Tests of cold-formed high strength stainless steel

compression members

Ben Young a,*, Wing-Man Lui b

a Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, Chinab Department of Civil Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

Received 31 May 2005; received in revised form 6 January 2006; accepted 24 January 2006

Available online 24 March 2006

Abstract

The paper describes a test program on cold-formed high strength stainless steel compression members. The duplex stainless steel having the

yield stress and tensile strength up to 750 and 850 MPa, respectively, was investigated. The material properties of the test specimens were

obtained from tensile coupon and stub column tests. The test specimens were cold-rolled into square and rectangular hollow sections. The

specimens were compressed between fixed ends at different column lengths. The initial overall geometric imperfections of the column specimens

were measured. The strength and behaviour of cold-formed high strength stainless steel columns were investigated. The test strengths were

compared with the design strengths predicted using the American, Australian/New Zealand and European specifications for cold-formed stainless

steel structures. Generally, it is shown that the design strengths predicted by the three specifications are conservative for the cold-formed high

strength stainless steel columns. In addition, reliability analysis was performed to evaluate the current design rules.

q 2006 Elsevier Ltd. All rights reserved.

Keywords: Cold-formed steel; Column; Duplex stainless steel; Experimental investigation; High strength; Material properties; Stainless steel structures; Structural

design; Tubular sections

1. Introduction

Stainless steel sections have been increasingly used in

architectural and structural applications. This is due to their

aesthetic appearance, superior corrosion resistance, ease of

maintenance and ease of construction. Since, its inception

during the early part of the 20th century, designers, engineers

and architects alike, have used stainless steel in both practical

and imaginative ways, with further use certain to arise as we

enter a global transition towards sustainable development and

reduction in environmental impacts [1].

Tests of cold-formed stainless steel columns have been

conducted by Rasmussen and Hancock [2], Talja and Salmi [3],

Macdonald et al. [4], Young andHartono [5], Gardner [1], Young

and Liu [6] and other researchers. These researchers proposed

design rules and design recommendations for stainless steel

columns. The current design rules in the American Society of

Civil Engineers Specification (ASCE) [7], Australian/New

Zealand Standard (AS/NZS) [8] and European Code (EC3) [9]

0263-8231/$ - see front matter q 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.tws.2006.01.006

* Corresponding author. Tel.: C852 2859 2674; fax: C852 2559 5337.

E-mail address: young@hku.hk (B. Young).

for cold-formed stainless steel structures as well as the design

rules proposed by the aforementioned researchers were mainly

based on the investigation of cold-formed austenitic stainless

steel type 304. However, little test data are available on cold-

formed high strength stainless steel columns, such as duplex

material. The current design rules may not be applicable to high

strength material. Therefore, there is a need to investigate the

appropriateness of the current design rules in the specifications

for high strength material.

A test program was performed to examine the strength and

behaviour of cold-formed high strength stainless steel columns

in this study. The test specimens were cold-rolled from flat

strips of duplex stainless steel. The square and rectangular

hollow section columns were compressed between fixed ends.

The column test strengths were compared with the design

strengths obtained using the American [7], Australian/New

Zealand [8] and European [9] specifications for cold-formed

stainless steel structures. Reliability analysis was also

performed to evaluate the current design rules.

2. Test specimens

High strength stainless steel square hollow section (SHS)

and rectangular hollow section (RHS) columns were

Thin-Walled Structures 44 (2006) 224–234

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Nomenclature

A gross area (unreduced cross-section);

Ae effective area (reduced cross-section);

B overall width of specimen;

D overall depth of specimen;

E0 initial Young’s modulus;

Et tangent modulus;

Fm mean value of fabrication factor;

L length of specimen;

le effective length (leZL/2);

Mm mean value of material factor;

n exponent in Ramberg–Osgood expression;

P compressive axial load;

PASCE unfactored design strengths calculated using

material properties obtained from tensile coupon

tests for the American specification;

P�ASCE unfactored design strengths calculated using

material properties obtained from stub column tests

for the American specification;

PAS/NZS unfactored design strengths calculated using

material properties obtained from tensile coupon

tests for the Australian/New Zealand Standard;

P�AS=NZS unfactored design strengths calculated using

material properties obtained from stub column tests

for the Australian/New Zealand standard;

PEC3 unfactored design strengths calculated using

material properties obtained from tensile coupon

tests for the European code;

P�EC3 unfactored design strengths calculated using

material properties obtained from stub column tests

for the European code;

PExp experimental ultimate load (test strength);

Pm mean value of tested-to-predicted load ratio;

ri inner corner radius of specimen;

ro outer corner radius of specimen;

ry radius of gyration about the minor y-axis;

t plate thickness of specimen;

VF coefficient of variation of fabrication factor;

VM coefficient of variation of material factor;

VP coefficient of variation of tested-to-predicted load

ratio;

x in-plane transverse coordinate;

y out-of-plane transverse coordinate;

a parameter used to define imperfection parameter;

b parameter used to define imperfection parameter;

b0, b1 reliability indices (safety indices);

d initial overall geometric imperfection at mid-

length;

3f elongation (tensile strain) after fracture based on a

gauge length of 50 mm;

f0, f1 resistance (capacity) factors;

lo parameter used to define imperfection parameter;

l1 parameter used to define imperfection parameter;

s0.01 static 0.01% tensile proof stress;

s0.2 static 0.2% tensile proof stress; and

su static tensile strength

B. Young, W.-M. Lui / Thin-Walled Structures 44 (2006) 224–234 225

investigated. The high strength material used in this study was

duplex stainless steel. The test specimens were cold-rolled

from flat strips. The test program consists of four test series that

include two SHS (Series SHS1 and SHS2) and two RHS

(Series RHS1 and RHS2). The nominal section sizes of the

SHS are 40!40!2 and 50!50!1.5 mm, and the nominal

section sizes of the RHS are 140!80!3 and 160!80!3 mm.

The overall depth (D) to thickness (t) ratios are 20.0, 33.3, 46.7

Table 1

Measured specimen dimensions for Series SHS1

Specimen Depth Width Thickness O

D (mm) B (mm) t r

SHS1L300 40.1 39.9 1.945 3

SHS1L300# 40.1 40.0 1.947 3

SHS1L650 40.1 39.5 1.933 3

SHS1L1000 40.1 40.0 1.937 3

SHS1L1500 40.1 40.0 1.924 3

SHS1L2000 40.1 40.0 1.916 3

SHS1L2500 40.2 40.0 1.918 3

SHS1L3000 40.2 40.0 1.940 3

Mean 40.1 39.9 1.932 3

COV 0.001 0.005 0.006 0

# second test; 1 in 25.4 mm; COV coefficient of variation.

and 53.3 for 40!40!2, 50!50!1.5, 140!80!3 and 160!80!3 sections, respectively. Tables 1–4 show the measured

cross-section dimensions and column length (L) of each test

specimen using the nomenclature defined in Fig. 1. The cross-

section dimensions shown in Tables 1–4 are the averages of

measured values at both ends for each test specimen. Each

specimen was cut to a specified length ranging from 300 to

3000 mm, and both ends were welded to steel end plates to

uter radius Inner radius Length Area

o (mm) ri (mm) L (mm) A (mm2)

.8 1.8 300 288

.8 1.8 300 289

.8 1.8 650 285

.8 1.8 1000 288

.8 1.8 1501 286

.8 1.8 2000 285

.8 1.8 2500 286

.8 1.8 3000 288

.8 1.8 – 287

.000 0.000 – 0.005

Table 2

Measured specimen dimensions for Series SHS2

Specimen Depth Width Thickness Outer radius Inner radius Length Area

D (mm) B (mm) t (mm) ro (mm) ri (mm) L (mm) A (mm2)

SHS2L300 50.1 50.3 1.584 2.8 1.5 300 295

SHS2L300# 50.0 50.3 1.548 2.8 1.5 300 289

SHS2L650 50.3 50.2 1.596 2.8 1.5 650 298

SHS2L1000 50.2 50.2 1.535 2.8 1.5 1000 287

SHS2L1500 50.0 50.2 1.533 2.8 1.5 1499 287

SHS2L2000 50.1 50.2 1.533 2.8 1.5 2000 287

SHS2L2500 50.2 50.2 1.543 2.8 1.5 2500 289

SHS2L3000 50.1 50.2 1.539 2.8 1.5 3000 288

Mean 50.1 50.2 1.551 2.8 1.5 – 290

COV 0.002 0.001 0.016 0.000 0.000 – 0.015

# second test; 1 in 25.4 mm; COV coefficient of variation.

Table 3

Measured specimen dimensions for Series RHS1

Specimen Depth Width Thickness Outer radius Inner radius Length Area

D (mm) B (mm) t (mm) ro (mm) ri (mm) L (mm) A (mm2)

RHS1L600 140.0 78.8 3.075 10.0 7.0 600 1258

RHS1L1400 139.9 79.9 3.070 10.0 7.0 1400 1262

RHS1L2200 139.9 80.0 3.066 10.0 7.0 2200 1262

RHS1L3000 140.1 79.9 3.011 10.0 7.0 3000 1244

Mean 140.0 79.7 3.056 10.0 7.0 – 1257

COV 0.001 0.007 0.010 0.000 0.000 – 0.007

1 in 25.4 mm; COV coefficient of variation.

B. Young, W.-M. Lui / Thin-Walled Structures 44 (2006) 224–234226

ensure full contact between specimen and end bearings. The

longest specimen lengths produced le/ry ratios of 99, 77, 46

and 44 for Series SHS1, SHS2, RHS1 and RHS2, respectively,

where le is the effective length of fixed-ended column (leZL/2)

and ry is the radius of gyration about the minor y-axis.

The column specimens were separated into four test series

of different cross-section dimensions. All specimens were

tested between fixed ends at various column lengths. The test

specimens were labeled such that the test series and specimen

length could be identified from the label. For example, the label

SHS1L300# defines the following specimen:

† The first four letters indicate that the specimen belongs to

test Series SHS1, where the letters ‘SHS’ refer to square

hollow section.

† The third letter ‘L’ indicates the length of the specimen.

† The last three or four digits are the nominal length of the

specimen in millimeters (300 mm).

Table 4

Measured specimen dimensions for Series RHS2

Specimen Depth Width Thickness O

D (mm) B (mm) t (mm) r

RHS2L600 160.1 80.8 2.869 9

RHS2L1400 160.1 80.8 2.868 9

RHS2L2200 160.1 80.8 2.864 9

RHS2L3000 160.4 80.9 2.878 9

Mean 160.2 80.8 2.870 9

COV 0.001 0.001 0.002 0

1 in 25.4 mm; COV coefficient of variation.

† If a test was repeated, the last symbol ‘#’ in superscript

indicates the repeated test.

The four test series SHS1, SHS2, RHS1 and RHS2 involved

columns with section sizes 40!40!2, 50!50!1.5, 140!80!3 and 160!80!3, respectively.

3. Material properties

3.1. Tensile coupon tests

Tensile coupon tests were conducted to determine the

material properties of the test specimens. Longitudinal tensile

coupons of each test series of specimens were tested. The

coupons were extracted from the untested specimens belonging

to the same batch of specimens as the column tests. The

coupons were taken from the centre of the face at 908 angle

from the weld, as shown in Fig. 1. The coupon dimensions

uter radius Inner radius Length Area

o (mm) ri (mm) L (mm) A (mm)

.0 6.3 600 1305

.0 6.3 1400 1304

.0 6.3 2200 1303

.0 6.3 3000 1311

.0 6.3 – 1306

.000 0.000 – 0.003

0

200

400

600

800

1000

0 10 20 30 40 50

Strain (%)

Stre

ss (

MPa

)

Fig. 2. Complete stress–strain curve obtained from tensile coupon test for

Series RHS2.

600

800

1000

Pa)

Fig. 1. Definition of symbols and location of tensile coupon in cross-section.

B. Young, W.-M. Lui / Thin-Walled Structures 44 (2006) 224–234 227

conformed to the Australian Standard AS 1391 [10] for the

tensile testing of metals using 12.5 mm wide coupon and a

gauge length of 50 mm.

The coupons were tested in a 250 kN capacity MTS

displacement controlled testing machine using friction grips.

Displacement control was used to drive the machine at a

speed of 0.04 mm/min within the elastic range of the stress–

strain curve, then the speed changed to 0.8 mm/min for the

range from proportional limit to a stress level beyond the

0.2% proof stress, and finally the speed changed to

1.35 mm/min until the fracture of the coupon specimen.

The static load was obtained by pausing the applied

straining for 1.5 min near the 0.2% proof stress and the

ultimate tensile strength. This allowed the stress relaxation

associated with plastic straining to take place. A calibrated

extensometer of 50 mm gauge length was used to measure

the longitudinal strain. Two linear strain gauges were

attached to each coupon at the center of each face. The

strain gauges readings were used to determinate the initial

Young’s modulus. A data acquisition system was used to

record the load and the readings of strain at regular

intervals during the tests.

The material properties obtained from the coupon tests are

summarized in Table 5. The measured material properties are

the static 0.2% proof stress (s0.2), static tensile strength (su),

initial Young’s modulus (E0) and elongation after fracture (3f)

based on a gauge length of 50 mm. The measured stress–strain

curves were used to determine the parameter n using the

Ramberg–Osgood expression [11]. The parameter n is used to

describe the shape of the curve, which was obtained from the

measured 0.01% (s0.01) and 0.2% (s0.2) proof stresses using

nZln(0.01/0.2)/ln(s0.01/s0.2). The values of n are also shown in

Table 5. The complete and the initial part of the stress–strain

curves obtained from the tensile coupon test for Series RHS2

are shown in Figs. 2 and 3, respectively.

Table 5

Measured material properties obtained from tensile coupon tests

Test

series

Section

D!B!t (mm)

s0.2(MPa)

su(MPa)

E0

(GPa)

3f(%)

n

SHS1 40!40!2 707 827 216 29 4

SHS2 50!50!1.5 622 770 200 37 5

RHS1 140!80!3 486 736 212 47 6

RHS2 160!80!3 536 766 208 40 5

1 in 25.4 mm; 1 ksi 6.89 MPa.

3.2. Stub column tests

Stub column tests were also conducted to determine the

material properties of the test specimens for the complete

cross-section in the cold-worked state. The shortest specimen

lengths complied with the Structural Stability Research

Council guidelines [12] for stub column lengths. A total of

six stub columns were tested which consisted of specimens

SHS1L300, SHS1L300#, SHS2L300, SHS2L300#, RHS1L600

and RHS2L600. The measured cross-section dimensions and

specimen length of the stub columns are shown in Tables 1–4.

A typical stub column test of specimen RHS2L600 is shown in

Fig. 4. Four longitudinal strain gauges were attached at mid-

length of the stub columns. The strain gauges were located at

the corners of the sections. Three laser displacement

transducers were used to measure the axial shortening of the

specimens.

The stub columns were compressed between fixed ends

using a 2500 kN capacity servo-controlled hydraulic testing

machine. The fixed-ended bearings were restrained against the

minor and major axis rotations as well as twist rotations and

warping. Displacement control was used to drive the hydraulic

actuator at a constant speed of 0.5 mm/min for all stub column

specimens. The static load was recorded by pausing the applied

straining for 1.5 min near the ultimate load of all the

specimens, except for specimens SHS2L300 and SHS2L300#.

The static ultimate loads for specimens SHS1L300,

0

200

400

0 0.2 0.4 0.6 0.8

Strain (%)

Stre

ss (

M

Fig. 3. Initial part of stress–strain curve obtained from tensile coupon test for

Series RHS2.

Table 6

Measured material properties obtained from stub column tests

Test series Section

D!B!t (mm)

s0.2(MPa)

su(MPa)

E0

(GPa)

n

SHS1 40!40!2 757 854 226 3

SHS2 50!50!1.5 608 618 200 4

RHS1 140!80!3 441 444 214 6

RHS2 160!80!3 390 411 213 9

1 in 25.4 mm; 1 ksi 6.89 MPa.

Fig. 4. Local buckling of specimen RHS2L600.

00 0.2 0.4 0.6 0.8

100

200

300

400

500

600

Strain (%)

Stre

ss (

MPa

)

Fig. 6. Initial part of stress–strain curve obtained from stub column test for

Series RHS2.

Table 7

Measured overall geometric imperfections at mid-length of columns

Specimen d/L

x y

SHS1L650 1/430 1/17060

SHS1L1000 1/19685 1/2386

SHS1L1500 1/11811 1/29528

SHS1L2000 1/10499 1/8288

SHS1L2500 1/29528 1/2140

B. Young, W.-M. Lui / Thin-Walled Structures 44 (2006) 224–234228

SHS1L300#, RHS1L600 and RHS2L600 were approximately

4–5% lower than their ultimate loads without pausing the

applied straining. Table 6 shows the measured material

properties obtained from the stub column tests, which included

the static 0.2% proof stress (s0.2), static tensile strength (su),

initial Young’s modulus (E0), and parameter n that calculated

using the same method as the tensile coupon tests. The material

properties were obtained from the average values of the four

strain gauges. The complete and the initial part of the stress–

strain curves obtained from the stub column test for Series

RHS2 are shown in Figs. 5 and 6, respectively.

Normally, the value of the 0.2% proof stress obtained from

stub column test would be greater than those obtained from

tensile coupon test. This is due to the cold-working at the

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Strain (%)

Stre

ss (

MPa

)

Fig. 5. Complete stress–strain curve obtained from stub column test for Series

RHS2.

corners of the section produced considerable enhancement to

the material properties. However, this is not the case for test

series SHS2, RHS1 and RHS2, where the values of the 0.2%

proof stress obtained from the stub column tests are less than

those obtained from the tensile coupon tests. This is due to

local buckling occurred in the stub column tests, and lower

values of 0.2% proof stress were obtained from the stub column

tests.

4. Geometric imperfection measurements

Initial overall geometric imperfections of the column

specimens were measured prior to testing. Minor axis flexural

imperfections were recorded for all specimens, except for the

stub columns of Series SHS1 and SHS2. Theodolites were used

to obtain readings at mid-length and near both ends of the

specimens. The overall geometric imperfections at mid-length

(d) normalized with respect to the specimen length (L) are

shown in Table 7. The average overall geometric imperfections

at mid-length were 1/2670, 1/1630, 1/4668 and 1/5614 of the

SHS1L3000 1/1390 1/11811

SHS2L650 1/2326 1/4653

SHS2L1000 1/1358 1/2316

SHS2L1500 1/2953 1/1790

SHS2L2000 1/4632 1/1500

SHS2L2500 1/775 1/3076

SHS2L3000 1/872 1/993

RHS1L600 – 1/4295

RHS1L1400 – 1/7349

RHS1L2200 – 1/5588

RHS1L3000 – 1/3236

RHS2L600 – 1/7874

RHS2L1400 – 1/5512

RHS2L2200 – 1/6663

RHS2L3000 – 1/3937

B. Young, W.-M. Lui / Thin-Walled Structures 44 (2006) 224–234 229

specimen length for Series SHS1, SHS2, RHS1 and RHS2,

respectively. The maximum initial local geometric imperfec-

tions of the specimens were 0.113, 0.164, 0.343 and 0.460 mm

for Series SHS1, SHS2, RHS1 and RHS2, respectively.

The local geometric imperfections measurements are detailed

in Young and Lui [13].

5. Column tests

The duplex stainless steel SHS and RHS columns were

compressed between fixed ends. The tests were performed over

a range of column lengths from 300 to 3000 mm. Therefore,

column curve for each series of tests were plotted. A 2500 kN

capacity DARTEC servo-controlled hydraulic testing machine

was used to apply compressive axial force to the column

specimens. Two steel end plates were welded to the ends of the

specimen. A moveable upper end support allowed the tests to

be conducted at various column lengths. A rigid flat bearing

plate was connected to the upper end support, and the top end

plate of the specimen was bolted to the rigid flat bearing plate,

which was restrained against the minor and major axis rotations

as well as twist rotations and warping. Hence, the top end of the

column was fixed in position. A special bearing was used at the

lower end support. Initially, the special bearing was free to

rotate in any direction. The ram of the actuator was moved

slowly toward the specimen until the special bearing was in full

contact with the bottom end plate of the specimen having a

small initial load of approximately 2 kN. This procedure

eliminated any possible gaps between the special bearing and

the bottom end plate of the specimen. The bottom end plate of

the specimen was bolted to the special bearing, and the bearing

was then restrained from rotations and twisting by using

vertical and horizontal bolts, respectively. The vertical and

horizontal bolts of the special bearing were used to lock the

Table 8

Comparison of test strengths with design strengths for Series SHS1

Specimen Test Comparison

PExp (kN) Failure mode le (mm) PExp

PASCE P

SHS1L300 245.3 Y 150 1.21 1

SHS1L300# 238.0 Y 150 1.17 1

SHS1L650 222.8 F 325 1.10 1

SHS1L1000 197.8 F 500 1.03 1

SHS1L1500 136.0 F 750 0.98 1

SHS1L2000 106.3 F 1000 1.04 1

SHS1L2500 71.3 F 1250 0.93 1

SHS1L3000 52.1 F 1500 0.90 0

Mean (Pm) – – – 1.05 1

COV (VP) – – – 0.106 0

Reliability

index (b0)

– – – 2.69 2

Resistance

factor (f0)

– – – 0.85 0

Reliability

index (b1)

– – – 2.69 2

Resistance

factor (f1)

– – – 0.85 0

# second test; 1 in 25.4 mm; 1 kip 4.45 kN; COV coefficient of variation; Y mater

*Calculated using material properties obtained from stub column tests.

bearing in position after full contact was achieved. Hence, the

special bearing became a fixed-ended bearing. The fixed-ended

bearing was considered to restrain both minor and major axis

rotations as well as twist rotations and warping.

Three laser displacement transducers were used to measure

the axial shortening of the specimen. Displacement control was

used to drive the hydraulic actuator at a constant speed of

0.5 mm/min for all specimens. The use of displacement control

allowed the tests to be continued into the post-ultimate range.

The static load was recorded by pausing the applied straining

for 1.5 min near the ultimate load of all the specimens, except

for the specimens of Series SHS2. The static ultimate load was

approximately 2–5% lower than the ultimate load without

pausing the applied straining for the specimens. A data

acquisition system was used to record the applied load and

the readings of the laser displacement transducers at regular

intervals during the tests.

The experimental ultimate loads (PExp) and failure modes of

the stub and long columns are shown in Tables 8–11 for Series

SHS1, SHS2, RHS1 and RHS2, respectively. The stub column

tests were repeated for Series SHS1 and SHS2. The test results

for the repeated tests are very close to the first test values, with

a difference of 3.0 and 1.1% for Series SHS1 and SHS2,

respectively. The failure modes observed at ultimate load of the

specimens involved yielding of material (Y), local buckling

(L), flexural buckling (F) and interaction of local and overall

flexural buckling (LCF), as shown in Tables 8–11. Flexural

buckling was observed for all specimens of Series SHS1,

except for the shortest specimens that failed by yielding of

material. Pure local buckling was observed for specimens with

effective lengths less than or equal to 700 mm (le%700 mm)

for Series SHS2, RHS1 and RHS2. Interaction of local and

overall flexural buckling was observed for specimens with

effective lengths greater than or equal to 1100 mm

PExp

AS=NZS

PExp

PEC3

PExp

P�ASCE

PExp

P�AS=NZS

PExp

P�EC3

.21 1.21 1.13 1.13 1.13

.17 1.17 1.10 1.10 1.10

.10 1.10 1.03 1.03 1.03

.03 1.12 0.93 0.91 1.04

.00 1.02 0.93 0.91 0.95

.09 1.14 1.00 1.02 1.06

.01 1.08 0.90 0.96 1.00

.99 1.07 0.87 0.95 0.99

.08 1.11 0.98 1.00 1.04

.077 0.054 0.096 0.083 0.057

.52 2.75 2.51 2.22 2.46

.90 0.91 0.85 0.90 0.91

.95 3.18 2.51 2.64 2.88

.85 0.85 0.85 0.85 0.85

ial yielding; F flexural buckling.

Table 9

Comparison of test strengths with design strengths for Series SHS2

Specimen Test Comparison

PExp (kN) Failure mode le (mm) PExp

PASCE

PExp

PAS=NZS

PExp

PEC3

PExp

P�ASCE

PExp

P�AS=NZS

PExp

P�EC3

SHS2L300 175.7 L 150 1.09 1.09 1.09 1.11 1.11 1.11

SHS2L300# 177.6 L 150 1.11 1.11 1.11 1.12 1.12 1.12

SHS2L650 181.0 L 325 1.13 1.13 1.13 1.14 1.14 1.14

SHS2L1000 175.1 L 500 1.09 1.09 1.10 1.11 1.11 1.12

SHS2L1500 156.8 LCF 750 1.11 1.14 1.11 1.11 1.11 1.12

SHS2L2000 124.7 F 1000 1.01 1.05 1.06 1.05 1.06 1.07

SHS2L2500 95.1 F 1250 0.92 1.00 1.06 1.00 1.04 1.06

SHS2L3000 72.4 F 1500 0.86 0.96 1.05 0.95 1.01 1.05

Mean (Pm) – – – 1.04 1.07 1.09 1.07 1.09 1.10

COV (VP) – – – 0.097 0.059 0.026 0.064 0.043 0.030

Reliability

index (b0)

– – – 2.72 2.58 2.74 3.00 2.69 2.78

Resistance

factor (f0)

– – – 0.85 0.90 0.91 0.85 0.90 0.91

Reliability

index (b1)

– – – 2.72 3.01 3.18 3.00 3.13

3.22

Resistance

factor (f1)

– – – 0.85 0.85 0.85 0.85 0.85

0.85

# second test; 1 in 25.4 mm; 1 kip 4.45 kN; COV coefficient of variation; L local buckling; F flexural buckling.

*Calculated using material properties obtained from stub column tests.

B. Young, W.-M. Lui / Thin-Walled Structures 44 (2006) 224–234230

(leR1100 mm) for Series RHS1 and RHS2 as well as for

specimen SHS2L1500. Flexural buckling was observed for

specimens SHS2L2000, SHS2L2500 and SHS2L3000. Fig. 4

shows the local buckling of specimen RHS2L600.

The specimen SHS1L3000 failed by flexural buckling is

shown in Fig. 7. The interaction of local and overall flexural

buckling of specimen RHS2L3000 at ultimate load is shown in

Fig. 8.

6. Design rules

The design strengths of the cold-formed stainless steel

concentrically loaded compression members were calculated

using the following specifications:

Table 10

Comparison of test strengths with design strengths for Series RHS1

Specimen Test Comparison

PExp (kN) Failure mode le (mm) PExp

PASCE P

RHS1L600 558.2 L 300 1.04 1

RHS1L1400 553.1 L 700 1.03 1

RHS1L2200 525.1 LCF 1100 1.06 1

RHS1L3000 513.5 LCF 1500 1.17 1

Mean (Pm) – – – 1.08 1

COV (VP) – – – 0.060 0

Reliability

index (b0)

– – – 2.89 2

Resistance

factor (f0)

– – – 0.85 0

Reliability

index (b1)

– – – 2.89 2

Resistance

factor (f1)

– – – 0.85 0

1 in 25.4 mm; 1 kip 4.45 kN; COV coefficient of variation; L local buckling; F fle

*Calculated using material properties obtained from stub column tests.

† American Society of Civil Engineers Specification (ASCE

2002) for the design of cold-formed stainless steel structural

members.

† Australian/New Zealand Standard (AS/NZS 2001) for cold-

formed stainless steel structures.

† European Code (EC3 1996) Eurocode 3: Design of steel

structures—Part 1.4: General rules—Supplementary rules

for stainless steels.

According to the design rules in the ASCE Specification,

tangent modulus (Et) was determined using Eq. (B-2) in

Appendix B of the ASCE Specification. The Ramberg–Osgood

parameter n, initial Young’s modulus (E0) and 0.2% proof

stress (s0.2) are required to determine the tangent modulus, thus

PExp

AS=NZS

PExp

PEC3

PExp

P�ASCE

PExp

P�AS=NZS

PExp

P�EC3

.04 1.04 1.13 1.13 1.13

.03 1.03 1.12 1.12 1.12

.08 1.02 1.14 1.15 1.09

.22 1.12 1.26 1.30 1.19

.09 1.05 1.16 1.18 1.13

.080 0.043 0.055 0.072 0.037

.39 2.50 3.22 2.73 2.83

.90 0.91 0.85 0.90 0.91

.78 2.92 3.22 3.13 3.26

.85 0.85 0.85 0.85 0.85

xural buckling.

Table 11

Comparison of test strengths with design strengths for Series RHS2

Specimen Test Comparison

PExp (kN) Failure mode le (mm) PExp

PASCE

PExp

PAS=NZS

PExp

PEC3

PExp

P�ASCE

PExp

P�AS=NZS

PExp

P�EC3

RHS2L600 537.3 L 300 1.00 1.00 1.00 1.28 1.28 1.28

RHS2L1400 537.2 L 700 1.00 1.00 1.00 1.28 1.28 1.28

RHS2L2200 515.3 LCF 1100 1.02 1.01 0.99 1.32 1.38 1.23

RHS2L3000 439.4 LCF 1500 0.99 1.02 0.93 1.21 1.26 1.13

Mean (Pm) – – – 1.00 1.01 0.98 1.27 1.30 1.23

COV (VP) – – – 0.013 0.011 0.033 0.036 0.042 0.056

Reliability

index (b0)

– – – 2.85 2.41 2.24 3.74 3.35 3.03

Resistance

factor (f0)

– – – 0.85 0.90 0.91 0.85 0.90 0.91

Reliability

index (b1)

– – – 2.85 2.87 2.68 3.74 3.78 3.44

Resistance

factor (f1)

– – – 0.85 0.85 0.85 0.85 0.85 0.85

1 in 25.4 mm; 1 kip 4.45 kN; COV coefficient of variation; L local buckling; F flexural buckling.

*Calculated using material properties obtained from stub column tests.

B. Young, W.-M. Lui / Thin-Walled Structures 44 (2006) 224–234 231

an iterative design procedure is involved. The design rules of

the AS/NZS Standard allow the use of Euler column strength

that is identical to the ASCE Specification or the Perry curve,

and the latter has been used for the purpose of comparison. In

calculating the AS/NZS design strengths, the values of the

parameters a, b, l0 and l1 are required, which depend on the

type of stainless steel. These parameters were determined from

the equations given by Rasmussen and Rondal [14], and the

values of the parameters are shown in Table 12. The material

properties obtained from both the tensile coupon tests and stub

column tests were used to determine these parameters. The

design rules of the EC3 Code, values of imperfection factor and

Fig. 7. Flexural buckling of specimen SHS1L3000.

limiting slenderness were taken as 0.49 and 0.4, respectively,

which were obtained from Table 5.2 of the Code. The three

specifications require the determination of effective cross-

section area (Ae) of the column. In the ASCE, AS/NZS and

EC3 specifications, the effective areas were generally found to

be equal to the gross areas of cross-section for Series SHS1 and

SHS2, except for the specimens with effective lengths less than

or equal to 750 mm (le%750 mm) for Series SHS2, whereas

the effective areas were less than the gross areas for Series

RHS1 and RHS2. This is in agreement with the local buckling

observed in the tests.

The fixed-ended columns were designed as concentrically

loaded compression members and the effective length (le) was

assumed equal to one-half of the column length (L) for fixed-

Fig. 8. Interaction of local and overall flexural buckling of specimen

RHS2L3000.

Table 12

Values of parameters a, b, l0 and l1 for design strength calculation

Test series Tensile coupon tests Stub column tests

a b l0 l1 a b l0 l1

SHS1 1.262 0.191 0.701 0.404 1.363 0.269 0.705 0.347

SHS2 1.066 0.117 0.686 0.488 1.304 0.205 0.695 0.383

RHS1 1.023 0.116 0.649 0.435 1.083 0.124 0.640 0.423

RHS2 1.067 0.117 0.666 0.467 0.721 0.132 0.597 0.291

B. Young, W.-M. Lui / Thin-Walled Structures 44 (2006) 224–234232

ended columns (leZL/2). The design strengths were calculated

using the average measured cross-section dimensions and the

measured material properties as detailed in Tables 1–6.

The 0.2% proof stress (s0.2) was used as the corresponding

yield stress.

0

50

100

150

200

250

300

0 500 1000 1500 2000

Effective length, le (mm)

Axi

al lo

ad, P

(kN

)

Tests

Flexural buckling

P*ASCE

P*AS / NZS

P*EC3

PEC3PAS / NZS

PASCE

Fig. 9. Column curves for Series SHS1.

160180200

)

Tests

Flexural buckling

7. Reliability analysis

The reliability of the column design rules was evaluated

using reliability analysis. Reliability analysis is detailed in the

Commentary of the ASCE Specification [7]. A target reliability

index (b0) of 3.0 for stainless steel structural members is

recommended as a lower limit in the ASCE Specification. The

design rules are considered to be reliable if the reliability index

is greater than 3.0. The resistance factors (f0) of 0.85, 0.9 and

1/1.1 for concentrically loaded compression members as

recommended by the ASCE, AS/NZS and EC3 specifications,

respectively, were used in the reliability analysis. The load

combinations of 1.2DLC1.6LL, 1.25DLC1.5LL and

1.35DLC1.5LL as specified in the ASCE, AS/NZS and EC3

specifications, respectively, were used in the analysis, where

DL is the dead load and LL is the live load. The statistical

parameters were obtained from Clause 6 of the ASCE

Specification for structural members, where MmZ1.10, FmZ1.00, VMZ0.10 and VFZ0.05 which are the mean values and

coefficients of variation of material and fabrication factors. The

statistical parameters Pm and VP are the mean value and

coefficient of variation of tested-to-predicted load ratios,

respectively, as shown in Tables 8–11. The values of the

reliability index (b0) of the design rules were determined using

the respective resistance factors and load combinations are

shown in Tables 8–11. For the purpose of direct comparison, a

constant resistant factor (f1) of 0.85 and a load combination of

1.2DLC1.6LL as specified in the ASCE Specification were

used to calculate the reliability index (b1) for the AS/NZS and

EC3 specifications, and the values of the reliability index are

also shown in Tables 8–11.

00 500 1000 1500 2000

20406080

100120140

Axi

al lo

ad, P

(kN

Effective length, le (mm)

P*ASCEP*AS / NZS

P*EC3

PEC3

PAS / NZSPASCE

Fig. 10. Column curves for Series SHS2.

8. Comparison of test strengths with design strengths

The column test strengths (PExp) are compared with the

unfactored design strengths predicted using the American

(ASCE) [7], Australian/New Zealand (AS/NZS) [8] and

European (EC3) [9] specifications for cold-formed stainless

steel structures. The design strengths were calculated using the

material properties obtained from both the tensile coupon tests

and stub column tests, and these material properties are shown

in Tables 5 and 6, respectively. Tables 8–11 show the

comparison of the column test strengths with the design

strengths, where PASCE, PAS/NZS and PEC3 are the design

strengths calculated using the material properties

obtained from the tensile coupon tests for American,

Australian/New Zealand and European specifications, respect-

ively. The P�ASCE; P

�AS=NZS and P�

EC3 are the design strengths

calculated using the material properties obtained from the stub

column tests. Figs. 9–12 also show the comparison of the test

strengths with the design strengths. Column curves were

plotted against the effective length of the columns for the

American, Australian/New Zealand and European specifica-

tions. The theoretical elastic minor axis flexural buckling loads

of the fixed-ended columns are also shown in Figs. 9–12. The

theoretical buckling loads were calculated using the effective

length equal to one-half of the column length.

100

0

200

300

400

500

600

700

800Tests Flexural buckling

0 500 1000 1500 2000 2500 3000Effective length, le (mm)

Axi

al lo

ad, P

(kN

)

P*ASCE

P*AS / NZSP*EC3

PEC3PAS / NZS

PASCE

Fig. 12. Column curves for Series RHS2.

0

100

200

300

400

500

600

700

800Tests

Flexural buckling

0 500 1000 1500 2000 2500 3000

Effective length, le (mm)

Axi

al lo

ad, P

(kN

)

P*ASCE

P*AS / NZS P*EC3

PEC3

PAS / NZS

PASCE

Fig. 11. Column curves for Series RHS1.

B. Young, W.-M. Lui / Thin-Walled Structures 44 (2006) 224–234 233

The design strengths predicted by the ASCE, AS/NZS and

EC3 specifications using the material properties obtained from

the tensile coupon and stub column tests are generally

conservative, except for a few specimens with long column

lengths in Series SHS2 and RHS2 calculated using the material

properties obtained from the tensile coupon tests, and some of

the specimens with intermediate and long column lengths in

Series SHS1. The mean values of PExp=PASCE; PExp=PAS=NZS

and PExp=PEC3 ratios are 1.05, 1.08 and 1.11 with the

coefficients of variation (COV) of 0.106, 0.077 and 0.054,

and the corresponding reliability indices (b0) of 2.69, 2.52 and

2.75 for Series SHS1, respectively, as shown in Table 8. The

mean values of PExp=P�ASCE; PExp=P

�AS=NZS and PExp=P

�EC3 ratios

are 0.98, 1.00 and 1.04 with the COV of 0.096, 0.083 and

0.057, and the corresponding reliability indices (b0) of 2.51,

2.22 and 2.46 for Series SHS1, respectively. The mean values

of the test strength to design strength ratios, COV and

reliability indices for Series SHS2, RHS1 and RHS2 are

shown in Tables 9–11, respectively.

Generally, the reliability indices (b0) are less than the target

value of 3.0 for all test series, except for Series SHS2, RHS1

and RHS2 that calculated using the material properties

obtained from the stub column tests for ASCE Specification.

The reliability indices (b1) based on the same resistant factor

and load combination are generally less than the target value

for all test series, except for Series SHS2, RHS1 and RHS2 that

calculated using the material properties obtained from the stub

column tests for ASCE, AS/NZS and EC3 specifications. It

should be noted that the design strengths calculated using the

material properties obtained from stub column tests of slender

sections, such as the Series SHS2, RHS1 and RHS2, have taken

the local buckling into account twice for the mechanical

properties and the calculation of effective area. Hence, the

design strengths of P�ASCE; P

�AS=NZS and P

�EC3 are quite con-

servative for slender sections subjected to local buckling.

9. Conclusions

A test program on cold-formed high strength stainless steel

columns has been presented. The duplex stainless steel was

investigated in this study. The test specimens had the yield

stress and tensile strength up to 750 and 850 MPa, respectively.

Two series of square hollow section and two series of

rectangular hollow section columns were compressed between

fixed ends. The fixed-ended columns were tested at different

column lengths, and column curves were obtained for each test

series. The test strengths were compared with the design

strengths predicted using the American, Australian/New

Zealand and European specifications for cold-formed stainless

steel structures. It is shown that the design strengths predicted

by the three specifications are generally conservative for the

cold-formed high strength stainless steel square and rectangu-

lar hollow section columns. Therefore, the current column

design rules specified in the three specifications are applicable

to high strength material, despite the fact that the specifications

were mainly based on the investigation of normal strength

material, such as the austenitic stainless steel type 304.

Acknowledgements

The authors are grateful to STALA Tube Finland for

supplying the test specimens. The authors are thankful to Mr

Chung Lee and Mr Pak-Kin Cheung for their assistance in this

research project.

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