1.99 145 18.1 19.6

ITF-S2T6-N50 39.9 39.9 2.00 169 18.0 32.1

ITF-S2T6-N75 39.9 40.0 2.00 194 18.0 43.5

ITF-S2T6-N100 39.9 39.9 2.00 221 18.0 58.8

ITF-S2T6-N150 39.9 40.0 2.00 270 18.0 84.7

ITF-S2T6-N200 39.9 40.0 1.90 322 19.0 105.0

ITF-S3T6-N30 39.8 39.8 4.82 150 6.3 56.9

ITF-S3T6-N60 39.8 39.8 4.82 179 6.3 92.8

ITF-S3T6-N90 39.8 39.8 4.82 210 6.3 137.8

ITF-S4T6-N25 44.6 44.6 1.14 148 37.1 6.7

ITF-S4T6-N50 44.6 44.6 1.15 191 36.8 8.2

ITF-S4T6-N75 44.6 44.6 1.15 206 36.8 10.4

ITF-S4T6-N100 44.5 44.6 1.15 232 36.7 11.6

ITF-S4T6-N150 44.5 44.5 1.15 282 36.7 17.7

ITF-S4T6-N200 44.5 44.5 1.15 330 36.7 21.1

ITF-S5T6-N30 50.7 50.7 1.97 183 23.7 14.3

ITF-S5T6-N60 50.7 50.7 1.96 213 23.9 18.6

ITF-S5T6-N90 50.8 50.7 1.96 243 23.9 23.5

ITF-S6T6-N30 50.8 50.4 3.05 182 14.7 32.1

ITF-S6T6-N60 50.8 50.3 3.04 212 14.7 42.5

ITF-S6T6-N90 50.7 50.4 3.04 242 14.7 54.9

ITF-S7T6-N30 63.9 63.9 3.00 222 19.3 33.0

ITF-S7T6-N60 63.9 63.9 3.01 252 19.2 43.0

ITF-S7T6-N90 63.9 63.9 2.97 282 19.5 58.3

ITF-S8T6-N60 76.0 76.0 3.08 288 22.7 44.0

ITF-S8T6-N90 76.0 76.0 3.06 318 22.8 64.4

ITF-S8T6-N120 76.1 76.1 3.08 348 22.7 81.6

ITF-S9T6-N60(1) 88.0 88.0 1.73 324 48.9 12.9

ITF-S9T6-N60(2) 88.0 88.0 1.73 324 48.9 13.2

ITF-S9T6-N90 88.0 88.0 1.72 354 49.2 14.5

ITF-S9T6-N120 88.0 88.0 1.74 385 48.6 16.8

ITF-S10T6-N90 101.7 101.9 2.31 396 42.0 27.7

ITF-S10T6-N120 101.7 101.8 2.31 426 42.0 31.8

ITF-S10T6-N150 101.8 101.8 2.31 456 42.1 36.9

ITF-S11T6-N90 112.0 111.6 3.16 427 33.4 72.7

ITF-S11T6-N120 111.5 112.1 3.16 456 33.3 81.3

ITF-S11T6-N150 111.5 112.1 3.15 486 33.4 92.5

ITF-S12T6-N90 153.2 153.1 3.30 548 44.4 50.3

ITF-S12T6-N120 153.1 153.3 3.27 579 44.8 55.9

ITF-S12T6-N150 153.2 153.1 3.29 608 44.6 71.5

ITF-R1T6-N25 100.1 44.1 1.35 325 72.1 6.6

ITF-R1T6-N50 100.1 44.2 1.35 350 72.1 6.7

ITF-R1T6-N75 100.1 44.1 1.35 373 72.1 7.5

ITF-R1T6-N100 100.1 44.1 1.35 401 72.1 8.2

ITF-R1T6-N150 100.0 44.0 1.34 449 72.6 9.5

ITF-R1T6-N200 100.1 44.1 1.35 499 72.1 11.2


�
The following notation is section geometry and materialtype of the specimens, where the section geometry isdefined in Table 1. The notation ‘‘S2T5’’ indicatessection S2 and material type of T5. � The notation ‘‘N50’’ indicates the length of bearing in
mm (50mm).
� If a test was repeated, then ‘‘(1)’’ indicates the first test
and ‘‘(2)’’ indicates the second test.

2.3. Material properties

Tensile coupon tests were carried out to determine thematerial properties of the aluminum specimens. The tensilecoupons were taken from the center of the web plate in thelongitudinal direction of the untested specimens. Thetensile coupons were prepared and tested according tothe American Society for Testing and Materials Standard

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d h

t

b

d

t

h

b

Fig. 1. Definition of symbols: (a) square hollow section and (b)

rectangular hollow section.

Table 6

Measured material properties of test specimens

Series E0 (GPa) s0.2 (MPa) su (MPa) ef (%)

S1T6 66.4 243.0 261.0 9.9

S2T5 65.0 184.9 220.4 5.7

S2T6 68.3 316.7 317.2 7.6

S3T6 69.5 226.0 246.0 10.8

S4T5 70.4 188.5 209.5 9.9

S4T6 67.8 296.2 300.4 8.0

S5T6 67.3 264.0 271.0 8.6

S6T6 63.6 268.0 273.0 10.2

S7T6 67.5 222.0 236.0 8.5

S8T6 68.1 246.0 264.0 9.5

S9T6 67.3 246.0 263.0 8.4

S10T6 67.9 234.0 258.0 9.6

S11T6 66.4 290.0 291.0 8.8

S12T6 71.8 244.0 267.0 10.5

R1T5 69.1 195.9 218.7 9.9

R1T6 70.3 260.0 276.3 7.6

R2T5 67.5 189.1 213.2 12.3

R2T6 68.9 275.4 283.1 10.1


[8] and the Australian Standard AS 1391 [9] for the tensiletesting of metals using 12.5mm wide coupons of gaugelength 50mm. The coupons were tested in an MTSdisplacement controlled testing machine using frictiongrips. Two strain gauges and a calibrated extensometer of50mm gauge length were used to measure the longitudinalstrain. A data acquisition system was used to record theload and strain at regular intervals during the tests. Thestatic load was obtained by pausing the applied strainingfor 1.5min near the 0.2% tensile proof stress and theultimate tensile strength. This allowed the stress relaxationassociated with plastic straining to take place. The materialproperties obtained from the tensile coupon tests aresummarized in Table 6, which includes the measured initial

Young’s modulus (E0), the static 0.2% tensile proof stress(s0.2), the static tensile strength (su), and the elongationafter fracture (ef) based on a gauge length of 50mm.

2.4. Loading conditions and test rig

The tubular sections were tested under two loadingconditions of ETF and ITF in accordance with the NASSpecification [5] and AS/NZS Standard [6]. For ETF andITF loading conditions, two identical bearing plates of thesame width were positioned at the end and mid-length ofeach specimen, respectively. Hinge supports were simulatedby two half rounds in the line of action of the force.Photographs of the ETF and ITF test setup are shown inFigs. 2a and 3a, respectively.A servo-controlled hydraulic testing machine was used

to apply a concentrated compressive force to the testspecimens. Displacement control was used to drive thehydraulic actuator at a constant speed of 0.05mm/min forall test specimens.

2.5. Test results

The experimental ultimate web crippling loads per web(PExp) are given in Tables 2–5 for ETF and ITF loadingconditions. Five tests were repeated and the specimens areETF-S2T5-N50, ETF-S2T5-N100, ETF-R1T5-N25, ITF-S4T5-N75, and ITF-S9T6-N60. The test result for therepeated test is very close to its first test value with adifference of less than 2.3%. This small difference betweenthe repeated tests demonstrated the reliability of the testresults.

3. Comparison of test strengths with different yield stresses

Sections S2, S4, R1, and R2 were fabricated by extrusionusing both the 6063-T5 and 6061-T6 heat-treated alumi-num alloys. The experimental web crippling loads per webobtained from these sections having normal strengthmaterial are compared with those sections having high-strength material, as shown in Tables 7 and 8 for ETF andITF loading conditions, respectively. The web cripplingloads per web were normalized with the yield stress of thespecimens. The values of ðPExp�T6=f y�T6Þ=ðPExp�T5=f y�T5Þ

ranged from 0.56 for section S4 with the bearing length (N)of 50mm to 0.92 for section R1 with N of 50mm underETF loading condition, and the values ranged from 0.69for section S4 with N of 200mm to 0.89 for section S2 withN of 25 and 150mm under ITF loading condition, asshown in Tables 7 and 8, respectively. The mean value ofðPExp�T6=f y�T6Þ=ðPExp�T5=f y�T5Þ is 0.8 for these sectionsunder both loading conditions of ETF and ITF. Thecoefficients of variation (COV) are 0.112 and 0.079 forETF and ITF loading conditions, respectively. It is shownthat the value of test strength-to-yield stress (PExp/fy) ratiofor normal strength material (T5) is larger than those forthe high-strength material (T6) by 20%.

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Fig. 2. Comparison of experimental and finite element analysis for end-two-flange (ETF) loading condition: (a) experimental and (b) FEA.


4. Comparison of test strengths with different bearing

lengths

The effect of the bearing length on the web cripplingstrength was examined. The experimental web cripplingloads per web obtained from the tubular sections withdifferent bearing lengths are compared with the webcrippling strengths of the specimens tested under a givenbearing length. The comparison is shown in Tables 9 and10 for ETF and ITF loading conditions, respectively. Ingeneral, the web crippling strength for ETF loadingcondition increases faster than those for ITF loadingcondition as the bearing length increases. For example,increasing the bearing length for sections S2, S4, R1, andR2 from 25 to 50, 75, 100, 150, and 200mm, the meanvalues of web crippling strength increased by 59%, 126%,192%, 352%, and 456% under ETF loading conditioncompared with 34%, 71%, 106%, 187%, and 255% underITF loading condition, as shown in Tables 9 and 10,respectively. Similarly, the web crippling strength for ETF

loading condition decreases faster than those for ITFloading condition as the bearing length decreases. Forexample, reducing the bearing length for sections S1, S3,and S5–S12 from 90 to 60 and 30mm, the mean values ofweb crippling strength reduced by 32% and 61% underETF loading condition compared with 24% and 48%under ITF loading condition, as shown in Tables 9 and 10,respectively. It is shown that the effect of bearing length onthe web crippling strength for ETF loading condition ismore severe than those for ITF loading condition.

5. Finite element analysis

5.1. General

The finite element program ABAQUS [7] version 6.6 wasused to simulate aluminum tubular sections subjected toweb crippling. Three main components have been carefullyconsidered in the FEM. These components are the bearing

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Fig. 3. Comparison of experimental and finite element analysis for interior-two-flange (ITF) loading condition: (a) experimental and (b) FEA.


plates, aluminum tubular section, and the interfacesbetween the bearing plates and the aluminum section.

In the FEM, the measured cross-section dimensions andmaterial properties obtained from the tests were used. Themodel was based on the centerline dimensions of the cross-sections.

5.2. Element type and mesh

The bearing plates were modeled using analytical rigidplates and the aluminum section was modeled using theS4R shell elements. The S4R element is a four-nodedoubly curved thin or thick shell element with reducedintegration, hourglass control, and finite membranestrains. It is mentioned in the ABAQUS Manualthat S4R element is suitable for complex bucklingbehavior. The S4R element has six degrees of freedomper node and provides accurate solutions to mostapplications [7]. The finite element mesh used in the modelwas investigated by varying the size of the elements in thecross-section to provide both accurate results and less

computational time. The finite element mesh sizes rangingfrom 2� 2mm (length by width) to 10� 10mm were usedfor the flanges and webs depending on the size of thesections. The typical finite element mesh of the squareand rectangular hollow sections under the ETF andITF loading conditions are shown in Figs. 2b and 3b,respectively.

5.3. Boundary condition and interface

Following the test procedure, the top bearing platewas restrained against all degrees of freedom, except forthe translational degree of freedom in the Y direction.Due to symmetry, only one half of the specimen wasmodeled, as shown in Figs. 2b and 3b. The nodes of thesymmetry of the section were prevented from translationaldisplacement in the X direction and rotation about the Y

and Z-axis.The interfaces between the bearing plates and the

aluminum section were modeled using the contact pair.The steel bearing plates are the master elements, while the

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Table 7

Comparison of web crippling tests with different yield stresses under ETF loading condition

Section Bearing length

N (mm)

Web

slenderness h/t

T5 T6 ComparisonðPExp�T6=f y�T6Þ

ðPExp�T5=f y�T5Þfy�T5 (MPa) PExp�T5 (kN) fy�T6 (MPa) PExp�T6 (kN)

S2 25 18.2 184.9 10.1 316.7 13.6 0.79

S2 50 18.4 184.9 17.4 316.7 25.3 0.85

S2 75 18.2 184.9 26.2 316.7 39.0 0.87

S2 100 18.5 184.9 35.5 316.7 54.3 0.89

S2 150 18.0 184.9 54.2 316.7 77.9 0.84

S2 200 18.0 184.9 71.7 316.7 90.0 0.73

S4 25 37.5 188.5 2.4 296.2 3.0 0.80

S4 50 37.1 188.5 5.2 296.2 4.6 0.56

S4 75 37.8 188.5 6.1 296.2 7.1 0.75

S4 100 37.4 188.5 8.0 296.2 8.9 0.70

S4 150 37.1 188.5 13.6 296.2 15.1 0.71

S4 200 36.7 188.5 16.5 296.2 17.7 0.68

R1 25 74.4 195.9 1.7 260.0 1.9 0.84

R1 50 74.5 195.9 2.1 260.0 2.5 0.92

R1 75 73.9 195.9 2.9 260.0 3.2 0.82

R1 100 73.9 195.9 3.4 260.0 3.9 0.88

R1 150 72.7 195.9 4.8 260.0 5.4 0.86

R1 200 73.3 195.9 5.9 260.0 6.7 0.86

R2 50 32.3 189.1 18.8 275.4 22.7 0.83

Mean 0.80

COV 0.112

Table 8

Comparison of web crippling tests with different yield stresses under ITF loading condition

Section Bearing length

N (mm)

Web

slenderness h/t

T5 T6 ComparisonðPExp�T6=f y�T6Þ

ðPExp�T5=f y�T5Þfy�T5 (MPa) PExp�T5 (kN) fy�T6 (MPa) PExp�T6 (kN)

S2 25 18.1 184.9 12.9 316.7 19.6 0.89

S2 50 18.0 184.9 21.6 316.7 32.1 0.87

S2 75 18.0 184.9 30.0 316.7 43.5 0.85

S2 100 18.0 184.9 39.1 316.7 58.8 0.88

S2 150 18.0 184.9 55.7 316.7 84.7 0.89

S2 200 19.0 184.9 72.7 316.7 105.0 0.84

S4 25 37.1 188.5 5.4 296.2 6.7 0.79

S4 50 36.8 188.5 6.6 296.2 8.2 0.80

S4 75 36.8 188.5 8.8 296.2 10.4 0.75

S4 100 36.7 188.5 10.4 296.2 11.6 0.71

S4 150 36.7 188.5 16.1 296.2 17.7 0.70

S4 200 36.7 188.5 19.5 296.2 21.1 0.69

R1 25 72.1 195.9 6.2 260.0 6.6 0.80

R1 50 72.1 195.9 6.7 260.0 6.7 0.75

R1 75 72.1 195.9 7.2 260.0 7.5 0.78

R1 100 72.1 195.9 7.6 260.0 8.2 0.81

R1 150 72.6 195.9 8.8 260.0 9.5 0.81

R1 200 72.1 195.9 9.8 260.0 11.2 0.86

Mean 0.80

COV 0.079


aluminum specimen is the slave element of the interfaceelements in the FEM. The contact pair allows the surfacesto separate under the influence of a tensile force. However,the two contact surfaces are not allowed to penetrate eachother.

5.4. Method of loading

The loading method used in the FEA was identical tothat used in the tests. The displacement control methodwas used for the analysis of the aluminum section subjected

ARTIC

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PRES

S

Table 9

Comparison of web crippling tests with different bearing lengths under ETF loading condition

Section PExp (N ¼ 25)

(kN)

PExp (N ¼ 50)

(kN)

PExp (N ¼ 75)

(kN)

PExp (N ¼ 100)

(kN)

PExp (N ¼ 150)

(kN)

PExp (N ¼ 200)

(kN)

Comparison

PExpðN ¼ 50Þ

PExpðN ¼ 25Þ

PExpðN ¼ 75Þ

PExpðN ¼ 25Þ

PExpðN ¼ 100Þ

PExpðN ¼ 25Þ

PExpðN ¼ 150Þ

PExpðN ¼ 25Þ

PExpðN ¼ 200Þ

PExpðN ¼ 25Þ

S2T5 10.1 17.4 26.2 35.5 54.2 71.7 1.72 2.59 3.51 5.36 7.09

S2T6 13.6 25.3 39.0 54.3 77.9 90.0 1.86 2.87 3.99 5.73 6.62

S4T5 2.4 5.2 6.1 8.0 13.6 16.5 2.17 2.52 3.33 5.65 6.88

S4T6 3.0 4.6 7.1 8.9 15.1 17.7 1.52 2.37 2.95 5.02 5.90

R1T5 1.7 2.1 2.9 3.4 4.8 5.9 1.21 1.71 1.97 2.79 3.47

R1T6 1.9 2.5 3.2 3.9 5.4 6.7 1.32 1.66 2.05 2.84 3.53

R2T5 14.0 18.8 29.6 36.2 59.0 76.3 1.34 2.12 2.59 4.23 5.47

R2T6 – 22.65 – – – – – – – – –

Mean 1.59 2.26 2.92 4.52 5.56

COV 0.216 0.202 0.260 0.279 0.273


(kN)

PExp (N ¼ 60)

(kN)

PExp (N ¼ 90)

(kN)

PExp (N ¼ 120)

(kN)

PExp (N ¼ 150)

(kN)

PExpðN ¼ 30Þ

PExpðN ¼ 90Þ

PExpðN ¼ 60Þ

PExpðN ¼ 90Þ

PExpðN ¼ 120Þ

PExpðN ¼ 90Þ

PExpðN ¼ 150Þ

PExpðN ¼ 90Þ

S1T6 14.4 27.5 40.8 – – 0.35 0.67 – –

S3T6 41.3 77.5 112.8 – – 0.37 0.69 – –

S5T6 7.5 12.2 17.4 – – 0.43 0.70 – –

S6T6 17.1 30.3 43.9 – – 0.39 0.69 – –

S7T6 20.9 32.9 50.9 – – 0.41 0.65 – –

S8T6 – 30.8 50.3 70.4 – – 0.61 1.40 –

S9T6 – 6.3 8.6 10.4 – – 0.73 1.21 –

S10T6 – – 17.3 22.2 27.5 – – 1.28 1.59

S11T6 – – 49.3 53.9 63.7 – – 1.09 1.29

S12T6 – – 27.0 39.3 51.3 – – 1.46 1.90

Mean 0.39 0.68 1.25 1.44

COV 0.082 0.057 0.103 0.146

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Table 10

Comparison of web crippling tests with different bearing lengths under ITF loading condition


(kN)

PExp (N ¼ 50)

(kN)

PExp (N ¼ 75)

(kN)

PExp (N ¼ 100)

(kN)

PExp (N ¼ 150)

(kN)

PExp (N ¼ 200)

(kN)

Comparison

PExpðN ¼ 50Þ

PExpðN ¼ 25Þ

PExpðN ¼ 75Þ

PExpðN ¼ 25Þ

PExpðN ¼ 100Þ

PExpðN ¼ 25Þ

PExpðN ¼ 150Þ

PExpðN ¼ 25Þ

PExpðN ¼ 200Þ

PExpðN ¼ 25Þ

S2T5 12.9 21.6 30.0 39.1 55.7 72.7 1.67 2.33 3.03 4.31 5.64

S2T6 19.6 32.1 43.5 58.8 84.7 105.0 1.64 2.22 3.00 4.32 5.36

S4T5 5.4 6.6 8.8 10.4 16.1 19.5 1.21 1.63 1.93 2.97 3.61

S4T6 6.7 8.2 10.4 11.6 17.7 21.1 1.22 1.55 1.73 2.64 3.15

R1T5 6.2 6.7 7.2 7.6 8.8 9.8 1.08 1.16 1.23 1.42 1.58

R1T6 6.6 6.7 7.5 8.2 9.5 11.2 1.02 1.13 1.24 1.43 1.69

R2T5 21.2 33.3 41.5 47.3 62.7 81.4 1.57 1.96 2.23 2.96 3.85

Mean 1.34 1.71 2.06 2.87 3.55

COV 0.204 0.279 0.363 0.414 0.448

Section PExp (N ¼ 30) (kN) PExp (N ¼ 60) (kN) PExp (N ¼ 90) (kN) PExp (N ¼ 120) (kN) PExp (N ¼ 150) (kN) PExpðN ¼ 30Þ

PExpðN ¼ 90Þ

PExpðN ¼ 60Þ

PExpðN ¼ 90Þ

PExpðN ¼ 120Þ

PExpðN ¼ 90Þ

PExpðN ¼ 150Þ

PExpðN ¼ 90Þ

S1T6 17.6 32.7 43.3 – – 0.41 0.76 – –

S3T6 56.9 92.8 137.8 – – 0.41 0.67 – –

S5T6 14.3 18.6 23.5 – – 0.61 0.79 – –

S6T6 32.1 42.5 54.9 – – 0.58 0.77 – –

S7T6 33.0 43.0 58.3 – – 0.57 0.74 – –

S8T6 – 44.0 64.4 81.6 – – 0.68 1.27 –

S9T6 – 12.9 14.5 16.8 – – 0.89 1.16 –

S10T6 – – 27.7 31.8 36.9 – – 1.15 1.33

S11T6 – – 72.7 81.3 92.5 – – 1.12 1.27

S12T6 – – 50.3 55.9 71.5 – – 1.11 1.42

Mean 0.52 0.76 1.17 1.30

COV 0.190 0.096 0.055 0.032

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Table 11

Comparison of experimental results with web crippling strengths predicted from finite element analysis under ETF loading condition

Specimen Web slenderness h/t Exp. load per web PExp (kN) FEA load per web PFEA (kN) Comparison PExp/PFEA

ETF-S2T5-N25 18.2 10.1 9.6 1.05

ETF-S4T5-N50 36.8 5.2 5.0 1.04

ETF-R1T5-N50 74.4 2.1 2.3 0.91

ETF-R1T5-N200 74.4 5.9 6.5 0.91

ETF-R2T5-N75 31.8 29.6 29.0 1.02

ETF-R2T5-N200 32.0 76.3 72.0 1.06

ETF-S1T6-N30 14.4 14.4 14.7 0.98

ETF-S2T6-N25 18.2 13.6 14.9 0.91

ETF-S3T6-N30 6.3 41.3 44.8 0.92

ETF-S12T6-N90 44.4 27.0 25.2 1.07

ETF-R1T6-N25 74.4 1.9 2.1 0.90

ETF-R1T6-N50 74.5 2.5 2.7 0.93

ETF-R1T6-N75 73.9 3.2 3.4 0.94

ETF-R1T6-N200 73.3 6.7 7.2 0.93

ETF-R2T6-N50 32.3 22.7 25.0 0.91

Mean 0.97

COV 0.066


to web crippling. Transverse compressive load was appliedto the specimen by specifying a displacement to thereference point of the analytical rigid plate that modeledthe bearing plate. Generally, a displacement of 5mm wasspecified.

5.5. Material modeling

The measured stress–strain curves of the specimenswere used in the FEA. The material behavior providedby ABAQUS allows for the multi-linear stress–straincurve to be used. The first part of the multi-linearcurve represents the elastic part up to the proportionallimit stress with measured Young’s modulus as well asPoisson’s ratio of 0.33. Since the analysis of postbucklinginvolves large in-elastic strains, the nominal (engineering)static stress–strain curve was converted to a true stress andlogarithmic plastic strain curve. The equations for truestress (strue) and plastic true strain (�pl

true) were specified inABAQUS [7].

6. Verification of FEM

In the verification of the FEM, a total of 30 aluminumtubular sections subjected to web crippling were analyzed.A comparison between the experimental results andthe finite element results was carried out. The mainobjective of this comparison is to verify and check theaccuracy of the FEM. The comparison of the test results(PExp) with the numerical results (PFEA) of web cripplingstrengths per web is shown in Tables 11 and 12 for ETFand ITF loading conditions, respectively. It can be seenthat good agreement has been achieved between bothresults for all specimens. The mean values of the PExp/PFEA

ratio are 0.97 and 0.95 with the corresponding COV

of 0.066 and 0.047 for ETF and ITF loadingconditions, respectively. A maximum difference of 10%was observed between the experimental and numericalresults for specimens ETF-R1T6-N25 and ITF-R1T6-N100. The web crippling failure mode observed fromthe tests has been also verified by the FEM for ETFand ITF loading conditions, as shown in Figs. 2and 3, respectively. It is shown that good agree-ment between the experimental and finite elementresults for both the web crippling strength and failuremode.

7. Conclusions

A test program on aluminum square and rectangularhollow sections subjected to web crippling has beenpresented. The test specimens were fabricated by extrusionusing 6063-T5 and 6061-T6 heat-treated aluminumalloys. The web slenderness value of the specimens rangingfrom 6.3 to 74.5 has been investigated. The test specimenswere tested under ETF and ITF loading conditions.The flanges of the square and rectangular hollow sectionswere not fastened to the bearing plates. The test specimenswith different yield stresses and bearing lengths havebeen investigated. It is shown that the value of teststrength-to-yield stress ratio for normal strength material(6063-T5) is larger than those for the high-strengthmaterial (6061-T6) by 20%. The web crippling strengthfor ETF loading condition increases faster than thosefor ITF loading condition as the bearing length increases.The effect of bearing length on the web cripplingstrength for ETF loading condition is more severe thanthose for ITF loading condition. The new web cripplingtest data presented in this paper can be used todevelop design rules for aluminum square and rectangular

ARTICLE IN PRESS

Table 12

Comparison of experimental results with web crippling strengths predicted from finite element analysis under ITF loading condition

Specimen Web slenderness h/t Exp. load per web PExp (kN) FEA load per web PFEA (kN) Comparison PExp/PFEA

ITF-S2T5-N25 18.0 12.9 13.7 0.94

ITF-S2T5-N50 18.0 21.6 21.3 1.01

ITF-R1T5-N50 72.6 6.7 7.2 0.93

ITF-R1T5-N200 72.1 9.8 10.8 0.91

ITF-R2T5-N50 31.8 33.3 36.4 0.91

ITF-R2T5-N100 31.8 47.3 49.5 0.96

ITF-S1T6-N30 14.4 17.6 18.0 0.98

ITF-S2T6-N25 18.1 19.6 21.2 0.92

ITF-S2T6-N50 18.0 32.1 33.5 0.96

ITF-S3T6-N30 6.3 56.9 60.2 0.95

ITF-S6T6-N30 14.7 32.1 32.7 0.98

ITF-S6T6-N60 14.7 42.5 45.9 0.93

ITF-S9T6-N60 48.9 12.9 12.1 1.07

ITF-R1T6-N100 72.1 8.2 9.1 0.90

ITF-R1T6-N200 72.1 11.2 12.3 0.91

Mean 0.95

COV 0.047


hollow sections. A FEM that incorporated the geometricand material non-linearities has been developed andverified against the experimental results. The FEM closelypredicted the behavior of aluminum square and rectangu-lar hollow sections subjected to web crippling.

Acknowledgments

The authors gratefully acknowledge the Asia AluminumManufacturing Company for supplying the test specimens.The authors are also grateful to Mr. Yiu-Man Wong andMr. Chun-Wai Chan for their assistance in the experi-mental program as part of their final year undergraduateresearch projects at university.

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[3] AS/NZS. Aluminium structures—part 1: limit state design, Australian/

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[4] EC9. Eurocode 9: design of aluminum structures—part 1.1: general

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aluminum tubular sections subjected to web crippling—part i:: tests and finite element analysis

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