J. Construct. Steel Research 34 (1995) 27-52
© 1995 Elsevier Science Limited
Printed in Malta. All rights reserved
0143-974X/95/$9.50
Tests of High Strength Steel Columns
K. J. R. R a s m u s s e n & G. J. H a n c o c k
School of Civil and Mining Engineering, University of Sydney, New South Wales 2006,
Australia
(Received for publication 25 January 1994)
ABSTRACT
The paper describes a test programme on columns fabricated from high strength
steel plates with nominal yield stress of 690 M P a. The programme comprised 13 box
and I-section specimens, including fixed-ended stub columns and pin-ended long
columns. For the pin-ended columns, two tests were performed for each length using
eccentric and concentric axial loading. The purpose of the test programme was to
select a curve for high strength steel columns with a nominal yield stress of 690 MPa
from the multiple column curves used in the Australian steel structures standard.
It is shown that the ctb= -0.5 curve is the appropriate curve for box and I-section
columns fabricated from flame-cut high strength steel plate with a nominal yield
stress of 690 MPa. This curve is higher than the otb = 0 curve for box and I-section
columns fabricated from ordinary steel because the effect of residual stresses is less
detrimental to the strength of high strength steel columns than to the strength of
ordinary steel columns.
The paper also shows a comparison of the tests with column design strengths of
the Australian steel structures standard AS4100, the load and Resistance Factor
Design Specification of the American Institute of Steel Construction, The British
Standc~rd BS5950: Part l, and the draft European Committee for Standardisation
(CEN) Eurocode3. The design strengths are shown to be in close agreement with the
tests except for Eurocode3 which conservatively predicts the test strengths.
NOTATION
A
Ae
A~
An
b
bf
bw
Cross-section area
Effective cross-section area (AS4100)
Gross cross-section area (AS4100)
Net cross-section area (AS4100)
Plate width
Clear flange width of I-section
Web width of I-section
27
28
Bf
e
eo
E
fE
I
I
kf
L
Le
Lt
Nc
Ns
Py
Pu
F
t
tf
tw
tw
V
VO
V
0~a
~b
~c
/3 u
r/
2,2.
O"
O'rf
O'rw
O"u
O'yc ~ O'yt
K. J. R. Rasmussen, G. J. Hancock
Total width of I-section flange
Total deviation of the centroid at mid-length from the line of
action of the force
Measured eccentricity of applied load
Young's modulus
Critical flexural buckling stress
Yield stress
Measured current during welding
Second moment of area about buckling axis
Form factor (AS4100)
Test specimen length
Effective column length
Total pin-ended column length
Column strength (AS4100)
Section capacity (AS4100)
Design strength (BS5950)
Ultimate load
Radius of gyration about buckling axis
Plate thickness
Thickness of flange plate of I-section
Thickness of web plate of 1-section
Leg length of fillet weld
Measured velocity of welding arc
Measured overall geometric imperfection at mid-length
Measured voltage during welding
Constant defining the imperfection parameter
Modified column slenderness (AS4100)
Constant defining multiple column curves of AS4100
Slenderness reduction factor
Average strain in coupon tests
Strain corresponding to ultimate tensile stress
Imperfection parameter
Column slenderness measures (AS4100)
Column slenderness 4fy/fl~
Constant (AS4100)
Average stress in coupon tests
Average residual stress in flanges of 1-section
Average residual stress in web of I-section
Ultimate tensile strength
Compressive/tensile yield stress
Parameter in Perry formula
Tests of hiah strenath steel columns
29
1 INTRODUCTION
The scope of the current Australian Standard 1 for steel structures is
limited to ordinary steel with yield stress less than 450 MPa. Consequently,
in Australia, structural members fabricated from high strength steel (defined in this paper as steel with a yield stress in excess of 450 MPa) are
usually designed according to overseas specifications which allow the use
of high strength steel, notably the American Institute of Steel Construction
(AISC) Load and Resistance Factor Design (LRFD) Specification. 2
A similar situation exists in Britain and Europe. Section 3.1.1 of the
British Standard BS5950: Part 13 specifies that 'the standard covers the
design of structures fabricated from steels supplied to BS4360;* other steels
may be used provided due allowance is made for variations in properties,
including ductility'. Hence, although high strength steels are not ruled out
explicitly, reference is given to BS4360 which concerns ordinary steels
only. Also, throughout the standard, the yield stresses quoted are those of
ordinary steels.
The 1983 draft of the Eurocode3 specification s contained separate rules
for high strength steels, including design curves for I-section columns
fabricated from high strength steels that were higher than those for
I-section columns fabricated from ordinary steels. These rules were not
included in the 1992 draft of the specification which gave reference to
separate rules for high strength steels, contained in Annex D of the
specification. However, this annex applies specifically to hot-rolled Isections with nominal yield stress less than or equal to 460 MPa.
The tests described in this paper form part of a research programme
into the strength of members fabricated from high strength steel. The aim
of the programme is to investigate whether high strength steel members
with yield stresses in the range from 450 MPa to 700 MPa can be designed
according to existing rules of the Australian steel structures standard
(AS4100) or whether these rules need to be modified to include high
strength steel.
According to the rules of AS4100, the column strength is determined as
a product: of the section capacity (stub column strength) and a slenderness
reduction factor which accounts for the reduction in strength resulting
from overall instability. The Australian Standard uses multiple column
curves, such that the appropriate slenderness reduction factor depends on
the type of cross-section and manufacturing process.
In Ref. 6, tests were described on stub columns fabricated from high
strength steel with a nominal yield stress of 690 MPa. These tests concerned the section capacity and were performed to investigate whether the
yield slenderness limits for welded uniformly compressed plates supported
30
K. J. R. Rasmussen, G. J. Hancock
along one or both longitudinal edges were applicable to high strength steel
plates. The yield slenderness limit was defined as the width to thickness
ratio (factored by x//~-y/250 where fy was the yield stress in MPa) beyond
which the ultimate load was reduced below the squash load as a result of
local buckling.
In this paper, tests are presented on long columns fabricated from high
strength steel with a nominal yield stress of 690 MPa. The purpose of the
tests was to determine the appropriate slenderness reduction factor to use
for columns fabricated from high strength steel with a nominal yield stress
of 690 MPa. The tests were performed on box and I-section column
fabricated by welding.
It was established from analytic modelling7 and testings that the
strength of columns fabricated from high strength steel exceeded the
strength of columns of equal length and cross-section fabricated from
ordinary steel when compared on a nondimensional basis. The difference
arose because the ratios of residual stress at critical points in the
cross-section to the yield stress were less for high strength steel columns
than for ordinary steel columns, and it was shown that it was the ratio of
residual stress to the yield stress, rather than the magnitude of residual
stress itself, which governed the reduction in strength. The ratio was lower
for high strength steel because the magnitude of residual stress was largely
independent of the yield stress. 9 Consequently, it should be expected that
it might be possible to use a higher value of the slenderness reduction
factor for columns fabricated from high strength steel than the value
adopted in AS4100 for columns fabricated from ordinary steel, so that ~he
influence of residual stress on the strength of high strength steel columns
is reduced in design.
Nishino and Tall s performed tests on columns rolled or fabricated from
high strength ASTM 514 steel with a nominal yield stress of 690 MPa. In
these tests, the columns were loaded 'concentrically' in accordance with
the American design philosophy which was to base the design strength on
straight concentrically loaded columns and to allow for imperfections by
using a comparatively high factor of safety. (The positions of the loading
points were adjusted such that the effects of geometric imperfections and
loading eccentricity counteracted approximately each other, and hence the
columns failed by nearly perfect bifurcation buckling.) Consequently, these
tests could not be used to select a column curve for high strength steel
columns in the Australian Standard, since the rules of this standard are
based on the strength of columns with overall geometric imperfections of
one-thousandth of the length.
Tests of high strength steel columns
31
The purpose of this paper is:
•
•
•
to present a test program on long box and I-section columns
fabricated from high strength steel with a nominal yied stress of
690 MPa;
to show the selection of a strength curve to be used in the Australian
Standard for columns fabricated from high strength steel with
nominal yield stress of 690 MPa;
to present a comparison of the test strengths with design strengths
obtained using the AS4100, AISC-LRFD, BS5950: Part 1, and draft
Eurocode3 specifications.
2 TEST PROGRAMME
2.1 OutLine of test programme
The test programme comprised 13 box and I-section columns tested as
fixed-ended stub columns and pin-ended long columns.
For each type of cross-section, the lengths of the pin-ended tests
produced column slenderness values (L/r) or about 30, 50 and 90, and
hence normalised slenderness value (~[= ~ y / f : ) of about 0.55, 0-95 and
1.70. For each pin-ended length, two tests were performed. In the first, the
load was applied approximately at the geometric centroid while in the
second, i~t was applied with a nominal eccentricity of one-thousandth of
the lengt]~. The second test was performed to determine the strengths of
columns with initial out-of-straightness, the allowable limit of which is
one-thou:~andth of the length according to AS4100. Since the initial
out-of-straightness of the test specimens was generally much less than a
thousandth of the length, a loading eccentricity of this magnitude was
introduced as an equivalent geometric imperfection. The test results of the
longest concentrically loaded I-section were considered unreliable and
have not been reported in this paper.
One stub column was tested between fixed ends for each type of
cross-section. The stub column lengths complied with the recommendations of Ref. 10, and so were sufficiently short to exclude overall
instability effects, yet sufficiently long to allow unrestrained development
of local buckles and to eliminate effects of frictional restraints at the ends
on the plate strength. Thus, the stub column strengths could be assumed
to be accurate measures of the compressive section capacities.
32
K. J. R. Rasmussen, G. J. Hancock
The slenderness values of the plates comprising the box and I crosssections were chosen slightly lower than the yield slenderness limits such
that the sections should be able to support their squash loads.
Separate specimens of each section type were prepared to determine
welding residual stresses, as described in Section 2.4. Tension and compression coupons were tested to determine the mechanical properties of
the steel, including Young's modulus, the tensile and compressive yield
stress values, and the ultimate tensile strength, as described in Section 2.5.
The test specimens have been labelled so that the cross-section and the
type of test can be identified from the label. The first letter signifies the
cross-section and is 'B' and T for the box and I-sections respectively. For
the long column test specimens, the numbers following the cross-section
type are the nominal pin-ended length in millimetres, and the letter
following signifies whether the load was applied concentrically (C) or
eccentrically (E). If the specimen was tested as a stub column or used for
residual stress measurement, the section type is followed by 'SC' or 'RS'
respectively rather than the column length.
2.2 Test specimen data and fabrication procedure
The test specimens were fabricated by manual Gas Metal Arc Welding
(GMAW) from nominal 5 and 8 mm plates of BISALLOY80 steel with
nominal yield stresses of 650 and 690 MPa respectively. BISALLOY80 is
an Australian-produced quenched and tempered steel complying with the
mechanical property requirements of ASTM A514 steel. The 5 mm plates
were guillotined into strips while the 8 mm plates were flame-cut. The
strips were tack-welded into sections before final welding. A preheat of
50 °C was used for the 8 mm plates while the 5 mm plates were welded at
ambient temperature. A single run of weld was laid along each fillet so that
four runs were laid for each section type, as shown in Fig. 1. To reduce
weld shrinkage deformations, the welds were laid alternately at the four
fillets, rather than continuously along each fillet, and were staggered (or
stepped-back) such that the staggered weld length was 400--600 mm The
welding parameters used in the fabrication of the test specimens are shown
in Table 1. In the table, I and V are the current and voltage displayed on
the welding machine respectively, and v is the observed velocity of the weld
arc. The electrode was a Lincolnweld L50 wire with a minimum nominal
yield stress of 360 MPa.
The nominal and measured cross-section dimensions of each column are
shown in Tables 2 and 3 for box and I-sections respectively. The symbols
used in these tables are defined in Fig. 1. The measurements are based on
average values of width and thickness of each component plate of the
Tests of high strength steel columns
a_
33
Bf
_¢
r- I
-I
I
b
b
•, ~ - - -
bf
t
I
Weld
a) Box-section
b) I-section
Fig. 1. Definition of symbols.
Table 1
Welding Parameters
Section
Box section
I-section
I
V
v
(amp)
(volt)
(mm/s)
260
240
22
22
8.1
3.8
cross-section. The tables also include the area (A), minor axis second
moment of area (I), and radius of gyration (r = ~ / ~ ) .
The measured specimen lengths (L) and the pin-ended column
lengths (Lt) are also shown in Tables 2 and 3. The pin-ended lengths
were obtained as the sum of the specimen length and the total length
(450 mm) of the end bearings. (At each end, the length from the axis of
rotation to the face of the end platen, on which the specimen bore, was
225 mm.)
The ends of the test specimens were milled fiat to within 0.005 mm
before testing to allow proper seating on the rigid end platens of the
testing rig:, and strain-gauges were attached to the pin-ended specimens at
mid-lengtih to measure longitudinal strains. For the box columns, one
gauge wa~ attached at the centre of each component plate, while for the
I-sections two gauges were attached at 5 mm from each free edge on either
side of the flange such that eight gauges in total were attached to each
I-section column.
K. J. R. Rasmussen, G. J. Hancock
34
Table 2
Measured Dimensions and Ultimate Loads of Box Section Test Specimens
Specimen
b
t
L
Lt
A
I
r
P,
(ram)
(ram)
(mm)
(mm)
(mm2)
(ram4)
(mm)
(kN)
Nominal
section
90
5
--
--
1850
2.75 x 106
38.6
--
Bll50C
B1150E
B1950C
B1950E
B3450C
B3450E
88"9
87'6
88"3
89"4
90"2
89"9
5"00
4"95
4"96
4"97
4'97
4"94
699
700
1500
1500
3001
3001
1149
1150
1950
1950
3451
3451
1828
1783
1801
1827
1843
1825
2"64 x 106
2"51 x 106
2"57 x 106
2'67 x 106
2"74 x 106
2"69 x 106
38"0
37-5
37"8
38"2
38"6
38"4
1174
1137
1078
926
469
438
BSC
88"8
4"95
400
400
1807
2"61 x 106
38"0
1236
2.3 Column tests
2.3.1 Geometric imperfections
Overall geometric imperfections are here defined as the deviation of the
column axis at mid-length from a straight line connecting the ends, and
are denoted by Vo, as shown in Fig. 2.
The imperfections of the box columns were measured in both principal
planes, whereas for the 1-sections only minor axis imperfections were
measured. During measurement, the ends were simply supported and the
specimen allowed to sag between the supports. Readings were taken using
the optical level at the ends and at the centre, allowing the deviation of the
column axis at mid-length from a straight line connecting the ends to be
calculated. This procedure was repeated after rotating the column by 180 °
a b o u t its longitudinal axis, and the two readings were averaged to
eliminate gravity effects.
The imperfections (v0) are shown in Tables 4 and 5 for box and
I-sections respectively. F o r the box sections, the imperfection is the largest
of the two measured values for each specimen. Only the largest imperfection has been included in Table 4 because all box columns failed by
bending in the principal plane that included the largest geometric imperfection.
bf
tf
bw
tw
tw
L
140
141"5
141-1
141"5
141"5
140"3
140"0
I1000C
I1000E
I1650C
I1650E
I2950E
ISC
66' 1
66"9
66"7
66"9
66"9
66'3
66
7'73
7"70
7"67
7"70
7"71
7"75
8
8
1 4 2 " 0 7"73
1 4 0 - 0 7"70
141"8 7"71
1 4 1 - 5 7"66
1 4 3 " 0 7"75
1 4 2 " 0 7"74
140
6"0
6"0
6'8
5"1
5"3
6"2
6
400
550
550
1199
1199
2500
--
(ram) (ram) (ram) (ram) (ram) (ram) (ram)
Bf
Nominal
section
Specimen
400
1000
1000
1649
1649
2950
--
(mm)
Lt
3334
3329
3350
3315
3346
3351
3430
(ram2)
A
106
106
106
106
10 6
10 6
3"54 × 106
3"64 X
3"60 x
3"64x
3"65 x
3"57 x
3.66 ×
(aim4)
I
Table 3
Measured Dimensions and Ultimate Loads of I-Section Test Specimens
32'6
33"1
32"8
33"1
33"0
32-6
32"7
(ram)
r
2369
2092
2192
1751
1682
745
--
(kN)
Pu
t~
t~
K. J. R. Rasmussen, G. J. Hancock
36
/
~
~ "
--
~--~.
_~
Fig. 2. Loading eccentricity and geometric imperfection.
Table 4
Nondimensional Test Strengths of Box Section Columns
Specimen
Vo
eo
e/Lt × 103
Le/r
2n = Le/r x/~r~/250
Pu/(A~rv,)
(ram)
(ram)
B1150C
B1150E
B1950C
B1950E
B3450C
B3450E
0"4
1"2
0"6
1"0
1"0
3"8
0-1
0"9
-0-1
2"2
-0"6
-0"9
0"43
1'83
0-26
1"64
~12
0'84
30"2
30'7
51"6
51"0
89-4
89"9
50"7
51"6
86-7
85'6
150"1
151"0
0"911
0'905
0"849
0"719
0"361
0'340
BSC
--
--
--
5"3
8.9
0"970
Table 5
Nondimensionai Test Strengths of I-Section Columns
Specimen
Vo
eo
e/Lt x 10a
Le/r
2n=L©/r x/~vJ250
Pu/(Aav~)
(ram)
(ram)
I1000C
I1000E
I1650C
I1650E
I2950E
0'0
0"1
0"3
0-5
0'6
0"7
1.2
0"1
0"5
1.4
0"70
1"30
0"25
0"61
0"68
30"2
30-5
49"8
50"0
90"5
49.1
49.5
81"0
81"2
147.0
0"952
0-991
0"800
0"762
0"337
ISC
--
--
--
6"1
10"0
1-077
2.3.2 Loading eccentricity
T h e e c c e n t r i c i t y (Co) o f t h e a p p l i e d l o a d at t h e s u p p o r t s , as s h o w n in Fig. 2,
w a s c a l c u l a t e d for e a c h l o n g c o l u m n d u r i n g initial l o a d i n g b y m e a s u r i n g
t h e d e f l e c t i o n a n d l o n g i t u d i n a l s t r a i n s at m i d - l e n g t h . T h e e c c e n t r i c i t y (eo)
Tests of high strength steel columns
37
and the total deviation (e=vo +eo) of the centroid at mid-length divided
by the pin-ended length (Lt) are shown in Tables 4 and 5 for each test
specimen. The deviation (e) was measured from a straight line connecting
the points of application of the force at the ends, as shown in Fig. 2.
In the tests of the long columns, the specimens were positioned in the rig
such that e/Lt x 10a was approximately zero and unity for the concentrically and eccentrically loaded columns respectively. As shown in Tables 4
and 5, the measured values of e/Lt x 103 differ slightly from these nominal
values, reflecting the difficulty of positioning the specimens accurately in
the rig.
2.3.3 Te.~t procedure
The long columns were tested between pinned end-bearings in a horizontal
serve-controlled Dartec test rig. The stub columns (BSC and ISC) were
tested between fixed ends.
The instrumentation of the pin-ended columns consisted of a load cell
measuring the axial force, transducers measuring axial compression,
deflections in the principal directions at mid-length, and end rotations, as
well as strain-gauges measuring longitudinal strains at mid-length. After
exceeding the proportionality stress of the material, readings were taken
approximately 1 rain after applying an increment of shortening to allow
the stres,; relaxation associated with the mobilisation and locking of
dislocatie,ns between metal crystals to take place, tl
The ultimate loads (Pu) of each long column and each stub column are
shown in Tables 2 and 3.
2.4 Residaai strains
The longitudinal membrane residual strains of the box and I-section were
obtained from specimens (BRS and IRS) with the same nominal crosssections its the long columns and stub columns. The residual stress
specimens were fabricated from the same virgin plates using the same
welding procedure as used for the long columns and stub columns, as
described in Section 2.2.
The strains were obtained using the sectioning technique. For the
I-section, readings were taken on each side of the component plates using
an extensometer before and after slicing the section into narrow strips to
release the residual strain. Readings on opposite sides were averaged to
obtain the membrane strain which was subsequently converted to a
membrane; stress by multiplying the strain by Young's modulus
(E=210GPa), as obtained from the compression coupon tests. The
residual stresses measured in the 1-section specimen are shown in Fig. 3.
K, J. R. Rasmussen, G. J. Hancock
38
-200
s
1
-100
0
100
200
MPa
qL
(, ~l 15m
/, • lOmm
MPa
200
100
0
-100
-200
% = -135HPa
or, = -32HPa
Fig. 3. R e s i d u a l stress m e a s u r e m e n t for I-section.
The figure also shows the locations of the residual stress measurements in
the cross-section and the average of the compressive residual stress
measurements in the web (~,,) and in the flanges (~rf), assumed to be
positive as tensile. The calculation of the average compressive residual
stress in the flanges (~rf) did not include the measurements closest to the
free edges of the flanges, since these measurements were tensile because the
virgin plates were flame-cut into strips. The average compressive residual
stress is a useful measure of the level of residual stress which may have a
weakening effect on a column.
The residual strains of the box sections were measured using strain
gauges. Gauges were attached on both sides of each component plate near
the half-width. Readings on opposite sides were averaged to provide the
membrane strain which was converted to a membrane residual stress using
the measured compressive Young's modulus. The residual stress measurements and their average (~r,= - 123 MPa) are shown in Table 6.
2.5 Tension and compression coupon tests
Tension and compression coupons were cut from the same 5 and 8 m m
virgin plates from which the long column, stub column and residual stress
specimens were manufactured. The coupons were cut parallel to the rolling
Tests of high strenoth steel columns
39
Table 6
Residual Stress of Box Columns
Residual stress
(MPa)
Side 1
- 145
Side 2
- 92
Side 3
- 148
Side 4
- 105
Average
- 123
direction and equipped with two strain gauges on opposing sides at
mid-length to measure longitudinal strains for accurate determination of
Young's modulus.
The compression coupons were tested in a jig preventing lateral buckling. The tension and compression coupons were tested in accordance with
AS1391 t2 using a low strain rate (< 15 #e/s) at strains less than 20 000 #5.
At strains greater than 20 000 #e, the strain rate of the tensile coupons was
increased to approximately 500#e/s. The ultimate tensile strength (o-u)
and the corresponding strain (eu) were measured near the conclusion of
the test after pausing the applied straining for 1 min.
The stress-strain curves obtained from the tension and compression
coupon tests are shown in Fig. 4(a) and (b) for the 5 and 8 mm plates
respectively. In the figures, the strain (5) is the average of the two strain
gauge readings and the stress (tr) is the measured load divided by the initial
area calc,ulated using the coupon dimensions measured before testing. For
strains greater than 20000#8, the strain of the tension coupons was
obtained by dividing the cross-head displacement by the initial parallel
length. As shown in Fig. 4(a) and (b), the scale on the strain axis changes
at 20 000/~e. This was also the strain at which the strain rate was increased
in the tests.
The mechanical properties obtained from the coupon tests are summarised Jin Table 7. In the table, Young's modulus (E) was obtained using a
linear regression analysis of the stress-strain points for stresses up to
300MPa. The compressive (trvc) and tensile (trvt) yield stresses were
obtained as the 0.2% proof stresses, as shown in Fig. 4(a) and (b). Table 7
also contains the nominal values of tensile yield stress, ultimate tensile
strength and equivalent percentage elongation based on a gauge length of
50 mm.
40
K. d. R. Rasmussen, G. J. Hancock
900
aye = 7kSMPa
/
800
0
(MPa)
Compression coupon
700
/
Te n : i : : S c ~ ; o n
600
50O
J r
!,
Strain rate: SOOpc/s
t,O0
300
200
100
0
f" re
Strain rate: 1Spe/s
//
/
I
0.2
1
Change of scale
eu= "/.6%
"
i
.
I
I
2
I
I
I
/,
¢
I
6
10z
x
I
I
8
I
I
10
I
I
12
I
I
16
1~
(a)
900
aye = 660MPa
Compression coupon
800
0
(MPa)
700
600
500
tl
7
~ O y t = 660MPa
%= 725MPa
Tension coupon
/
L,O0
Strain rate: SOOp¢/s
Fraci'ure
Str~n rate: 15pe/s
3O0
200
I
0
eu= 8./.%
Changeof scale
IO0
I
0 0.2
.
I
"
I
i
2
4
I
~: x
I
t
6
t
i
8
i
i
10
i
i
12
t
i
1/,
102
(b)
Fig. 4. Stress-strain curves for (a) a 5 mm plate and (b) an 8 mm plate.
i
16
Table 7
Tension
Compression
Tension
Compression
5
5
8
8
690
650
tryt
(MPa)
° Based o n 50 m m gauge length.
Compression
or tension
test
Nominal
plate
thickness
790-930
750-900
(MPa)
o.
18
18
(%)
Percentage
elongationa
Nominal values
208
213
214
213
(GPa)
E
725
--
-660
660
750
o"u
745
--
(MPa)
Oyc
--
705
6"yt
Measured values
N o m i n a l a n d M e a s u r e d M e c h a n i c a l Properties of 5 a n d 8 m m Plates
10
10
(%)
Eu
42
K. J. R. Rasmussen, G. J. Hancock
3 COLUMN CURVE SELECTION
3.1 Column design rules of AS4100
According to Section 6 of AS4100,1 the capacity of a column is obtained as
(1)
N<=~¢N,
where ~c is the member slenderness reduction factor and N, is the section
capacity.
3.1.1 Section capacity
The section capacity (N,) is calculated a~
(2)
Ns=krAnfy
where A, is the net cross-section area, fy the yield stress, and kf the form
factor, given by
kf=~
(3)
In eqn (3), A e and A s are the effective and gross cross-section areas
respectively.
It was recommended in Ref. 6 that the yield slenderness limits specified
in AS4100 should also be used for high strength steel plates. The yield
slenderness limit was defined as the width to thickness ratio (factored by
x/fy/250 where fy was the yield stress in MPa) beyond which the ultimate
load was reduced below the squash load as a result of local buckling, In
the present paper, the slenderness values of the plates comprising the test
sections were chosen slightly lower than the yield slenderness limits, and so
the net and gross areas were the same and equal to the cross-section area
(A) shown in Tables 2 and 3. Consequently, the section capacity (Ns) was
equal to the squash load (,4 fy) for both cross-sections.
3.1.2 Slenderness reduction factor
The slenderness reduction factor (0t~) accounts for the reduction in
capacity resulting from overall instability. It is calculated as
]
(4)
Tests of high strength steel columns
43
where
+1+7
(5)
2=2,+=a~b
(6)
r/=0-£03 26(4-13-5)>10
(7)
(8)
2100(2.- J3.5)
2gl- 15"34, + 2050
(9)
In eqn (8), L, and r are the effective length and radius of gyration
respectively, and in eqn (6), the member section constant (~tb) attains one of
the values, -1.0, -0.5, 0, 0.5, 1.0, depending on the method of manufacture, type of cross-section and thickness of component plates.
The five values of ~b define the multiple column curves used in AS4100,
as shown in Fig. 5. For welded I-sections fabricated from flame-cut plates
and for welded box sections, the column curve specified in AS4100 is the
~b = 0 curve.
3.2 Comparison of test strengths with design strengths according to AS4100
The column slenderness (2. = Le/rx/~vJ250) and nondimensional strength
(P,/(Atrv,)) of the box and I-sections are shown in Tables 4 and 5
respectiw;ly. In determining 2 , and Pu/(Atrv,), Le was equal to the
pin-endecl column length (Lt), r and A were calculated using measured
values of length and cross-section dimension, as shown in Tables 2 and 3,
and try, was the measured tensile yield stress shown in Table 7.
The nondimensional test strengths of the box and 1-sections are compared with the five column curves of AS4100 in Fig. 5(a) and (b)
respectively. As shown in Fig. 5(a), the nondimensional strength
(P,/(Aav,)=0"970) of the box section stub column is 3% lower than the
squash load. This discrepancy is a result of the plate strength formulae
adopted :in AS4100 which produce optimistic section capacities when
44
K. J. R. Rasmussen, G. J. Hancock
1.4
I
I
I
I
I
I
I
I
I
/
1.2
1.0
e~
0.8
0.6
OA
ab
0.5
0.2
0
(a)
o
•
Concentric loading
Eccentric loading
0
I
I
I
I
I
I
I
I
l
20
40
60
80
100
120
140
160
180
200
1.4
12
Tt
10
,
0.8 -- ~
~
,
/
Pu
Ao~t
Euler
0.6 --
-1.
-0.5
°
loading
•
0
Eccentric loading
I
I
I
I
I
h
I
I
I
20
40
60
80
100
120
140
160
180
200
(b)
Fig. 5. C o l u m n curves o f A S 4 1 0 0 a n d test strengths for (a) b o x c o l u m n s a n d (b) I-section
columns.
applied to high strength steel plates supported along both longitudinal
edges with slenderness values near the yield slenderness limit, as discussed
in detail in Ref. 6.
The discrepancy is not related to the choice of column curve, since the
five curves merge at short column lengths. It should be noticed that the
lack of conservatism would have been less if the c o m p o n e n t plates had
Tests of high strength steel columns
45
been either stockier or more slender, since the plate slenderness value of
the BSC section was close to the yield slenderness limit, which was the
slenderness value for which the standard produced the most optimistic
plate strengths.
The strengths of the shortest pin-ended box columns (Bll50C and
Bll50E) are approximately equal, despite the larger loading eccentricity
applied in the test of Bll50E compared to the test of Bl150C. This result
may be explained by the fact that short columns are fairly insensitive to
eccentric: loading. The strength of the nominally concentrically loaded box
column of intermediate length (B1950C) is 18 % higher than the strength of
the eccentrically loaded specimen (B1950E) of equal length, as shown in
Fig. 5(a). The difference is primarily attributed to the larger eccentricity
used in the test of B1950E compared to that used in the test of B1950C. It
should be noticed that the eccentricity (e = 1.64 Lt/1000 ) used in the test of
B1950E exceeded the nominal value of Lt/lO00.
The strength of the longest concentrically loaded box column (B3450C)
is nearly equal to the Euler load, as shown in Fig. 5(a). In the test, the
column remained nearly straight until reaching the ultimate load, at which
the mid-length deflection increased rapidly, exhibiting nearly perfect
bifurcation behaviour. As a result of the eccentricity incorporated in the
test of B3450E, the strength of this column is 6% lower than the
concentr~ically loaded column (B3450C). However, the eccentricity
(e=0.84Lt/1000) used in the test of B3450E was less than the nominal
value (Lt/1000).
In sele,cting a strength curve for box columns fabricated from high
strength steel, the test strengths of the eccentrically loaded columns shall
be compared with the multiple column curves shown in Fig. 5(a). The
~b = --0"5 curve is in closest agreement with the strengths of the test
sections of intermediate lengths. The shortest pin-ended column strength
(Bll50E) is slightly lower than the ~b = - 0 " 5 curve because at short
lengths the strength approaches the stub column strength which is less
than the squash load for reasons explained previously. Considering the full
range of lengths, the ~b = --0"5 curve appears to be the appropriate curve
for box columns fabricated from high strength steel with nominal yield
stress of 690 MPa.
As shovcn in Fig. 5(b), the strength (Pu/(Atrvt)= 1'077) of the I-section
stub column (ISC) is 8% higher than the squash load. The strength of the
shortest concentrically loaded pin-ended I-section (I1000C) is less than the
strength of the eccentrically loaded I-section (I1000E) of equal length, as
shown in Fig. 5(b), despite the larger loading eccentricity used in the test of
I1000E. This result may be explained by the fact that the strengths were
K. J. R. Rasmussen, G. J. Hancock
46
influenced by random variations of residual stresses and geometric plate
imperfections and that these variations may have had a greater influence
on the strengths than the loading eccentricity.
The strengths of the eccentrically loaded I-section specimens of intermediate and long length are slightly higher than the 0%= -0"5 curve, as
shown in Fig. 5(b). However, the loading eccentricity used in these tests
was slightly smaller than Lt/lO00, as shown in Table 5. As for box
columns, the ~b = --0"5 curve appears to be the appropriate column curve
for I-sections (minor axis buckling) fabricated from flame-cut high strength
steel plate.
On the basis of the comparison shown in Fig. 5(a) and (b), it has been
recommended that the ~b = --0"5 curve be used in the Australian Standard
for welded box columns and welded I-section columns (minor axis
buckling) fabricated from flame-cut high strength steel plate (t < 40 mm)
with a nominal yield stress of 690 MPa.
4 C O M P A R I S O N O F TEST S T R E N G T H S W I T H T H E
A U S T R A L I A N , A M E R I C A N , BRITISH A N D E U R O P E A N
S P E C I F I C A T I O N S F O R STEEL S T R U C T U R E S
4.1 General
The test results of the box and I-section columns are compared in Figs 6
and 7 with design strengths obtained using the Australian, 1 American,2
British 3 and European 5 specifications for steel structures. The figures also
include the measured nondimensional eccentricities (e/Lt x 103), as obtained from the eccentrically loaded tests. The comparison is based on the
nominal cross-sections detailed in Tables 2 and 3, and a nominal yield stress
of 690 MPa.
The Eurocode3 design curves shown in Figs 6 and 7 are based on
Section 5.5.1 of the specification. (Annex D of Eurocode3 allows a higher
design curve to be used for I-sections of nominal 420 and 460 MPa yield
stress than sections of ordinary European steel, having nominal yield
stresses of 225, 275 and 355 MPa. However, this annex applies specifically
to hot-rolled sections.)
For each specification, the component plates of the cross-sections were
sufficiently stocky that the section capacity was equal to the squash load
(Afy). However, in using the British Standard, the design strength (py) was
reduced by 20 MPa in accordance with Section 4.7.5 of that standard
because the columns were fabricated by welding.
Tests of high strength steel columns
47
\1
1.500
/
1,250
1,000
750
500
250 _
- -
.....
0
0
AISC - LRFD
BS5950: Part 1
Eurocode 3
I
I
20
40
I
60
o Concentric loading
* Eccentric loading
I
80
100
L/r
Fig. 6. C o m p a r i s o n of design s t r e n g t h s a n d test s t r e n g t h s for b o x c o l u m n s using n o m i n a l
values.
3,000
[
I
\
[
1,01111
I
"L~/I"~" "
-
AS4100
-
500
-.....
0
0
©= 0.68
AISC - LRFD
BS5950: Part 1
Eurocode 3
I
I
20
40
I
60
~
~0
o Concentric loading
• Eccentric loading
I
80
100
L/r
Fig. 7. C o r a p a r i s o n o f design s t r e n g t h s a n d test s t r e n g t h s for I-section c o l u m n s using
n o m i n a l values.
In the following comparison, the Eurocode3 adoption of the RondalMaquoi I~L approximations to the multiple ECCS 7 'a', 'b' and 'c' column
curves is used as reference. Consequently, using a notation consistent with
that of Section 3.1, the ECCS 'a', 'b' and 'c' curves are approximated
K. J. R. Rasmussen, G. J. Hancock
48
closely by the slenderness reduction factor,
1
~c
~+~~<1
(10)
~b=½ I-(1+ r/) + ~.2]
(11)
~.--~f~
(12)
n2E
fE = (Lc/r)2
(13)
r/= ~(2-0-2)
(14)
(0-21 'a' curve
0e = ~0-34 'b' curve
{,0.49 'c' curve
(15)
where
It follows from eqns (10)--(15) that for a given value of 0~, the slenderness
reduction factor (~c(2)) is uniquely defined by the slenderness ().).
The strength curves of the Australian, American, British and European
specifications were obtained on the following basis:
•
•
•
In using the Australian Standard, the 0cb= - 0 . 5 curve was used in
accordance with the recommendations made in Section 3.2 above.
The ~b = --0"5 curve is a close fit TM to the 'a' curve of the ECCS
Recommendations.
The American Specification has not adopted the multiple column
curve concept, but uses a single curve which is a fit to the SSRC 2P
curve. 1° The SSRC 2P curve is based on a mean overall geometric
imperfection of 1/1470 of the length, Is and lies between the 'a' and
'b' curves of the ECCS Recommendations at intermediate and long
column lengths but below the 'b' curve at short lengths.
The column curves of the British Standard are defined by eqns
(10)--(15), except that the imperfection parameter (r/) is given by
i/= O.O01a ~f~-~ (2-0.2)
(16)
Tests of high strenyth steel columns
49
rather than by eqn (14). The constant a takes the values 2.0, 3.5 and 5.5
for the British 'a', 'b' and 'c' curves respectively. Consequently, in using
the British Standard, the slenderness reduction factor (0~c(2, fy)) is a
function of the yield stress. The curve to be used for box and I-section
(minor axis bending) columns fabricated from flame-cut plates
(t < 40 ram) is the 'b' curve. For mild steel (fy = 235 MPa) this curve
coJincides with the ECCS 'b' curve, but for high strength steel
(fy = 690 MPa) the imperfection parameter (eqn (16)) becomes,
r/=0.190(2-0.2)
•
(17)
and so for this value of yield stress the British 'b' curve is nearly the
same as the ECCS 'a' curve, as defined by eqns (14) and (15),
alt]aough slightly higher.
The Eurocode3 column curves are defined by eqns (10)--(15). The
curve specified for welded box columns is the 'b' curve. For welded
I-sections bent about their minor axis, the specified column curve is
the 'c' curve. This curve is lower than those specified in AS4100 and
BS5950, partly because I-sections fabricated from flame-cut plates
may be designed using a higher column curve than sections fabricated from as-rolled plates according to AS4100 and BS5950,
whereas no such distinction is made in Eurocode3.
In summary, the column curves of the Australian, American and British
specifications to be used in the comparison with test strengths all fit closely
the ECCS 'a' curve. However, the column curves specified in Eurocode3
are the 'b' and 'c' curves for welded box sections and welded I-sections
bent about their minor axis respectively.
4.2 Box c,olumns
The design strengths are compared with test strengths in Fig. 6. Generally,
the design strengths are in close agreement with the tests of the eccentrically loaded columns, although the Eurocode3 design curve is conservative
at intermediate and long lengths. The design strength of the Australian
Standard is slightly higher than the strength of test specimen Bll50E.
However, the eccentricity (1.83 Lt/1000) used in this test was significantly
higher them the nominal value of Lt/lO00.
4.3 I-section columns
The design strengths are compared with the test strengths in Fig. 7. The
Australian, American and British specifications generally agree with the
50
K. J. R. Rasmussen, G. J. Hancock
tests, although the design specifications are conservative at short to
intermediate lengths. The Eurocode3 design curve is significantly lower
than the tests at intermediate and long lengths. This is partly because
I-sections fabricated from flame-cut plates are designed using the same
column curve as sections fabricated from as-rolled plates, as explained
above. The test strengths of I1650E and I2950E are 22% and 18% higher
than the design strengths respectively.
5 CONCLUSIONS
A test programme on long box and I-section columns fabricated from high
strength steel with a nominal yield stress of 690 MPa has been described.
The purpose of the programme was to select a curve for high strength steel
columns from the multiple column curves used in the Australian Standard.
It was shown that the appropriate column curve for welded box
columns with plate thickness less than 4 0 m m was the ~b = --0"5 curve.
This was also the appropriate curve for welded I-section columns (minor
axis buckling) fabricated from flame-cut plate with thickness less than
40 ram. The 0Cb= --0"5 curve of the Australian Standard fits closely the 'a'
curve of the ECCS Recommendations.
If the test specimens had been fabricated from ordinary steel, the
column curve would have been the 0Cb= 0 curve according to the Australian Standard. This curve is lower than the ~b=--0"5 curve, and so the
recommendation of using the ~b = --0"5 curve for high strength steel
implies that columns fabricated from high strength steel are stronger than
columns fabricated from ordinary steel when compared on a nondimensional basis.
The design strengths of short box columns (and other cross-sections
composed mainly of high strength plates supported along both longitudinal edges) may be optimistic if the slenderness of the component plates is
near the yield slenderness limit. This is a result of the strength curves of the
Australian, American and Eurocode3 specifications for high strength steel
plates supported along both longitudinal edges which are optimistic for
plate slenderness values near the yield slenderness limit. 6 This conclusion
applies to a lesser extent to the British Standard which generally produces
conservative strengths for plates supported along both longitudinal edges.
The test strengths were compared with nominal design strengths using
the Australian, 1 American, 2 British a and Eurocode35 specifications for
steel structures. The design curves of the Australian, American and British
specifications were nearly identical for welded high strength box columns
and 1-sections bent about their minor axis, and were shown to be in close
Tests of high strength steel columns
51
agreement with the test strengths. However, the Eurocode3 design curves
were conservative c o m p a r e d with the tests. This was because the specification uses the ECCS 'b' curve for welded box sections, whereas curves
similar to the higher ECCS 'a' curve are specified in the Australian,
American and British specifications. The British curve closely fits the
ECCS 'a' curve because the imperfection parameter is a function of the
yield stress in the British Standard. F o r welded I-sections bent about their
m i n o r axis, the Eurocode3 design curve was conservative because it was
based on the ECCS 'c' curve whereas the Australian, American and British
specifications were based on curves similar to the ECCS 'a' curve. In the
comparison, the Eurocode3 design curves were obtained from Section
5.5.1 of Eurocode3. It is possible that changes to these rules m a y be
specified in Annex D of Eurocode3. This annex applies to high strength
steel members and is currently in preparation.
ACKNOWLEDGEMENTS
The authors wish to thank Bisalloy Industrial Steels Pty Limited for
permitting release of the B I S A L L O Y 80 test results.
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1990.
2. Load and resistance factor design specification for structural steel buildings.
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Institution, London, 1990.
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buildings. Draft Document ENV 1993-1-1: 1992, European Committee for
Standardisation (CEN), Brussels, 1992.
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K. J. R. Rasmussen, G. J. Hancock
10. Galambos, T.V. (ed.), Guide to Stability Desiffn Criteria for Metal Structures,
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