AISC_coldformed Tubulars & Connections 2000

1

Research into the Behaviour and Design of Cold-Formed Tubular Members and Connections

Gregory Hancock and Tim Wilkinson Centre for Advanced Structural Engineering

Department of Civil Engineering, University of Sydney NSW, 2006, Australia

Xiao-Ling Zhao

Department of Civil Engineering, Monash University Clayton, Victoria, Australia

ABSTRACT For nearly 20 years, a major research program has been performed at the University of Sydney investigating the structural behaviour and design of cold-formed tubular structural members and connections. This research has been progressively incorporated in the Australian Standard AS 4100 Steel Structures. In the last 5 years, several major steel structures have been built for the Olympics 2000 and these have been made mainly from cold-formed tubular members designed to AS 4100. Hence the Olympic structures have benefited from the research and design developments. Cold-formed tubular members are manufactured in Australia to the Australian Standard AS 1163 Structural Steel Hollow Sections. In 1990, the Australian Steel Structures Standard was published as AS 4100 in limit states format and included the University of Sydney research available at that time. In 1998, a revision of AS 4100 was published and included all of the latest research on cold-formed tubular members The lecture summarises the research which has been performed to date including plate strength, compression members, flexural members, beam-columns, portal frames, and welded and bolted connections. Emphasis is placed on the experimental data and its use in formulating design equations for use in AS 4100-1998. INTRODUCTION Cold-formed structural members are being used more widely in routine structural design as the world steel industry moves from the production of hot-rolled section and plate to coil and strip, often with galvanised and/or painted coatings. Steel in this form is more easily delivered from the steel mill to the manufacturing plant where it is usually cold-rolled into open and closed section members. In Australia, of the approximately one million tonnes of structural steel used each year, 125,000 tonnes is used for cold-formed open sections such as purlins and girts and 400,000 tonnes is used for tubular members. Tubular members are normally produced by cold-forming with an electric resistance weld (ERW) to form the tube. In some applications of tubular members, the sections are in-line galvanised

Prepared for a lecture series given by Professor Greg Hancock and Dr Xiao-Ling Zhao, organised by the Australian Institute of

Steel Construction, June 2000.

2

with a subsequent enhancement of the tensile properties. The resulting product is called DuraGal (BHP (1997)). In Australia, the total quantity of cold-formed products now exceeds the total quantity of hot-rolled products. Structural steel hollow sections are normally produced to the Australian Standard AS 1163 (1991). They are all cold-formed and usually have stress grades of 250 MPa (called C250), 350 MPa (called C350) and 450 MPa (called C450). The most common grade is C350 which has the yield strength enhanced from 300 MPa to 350 MPa during the forming process. The C450 grade is often achieved by in-line galvanising (BHP, 1997) but may be achieved by alloying elements in the steel feed. The Australian Standard for the design of steel structures AS 4100 was first published in limit states format in 1990 and permitted the use of cold-formed tubular members to AS 1163. Cold-formed tubular members had been permitted to be designed to the permissible stress steel structures design standard AS 1250 (Standards Australia 1981) since an amendment in 1982. However, the research on cold-formed tubular members was limited in many areas, particularly flexural members and connections, and so a significant research program was undertaken. This paper summarises research in the following areas: • Plate slenderness limits for tube faces in both compression and bending (Section 1) • Compression members (Section 2) • Flexural members including lateral buckling (Section 3) • Web crippling under bearing and combined bending and web crippling under bearing (Section 4) • Combined compression and bending (beam-columns) for both compact and slender sections

(Section 5) • Welded connections less than 3 mm thick (Section 6) • Bolted moment end-plate connections (Section 7) • Plastic design of portal frames (Section 8) 1. PLATE SLENDERNESS LIMITS 1.1 Flange Slenderness Limits in Compression Design rules for the plate slenderness limits (yield slenderness limit 8ey and plastic slenderness limit 8ep) of cold-formed tubular sections are included in AS 4100-1998. These plate slenderness limits were based on tests of C350 SHS and RHS produced by BHP Structural and Pipeline Products. The test results were published in Hasan and Hancock (1989), Key and Hancock (1985) and Key, Hasan and Hancock (1988). To ascertain whether these plate slenderness limits were applicable to C450 tubular sections, compression tests on stub columns and plastic bending tests on beams were performed on sections produced by Palmer Tube Mills (Aust) Pty Limited. The test results were published by Zhao and Hancock (1991a). 1.2 Yield Slenderness Limit for Flange in Compression The yield slenderness limit (8ey) defines a plate element slenderness (8e) below which the plate can be considered as fully effective when subjected to compression. The effective width (be) of a flat element of clear width (b) is defined as:

250y

ey

e

eye f

tbb

λλλ

=

= (1)

3

in which fy is the yield stress used in design. The nominal section capacity of a concentrically loaded compression member is defined in Clause 6.2 of AS 4100-1998 as:

Ns = kf An fy (2)

in which An is the net area of the cross-section and kf is the form factor defined as:

g

ef A

Ak = (3)

where Ag is the gross area of the section. Ae is the effective area which is calculated from the gross area by summing the effective areas of the individual elements, whose effective widths are given by Eq. 1. For SHS and RHS, the formulae for kf are given in Zhao and Hancock (1991a). They are summarised below, where E = 200000 MPa, < = 0.3 and kb = 4.0 (the adoption of 4.0 for the elastic buckling coefficient was explained in Key et al. (1988). For SHS:

c

eyef Sb

bk

λ01858.0== (4)

For RHS:

db

db

Sk c

ey

f

+

+=

1

01858.0 λ

(5)

where

b

yc kE

ftbS 2

2 )1(π

ν−

= (6)

The parameter Sc is called the modified plate slenderness. For RHS, d (the clear depth of RHS) should be used for the calculation of Sc in place of b (the clear width of RHS). Eq. (5) assumes that for RHS only the more slender face is not fully effective. For 8ey = 40, from Eq. (4) for SHS:

c

f Sk 743.0= (7)

and from Eq. (5) for RHS:

4

db

db

Sk c

f

+

+=

1

743.0

(8)

in which Sc is given by Eq. (6). The dimensionless stub column failure strengths (Pu / AmFyf) have been plotted in Fig. 1 against the modified plate slenderness ( ) byfmmc kEtbS 22 /)1(12/ πνσ −= . Fig. 1(a) compares the results for the

Fig. 1 Section Strength versus Modified Plate Slenderness

different section sizes for C450 SHS and RHS, whereas Fig. 1(b) compares the results for the C350 tests and for the C450 tests. The form factor kf is also plotted in Figs 1(a) and (b) for SHS and RHS with a b/d ratio equal to 0.6. The comparison is based on the measured yield stress (Fyf) and the measured dimensions (bm,, tm and Am). From Fig. 1(b), it can be concluded that the plate yield slenderness limit (8ey = 40) specified in AS 4100-1998 is adequate for both C350 and C450 SHS and RHS. The reason for some tests having Pu / AmFyf greater than 1.0 is a result of the fact that Fyf is based on the face yield strength whereas the average yield strength is greater than Fyf as a result of the higher yield in the corners. 1.3 Plastic Slenderness Limit for Flange in Compression For SHS and RHS, the plastic slenderness limit (8ep) defines a flange plate slenderness below which the section can be used for plastic design. The usual method to judge whether a section can be used

(b) C350 and C450 SHS and RHS

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Modified Plate Slenderness (S )

0

0.2

0.4

0.6

0.8

1.0

1.2

P /AC450C350

c

σu m yf

(a) C450 SHS and RHS

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Modified Plate Slenderness (S )

0

0.2

0.4

0.6

0.8

1.0

1.2

P /A

k for RHSwith b/d =0.6

100 x 100 x 3.8 SHS100 x 100 x 3.3 SHS100 x 100 x 2.8 SHS75 x 75 x 3.3 SHS75 x 75 x 2.8 SHS75 x 75 x 2.3 SHS65 x 65 x 3.3 SHS125 x 75 x 3.8 RHS125 x 75 x 3.3 RHS100 x 50 x 2.8 RHS

f

k for SHSf

Elastic Local Bucklingk = 4.0b

c

σu m yf

k for RHSwith b/d =0.6

b

Elastic Local Bucklingk = 4.0b

k for SHSf

5

for plastic design is to check its plastic hinge rotation capacity (R) as defined by Korol and Hudoba (1978) and Hasan and Hancock (1989). A value of R equal to 4.0 was assumed to be sufficient to allow redistribution of moment for plastic design. From the measured plastic hinge rotation capacity (Rt) determined in tests for a range of sections, a value of b/t = 25 was obtained for C350 RHS by Hasan and Hancock (1989), and a value of b/t = 22 was obtained for C450 RHS by Zhao and Hancock (1991) as the satisfactory lower bound limits for defining the maximum flange slenderness of cold-formed RHS that may be used for plastic design. From Clause 5.2 of AS 4100-1998

epy

e

ftb λλ ≤=

250 (9)

Hence, for C350 RHS, using b/t = 25, Eq. (9) gives 8ep = 29.6, and for C450 RHS, using b/t = 22, Eq. (9) gives 8ep = 29.5. A direct comparison of 8e versus Rt is shown in Fig. 2 using the measured values of bm, tm and Fyf. It can be seen that at an Rt value of 4.0, both the C350 and C450 give a similar plate element plastic slenderness limit (8ep) of approximately 30. If a higher value of Rt was required, then the C450 RHS would require a lower plate element plastic slenderness limit than the C350 RHS.

Fig. 2 Plate Element Slenderness versus Plastic Hinge Rotation Capacity

It can be concluded that the plate element plastic slenderness limit (8ep = 30) specified in AS 4100-1998 is adequate for both C350 and C450 SHS and RHS. It should be noted that at this stage, plastic design of SHS and RHS is not permitted by AS 4100-1998 so that the 8ep value is currently used to define the limit for compact sections which can resist the plastic moment Mp without moment redistribution. 1.4 Plastic Slenderness Limit for Web in Bending To further investigate the suitability of RHS sections with low b/d for plastic design, a series of bending tests examined the influence of web slenderness on the rotation capacity of cold-formed rectangular hollow sections (Wilkinson and Hancock (1998). The results indicate that the plastic (Class 1) web slenderness limits in design standards, which are based on tests of I-sections, are not conservative for RHS. Some sections, which are classified as compact or Class 1 by current steel

0 2 4 6 8 10 12Plastic Hinge Rotation Capacity (R )

0

10

20

30

40

50

Plat

eEl

emen

tSle

nder

ness

Linear Regression (C450)

Linear Regression (C350)

Lower Bound

Lower BoundC450C350

t

b ------m t m

σ ------yf

250

√()

6

specifications, do not demonstrate rotation capacity suitable for plastic design. The common approach in which the flange and web slenderness limits are given independently is inappropriate for RHS. There is considerable interaction between the webs and the flange, which influences the rotation capacity, as shown by the approximate iso-rotation curves in Fig. 3 where the numbers next to the markers are the value of Rt. A proposal for a bilinear interaction formula between the web and flange slenderness limits for compact RHS is also shown in Fig. 4. The reference to “this paper” in Fig. 3 means Wilkinson and Hancock (1998).

Fig. 3 Rotation Capacity and Isorotation Curves for Tests of RHS

Fig. 4 Iso-rotation Curves and Proposed Compact Limit for Webs of RHS 2. COMPRESSION MEMBERS The formulae for column design adopted in AS 4100-1998 are based on the ‘modifying factor’ method for multiple column curves described by Rotter (1982). The nominal member capacity (Nc) of a column is defined in Clause 6.3.3 of AS 4100-1998 as:

0

5

10

15

20

25

30

35

40

45

50

20 30 40 50 60 70 80 90

Web Slenderness (AS 4100) λw = (d -2t )/t·√(f y/250)

Flan

ge S

lend

erne

ss (A

S 41

00)

λ w =

(d-2

t)/t

· √(f

y/250

)

AS 4100Compact

Limit

R = 1R = 2

R = 4

R = 6

Possible newCompact Limitλw < 70 - 5λf /6

λf < 30

0

5

10

15

20

25

30

35

40

45

50

20 30 40 50 60 70 80 90

Web Slenderness (AS 4100) λw

Flan

ge S

lend

erne

ss (A

S 41

00)

λ f

This Paper Grade C450

This Paper Grade C350

Zhao & Hancock (1991) Grade C450

Hasan & Hancock (1988) Grade C350

AS 4100Compact Limit

0

3.82.3

2.6

0

1.3

0.81.2

1.8 1.5

4.8

7.1

6.07.4

1114

9.0

12

8.5

9.08.0

5.6

5.0 4.34.2

2.72

3.51.2

1.40.8

5.7

6.5

R = 1

R = 2

R = 4R = 6

13 11

7

scsc NNN ≤= α (10)

in which Ns is given by Eq. (2). The member slenderness reduction factor "c is determined by the following formulae:

−−=

29011ξλ

ξα c (11a)

2

2

902

190

++

=λ

ηλ

ξ (11b)

ban ααλλ += (11c)

( ) 05.1300326.0 ≥−= λη (11d)

250y

fe

n

fk

rL

=λ (11e)

( )

20503.155.132100

2 +−−

=nn

na λλ

λα (11f)

The appropriate member section constant ("b) is given in Table 6.3.3(1) or 6.3.3(2) of AS 4100-1998. The form factor (kf) is given by Eq. (3). The effective length (Le) is the product of the actual length (L) and the member effective length factor (ke) determined in accordance with Clause 4.6.3 of AS 4100-1998. The results of long column tests on SHS sections performed by Key, Hasan and Hancock (1988) are compared in Fig. 5 with three column curves with different values of the appropriate member section constant ("b). The test strengths are nondimensionalised with respect to the stub column strength (kf Pyf) based on the measured yield stress of each specimen and the measured dimensions. The curves with "b = -1.0 and 0.0 correspond approximately with the SSRC1 and SSRC2 column curves respectively.

8

Fig. 5 Comparison of AS 4100 Column Curves with Test Results

The test results on the loaded columns with load eccentricity equal to L/1000 have been adopted in AS 4100-1998 for the design of cold-formed SHS and RHS columns. The use of an eccentricity of L/1000 resulted from the fact that the SHS tested were particularly straight and so no significant geometric imperfections existed in the columns. The curve chosen in AS 4100-1990 for non-stress relieved SHS and RHS is "b = -0.5 3. FLEXURAL MEMBERS Lateral Buckling Beam Curves The beam design curve in AS 4100-1998 is very conservative when applied to RHS sections, since it was based on the lower bounds of tests on I-sections. Inelastic lateral buckling tests on RHS sections were performed and formulae for member capacity of RHS beams were proposed (Zhao, Hancock and Trahair (1995) and are shown in Fig. 6. A finite element (FE) model was developed to simulate the lateral buckling behaviour of RHS sections. The analysis included the effects of the prebuckling deflections, material inelasticity, residual stresses and initial imperfections (Pi and Trahair, (1994)) and Zhao, Hancock, Trahair and Pi (1995)). The proposal of Pi and Trahair (1994) is shown in Fig. 6. An alternative lateral buckling moment (Mbx) under uniform bending moment is given by:

( ) pxbx MM 2278.0056.1 λ−= for 40.145.0 ≤≤ λ (12)

yzbx MM = for 40.1>λ (13)

yz

px

MM

=λ (14)

GJEIL

M yyz

= π (15)

0 0.5 1.0 1.5(Non-Dimensional Slenderness)

0

0.5

1.0

k P

76 x 76 x 2.0 SHS - Concentric

-----------Pmax

f yf

k P--------------PE

f yf√( )

76 x 76 x 2.0 SHS - Eccentric (e = L/1000)152 x 152 x 4.9 SHS - Concentric152 x 152 x 4.9 SHS - (Eccentric (e = L/1000)203 x 203 x 6.3 SHS - Concentric203 x 203 x 6.3 SHS - Eccentric (e = L/1000)

Euler (P )E

= - 1.0- 0.5

0.0

αb

9

in which Mpx is the fully plastic moment capacity, 8 is the nondimensional slenderness ratio, Myz is the elastic buckling moment, E is the elastic modulus, G is the shear modulus, Iy is the second moment of area about minor y-axis and J is the torsion constant of the tubular section. The alternative proposal given by Eqs 12 and 13 is also shown in Fig. 6 as ”This Paper”. The proposal is very much higher than the AS 4100-1998 beam curve. It has not been incorporated in AS 4100-1998 at this time.

Fig. 6 Proposed Design Rules for RHS Beams 4. WEB CRIPPLING UNDER BEARING 4.1 Beams under Bearing Tests were performed on a range of cold-formed RHS subject to transverse bearing force (Zhao and Hancock (1992a, 1995a). Two types of failure modes were observed for RHS sections under a transverse bearing force. They are web buckling failure and flange-face yielding failure. The load- carrying capacities of RHS under transverse bearing force depend on the following key parameters (where the symbols are defined in Fig. 7). q Loading position, ie interior bearing (when 55.1 dbd ≥ ) or end bearing (when 55.1 dbd < ) q Ratio (() of bearing length (bs) to section width (b) q Ratio of web depth (d – 2t) to section thickness (t) q External corner radius of the section (rext)

Comparison with AS 4100 and Proposed Design Rules for RHS Beams

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0Non-Dimensional Slenderness

0

0.2

0.4

0.6

0.8

1.0

M /M

λ

pxbx RHS Beams (uniform moment)Test Values (maximum)Test Values (at )Basic FEM M odel (Pi and Trahair)Proposed (Pi and Trahair)AS 4100 - 1990This Paper

∆ t

10

Fig. 7 RHS Sections under Transverse Bearing Forces

Fig. 8 End Bearing Failure

b

d

rext

(a) Section

(b) Interior force

11

1

2.5

(c) End force

11

1

2.5

rext

d5 = d -2rext

rext

bd bs

bb

bbfbbw bbw

bb = bbf + 2 bbw

bbf = bbs + 5rext

bbw = d5 /2

d5 /2

bs

rext

d5 /2

bb = bbf + bbw

bbf = bbs + 2.5rext

bbw = d5 /2

bb

bbf bbw

11

The load carrying capacity of RHS under end-bearing force was found to be less on average than half of that of RHS under interior bearing force. The effect of reducing the bearing length in end-bearing tests was found more severe than in interior bearing tests. Reducing the bearing length by one-half in end-bearing tests reduces the bearing capacity by 30%, while reducing the bearing length by one-half in interior bearing tests reduces the bearing capacity by 8% to 20% depending on the web slenderness. A typical end bearing specimen after testing is shown in Fig. 8 for RHS under transverse bearing forces. The design rules for calculating web bearing capacities (bearing yield capacity and bearing buckling capacity) in AS 4100-1990 were based on tests of hot-rolled I-sections. It was found that the predictions in AS 4100-1990 were too high to be used for RHS sections under transverse bearing force, since the formulae in AS 4100-1990 applied to webs of I-sections that are loaded concentrically, while in the case of RHS sections the bearing load is applied eccentrically as a result of the corner radii. The eccentric loading produces primary bending of the web out of its plane and a subsequent reduction in capacity. Plastic mechanism analysis was used to establish design formulae for bearing yield capacity. The mechanism models were based on experimental observations. The nominal bearing yield capacity (Rby) of both webs can be calculated using Clause 5.13.3 of AS 4100-1998. They are summarised below, where most of the symbols are defined in Fig. 7.

pybby tfbR α2= (16)

in which fy is the yield stress of the material, bb and "p can be determined as follows: q for interior bearing ( 55.1 dbb ≥ )

55 drbb extsb ++= ( ) ( ) ( ){ }[ ]222 /25.0 1/111/5.0 vpmvspmsp kkkk ×−−+−+= ααα

q for end bearing ( 55.1 dbb < )

2/5.2 5drbb extsb ++=

ssp kk −+= 22α in which vspm kk /5.0/1 +=α

1/2 −= trk exts tdkv /5= The design rules for bearing buckling capacity of RHS sections are similar to those for I-sections in AS 4100. The nominal bearing buckling capacity of a web shall be taken as the axial load capacity determined in accordance with Section 6 of AS 4100-1998 using 5.0=ba and kf = 1.0 for a compression member of area twbb and slenderness ratio we tdrL /5.3/ 5= for interior bearing and

we tdrL /8.3/ 5= for end bearing. The term tw is web thickness and bb is defined in Fig. 7. The higher values of slenderness rLe / used for tubular sections when compared with other sections reflects the smaller degree of restraint provided by the flanges to the web.

12

4.2 Beams under Combined Bending and Bearing

A series of interaction tests of bending and transverse concentrated force were performed, where the concentrated force was applied either by a welded SHS branch to form a T-joint or by a bearing plate (Zhao and Hancock, 1991b, 1992a). The interaction curves for the RHS sections under bending and bearing force are compared in Fig. 9 with those of similar tests on RHS with welded branch. The interaction is more severe for the tests with bearing plate whereas the interaction is less for the welded T-joints due to the restraint against web rotation provided by the welded branch. It was found that the interaction behaviour depends on the ratio (() of bearing length (bs) to section width (b) and the ratio of web depth (d – 2t) to section thickness (t) (Zhao and Hancock, 1992b).

A new clause was added to AS 4100-1998 to account for combined bearing and bending. It can be summarised as follows.

Rectangular and square hollow sections to AS 1163 subjected to combined bending and bearing force shall satisfy either:

5.12.1**

≤

+

sb MM

RR

φφ (17)

for 0.1/ ≥bbs and ( ) 30/2 ≤− ww ttd or

0.18.0**

≤

+

sb MM

RR

φφ otherwise (18)

where N = capacity factor = 0.9 Rb = nominal bearing capacity of webs specified in Clause 5.13.2 of AS 4100-1998 Ms = nominal section moment capacity determined in accordance with Clause 5.2 of

AS 4100-1998 bs = stiff bearing length b = total width of section tw = web thickness

13

Fig. 9 RHS Sections under Combined Bending and Transverse

Bearing Force

5. BEAM-COLUMNS 5.1 Introduction The design rules in AS 4100-1998 Section 8 for members subject to combined actions have a two tier approach. For both the section capacity rules in Clause 8.3, and the member capacity rules in Clause 8.4, simple linear interaction formulae are specified. However, for doubly symmetric, compact I-sections, more advanced interaction rules were specified as higher tiers in AS 4100-1990. Recently, a detailed research program (Sully and Hancock, 1996) was performed on compact cold-formed SHS to AS 1163 to ascertain whether the more advanced interaction rules are applicable to these sections. Further research has also been performed on slender cold-formed SHS sections (Sully and Hancock, 1995). The results of this research, which are described briefly in this section, have been used to extend the applicability of the advanced interaction rules in AS 4100-1998 to compact rectangular and square hollow sections. In particular, Clause 8.3.2 for the section capacity for uniaxial bending about the major principal axis, Clause 8.3.3 for the section capacity for uniaxial bending about the minor principal axis, Clause 8.4.2 for the member in-plane capacity using an elastic structural analysis have been extended in AS 4100-1998 to allow the advanced rules for compact I-sections to be used for rectangular and square hollow sections to AS 1163. In the USA, in the AISC Specification (AISC 1993), there is an advanced interaction rule which applies to all sections, whether I- or tubular. This design curve, which is invariant with end-moment ratio, is higher than the Australian curve in some cases and lower in others. This section describes the Australian theoretical and experimental research used to support the Australian extensions. 5.2 Test Program on Compact Sections A test rig was purpose-built for this test program. It consisted of a 2000 kN hydraulic actuator used to apply compressive axial force and a 250 kN hydraulic actuator used to apply bending moment to the specimen as shown in Fig. 10. The moment was applied to the specimens by the bending actuator via lever arms attached to each end of the specimen. The layout of the rig allowed for a range of end moment ratios ($) from around $ = - 4/1 to $ = -1 (ie specimen bent in single curvature). The rig did not allow for positive values of $ (ie specimens bent in double curvature).

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0 1.61.41.21.00.80.60.40.2

Dimensionless Loading P/Pf

Dim

ensi

onle

ss M

omen

t M

/ M

f

Dash (T-Joint)

S3B1C11S3B1C12S3B1C13

Solid (Bearing)

S3B1C11S3B1C12S3B1C13

14

The two actuators could be operated independently or coupled depending on the loading type being investigated. For this test program, the actuators were linked together so that by controlling one, in either load or displacement, loads would be applied in a constant ratio.

Fig. 10 Plan View of Test Rig Layout

The specimens tested were 125 × 125 × 6.0 SHS in Grade C350 which could be classified as compact according to AS 4100-1998. In order to determine the section axial compression capacity of the specimens, two stub column tests were carried out in a 2000 kN hydraulic actuator. Both specimens reached similar ultimate loads (1173 kN and 1196 kN). A plastic bending test was conducted using a 2000 kN hydraulic actuator in a four point bending test configuration. The plastic bending test reached a moment of 53 kNm at ultimate and, after substantial deformation, was concluded when a local buckle had formed in the specimen. A column test was conducted in the test rig by application of the compression actuator only. The column specimen was 3000 mm long. Adding this to the 225 mm at each end of the test rig, from the centre of the pins to the ends of the test specimen, gave the columns an effective length of 3450 mm between the pinned bearings. This length was chosen because it gave a non-dimensionalised

Lever arm

High tensilesteel bars

SHS Test specimenRigid joint

Rigid joint

2000 kNdartec jack

Northern Head stock(fixed to floor)

Southern end frame(roller joint with floor)

Pin joint

250 kNMTS jack

Support frames(stainless steel onteflon pads to allowmovement in horizontalplane)

Packingplates

Channel

Transferplates

SHS testspecimen

Section A-A

A A

Lever arm

Spherical joint

Spherical joint

Ball joint

15

slenderness (8) of approximately 1 when the nominal yield stress (Fy = 350 MPa) and nominal dimensions were used.

=

ErL yc

2πσ

λ (19)

An eccentricity of 3mm was added at each end in the plane of bending. This was considerably greater than the measured geometric imperfection of 0.4 mm. The specimen exhibited stable unloading characteristics, after reach an ultimate axial load (Puc) of 632 kN. Interaction tests were performed using the test rig in Fig. 10. All of the specimens tested were 3000 mm long which was the same as the column tests. Two series of interaction beam-column tests were conducted. For the first series with $ = -1 (referred to as B1 series), four tests were conducted with varying ratios of applied load and moment. In order of descending applied load/moment ratio they are B1R1 to B1R4. For the second series with $ = -0.5 (referred to as B2 series), three tests were conducted, known as B2R1 to B2R3, again in descending order of applied load/moment ratio. Plots of load versus central moment for the four B1 series of tests are shown in Fig. 11. This central moment is the sum of the moment applied directly from the bending actuator and the moment indirectly applied via the P - ) effect from both the compression and bending actuators.

Fig. 11 Maximum Moment versus Load for B1 Series of Compact Interaction Tests

Unlike the B1 series, the region of maximum moment for the B2 series shifted during the tests. At low loads, the peak moment was at the point of application of greatest applied moment, ie at the southern end. As the deflections increased, the P - ) effect increased and the peak moment shifted towards the centre of the specimen. The extent to which the shift occurred was dependent on the applied load/moment ratio. 5.3 Finite Element Analysis of Compact Sections An advanced finite element nonlinear analysis, developed at the University of Sydney (Clarke 1993) was used to simulate each of the tests. The advanced analysis could include the effects of large deflections, residual stresses, material nonlinearity, gradual yielding, elastic unloading and geometric

0 10 20 30 40 50 60Maximum Moment (kNm)

0

100

200

300

400

500

600

700

Load

(kN

)

Test resultsFinite element analysis

B1R1

B1R2

B1R3

B1R4

(NIFA)

16

imperfections. Material properties for the finite element analysis were taken from the results of the tensile coupon tests and residual stress tests. Material curves were multi-linear functions derived directly from the stress-strain curves. Membrane residual stresses were taken as zero. The end platens were included as a third material type to account for their increased stiffness. Measured eccentricities between the specimens and the end platens were included. Geometric imperfections were taken as sinusoidal over the length of the specimen with a mid-span deflection of 0.4 mm. Comparison of analysis and tests results for the B1 series of interaction tests is shown in Fig. 11. There is good agreement especially for tests B1R3 and B1R4. Similar good agreement has been achieved for the B2 series. Hence it was concluded that the finite element analysis is able to accurately simulate the test results. To compare the test sections with current design rules, for a wider range of parameters that was tested, further finite element analyses were undertaken for $ = -1, $ = -½, $ = 0, $ = ½, $ = 1. From each of these analyses, the maximum applied load was found with the corresponding maximum applied end moment. Using the equations from Trahair and Bradford (1998), the equivalent maximum second order elastic moment within the section was calculated:

2

cot cosec 1

+

+=

xxm P

PPPMM ππβ (20)

and , cosfor

− <

xPPπβ

MM m = (21)

− ≥

xPPπβ cosfor

where Mm = maximum second order elastic moment M = maximum applied end moment P = Maximum applied axial load Px = Euler buckling load for the section $ = ratio of applied end moments This is of course very different from the actual maximum moment within the section, which is the sum of the applied maximum end moment and moment due to the mid-span deflection and load. These maximum second-order elastic moments are compared with the current interaction design rules in Clause 8.4.2.2 of AS 4100-1998, for doubly symmetric compact I-sections and the interaction rule from the AISC Specification (AISC-US 1993). Graphs of these plots for 1,0,1 ==−= βββ are shown in Fig.12.

Ν−1

++

Ν−1

+−=

ccs NN

MMφ

βφ

β 2

1 18.1 2

1133

(22)

17

M = Maximum allowable applied end moment Ms = section moment capacity = Ze fy N = applied compressive axial load Nc = member axial load capacity given by Eq. 10 $ = ratio of applied end moments N = 0.9 The graphs have been non-dimensionalised against the short column load (Psq) and the plastic moment (Mpt) capacity, Psq is calculated from the measured cross-sectional area and the proof stress of the material from the flats, determined from the tensile coupon tests. Mpt is calculated using the measured section dimensions to determine the actual plastic section modulus, and the proof stress of the material from the flats, determined from the tensile coupon tests. The cold-formed, compact square hollow sections tested showed adequate ductility and adequate capacity to absorb moment past the maximum axial load. Comparing the equivalent second order elastic moments with the design rules shows that even at $ = -1 there is some capacity to absorb small axial forces without reducing the moment capacity. This effect increases with an increase in $. The current interaction design rules in AS 4100 for doubly symmetric I-sections are applicable to cold-formed RHS as specified in AS 4100-1998. They are however conservative for larger values of $ and there is scope for improved design rules to be developed. The current interaction rules in the AISC-US Specification (AISC 1993) are more conservative than the theoretical and experimental values except for the $ = -1 case. 5.4 Test Program on Slender Sections The same test rig and loading arrangements as used for the compact sections were used for a second test series on slender sections. The slender square hollow sections tested were of nominal overall dimension 200 mm square with nominal thickness 5 mm and nominal yield stress 350 MPa. The slenderness (b/t) of the faces was 38 based on the clear width of the flanges. Two specimen lengths were tested. The distance between the centres of the pinned bearings in Fig. 10 were 5550 mm for the long sections and 1246 mm to 1560 mm for the short specimens. The length of the long specimens was chosen to produce a non-dimensional column slenderness of approximately 1.0. Two different ratios of end moment were used for the long specimens both producing overall bending in single curvature. These were equal and opposite end moment (β = −1.0) and the moment at one end half the other (β = −0.5). The tests are labelled B1 and B2 respectively as for the compact sections. However a symbol ‘s’ has been included to indicate that the test is on a slender section. The full set of results is given in Sully and Hancock (1995) and summarised in Sully and Hancock (1998).

18

Fig. 12 Comparison of Design Rules with Interaction Surface

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Maximum Moment (M/M )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Load

(P/P

)sq

pt

AS 4100 interaction ruleAISC interaction ruleSHS interaction curve

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Maximum Moment (M/M )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Load

(P/P

)sq

pt

AS 4100 interaction ruleAISC interaction ruleSHS interaction curve

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Maximum Moment (M/M )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Load

(P/P

)sq

pt

AS 4100 interaction ruleAISC interaction ruleSHS interaction curve, flats onlySHS interaction curve, flats and corners

(a) Comparison of Design Rules with Interaction Surface for = -1β

(b) Comparison of Design Rules with Interaction Surface for = 0β

(c) Comparison of Design Rules with Interaction Surface for = 1β

19

Fig 13 Slender Long SHS Axial Force/Moment Interaction ($ = -1.0)

Fig. 14 Slender Long SHS Axial Force/Moment Interaction ($ = -0.5)

0 10 20 30 40 50 60 70 80 90 1000

100

200

300

400

500

600

700

800

900

1000

Axi

alLo

ad(k

N)

LC1s

B1R1s

B1R2s

B1R2as

B1R3s

PB1NTs PB4PT

AS4100AISC-LRFDEurocode3Tests

Moment, M = M , (kN.m)me δb e

0 10 20 30 40 50 60 70 80 90 1000

100

200

300

400

500

600

700

800

900

1000

Axi

alLo

ad(k

N)

LC1s

B2R1s

B2R2s

B2R3s

PB4PTsPB1NTs

Moment, M = M , (kN.m)me δb e

AS4100AISC-LRFDEurocode3Tests

20

Fig. 15 Slender Short SHS Axial Force/Moment Interaction ($ = -1.0)

The axial force-moment interaction graphs are shown in Figs 13, 14 and 15 where the moment on the horizontal axis is the second-order elastic moment. The second order moment was derived for the test results by amplifying the applied end moment from the tests by the appropriate amplification factor which depends on the ratio of the applied axial load to the Euler buckling load of the member based on the length between the pinned ends. The amplification factor is specified in Clause 4.4.2.2 of AS 4100-1998 as

δbm

E

CN N

=−1 /

(22)

where N is the applied axial load, NE is the Euler buckling load, and Cm is a moment distribution factor equal to unity in the case of uniform moment (β = −1.0) and 0.8 in the case of the moment at one end half the other (β = −0.5). On the vertical axis of Fig. 15, the ultimate load for a test of a column with no end moment is shown where the column strength of the specimen STC is a stub column test. On the horizontal axes of Figs 13, 14 and 15, the results of two different tests with pure bending and no axial force are shown. The test labelled PB4PT is a four point bending test where a region of pure moment derived from lateral loads on a beam section is achieved. The test labelled PBINT was performed using the test rig in Fig. 10 to achieve pure bending by applying a tension through the 250 kN MTS actuator and a balancing compression through the 2000 kN Dartec actuator. This test failed by inelastic local buckling in the compression flange and webs of the SHS section adjacent to the point where the loading plates were welded to the webs of the section. The applied moment at failure for the PBINT test was significantly below the PB4PT test probably as a result of the different method of application of the end moment. In the case of the P4PBT test, the moment was applied by the section of SHS extending beyond the interior loading point whereas in the PBINT test, the moment was applied by the channel lever arms through the plates welded to the webs. It is clear from these results that the method of connection of slender tubes can play an important part in the strength of the section, particularly in bending.

0 10 20 30 40 50 60 70 80 90 1000

200

400

600

800

1000

1200

1400

1600

Axi

alLo

ad(k

N)

STC

S1T1

S1T2

S1T3

PB4PTsPB1NTs

Moment, M = M , (kN.m)me δb e

AS4100AISC-LRFDEurocode3Tests

21

The results for the interaction tests are compared in Figs 13, 14 and 15 with the predictions by AS 4100-1998, the AISC-LRFD Specification (AISC-US (1993)) and Eurocode3 (Eurocode (1992)). In computing these standards, the mean measured section geometry and mean measured yield stress of the flat material have been used. All three specifications are conservative except for the PBINT test result. A line fitted between the column test strength and the PB4PT test for each case is approximately aligned with the test results indicating that a linear interaction graph between axial force and moment is most appropriate for slender sections. The conservatism of the code predictions is mainly a consequence of the conservatism of the prediction of the pure axial and pure moment cases. In AS 4100-1998 a linear interaction curve has been retained in Clause 8.4.2.2 for slender sections unlike the compact sections described in Sections 5.2 and 5.3 above. 6. WELDED CONNECTIONS The Australian Standard AS 4100-1990 when originally produced only applied to steel that is 3 mm or thicker. Tubular sections less than 3 mm thick could not be designed to this standard, and had to be designed to the Australian Cold-Formed Steel Structures Standard AS 1538-1988 (now in Limit State Format as AS/NZS 4600:1996). Since the design rules for welded connections in AS/NZS 4600 are based on tests on sheet steel performed in the USA in the early 1980s (Pek`z and McGuire (1981)), they may be inappropriate when applied to RHS sections. Consequently, a large number of tests were performed on butt welds, transverse fillet welds and longitudinal fillet welds in both C350 and C450 RHS members (Zhao and Hancock (1995b, 1995c, 1996)). Proposed design rules were calibrated using reliability analysis method. They are now included in AS 4100-1998. 6.1 Butt Welds The dominant failure mode found in the tests of butt welds in C350 RHS members was tube tearing failure. Significant necking of RHS was observed at the failure cross section. Most of the tearing occurred along the seam of the RHS as shown in Fig. 16. This may be due to the lower ductility of the seam. The dominant failure mode in the tests of butt welds in C450 RHS members was tube failure in the heat affected zone as shown in Figure 17. No significant necking of RHS was observed.

22

Fig. 16 Butt Weld in C350 SHS – Typical Failure

Fig. 17 Butt Weld in C450 SHS – Typical Failure The complete penetration butt weld along a full perimeter was found to be stronger than the RHS itself. The complete penetration butt welds can be designed in accordance with the tension member rule in AS 4100-1998 with a capacity factor (φ) of 0.9. The nominal capacity of a tension member is governed by the lesser of fyA and 0.85fuA, where A is the cross-section area, fy is the yield stress and fu is the ultimate tensile strength. For grade C350 RHS sections, fyA is less than 0.85fuA. For grade C450 RHS sections, 0.85fuA is less than fyA.

23

6.2 Transverse Fillet Welds The actual weld sizes (leg lengths) in the test specimens less than 3.0 mm thick were found to be oversized. This finding agrees with the trend found in the international test series (Pham and Bennetts (1983)) as shown in Figure 18, ie. welds are slightly oversized when the nominated size is small and are slightly undersized when the nominated size is large. Weld failure (shear across the weld throat) was observed in tests where transverse fillet welds were not applied to the full perimeter of an RHS section. The full strengths of RHS sections were achieved if the full perimeter was welded using transverse fillet welds.

Fig. 18 Variation of Actual Throat Thickness

The design rules for transverse fillet welds and those for longitudinal fillet welds are the same in AS 4100-1998, ie φ0.6XuaL where φ is the capacity factor, Xu is the weld metal strength, a is the weld throat thickness and L is the weld length. The predictions in AS 4100-1998 were found conservative for design of transverse fillet welds. The design strength of transverse fillet welds in the American Institute of Steel Construction Specification (AISC (1993)) has now been increased from φ0.6XuaL to 1.5 x φ0.6XuaL where the capacity factor is 0.75. However, for simplicity no changes have been made to the existing design rules for transverse fillet welds in AS 4100-1998.

6.3 Longitudinal Fillet Welds A schematic view of longitudinal fillet welds is shown in Fig. 19. The failure mode observed in the tests without end return welds was tube failure at the end of the weld adjacent to the end of the plate as shown in Fig.19. The failure may be due to the stress concentration in the area between the weld and the end of the plate. The failure mode observed in tests where end return welds were applied was tube failure in the heat-affected zone adjacent to the end return weld as shown in Fig. 19. The shift of the failure position is most likely due to the fact that the end return weld formed a continuous path of load transfer along the end of the plate. The variation of the weld strength with respect to the ratio of weld length to wall thickness derived by Pek`z and McGuire (1981) and that with respect to the ratio of weld length to plate width derived by Stark and Soetens (1980) were not confirmed in the current tests. This may be because these two formulae were based on regression analysis of tests on lap-joint fillet welds in sheet steel, while T-joint fillet welds in RHS sections were used in the current tests.

2.0

1.5

1.0

0.5

0 4 8 12

Nominal Throat Thickness (mm)

Actu

al /

Nom

inal

( M

ean

)International Test Series

Current Test Series

24

The strength of the longitudinal fillet welds ranges from 68% to 81% of the strength of the transverse fillet welds, and the corresponding deformation of the longitudinal fillet welds ranges from 1.3 to 2.1 times larger than that of the transverse fillet welds. The variation in values of strength and deformation in different tests is mainly due to the differences in orientation of RHS sections, the weld length, and the inclusion or exclusion of the end return welds.

Fig. 19 Longitudinal Fillet Welds – Typical Failure Positions The existing design rule for longitudinal fillet welds in AS 4100-1998 is φ0.6XuaL where φ is the capacity factor (0.8), Xu is the weld metal strength, a is the weld throat thickness and L is the weld length. The predictions in AS 4100-1990 were found to produce an inadequate reliability index for design of longitudinal fillet welds in RHS sections less than 3mm thick. Two options can be used to produce adequate reliability index (Zhao and Hancock (1994)). Option No.1: Keep the same design rule, but specify the need for end return welds as a requirement in AS 4100. Option No.2: Change the capacity factor from 0.8 to 0.7 without specifying the end return welds as a requirement in AS 4100. The second option has been adopted in AS 4100-1998. 7. BOLTED CONNECTIONS Moment end plate connections joining I-section members are used extensively and considerable documentation on their behaviour exists in the literature. In contrast, research on moment end plate connections joining rectangular and square hollow sections is limited and satisfactory design models are not widely available. The research on tubular end plate connections that has been conducted has concentrated on pure tensile loading or combined compression and bending. An analytical model to predict the serviceability limit moment and ultimate moment capacities of end plate connections joining rectangular hollow sections has been presented in Wheeler, Clarke, Hancock and Murray (1998). The connection geometry considered utilises two rows of bolts, one of which is located above the tension flange and the other of which is positioned symmetrically below the compression flange.

10 mmPlate

RHS

Tubefailure

(a) Without End Return

10 mmPlate

RHS

Tubefailure

(b) With End Return

25

Using a so-called modified stub-tee approach, the model considers the combined effects of prying action caused by flexible end plates and the formation of yield lines in the end plates as shown in Fig. 20. The model has been calibrated against experimental data from an extended test program forming part of the research project (Wheeler, Clarke and Hancock, 1995). Of the three types of end plate behaviour considered in the stub-tee model (thick, thin and intermediate), the paper recommends that the end plate connections be designed to behave in an intermediate fashion, with the connection strength being governed by tensile bolt failure. Thin plate behaviour results in connections that are of very ductile and exhibit extremely high rotations, while connections exhibiting thick plate behaviour are very brittle and may be uneconomical.

M

M

M

u

(a) Mode 1 (b) Mode 2 (c) Mode 3

Fig. 20 Yield Line Mechanisms for Bolted Moment End Plate Connection 8. PLASTIC DESIGN OF PORTAL FRAMES 8.1 Introduction Plastic design of statically indeterminate frames, can lead to higher ultimate loads with associated higher deformations compared to traditional elastic design methods. As some point in the frame reaches its plastic moment (Mp), a plastic zone is created. The zone forms a hinge and rotates further, maintaining Mp, while redistributing additional load to other parts of the structure. The hinge process is repeated as other hinges form, until there is a sufficient number of hinges to create a plastic collapse mechanism for the whole structure or part of the structure. All hinges, particularly those which form early, must be able to rotate sufficiently for this mechanism to form. There are specific requirements for the suitability of sections for plastic design. A Compact or Class 1 section is deemed suitable for plastic design. The flanges and webs of the RHS must be sufficiently stocky to avoid local buckling before large plastic rotations occur. Beam tests have examined the appropriate slenderness limits for cold-formed RHS (Wilkinson and Hancock (1998)) as described in Section 1.4. The rotation capacity of knee joints has also been examined (Wilkinson and Hancock (2000), since plastic hinges often form at the connections of portal frames.

26

Due to the large strains occurring in plastic hinges, material ductility requirements are imposed by design standards. Most cold-formed RHS do not satisfy the requirements of Clause 3.2.2.2 of Eurocode 3 or Clause 4.5.2 of Australian Standard AS 4100-1998. The AISC-US Specification (AISC, 1993) permits plastic design of frames composed of cold-formed RHS. This section briefly describes tests on portal frames manufactured from cold-formed RHS. The aims of the test series included: (1) investigation of the ultimate load capacity of RHS frames; (2) whether a plastic collapse mechanism can form in such a frame; (3) a study of rotation capacity requirements for portal frames. 8.2 Test Frame Layout Three frames were tested under simulated combined gravity and transverse wind loads. The ratio of vertical load (V) to horizontal load (H) is summarised in Table 1. The general layout of each frame is shown in Figure 21. Each frame spanned 7 metres, with an eaves height of 3 metres, and a total height of 4 metres. There was a collar tie which joined the midpoint of each rafter. The frames were constructed from RHS, and the collar tie was made from a pair of channel sections. The RHS were manufactured by BHP Structural and Pipeline Products. Two strength grades were selected, Grade C350L0 and C450L0 (nominal yield stress fyn of 350 MPa and 450 MPa respectively), manufactured to Australian Standard AS 1163. The Grade C450 specimens are called DuraGal, produced using a unique cold-forming and in-line galvanising process.

Fig. 21 Portal Frame Test Arrangement

8.3 Connections The welded internal sleeve joint (Wilkinson and Hancock (2000)), as shown in Fig. 22, was selected for the knee joints of the portal frame. A welded box section, cut in an open •V• shape (to match the angle of the portal frame knee), was fabricated from 10 mm Grade 250 plate. The sleeve was sized to fit tightly inside the RHS. The sleeve extended 300 mm into both the column and the rafter of each knee joint and required a sledge hammer to insert the sleeve in place. The sleeve connection forces the plastic hinge at the knee to form away from the connection centreline.

StrongFloor

Gravity loadsimulator

1000

1000

2000

7000

(Restraint forFrames 2 & 3 only)

Horizontal loadcradle

Pinned base

Internal sleeveknee joint

Points of lateral restraint

SOUTH NORTH

Bolted endplate

MTS actuator

Collar tie (channel) Roller bearing supportedby auxiliary frame(not shown)

27

A moment resisting bolted end plate connection was used at the apex of the frame. A 10 mm plate was butt welded to the end of each rafter, and the two plates were bolted together with eight high strength fully-tensioned M16 bolts positioned symmetrically about the x-axis of the RHS. A common connection for portal frames is the bolted base plate connection to a concrete footing. To simulate the column base plate, a pinned connection was used. The webs of the RHS were stiffened locally by a steel plate, and a 30 mm diameter high strength steel pin was inserted through the neutral axis of the RHS. A thick steel base plate supported the pin. The base plate was securely fastened to the strong floor of the laboratory. The pin connection was greased to reduce friction.

Fig. 22 Internal sleeve knee joint connection 8.4 Loading Method A combination of vertical gravity and transverse wind loads was selected for the test series. In a prototype portal frame, gravity and wind loads are transferred to the frame from the sheeting via purlins and girts, similar to a distributed load. It is difficult to replicate distributed loads in a laboratory, and hence the loads were applied as point loads. The vertical load was applied at the midpoint of the collar tie. Large in-plane sway displacements were anticipated and it was essential that the downwards loads remained vertical to simulate true gravity loading. A hydraulic jack was required to achieve the large vertical load. However, a jack connected directly to the strong floor of the laboratory would produce a non-vertical load as the frame swayed horizontally. A gravity load simulator was attached to the strong floor of the laboratory as shown in Fig. 21. The simulator had two inclined members, pinned together by a rigid triangular unit, and pinned at the other end to the base. The jack was bolted to the top of another vertical member, which was pinned to the base of the triangular section. 8.5 Results The ultimate loads are given in Table 1 and compared with the results of a first order plastic analysis using program PRFSA (CASE, 1997). The first order plastic analysis of the frames does not include second order effects and the reduction of plastic moment to account for interaction with axial force.

B

B

Limit ofsleeve Fillet

weld

RHS wall

Sleeve

Full penetrationbutt weld

300

300

(i) Column – rafter joint (ii) Section B-B (iii) Section C-C

RHS

Sleeve

CC

Groove cutfor RHS

seam weld

28

Load at ultimate (kN) Specimen Cut from section

Load ratio V/H Vertical Horizontal

1

loadanalysisPlasticloadverticalUltimate

Frame 1 150 × 50 × 4.0 C350 40 68.2 1.75 1.00

Frame 2 150 × 50 × 4.0 C450 40 71.5 1.87 0.98

Frame 3 150 × 50 × 4.0 C450 3.3 45.7 13.8 0.91 Note: (1) Plastic analysis load based on measured properties

Table 1 Results of Tests and Analyses

In particular, the ultimate load for Frame 3, is low compared with the first order plastic analysis. However, preliminary advanced analysis has shown that the second order effects are substantial and reduce the ultimate load of Frame 3 by approximately 10%. Results of the advanced analysis are available in Wilkinson and Hancock (1999). 8.6 Discussion of Portal Frame Tests The following important points can be derived from the results: C Plastic collapse mechanisms were formed in all three frames. Large curvatures (hinges)

occurred in (or very close to) the locations predicted by the computer analysis. C The ultimate loads were similar to or smaller than those predicted by the first order plastic

analysis. C There was no significant difference in the behaviour of the Grade C350 and Grade C450

frames (Frame 1 and Frame 2). C There was no failure due to insufficient material ductility. C The welded internal sleeve knee joints performed without any signs of distress. C The lateral restraints performed adequately and the frame did not buckle out-of-plane. C Frames with large sway deflections (Frame 3) require a second order elastic analysis to predict

the ultimate load. 9. CONCLUSIONS The paper has described a substantial research program based mainly on testing of cold-formed square and rectangular hollow sections produced to the Australian Standard AS 1163 Structural Steel Hollow Sections but including some finite element analyses. The purpose of the research was to understand the behaviour of cold-formed hollow sections in order to produce design rules for use in structural steel design standards, especially the Australian Steel Structures Standard AS 4100. Design rules for plate slenderness, long columns, beams in bearing, beam-columns and welded connections less than 3 mm thick have been produced and incorporated in AS 4100–1998. Design rules have also been produced for lateral buckling but not yet incorporated in AS 4100. Ongoing research on plastic design includes plastic bending of sections in combined compression and bending and fracture in welded steel connections.

29

The research has allowed cold-formed tubular members to be safely designed to the Australian Steel Structures Standard AS 4100. Future and ongoing research will enhance the capability of AS 4100 when applied to cold-formed tubular members and connections. 10. REFERENCES AISC (1993), “Load and Resistance Factor Design Specification for Structural Steel Buildings”, American Institute of Steel Construction, Chicago, Illinois. BHP Structural and Pipeline Products (1997), “DuraGal Design Capacity Tables for Structural Steel Angles, Channels and Flats”, BHP Sydney, Australia. Clarke, M.J. (1993), “Plastic-Zone Analysis of Frames”, Chapter 6 in Advanced Analysis of Steel Frames: Theory, Software and Applications, editors WF Chen and S Toma, CRC Press, Boca Raton, Florida, pp 259-319. Eurocode 3, (1992), “Design of Steel Structures, Part 1.1: General Rules for Buildings, Metric”, European Committee for Standardisation, Draft Document ENV 1993-1-1, Brussels. Hasan, SW. and Hancock, G.J (1989), “Plastic Bending Tests of Cold-Formed Rectangular Hollow Sections”, Journal of the Australian Institute of Steel Construction, Vol 23, No 4, pp 2-19. Key, PW and Hancock, GJ (1985), “Strength Tests of Cold-Formed Square Hollow Section Columns”, Civil Engineering Transactions, Institution of Engineers, Australia, Vol CE27, No 4, pp 341-346. Key, PW, Hasan, SW and Hancock, GJ (1988), “Column Behaviour of Cold-Formed Hollow Sections”, Journal of Structural Engineering, ASCE, Vol 114, No 2, pp. 390-407. Korol, RM and Hudoba, J, (1972), “Plastic Behaviour of Hollow Structural Sections”, Journal of Structural Division, ASCE, Vol 8 ST5, pp 1007-23. Pek`z, T and McGuire, W (1981), “Sheet Steel Welding”, Journal of Structural Engineering, ASCE, Vol 107 No 8, pp 1657-1673. Pi, YL and Trahair, NS (1995), “Lateral Buckling Strengths of Cold-formed Rectangular Hollow Sections”, Thin-Walled Structures, Vol 22, No 2, pp 71-95. Pi, YL and Trahair, NS (1994b), “Nonlinear Inelastic Analysis of Steel Beam-Columns. II: Applications”, Journal of Structural Engineering, ASCE, Vol 120, No 7, pp 2062-2085. Rotter, JM , (1982), “Multiple Column Curves by Modifying Factors”, Journal of Structural Engineering, ASCE, 108, pp1665-9. Pham, L and Bennetts, ID (1983), “Reliability of Fillet Weld Design”, Civil Engineering Transactions, Institute of Engineers, Australia, CE26, No 2, pp 119-124. Standards Association of Australia (1981), “SAA Steel Structures Code”, AS 1250. Standards Association of Australia (1998), “Steel Structures”, AS 4100-1998.

30

Standards Association of Australia (1991). “Structural Steel Hollow Sections”, Australian Standard AS 1163. Stark, JWB and Soetens, F (1980), “Welded Connections in Cold-Formed Sections”, Proceedings, 5th International Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, MO, USA. Sully, R and Hancock, GJ (1995), “Behaviour of Cold-Formed Slender SHS Beam-Columns”, Research Report, School of Civil and Mining Engineering, University of Sydney, R707, September 1995. Sully, RM and Hancock, GJ (1996a), “Behaviour of Cold-Formed SHS Beam-Columns”, Journal of Structural Engineering, ASCE, 122 (3), pp 326-226. Sully, R and Hancock, GJ (1998), “The Behaviour of Cold-Formed Slender Square Hollow Sections Beam-Columns”, Proceedings, Eighth International Symposium on Tubular Structures, Singapore, August, pp 445-454. Trahair, NS and Bradford, MA (1998), “The Behaviour and Design of Steel Structures to AS 4100”, third edition, Chapman and Hall. Wheeler, AT, Clarke, MJ and Hancock, GJ (1995), “Tests of Bolted End Moment End Plate Connections in Tubular Members”, Proceedings, Fourteenth Australasian Conference on the Mechanics of Structures and Materials, Hobart, Tasmania, University of Tasmania, pp 331-336. Wheeler, AT, Clarke, MJ and Hancock, GJ and Murray, TM (1998), “Design Model for Bolted Moment End Plate Connections using Rectangular Hollow Sections”, Journal of Structural Engineering, ASCE, Vol 124 No 2, pp Wilkinson, TJ and Hancock, GJ, (1998), “Tests to Examine Compact Web Slenderness of Cold-Formed RHS”, Journal of Structural Engineering, ASCE, Vol 124 (10), pp1166-1174. Wilkinson, TJ and Hancock, GJ (1999), “Comparison of Analyses with Tests of Cold-Formed RHS Portal Frames”, Mechanics of Structures and Materials, editors, MA Bradford, RQ Bridge and SJ Foster, Balkema, pp 245-250. Wilkinson, TJ and Hancock, GJ (2000), “Tests to Examine Plastic Behaviour of Knee Joints in Cold-Formed RHS”, Journal of Structural Engineering, ASCE, Vol 126, No 3, pp 297-305. Zhao, X-L and Hancock, GJ (1991a), “Tests to Determine Plate Slenderness Limits for Cold-Formed Rectangular Hollow Sections of Grade C450”, Journal of the Australian Institute of Steel Construction, Vol. 25, No 4, pp 2-16. Zhao, X-L and Hancock, G.J. (1992a), “Square and Rectangular Hollow Sections subject to Combined Actions”, Journal of Structural Engineering, ASCE, Vol 118, No 3, pp 648-668.

Zhao, X-L. and Hancock, GJ (1991b), “T-Joints in Rectangular Hollow Sections subject to Combined Actions”, Journal of Structural Engineering Engineering, ASCE, Vol 117, No 8, pp 2258-2277. Zhao, X-L and Hancock, GJ (1992), “Design Formulae for Web Crippling of Rectangular Hollow Sections”, 3rd Pacific Structural Steel Conference, Tokyo, Japan, October, pp

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Zhao, X-L and Hancock, GJ (1994), “Tests and Design of Butt Welds and Fillet Welds in Thin Cold-Formed RHS Members”, In: Tubular Structures VI, editors G Grundy, A Holgate and B Wong, Balkema, Rotterdam, pp 465-472. Zhao, X-L and Hancock, G. J. (1995a), “Square and Rectangular Hollow Sections under Transverse End Bearing Force”, Journal of Structural Engineering, ASCE, Vol 121, No 9, pp 1323-1329. Zhao, X-L and Hancock, GJ (1995b), “Butt Welds and Transverse Fillet Welds in Thin Cold-Formed RHS Members”, Journal of Structural Engineering, Vol 121, No 11, pp 1674-1682. Zhao, X-L and Hancock, GJ (1995c), “Longitudinal Fillet Welds in Thin Cold-Formed RHS Members”, Journal of Structural Engineering, ASCE, Vol 121, No 11, pp 1683-1690. Zhao, X-L and Hancock, GJ (1996), “Welded Connections in Thin Cold-Formed RHS”, Connections in Steel Structures III, editors R Bjorhovde, A Colson and R Zandonini, pp 89-98. Zhao, X-L, Hancock, GJ and Trahair, NS (1995), “Lateral Buckling Tests in Cold-Formed RHS Beams”, Journal of Structural Engineering, ASCE, Vol 121, No 11, pp 1565-1573. Zhao, X-L, Hancock, GJ, Trahair, NS and Pi, YL (1995), “Lateral Buckling of Cold-Formed RHS Beams”, In: Structural Stability and Design, editors S Kitipornchai, GJ Hancock, and M Bradford, Balkema, Rotterdam, pp 55-60.

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APPENDIX 1

Fig. A1 Olympic Stadium Australia (under construction)

Fig. A2 Olympic Aquatic Centre, Homebush Bay, Sydney (under construction)