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Experiments of Class 4 open section beams at elevated temperature
Martin Prachar an Jan Hricak a Michal Jandera an Frantisek Wald a Bin Zhao b
a Faculty of Civil Engineering Czech Technical University in Prague Thakurova 7 Praha Czech Republic b CTICM Centre Technique Industriel de la Construction Meacutetallique Saint-Aubin France
a r t i c l e i n f o
Keywords
Slender section
Elevated temperature
Lateral torsional buckling
Tapered beam
a b s t r a c t
At elevated temperature behaviour of Class 1 to 3 open cross-section beams have been investigated
experimentally and numerically whereas for slender Class 4 sections only few experimental data have
been collected Due to the economic assumptions of members with Class 4 cross section and general
validity of the existing design rules further investigation is desired This paper presents tests and
numerical simulation of welded slender (Class 4) I-section beams at elevated temperature The design of
the test set-up as well as progress of the experiments is presented Detailed information about the
geometrical data measured geometrical imperfections temperature load and actual mechanical
properties were collected The tests were subsequently used for a FE model validation The described
research allows better understanding to the 1047297re behaviour of steel members of Class 4 cross-
section beams
amp 2015 Elsevier Ltd All rights reserved
1 Introduction
The area of research in slender cross-sections in case of 1047297re is
very important as only little investigation was made and structural
1047297re design became an inseparable part of structural design The
correctness of the design is essential regarding safety of the
structure as well as its economy concerning also possible addi-
tional 1047297re protection costs Therefore well representing design
models which simulate the actual behaviour of the structures
exposed to 1047297re are crucial as a base of such design formulas
Steel members with thin-walled cross-sections are commonly
used in buildings due to its lightness and long span capacity The
design principles of Class 4 sections are very speci1047297c and usually
more dif 1047297cult than for stocky sections Despite the current EC3
contains a number of simple rules for design of Class 4 cross-
sections at elevated temperature based on recent numerical
simulations they were found to be not accurate [1] Through
re1047297ning these rules a signi1047297cant material savings could be
achieved which would lead to higher competitiveness of the steelstructures However the lack of numerical and experimental data
have been collected until now which may serve as a base to such
changes
The structural steel members of slender cross-sections (Class
4 section according to EC3 11 [2]) subjected to bending are
characterized by having the possibility of failure by both local
and global buckling modes The local buckling mode occurs due to
the compression of thin plates in the section (see Fig 1a) There-
fore the section resistance is signi1047297cantly affected by deforma-
tions of the area in compression The lateral torsional buckling
(global buckling mode for members in bending) is an instability
induced by the compressed 1047298ange of unrestrained open section
beams subjected to bending around the major axis as shown in
Fig 1b The actual bending resistance is reduced by this effect
compared to simple bending (section) resistance
The effect of local buckling may be considered in the structural
design by using the effective areas of plate elements in compres-
sion for Class 4 sections by effective sectional properties (effective
cross section method) or using stress limits for plates (reduced
stress method) The reduction factor ρ depending on the plate
slenderness λ p is used in both of these two methods In the 1047297rst
method the effective cross-section method the reduction factor
reduces cross-section area Ac (resp the section modulus) The
effective area of the compression zone Aceff should be obtainedfrom (1) as a result of effective (reduced) widths of the plates
Aceff frac14 ρ Ac eth1THORN
In the second method the reduced stress method the reduc-
tion factor reduces the maximum allowed stress where the
components of the stress 1047297eld ethσ xEd σ zEd τ EdTHORN in the ultimate
limit state are considered as acting together This method does not
take into account the second-order effect in the possible shift of
the neutral axis position The advantage of this method is the
possibility to use gross cross section properties for calculation
resulting in lower computational cost as it isnrsquot necessary to
Contents lists available at ScienceDirect
jo ur nal ho me pa ge wwwelseviercomlocatetws
Thin-Walled Structures
httpdxdoiorg101016jtws201504025
0263-8231amp 2015 Elsevier Ltd All rights reserved
n Corresponding authors
E-mail addresses martinpracharfsvcvutcz (M Prachar)
janhricakfsvcvutcz (J Hricak) michaljanderafsvcvutcz (M Jandera)
waldfsvcvutcz (F Wald) BZHAOCTICMcom (B Zhao)
Please cite this article as Prachar M et al Experiments of Class 4 open section beams at elevated temperature Thin-Walled Structures(2015) httpdxdoiorg101016jtws201504025i
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determine effective section properties One (general) possibility of
the veri1047297cation formula is given by (2) others are given by EC3 15
[3]
σ xEd
ρx f y=γ M1
2
thorn σ zEd
ρz f y=γ M1
2
σ xEd
ρx f y=γ M1
σ zEd
ρz f y=γ M1
thorn 3 τ Ed
χ w f y=γ M1
2
r ρ2
eth2THORN
As described above the reduction factor depends on the plate
slenderness According to EC3 15 [3] the plate slenderness λp is
given by Eq (3)
λ p frac14
ffiffiffiffiffiffiffi f yσ cr
s frac14
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f y
kσ π 2E 12 1 ν2eth THORN
t b
2
v uut frac14 b=t
095 ffiffiffiffiffiffiffi
E f y
q ffiffiffiffiffikσ
p frac14 b
284 t ε ffiffiffiffiffi
kσ
p eth3THORN
where σ cr is the elastic critical plate buckling stress kσ is the
buckling factor t is the thickness of the plate b is the appropriate
width ε is a factor depending on f y and E ( f y and E to be expressed
in N=mm2)
ε frac14
ffiffiffiffiffiffiffiffiffi235
f y
s eth4THORN
Both highlight values in Eq (3) depends on temperature It
brings additional term which re1047298ects degradation of material
properties see Eq (5)
ffiffiffiffiffiffiffiffikEθ
kyθ
s ffiffiffiffiffiE
f y
s eth5THORN
The cross-section classi1047297cation is therefore different at 1047297re
situation than at normal temperature According to EC3 12 [4]
for the purpose of these simpli1047297ed rules the cross-sections may be
classi1047297ed as for normal temperature design with a reduced value
Fig 1 Buckling mode shapes (a) local buckling (left) (b) lateral-torsional buckling (right)
Fig 2 Ratio of material properties reduction as a function of temperature
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for ε as given by Eq (6)
εθ frac14 085 235
f y
05
eth6THORN
where the reduction coef 1047297cient 085 represents the effect of the
degradation of material properties regardless temperature and
material The correct relationship for ε taking into account
in1047298uence of different temperature can be written as (7)
εθ frac14
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikEθ
kyθ or kp02θ
s 235
f y
05
eth7THORN
Compared to the real dependence of reduced material proper-
ties on temperature apparently the simple reduction by 085 is
suf 1047297cient and mostly safe approximation see Fig 2a)
The Informative Annex E of EC3 12 [4] recommends using
different value of yield strength for Class 4 section (02 proof
strength for Class 4 instead of 20 total strain for stockier Class
1 to 3 sections) The effective cross-section characteristics should
be calculated according the EC3 15 [3] (resp EC3 13 [5]) This
means the effective section is based on the material properties at
20 1C The actual relationship for ε depending on temperature is
shown in Fig 2b)Determination of the bending resistance for members sub-
jected to lateral torsional buckling of Classes 1 to 3 cross sections
at elevated temperature is based on the same principles as the
design at room temperature according to EC3 11 [2] However it
differs in using one imperfection factor only for all types of cross-
sections The procedure may be used for Class 4 sections as well
however with restriction for the maximum critical temperature
and different reduction for the yield strength (Annex E)
For web-tapered beams a limited design procedure is given in
the informative Annex BB of the standard EC3 11 [2] applicable for
the room temperature only The additional procedure is the clause
634 (General Method) given in EC3 11 [2] The suitability of this
approach for Class 1 to 3 cross-section and ambient temperature
was veri1047297ed in [6] The resistance of the non-uniform members
according to the General Method was analysed and compared with
numerical results and the procedures of clauses 631 to 633 of
EC3 11 [2] For elevated temperature the General method was
validated for selected stocky sections by Couto et al [7] EC3 15
Annex B [3] gives another possible approach for non-uniform
members It considers the effect of both plate (local) and lateraltorsional buckling (global) by one reduction factor In case of
member subjected to the lateral torsional buckling the reduction
factor used should be the minimum of the reduction factor ρ given
by EC3 15 [3] in clause B1 (used for the reduction due to the local
buckling) and χ LTmdashthe reduction for lateral torsional buckling
according to EC3 11 632 [2] This in fact leads to the method in
clause 632 but with neglecting the local buckling effect by
considering the elastic section modulus for slender beams Resis-
tance of non-uniform members at room temperature was also
published by Marques et al [8] or using Merchant-Rankine
procedure by Braham and Hanikenne [9] The possibility of using
any of the above described rules for lateral-torsional buckling in
case of 1047297re has not been investigated yet
In the framework of the RFCS project FIDESC4mdashFire Design of
Steel Members with Welded or Hot-rolled Class 4 Cross-sections
several simple supported beams submitted to four-point bending
were tested to study the pure bending and the lateral torsional
buckling at different temperatures
2 Description of the experiments
In the described research of slender sections at elevated tempera-
ture four tests were carried out to study the simple bending (section
resistance) and three tests for beams subjected to lateral torsional
buckling First a preliminary numerical model for calibration of
experiments was made using FE software ABAQUS [10] In order to
achieve local or global failure mode as main failure mode different
boundary condition and load distributions were modelled Based on
the numerical model development and laboratory conditions appro-
priate cross-sections and procedures were chosenFig 3 Scheme of tested beam
Table 1
Tested sectionsmdashsimple bending
Test number Dimensions [mm] Classi1047297cation
Test 1 (450 1C) and Test 2 (650 1C) hfrac14 680 WebmdashClass 4
b frac14250 λ p frac14 144
t f frac14 12 FlangemdashClass 4
t wfrac144 λ p frac14 066
Test 3 (450 1C) and Test 4 (650 1C) hfrac14 846 WebmdashClass 4
b frac14300 λ p frac14 145
t f frac14 8 FlangemdashClass 4
t wfrac145 λ p frac14 118
NOTE Classi1047297cationmdashaccording to EN 1993-1-2
Plate slendernessmdashaccording to EN 1993-1-2 Annex E
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Fig 4 Tested beams 1 to 7
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A simply supported beam with two equal concentrated point
loads applied symmetrically was chosen for the test see Fig 3 The
central part of the beam (between the point loads) subjected to
uniform bending moment was the only heated part The tempera-
ture affects the plate slenderness as described above and shown in
Fig 2b The two temperatures selected for the tests were decided
to represent the most signi1047297cant change of the slenderness for the
same section These were namely 450 1C and 650 1C
Seven tests vary in the cross-sections length of the middle
and side span and temperature Table 1 present the used
Table 2
Tested sectionsmdashlateral torsional buckling
Test number Dimensions [mm] Classi1047297cation Non-dimensional slenderness
Test 5 (450 1C) hfrac14460 WebmdashClass 4
bfrac14150 λp frac14 107 λLT frac14 091
t f frac145 FlangemdashClass 4
t wfrac144 λp frac14 096 λLTθ frac14 086
Test 6 (450 1C) hfrac14460 WebmdashClass 4 λLT frac14 092
bfrac14150 λp frac14 101 λLTθ frac14 088
t f frac147 FlangemdashClass 4
t wfrac144 λp frac14 069
Test 7 Tapered beam (650 1C) h Afrac14460 Endmdashsection A-B WebmdashClass 4
hBfrac14620 λpethATHORN frac14 107
bfrac14150 λpethBTHORN frac14 152
t f frac147 FlangemdashClass 4
t wfrac144 λpethABTHORN frac14 096
Fig 5 Simple bending test setup (upper) and lateral torsional buckling test setup (lower)
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 5
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cross-sections which were fabricated by one side 1047297llet welding
Fig 4 summarises the tested beams dimensions and used steel
plates S1ndashS7 for which the material properties are given later
(Table 5) In case of the simple bending two cross-sections of
constant height were tested for each temperature In these tests
the lateral movement of the beam was prevented at smalldistances so the failure mode was not affected by lateral torsional
buckling The length of the middle part was approximately
1500 mm (after heating) Each section was tested at temperatures
450 1C and 650 1C The other three tests were designed to fail with
major contribution of lateral torsional buckling and the lateral
restrains were at larger distances Two of the tests were performed
on beams of constant section height One test was made on a
tapered beam where the height of the web varied linearly from
one end to another The length of the middle part (between the
load points) of the beams was approximately 2800 mm (after
heating) Free rotation and transverse de1047298ection was allowed
between load points The section rotation was also allowed at
the supports The temperature for each section is detailed in
Tables 1 and 2
All tests were controlled by displacement (vertical de1047298ection)
which was estimated as 45 mm per minute for simple bending
tests Final de1047298ection at midspan was 70 mm For beams subjected
Fig 6 Lateral restraints
Fig 7 Simple bending test supports (a) pinned (b) roller
Fig 8 Lateral restraints at the end of the tested beams (simple bending and LTB)
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to lateral torsional buckling deformation increase was estimated
as 35 mm per minute and the 1047297nal de1047298ection was 50 mm The
load was introduced via a distributing beam at the edges of the
heated part (middle span) The load was applied by means of one
hydraulic jack of 650 kN capacity All the tests were performed on
steady state it means that the beams were 1047297rst heated and then
the load was applied until failure
The additional test equipment was designed as universal for
the experiments It respected boundary conditions based on the
numerical analyses and is described below Test setup for both
types of the tests is illustrated in Fig 5 It consisted of lateral
restraints supports and the load distributing beam At the location
of the load application (at the edge of the heated part) the top and
the bottom 1047298ange were laterally restrained by two vertical CHS
80 56 supported transversally by diagonal members Bolts above
and below the tested pro1047297le section interconnected these two
vertical pro1047297les The lateral restraints are depicted in Fig 6
For all tests the beams were supported at the ends under the
lower 1047298ange In the case of simple bending tests both supports
were pinned (free rotation in the direction of the strong axis) One
of the supports was designed as a rolling bearing (set of horizontal
rods) and allowed free horizontal displacement in the longitudinal
direction (beam axismdashroller) Other displacements and rotations
were restricted see Fig 7 The restriction of lateral displacementand lateral rotation was ensured by couple of vertical pro1047297les (UPE
100) see Fig 8 The horizontal recti1047297cation of the vertical pro1047297les
was allowed to 1047297t to both tested section widths
In the case of the lateral torsional buckling tests the end
supports were considered just by one point support It was made
using a high-resistance steel sphere bearing placed between two
steel plates Both end supports allowed free torsion of the end
cross-section around the sphere bearing One restrained the
displacement in all directions (pinned) The second allowed also
free horizontal displacement in the direction along the beam axis
(roller) The prevented transverse displacement in at the supports
was found to have very little effect on the beam resistance and was
much easier to reach in the test Fig 9 shows both pinned and
roller supports of the beam
Fig 9 Lateral torsional buckling test supports (a) pinned (b) roller
Fig 10 Manual measurement
Fig 11 Simple bending testsmdashpoints of the measurement (the web and the upper
1047298ange)
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21 Measurement of the initial geometric imperfections
Before the experiment after placing the beam on the support
the initial geometry of the specimens was established using the
two methods namely manual measurements and laser scanningThe 1047297rst methodmdashmanual measurement consists of amplitude
measurement for global and local imperfection Amplitude of
global imperfection was measured as a deviation from a string
spanned between the stiffeners (load application points) For
measurements of local imperfection amplitude a special device
set with a centesimal displacement meter was used see Fig 10
The length of device set was chosen according to the half sine
wave length corresponding to the local buckling shape for each
beam calculated in ABAQUS The investigation was made in
compression zone of the beams only Figs 11 and 12 show the
position of the measurements The local imperfection amplitudes
of the web and 1047298ange for beam test 1 to 4 are in Figs 13ndash16 and in
Figs 17 and 18 for the beam test 5 to 7 For these the side of the
1047298ange with higher imperfection amplitude is shown Table 3
summarises the maximum amplitude of the local and global
imperfection along each beam
The second method of imperfection measurement (see Fig 19)
was the laser scanning method It is still comparatively new
technology (1047297rst instrument were used about 15 years ago) andit is very effective for measuring of complex surface topography
Therefore it was used as control method to measure the global
and local initial imperfections All tested beams were scanned
before testing Scanning resolution was set to average grid
5 5 mm on the beam surface The result were plotted as set of
longitudinal and transverse sections trough the tested beams
which adequately describes each beams geometrical properties
Eight standpoints were used to reach maximum covering of the
beam surface It took about 5 min to carry out one standpoint
Surphaser 25HSX with IR_X con1047297guration (the second most
accurate con1047297guration) was used in all cases It is the most
accurate polar laser scanning system on the market The most
important speci1047297cation of the scanner are measurement speed up
to 12 million points per second 1047297eld of view panoramic accuracy
Fig 14 Distribution of the imperfection amplitude along the beammdashTest 2
Fig 12 Lateral torsional buckling testsmdashpoints of the measurement (the web and the upper 1047298ange)
Fig 13 Distribution of the imperfection amplitude along the beammdashTest 1
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better than 05 mm (absolute) at 5 m noise 01 mm at 3 m
measurement range 04ndash30 m Scanner 3D data from eight stand-
points was transformed to unique coordinate system using sphe-
rical control points in the Leica Cyclone software Then the beam
part from point cloud was cut out and 3D model in the form of
triangular mesh was created in the software Geomagic Studio see
Fig 20 The last step was generation of cross and horizontal
sections in 5 cm intervals see Fig 21 Detailed information about
scanning of these beams can be found in [11] In comparison of
both methods laser scanning and manual measurement found
the imperfection amplitudes very similar see Fig 22
22 Heating of specimens
There is not much experimental work on the behaviour of Class
4 beams at elevated temperature but similar experiments using the
same type of heating equipment were made on the lateral-torsional
buckling of Class 1 section beams in 2003 [12] and in 2005 [13] For
the described tests Mannings 70 kV A heat power units with
6 channels were used to heat the specimens see Fig 23 This unit
provides a 60 V supply for powering various types of low voltage
heating elements It consists of an air natural 3 phase transformer
switching is by contactors The output channels are controlled by
means of energy regulators and the temperature controllers Each
channel has its own automanual switch so any combination of
channels can be operated either auto or manual
Cable connection of 70 kV A consists of 6 triple cable sets and
4-way splitter cables can accommodate total of 24 1047298exible ceramic
heating pads attached Maximum connected load for the 70 kV A
unit is 648 kW In order to be able to heat two different beams of
the experimental tests universal size of the ceramic pads was
used 305 165 mm Ceramic heating elements are constructed
from nickel-chrome core wire and nickel cold tail wire which is
electrically insulated by interlocking high grade sintered alumina
ceramic beads The construction allows the heating element to be
1047298exible and provides high heat transfer ef 1047297ciency The heating
pads are able to reach a maximum temperature of 1200 1C
working temperature capability is 1050 1C at a heating rate
10 1Cmin
In the 1047297rst step the pads were put on the rod rack in order to
maintain the position of the heating elements on the web On the
bottom 1047298ange the pads were 1047297xed with steel wire On the top
1047298ange the pads were 1047297xed with adhesive tape only They were
placed on the outer surface of the 1047298anges For the web they were
attached from one side only where the side was alternated along
the beam length (Fig 24)
Two types of material were used for the beams insulation First
the space between the 1047298anges and the outer surface of the 1047298anges
was insulated by standard mineral wool (ROCKWOOL Airrock HD)
The wool was 1047297xed on the beam with steel wires Second themiddle span was wrapped by super wool insulation material see
Fig 25
Seventeen thermocouples were used for the temperature
measurement Eleven of them were placed in the middle span
and six were placed in the side spans for monitoring of the
temperature in not-heated section For lateral torsional buckling
test where the middle span was longer twenty thermocouples
were used in the middle span and four in the side spans The
thermocouples were distributed on the beam according to the
position of ceramic pads as shown and numbered in Fig 24 Beam
temperatures were recorded from the beginning of heating to the
end of the experiment The average measured temperatures
during the loading can be found in Table 4 for each part of the
beam separately The temperature of the bottom 1047298ange was lower
Table 3
Local and global geometric imperfection amplitudes
Test number Imperfection amplitude [mm]
Local-web Local-1047298ange Global
Test 1 4 77 120 ndash
Test 2 1 34 198 ndash
Test 3 2 36 192 ndash
Test 4 1 60 067 ndash Test 5 736 227 25
Test 6 58 069 15
Test 7 759 213 15
Fig 15 Distribution of the imperfection amplitude along the beammdashTest 3
Fig 16 Distribution of the imperfection amplitude along the beammdashTest 4
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as result of worse contact between beam and ceramic pads The
sets of four heating pads were controlled by one thermocouple
The displacements were measured by potentiometers For the
simple bending test two potentiometers were used for measure-
ment of the vertical displacement in the locations of load applica-
tion and one at the mid span For the lateral torsional bending test
two potentiometers were place in the locations of load application
as in the previous case Vertical (VD) and horizontal (HD) de1047298ec-
tion of the bottom 1047298ange centre and section rotation (R) of the
beam at mid-span were calculated from measurement of four
potentiometers Two measured vertical de1047298ection and two hor-
izontal one for two points of the section (see Fig 26)
Fig 17 Local imperfection amplitude along the webmdashlateral torsional buckling Test 5 to 7
Fig 18 Local imperfection amplitude along the upper 1047298angemdashlateral torsional buckling Test 5 to 7
Fig 19 Laser scanner
Fig 20 Beam triangular mesh model
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23 Material properties
For possible model validation material properties for each part
of the welded section were measured at ambient temperature and
at elevated temperature namely 450 1C and 650 1C The tensile
coupon tests were carried out in accordance with EN ISO 6892-1
[14] to determine the basic engineering stress-strain response of
the material The measured values of yield strength for each plate
as were de1047297ne in Fig 4 and temperature are presented in Table 5
3 Numerical analyses and its comparison with experiments
The tests were replicated by means of the 1047297nite element
method program ABAQUS [10] The ABAQUS code is general
software and allows a complete solution for a large range of
problems including the analysis of structures under 1047297re Static
calculation was used in this case The same models as for
preliminary numerical simulation were used The beam was
meshed using quadrilateral conventional shell elements (namely
type S4) Conventional shell elements discretize a body by de1047297ning
the geometry at a reference surface In this case the thickness is
de1047297ned through the section property de1047297nition Conventional
shell elements have 3 displacement and 3 rotational degrees of
freedom per node Element type S4 is a fully integrated general-
purpose 1047297nite-membrane-strain shell element The element has
four integration points per element
All experimental data have been used for validation of thenumerical model Both local and global (if any) geometrical
imperfections were introduced into the geometrically and materi-
ally nonlinear analysis
The material law was de1047297ned by elasticndashplastic nonlinear
stressndashstrain diagram where enough data points were used The
true material stressndashstrain relationship was calculated from the
static engineering strassndashstrain curves obtained from the coupon
tests at room temperature The reductions of material properties
as well as the material nonlinearity were taken from the EC3 12
[4] as only two levels of elevated temperature were tested and
mostly con1047297rmed the established reduction factors The measured
average temperatures from each heated part of the beams were
introduced to the model Adjacent parts of the beam and stiffeners
were modelled as in room temperature (20 1C)
Fig 21 Cross and horizontal beam sections
Fig 22 Comparison between manual measurement and laser scanning for web
of beam
Fig 23 Mannings heat power units
Table 4
Temperature during the tests
Test number Average temperature [1C]
Upper 1047298ange Bottom 1047298ange Web
Test 1 444 469 458
Test 2 654 636 649
Test 3 481 425 431
Test 4 661 631 641
Test 5 457 354 444
Test 6 481 369 443
Test 7 624 416 567
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
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across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
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determine effective section properties One (general) possibility of
the veri1047297cation formula is given by (2) others are given by EC3 15
[3]
σ xEd
ρx f y=γ M1
2
thorn σ zEd
ρz f y=γ M1
2
σ xEd
ρx f y=γ M1
σ zEd
ρz f y=γ M1
thorn 3 τ Ed
χ w f y=γ M1
2
r ρ2
eth2THORN
As described above the reduction factor depends on the plate
slenderness According to EC3 15 [3] the plate slenderness λp is
given by Eq (3)
λ p frac14
ffiffiffiffiffiffiffi f yσ cr
s frac14
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f y
kσ π 2E 12 1 ν2eth THORN
t b
2
v uut frac14 b=t
095 ffiffiffiffiffiffiffi
E f y
q ffiffiffiffiffikσ
p frac14 b
284 t ε ffiffiffiffiffi
kσ
p eth3THORN
where σ cr is the elastic critical plate buckling stress kσ is the
buckling factor t is the thickness of the plate b is the appropriate
width ε is a factor depending on f y and E ( f y and E to be expressed
in N=mm2)
ε frac14
ffiffiffiffiffiffiffiffiffi235
f y
s eth4THORN
Both highlight values in Eq (3) depends on temperature It
brings additional term which re1047298ects degradation of material
properties see Eq (5)
ffiffiffiffiffiffiffiffikEθ
kyθ
s ffiffiffiffiffiE
f y
s eth5THORN
The cross-section classi1047297cation is therefore different at 1047297re
situation than at normal temperature According to EC3 12 [4]
for the purpose of these simpli1047297ed rules the cross-sections may be
classi1047297ed as for normal temperature design with a reduced value
Fig 1 Buckling mode shapes (a) local buckling (left) (b) lateral-torsional buckling (right)
Fig 2 Ratio of material properties reduction as a function of temperature
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for ε as given by Eq (6)
εθ frac14 085 235
f y
05
eth6THORN
where the reduction coef 1047297cient 085 represents the effect of the
degradation of material properties regardless temperature and
material The correct relationship for ε taking into account
in1047298uence of different temperature can be written as (7)
εθ frac14
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikEθ
kyθ or kp02θ
s 235
f y
05
eth7THORN
Compared to the real dependence of reduced material proper-
ties on temperature apparently the simple reduction by 085 is
suf 1047297cient and mostly safe approximation see Fig 2a)
The Informative Annex E of EC3 12 [4] recommends using
different value of yield strength for Class 4 section (02 proof
strength for Class 4 instead of 20 total strain for stockier Class
1 to 3 sections) The effective cross-section characteristics should
be calculated according the EC3 15 [3] (resp EC3 13 [5]) This
means the effective section is based on the material properties at
20 1C The actual relationship for ε depending on temperature is
shown in Fig 2b)Determination of the bending resistance for members sub-
jected to lateral torsional buckling of Classes 1 to 3 cross sections
at elevated temperature is based on the same principles as the
design at room temperature according to EC3 11 [2] However it
differs in using one imperfection factor only for all types of cross-
sections The procedure may be used for Class 4 sections as well
however with restriction for the maximum critical temperature
and different reduction for the yield strength (Annex E)
For web-tapered beams a limited design procedure is given in
the informative Annex BB of the standard EC3 11 [2] applicable for
the room temperature only The additional procedure is the clause
634 (General Method) given in EC3 11 [2] The suitability of this
approach for Class 1 to 3 cross-section and ambient temperature
was veri1047297ed in [6] The resistance of the non-uniform members
according to the General Method was analysed and compared with
numerical results and the procedures of clauses 631 to 633 of
EC3 11 [2] For elevated temperature the General method was
validated for selected stocky sections by Couto et al [7] EC3 15
Annex B [3] gives another possible approach for non-uniform
members It considers the effect of both plate (local) and lateraltorsional buckling (global) by one reduction factor In case of
member subjected to the lateral torsional buckling the reduction
factor used should be the minimum of the reduction factor ρ given
by EC3 15 [3] in clause B1 (used for the reduction due to the local
buckling) and χ LTmdashthe reduction for lateral torsional buckling
according to EC3 11 632 [2] This in fact leads to the method in
clause 632 but with neglecting the local buckling effect by
considering the elastic section modulus for slender beams Resis-
tance of non-uniform members at room temperature was also
published by Marques et al [8] or using Merchant-Rankine
procedure by Braham and Hanikenne [9] The possibility of using
any of the above described rules for lateral-torsional buckling in
case of 1047297re has not been investigated yet
In the framework of the RFCS project FIDESC4mdashFire Design of
Steel Members with Welded or Hot-rolled Class 4 Cross-sections
several simple supported beams submitted to four-point bending
were tested to study the pure bending and the lateral torsional
buckling at different temperatures
2 Description of the experiments
In the described research of slender sections at elevated tempera-
ture four tests were carried out to study the simple bending (section
resistance) and three tests for beams subjected to lateral torsional
buckling First a preliminary numerical model for calibration of
experiments was made using FE software ABAQUS [10] In order to
achieve local or global failure mode as main failure mode different
boundary condition and load distributions were modelled Based on
the numerical model development and laboratory conditions appro-
priate cross-sections and procedures were chosenFig 3 Scheme of tested beam
Table 1
Tested sectionsmdashsimple bending
Test number Dimensions [mm] Classi1047297cation
Test 1 (450 1C) and Test 2 (650 1C) hfrac14 680 WebmdashClass 4
b frac14250 λ p frac14 144
t f frac14 12 FlangemdashClass 4
t wfrac144 λ p frac14 066
Test 3 (450 1C) and Test 4 (650 1C) hfrac14 846 WebmdashClass 4
b frac14300 λ p frac14 145
t f frac14 8 FlangemdashClass 4
t wfrac145 λ p frac14 118
NOTE Classi1047297cationmdashaccording to EN 1993-1-2
Plate slendernessmdashaccording to EN 1993-1-2 Annex E
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Fig 4 Tested beams 1 to 7
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A simply supported beam with two equal concentrated point
loads applied symmetrically was chosen for the test see Fig 3 The
central part of the beam (between the point loads) subjected to
uniform bending moment was the only heated part The tempera-
ture affects the plate slenderness as described above and shown in
Fig 2b The two temperatures selected for the tests were decided
to represent the most signi1047297cant change of the slenderness for the
same section These were namely 450 1C and 650 1C
Seven tests vary in the cross-sections length of the middle
and side span and temperature Table 1 present the used
Table 2
Tested sectionsmdashlateral torsional buckling
Test number Dimensions [mm] Classi1047297cation Non-dimensional slenderness
Test 5 (450 1C) hfrac14460 WebmdashClass 4
bfrac14150 λp frac14 107 λLT frac14 091
t f frac145 FlangemdashClass 4
t wfrac144 λp frac14 096 λLTθ frac14 086
Test 6 (450 1C) hfrac14460 WebmdashClass 4 λLT frac14 092
bfrac14150 λp frac14 101 λLTθ frac14 088
t f frac147 FlangemdashClass 4
t wfrac144 λp frac14 069
Test 7 Tapered beam (650 1C) h Afrac14460 Endmdashsection A-B WebmdashClass 4
hBfrac14620 λpethATHORN frac14 107
bfrac14150 λpethBTHORN frac14 152
t f frac147 FlangemdashClass 4
t wfrac144 λpethABTHORN frac14 096
Fig 5 Simple bending test setup (upper) and lateral torsional buckling test setup (lower)
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cross-sections which were fabricated by one side 1047297llet welding
Fig 4 summarises the tested beams dimensions and used steel
plates S1ndashS7 for which the material properties are given later
(Table 5) In case of the simple bending two cross-sections of
constant height were tested for each temperature In these tests
the lateral movement of the beam was prevented at smalldistances so the failure mode was not affected by lateral torsional
buckling The length of the middle part was approximately
1500 mm (after heating) Each section was tested at temperatures
450 1C and 650 1C The other three tests were designed to fail with
major contribution of lateral torsional buckling and the lateral
restrains were at larger distances Two of the tests were performed
on beams of constant section height One test was made on a
tapered beam where the height of the web varied linearly from
one end to another The length of the middle part (between the
load points) of the beams was approximately 2800 mm (after
heating) Free rotation and transverse de1047298ection was allowed
between load points The section rotation was also allowed at
the supports The temperature for each section is detailed in
Tables 1 and 2
All tests were controlled by displacement (vertical de1047298ection)
which was estimated as 45 mm per minute for simple bending
tests Final de1047298ection at midspan was 70 mm For beams subjected
Fig 6 Lateral restraints
Fig 7 Simple bending test supports (a) pinned (b) roller
Fig 8 Lateral restraints at the end of the tested beams (simple bending and LTB)
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to lateral torsional buckling deformation increase was estimated
as 35 mm per minute and the 1047297nal de1047298ection was 50 mm The
load was introduced via a distributing beam at the edges of the
heated part (middle span) The load was applied by means of one
hydraulic jack of 650 kN capacity All the tests were performed on
steady state it means that the beams were 1047297rst heated and then
the load was applied until failure
The additional test equipment was designed as universal for
the experiments It respected boundary conditions based on the
numerical analyses and is described below Test setup for both
types of the tests is illustrated in Fig 5 It consisted of lateral
restraints supports and the load distributing beam At the location
of the load application (at the edge of the heated part) the top and
the bottom 1047298ange were laterally restrained by two vertical CHS
80 56 supported transversally by diagonal members Bolts above
and below the tested pro1047297le section interconnected these two
vertical pro1047297les The lateral restraints are depicted in Fig 6
For all tests the beams were supported at the ends under the
lower 1047298ange In the case of simple bending tests both supports
were pinned (free rotation in the direction of the strong axis) One
of the supports was designed as a rolling bearing (set of horizontal
rods) and allowed free horizontal displacement in the longitudinal
direction (beam axismdashroller) Other displacements and rotations
were restricted see Fig 7 The restriction of lateral displacementand lateral rotation was ensured by couple of vertical pro1047297les (UPE
100) see Fig 8 The horizontal recti1047297cation of the vertical pro1047297les
was allowed to 1047297t to both tested section widths
In the case of the lateral torsional buckling tests the end
supports were considered just by one point support It was made
using a high-resistance steel sphere bearing placed between two
steel plates Both end supports allowed free torsion of the end
cross-section around the sphere bearing One restrained the
displacement in all directions (pinned) The second allowed also
free horizontal displacement in the direction along the beam axis
(roller) The prevented transverse displacement in at the supports
was found to have very little effect on the beam resistance and was
much easier to reach in the test Fig 9 shows both pinned and
roller supports of the beam
Fig 9 Lateral torsional buckling test supports (a) pinned (b) roller
Fig 10 Manual measurement
Fig 11 Simple bending testsmdashpoints of the measurement (the web and the upper
1047298ange)
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21 Measurement of the initial geometric imperfections
Before the experiment after placing the beam on the support
the initial geometry of the specimens was established using the
two methods namely manual measurements and laser scanningThe 1047297rst methodmdashmanual measurement consists of amplitude
measurement for global and local imperfection Amplitude of
global imperfection was measured as a deviation from a string
spanned between the stiffeners (load application points) For
measurements of local imperfection amplitude a special device
set with a centesimal displacement meter was used see Fig 10
The length of device set was chosen according to the half sine
wave length corresponding to the local buckling shape for each
beam calculated in ABAQUS The investigation was made in
compression zone of the beams only Figs 11 and 12 show the
position of the measurements The local imperfection amplitudes
of the web and 1047298ange for beam test 1 to 4 are in Figs 13ndash16 and in
Figs 17 and 18 for the beam test 5 to 7 For these the side of the
1047298ange with higher imperfection amplitude is shown Table 3
summarises the maximum amplitude of the local and global
imperfection along each beam
The second method of imperfection measurement (see Fig 19)
was the laser scanning method It is still comparatively new
technology (1047297rst instrument were used about 15 years ago) andit is very effective for measuring of complex surface topography
Therefore it was used as control method to measure the global
and local initial imperfections All tested beams were scanned
before testing Scanning resolution was set to average grid
5 5 mm on the beam surface The result were plotted as set of
longitudinal and transverse sections trough the tested beams
which adequately describes each beams geometrical properties
Eight standpoints were used to reach maximum covering of the
beam surface It took about 5 min to carry out one standpoint
Surphaser 25HSX with IR_X con1047297guration (the second most
accurate con1047297guration) was used in all cases It is the most
accurate polar laser scanning system on the market The most
important speci1047297cation of the scanner are measurement speed up
to 12 million points per second 1047297eld of view panoramic accuracy
Fig 14 Distribution of the imperfection amplitude along the beammdashTest 2
Fig 12 Lateral torsional buckling testsmdashpoints of the measurement (the web and the upper 1047298ange)
Fig 13 Distribution of the imperfection amplitude along the beammdashTest 1
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better than 05 mm (absolute) at 5 m noise 01 mm at 3 m
measurement range 04ndash30 m Scanner 3D data from eight stand-
points was transformed to unique coordinate system using sphe-
rical control points in the Leica Cyclone software Then the beam
part from point cloud was cut out and 3D model in the form of
triangular mesh was created in the software Geomagic Studio see
Fig 20 The last step was generation of cross and horizontal
sections in 5 cm intervals see Fig 21 Detailed information about
scanning of these beams can be found in [11] In comparison of
both methods laser scanning and manual measurement found
the imperfection amplitudes very similar see Fig 22
22 Heating of specimens
There is not much experimental work on the behaviour of Class
4 beams at elevated temperature but similar experiments using the
same type of heating equipment were made on the lateral-torsional
buckling of Class 1 section beams in 2003 [12] and in 2005 [13] For
the described tests Mannings 70 kV A heat power units with
6 channels were used to heat the specimens see Fig 23 This unit
provides a 60 V supply for powering various types of low voltage
heating elements It consists of an air natural 3 phase transformer
switching is by contactors The output channels are controlled by
means of energy regulators and the temperature controllers Each
channel has its own automanual switch so any combination of
channels can be operated either auto or manual
Cable connection of 70 kV A consists of 6 triple cable sets and
4-way splitter cables can accommodate total of 24 1047298exible ceramic
heating pads attached Maximum connected load for the 70 kV A
unit is 648 kW In order to be able to heat two different beams of
the experimental tests universal size of the ceramic pads was
used 305 165 mm Ceramic heating elements are constructed
from nickel-chrome core wire and nickel cold tail wire which is
electrically insulated by interlocking high grade sintered alumina
ceramic beads The construction allows the heating element to be
1047298exible and provides high heat transfer ef 1047297ciency The heating
pads are able to reach a maximum temperature of 1200 1C
working temperature capability is 1050 1C at a heating rate
10 1Cmin
In the 1047297rst step the pads were put on the rod rack in order to
maintain the position of the heating elements on the web On the
bottom 1047298ange the pads were 1047297xed with steel wire On the top
1047298ange the pads were 1047297xed with adhesive tape only They were
placed on the outer surface of the 1047298anges For the web they were
attached from one side only where the side was alternated along
the beam length (Fig 24)
Two types of material were used for the beams insulation First
the space between the 1047298anges and the outer surface of the 1047298anges
was insulated by standard mineral wool (ROCKWOOL Airrock HD)
The wool was 1047297xed on the beam with steel wires Second themiddle span was wrapped by super wool insulation material see
Fig 25
Seventeen thermocouples were used for the temperature
measurement Eleven of them were placed in the middle span
and six were placed in the side spans for monitoring of the
temperature in not-heated section For lateral torsional buckling
test where the middle span was longer twenty thermocouples
were used in the middle span and four in the side spans The
thermocouples were distributed on the beam according to the
position of ceramic pads as shown and numbered in Fig 24 Beam
temperatures were recorded from the beginning of heating to the
end of the experiment The average measured temperatures
during the loading can be found in Table 4 for each part of the
beam separately The temperature of the bottom 1047298ange was lower
Table 3
Local and global geometric imperfection amplitudes
Test number Imperfection amplitude [mm]
Local-web Local-1047298ange Global
Test 1 4 77 120 ndash
Test 2 1 34 198 ndash
Test 3 2 36 192 ndash
Test 4 1 60 067 ndash Test 5 736 227 25
Test 6 58 069 15
Test 7 759 213 15
Fig 15 Distribution of the imperfection amplitude along the beammdashTest 3
Fig 16 Distribution of the imperfection amplitude along the beammdashTest 4
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as result of worse contact between beam and ceramic pads The
sets of four heating pads were controlled by one thermocouple
The displacements were measured by potentiometers For the
simple bending test two potentiometers were used for measure-
ment of the vertical displacement in the locations of load applica-
tion and one at the mid span For the lateral torsional bending test
two potentiometers were place in the locations of load application
as in the previous case Vertical (VD) and horizontal (HD) de1047298ec-
tion of the bottom 1047298ange centre and section rotation (R) of the
beam at mid-span were calculated from measurement of four
potentiometers Two measured vertical de1047298ection and two hor-
izontal one for two points of the section (see Fig 26)
Fig 17 Local imperfection amplitude along the webmdashlateral torsional buckling Test 5 to 7
Fig 18 Local imperfection amplitude along the upper 1047298angemdashlateral torsional buckling Test 5 to 7
Fig 19 Laser scanner
Fig 20 Beam triangular mesh model
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23 Material properties
For possible model validation material properties for each part
of the welded section were measured at ambient temperature and
at elevated temperature namely 450 1C and 650 1C The tensile
coupon tests were carried out in accordance with EN ISO 6892-1
[14] to determine the basic engineering stress-strain response of
the material The measured values of yield strength for each plate
as were de1047297ne in Fig 4 and temperature are presented in Table 5
3 Numerical analyses and its comparison with experiments
The tests were replicated by means of the 1047297nite element
method program ABAQUS [10] The ABAQUS code is general
software and allows a complete solution for a large range of
problems including the analysis of structures under 1047297re Static
calculation was used in this case The same models as for
preliminary numerical simulation were used The beam was
meshed using quadrilateral conventional shell elements (namely
type S4) Conventional shell elements discretize a body by de1047297ning
the geometry at a reference surface In this case the thickness is
de1047297ned through the section property de1047297nition Conventional
shell elements have 3 displacement and 3 rotational degrees of
freedom per node Element type S4 is a fully integrated general-
purpose 1047297nite-membrane-strain shell element The element has
four integration points per element
All experimental data have been used for validation of thenumerical model Both local and global (if any) geometrical
imperfections were introduced into the geometrically and materi-
ally nonlinear analysis
The material law was de1047297ned by elasticndashplastic nonlinear
stressndashstrain diagram where enough data points were used The
true material stressndashstrain relationship was calculated from the
static engineering strassndashstrain curves obtained from the coupon
tests at room temperature The reductions of material properties
as well as the material nonlinearity were taken from the EC3 12
[4] as only two levels of elevated temperature were tested and
mostly con1047297rmed the established reduction factors The measured
average temperatures from each heated part of the beams were
introduced to the model Adjacent parts of the beam and stiffeners
were modelled as in room temperature (20 1C)
Fig 21 Cross and horizontal beam sections
Fig 22 Comparison between manual measurement and laser scanning for web
of beam
Fig 23 Mannings heat power units
Table 4
Temperature during the tests
Test number Average temperature [1C]
Upper 1047298ange Bottom 1047298ange Web
Test 1 444 469 458
Test 2 654 636 649
Test 3 481 425 431
Test 4 661 631 641
Test 5 457 354 444
Test 6 481 369 443
Test 7 624 416 567
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
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across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
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for ε as given by Eq (6)
εθ frac14 085 235
f y
05
eth6THORN
where the reduction coef 1047297cient 085 represents the effect of the
degradation of material properties regardless temperature and
material The correct relationship for ε taking into account
in1047298uence of different temperature can be written as (7)
εθ frac14
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffikEθ
kyθ or kp02θ
s 235
f y
05
eth7THORN
Compared to the real dependence of reduced material proper-
ties on temperature apparently the simple reduction by 085 is
suf 1047297cient and mostly safe approximation see Fig 2a)
The Informative Annex E of EC3 12 [4] recommends using
different value of yield strength for Class 4 section (02 proof
strength for Class 4 instead of 20 total strain for stockier Class
1 to 3 sections) The effective cross-section characteristics should
be calculated according the EC3 15 [3] (resp EC3 13 [5]) This
means the effective section is based on the material properties at
20 1C The actual relationship for ε depending on temperature is
shown in Fig 2b)Determination of the bending resistance for members sub-
jected to lateral torsional buckling of Classes 1 to 3 cross sections
at elevated temperature is based on the same principles as the
design at room temperature according to EC3 11 [2] However it
differs in using one imperfection factor only for all types of cross-
sections The procedure may be used for Class 4 sections as well
however with restriction for the maximum critical temperature
and different reduction for the yield strength (Annex E)
For web-tapered beams a limited design procedure is given in
the informative Annex BB of the standard EC3 11 [2] applicable for
the room temperature only The additional procedure is the clause
634 (General Method) given in EC3 11 [2] The suitability of this
approach for Class 1 to 3 cross-section and ambient temperature
was veri1047297ed in [6] The resistance of the non-uniform members
according to the General Method was analysed and compared with
numerical results and the procedures of clauses 631 to 633 of
EC3 11 [2] For elevated temperature the General method was
validated for selected stocky sections by Couto et al [7] EC3 15
Annex B [3] gives another possible approach for non-uniform
members It considers the effect of both plate (local) and lateraltorsional buckling (global) by one reduction factor In case of
member subjected to the lateral torsional buckling the reduction
factor used should be the minimum of the reduction factor ρ given
by EC3 15 [3] in clause B1 (used for the reduction due to the local
buckling) and χ LTmdashthe reduction for lateral torsional buckling
according to EC3 11 632 [2] This in fact leads to the method in
clause 632 but with neglecting the local buckling effect by
considering the elastic section modulus for slender beams Resis-
tance of non-uniform members at room temperature was also
published by Marques et al [8] or using Merchant-Rankine
procedure by Braham and Hanikenne [9] The possibility of using
any of the above described rules for lateral-torsional buckling in
case of 1047297re has not been investigated yet
In the framework of the RFCS project FIDESC4mdashFire Design of
Steel Members with Welded or Hot-rolled Class 4 Cross-sections
several simple supported beams submitted to four-point bending
were tested to study the pure bending and the lateral torsional
buckling at different temperatures
2 Description of the experiments
In the described research of slender sections at elevated tempera-
ture four tests were carried out to study the simple bending (section
resistance) and three tests for beams subjected to lateral torsional
buckling First a preliminary numerical model for calibration of
experiments was made using FE software ABAQUS [10] In order to
achieve local or global failure mode as main failure mode different
boundary condition and load distributions were modelled Based on
the numerical model development and laboratory conditions appro-
priate cross-sections and procedures were chosenFig 3 Scheme of tested beam
Table 1
Tested sectionsmdashsimple bending
Test number Dimensions [mm] Classi1047297cation
Test 1 (450 1C) and Test 2 (650 1C) hfrac14 680 WebmdashClass 4
b frac14250 λ p frac14 144
t f frac14 12 FlangemdashClass 4
t wfrac144 λ p frac14 066
Test 3 (450 1C) and Test 4 (650 1C) hfrac14 846 WebmdashClass 4
b frac14300 λ p frac14 145
t f frac14 8 FlangemdashClass 4
t wfrac145 λ p frac14 118
NOTE Classi1047297cationmdashaccording to EN 1993-1-2
Plate slendernessmdashaccording to EN 1993-1-2 Annex E
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Fig 4 Tested beams 1 to 7
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A simply supported beam with two equal concentrated point
loads applied symmetrically was chosen for the test see Fig 3 The
central part of the beam (between the point loads) subjected to
uniform bending moment was the only heated part The tempera-
ture affects the plate slenderness as described above and shown in
Fig 2b The two temperatures selected for the tests were decided
to represent the most signi1047297cant change of the slenderness for the
same section These were namely 450 1C and 650 1C
Seven tests vary in the cross-sections length of the middle
and side span and temperature Table 1 present the used
Table 2
Tested sectionsmdashlateral torsional buckling
Test number Dimensions [mm] Classi1047297cation Non-dimensional slenderness
Test 5 (450 1C) hfrac14460 WebmdashClass 4
bfrac14150 λp frac14 107 λLT frac14 091
t f frac145 FlangemdashClass 4
t wfrac144 λp frac14 096 λLTθ frac14 086
Test 6 (450 1C) hfrac14460 WebmdashClass 4 λLT frac14 092
bfrac14150 λp frac14 101 λLTθ frac14 088
t f frac147 FlangemdashClass 4
t wfrac144 λp frac14 069
Test 7 Tapered beam (650 1C) h Afrac14460 Endmdashsection A-B WebmdashClass 4
hBfrac14620 λpethATHORN frac14 107
bfrac14150 λpethBTHORN frac14 152
t f frac147 FlangemdashClass 4
t wfrac144 λpethABTHORN frac14 096
Fig 5 Simple bending test setup (upper) and lateral torsional buckling test setup (lower)
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cross-sections which were fabricated by one side 1047297llet welding
Fig 4 summarises the tested beams dimensions and used steel
plates S1ndashS7 for which the material properties are given later
(Table 5) In case of the simple bending two cross-sections of
constant height were tested for each temperature In these tests
the lateral movement of the beam was prevented at smalldistances so the failure mode was not affected by lateral torsional
buckling The length of the middle part was approximately
1500 mm (after heating) Each section was tested at temperatures
450 1C and 650 1C The other three tests were designed to fail with
major contribution of lateral torsional buckling and the lateral
restrains were at larger distances Two of the tests were performed
on beams of constant section height One test was made on a
tapered beam where the height of the web varied linearly from
one end to another The length of the middle part (between the
load points) of the beams was approximately 2800 mm (after
heating) Free rotation and transverse de1047298ection was allowed
between load points The section rotation was also allowed at
the supports The temperature for each section is detailed in
Tables 1 and 2
All tests were controlled by displacement (vertical de1047298ection)
which was estimated as 45 mm per minute for simple bending
tests Final de1047298ection at midspan was 70 mm For beams subjected
Fig 6 Lateral restraints
Fig 7 Simple bending test supports (a) pinned (b) roller
Fig 8 Lateral restraints at the end of the tested beams (simple bending and LTB)
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to lateral torsional buckling deformation increase was estimated
as 35 mm per minute and the 1047297nal de1047298ection was 50 mm The
load was introduced via a distributing beam at the edges of the
heated part (middle span) The load was applied by means of one
hydraulic jack of 650 kN capacity All the tests were performed on
steady state it means that the beams were 1047297rst heated and then
the load was applied until failure
The additional test equipment was designed as universal for
the experiments It respected boundary conditions based on the
numerical analyses and is described below Test setup for both
types of the tests is illustrated in Fig 5 It consisted of lateral
restraints supports and the load distributing beam At the location
of the load application (at the edge of the heated part) the top and
the bottom 1047298ange were laterally restrained by two vertical CHS
80 56 supported transversally by diagonal members Bolts above
and below the tested pro1047297le section interconnected these two
vertical pro1047297les The lateral restraints are depicted in Fig 6
For all tests the beams were supported at the ends under the
lower 1047298ange In the case of simple bending tests both supports
were pinned (free rotation in the direction of the strong axis) One
of the supports was designed as a rolling bearing (set of horizontal
rods) and allowed free horizontal displacement in the longitudinal
direction (beam axismdashroller) Other displacements and rotations
were restricted see Fig 7 The restriction of lateral displacementand lateral rotation was ensured by couple of vertical pro1047297les (UPE
100) see Fig 8 The horizontal recti1047297cation of the vertical pro1047297les
was allowed to 1047297t to both tested section widths
In the case of the lateral torsional buckling tests the end
supports were considered just by one point support It was made
using a high-resistance steel sphere bearing placed between two
steel plates Both end supports allowed free torsion of the end
cross-section around the sphere bearing One restrained the
displacement in all directions (pinned) The second allowed also
free horizontal displacement in the direction along the beam axis
(roller) The prevented transverse displacement in at the supports
was found to have very little effect on the beam resistance and was
much easier to reach in the test Fig 9 shows both pinned and
roller supports of the beam
Fig 9 Lateral torsional buckling test supports (a) pinned (b) roller
Fig 10 Manual measurement
Fig 11 Simple bending testsmdashpoints of the measurement (the web and the upper
1047298ange)
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21 Measurement of the initial geometric imperfections
Before the experiment after placing the beam on the support
the initial geometry of the specimens was established using the
two methods namely manual measurements and laser scanningThe 1047297rst methodmdashmanual measurement consists of amplitude
measurement for global and local imperfection Amplitude of
global imperfection was measured as a deviation from a string
spanned between the stiffeners (load application points) For
measurements of local imperfection amplitude a special device
set with a centesimal displacement meter was used see Fig 10
The length of device set was chosen according to the half sine
wave length corresponding to the local buckling shape for each
beam calculated in ABAQUS The investigation was made in
compression zone of the beams only Figs 11 and 12 show the
position of the measurements The local imperfection amplitudes
of the web and 1047298ange for beam test 1 to 4 are in Figs 13ndash16 and in
Figs 17 and 18 for the beam test 5 to 7 For these the side of the
1047298ange with higher imperfection amplitude is shown Table 3
summarises the maximum amplitude of the local and global
imperfection along each beam
The second method of imperfection measurement (see Fig 19)
was the laser scanning method It is still comparatively new
technology (1047297rst instrument were used about 15 years ago) andit is very effective for measuring of complex surface topography
Therefore it was used as control method to measure the global
and local initial imperfections All tested beams were scanned
before testing Scanning resolution was set to average grid
5 5 mm on the beam surface The result were plotted as set of
longitudinal and transverse sections trough the tested beams
which adequately describes each beams geometrical properties
Eight standpoints were used to reach maximum covering of the
beam surface It took about 5 min to carry out one standpoint
Surphaser 25HSX with IR_X con1047297guration (the second most
accurate con1047297guration) was used in all cases It is the most
accurate polar laser scanning system on the market The most
important speci1047297cation of the scanner are measurement speed up
to 12 million points per second 1047297eld of view panoramic accuracy
Fig 14 Distribution of the imperfection amplitude along the beammdashTest 2
Fig 12 Lateral torsional buckling testsmdashpoints of the measurement (the web and the upper 1047298ange)
Fig 13 Distribution of the imperfection amplitude along the beammdashTest 1
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better than 05 mm (absolute) at 5 m noise 01 mm at 3 m
measurement range 04ndash30 m Scanner 3D data from eight stand-
points was transformed to unique coordinate system using sphe-
rical control points in the Leica Cyclone software Then the beam
part from point cloud was cut out and 3D model in the form of
triangular mesh was created in the software Geomagic Studio see
Fig 20 The last step was generation of cross and horizontal
sections in 5 cm intervals see Fig 21 Detailed information about
scanning of these beams can be found in [11] In comparison of
both methods laser scanning and manual measurement found
the imperfection amplitudes very similar see Fig 22
22 Heating of specimens
There is not much experimental work on the behaviour of Class
4 beams at elevated temperature but similar experiments using the
same type of heating equipment were made on the lateral-torsional
buckling of Class 1 section beams in 2003 [12] and in 2005 [13] For
the described tests Mannings 70 kV A heat power units with
6 channels were used to heat the specimens see Fig 23 This unit
provides a 60 V supply for powering various types of low voltage
heating elements It consists of an air natural 3 phase transformer
switching is by contactors The output channels are controlled by
means of energy regulators and the temperature controllers Each
channel has its own automanual switch so any combination of
channels can be operated either auto or manual
Cable connection of 70 kV A consists of 6 triple cable sets and
4-way splitter cables can accommodate total of 24 1047298exible ceramic
heating pads attached Maximum connected load for the 70 kV A
unit is 648 kW In order to be able to heat two different beams of
the experimental tests universal size of the ceramic pads was
used 305 165 mm Ceramic heating elements are constructed
from nickel-chrome core wire and nickel cold tail wire which is
electrically insulated by interlocking high grade sintered alumina
ceramic beads The construction allows the heating element to be
1047298exible and provides high heat transfer ef 1047297ciency The heating
pads are able to reach a maximum temperature of 1200 1C
working temperature capability is 1050 1C at a heating rate
10 1Cmin
In the 1047297rst step the pads were put on the rod rack in order to
maintain the position of the heating elements on the web On the
bottom 1047298ange the pads were 1047297xed with steel wire On the top
1047298ange the pads were 1047297xed with adhesive tape only They were
placed on the outer surface of the 1047298anges For the web they were
attached from one side only where the side was alternated along
the beam length (Fig 24)
Two types of material were used for the beams insulation First
the space between the 1047298anges and the outer surface of the 1047298anges
was insulated by standard mineral wool (ROCKWOOL Airrock HD)
The wool was 1047297xed on the beam with steel wires Second themiddle span was wrapped by super wool insulation material see
Fig 25
Seventeen thermocouples were used for the temperature
measurement Eleven of them were placed in the middle span
and six were placed in the side spans for monitoring of the
temperature in not-heated section For lateral torsional buckling
test where the middle span was longer twenty thermocouples
were used in the middle span and four in the side spans The
thermocouples were distributed on the beam according to the
position of ceramic pads as shown and numbered in Fig 24 Beam
temperatures were recorded from the beginning of heating to the
end of the experiment The average measured temperatures
during the loading can be found in Table 4 for each part of the
beam separately The temperature of the bottom 1047298ange was lower
Table 3
Local and global geometric imperfection amplitudes
Test number Imperfection amplitude [mm]
Local-web Local-1047298ange Global
Test 1 4 77 120 ndash
Test 2 1 34 198 ndash
Test 3 2 36 192 ndash
Test 4 1 60 067 ndash Test 5 736 227 25
Test 6 58 069 15
Test 7 759 213 15
Fig 15 Distribution of the imperfection amplitude along the beammdashTest 3
Fig 16 Distribution of the imperfection amplitude along the beammdashTest 4
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as result of worse contact between beam and ceramic pads The
sets of four heating pads were controlled by one thermocouple
The displacements were measured by potentiometers For the
simple bending test two potentiometers were used for measure-
ment of the vertical displacement in the locations of load applica-
tion and one at the mid span For the lateral torsional bending test
two potentiometers were place in the locations of load application
as in the previous case Vertical (VD) and horizontal (HD) de1047298ec-
tion of the bottom 1047298ange centre and section rotation (R) of the
beam at mid-span were calculated from measurement of four
potentiometers Two measured vertical de1047298ection and two hor-
izontal one for two points of the section (see Fig 26)
Fig 17 Local imperfection amplitude along the webmdashlateral torsional buckling Test 5 to 7
Fig 18 Local imperfection amplitude along the upper 1047298angemdashlateral torsional buckling Test 5 to 7
Fig 19 Laser scanner
Fig 20 Beam triangular mesh model
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23 Material properties
For possible model validation material properties for each part
of the welded section were measured at ambient temperature and
at elevated temperature namely 450 1C and 650 1C The tensile
coupon tests were carried out in accordance with EN ISO 6892-1
[14] to determine the basic engineering stress-strain response of
the material The measured values of yield strength for each plate
as were de1047297ne in Fig 4 and temperature are presented in Table 5
3 Numerical analyses and its comparison with experiments
The tests were replicated by means of the 1047297nite element
method program ABAQUS [10] The ABAQUS code is general
software and allows a complete solution for a large range of
problems including the analysis of structures under 1047297re Static
calculation was used in this case The same models as for
preliminary numerical simulation were used The beam was
meshed using quadrilateral conventional shell elements (namely
type S4) Conventional shell elements discretize a body by de1047297ning
the geometry at a reference surface In this case the thickness is
de1047297ned through the section property de1047297nition Conventional
shell elements have 3 displacement and 3 rotational degrees of
freedom per node Element type S4 is a fully integrated general-
purpose 1047297nite-membrane-strain shell element The element has
four integration points per element
All experimental data have been used for validation of thenumerical model Both local and global (if any) geometrical
imperfections were introduced into the geometrically and materi-
ally nonlinear analysis
The material law was de1047297ned by elasticndashplastic nonlinear
stressndashstrain diagram where enough data points were used The
true material stressndashstrain relationship was calculated from the
static engineering strassndashstrain curves obtained from the coupon
tests at room temperature The reductions of material properties
as well as the material nonlinearity were taken from the EC3 12
[4] as only two levels of elevated temperature were tested and
mostly con1047297rmed the established reduction factors The measured
average temperatures from each heated part of the beams were
introduced to the model Adjacent parts of the beam and stiffeners
were modelled as in room temperature (20 1C)
Fig 21 Cross and horizontal beam sections
Fig 22 Comparison between manual measurement and laser scanning for web
of beam
Fig 23 Mannings heat power units
Table 4
Temperature during the tests
Test number Average temperature [1C]
Upper 1047298ange Bottom 1047298ange Web
Test 1 444 469 458
Test 2 654 636 649
Test 3 481 425 431
Test 4 661 631 641
Test 5 457 354 444
Test 6 481 369 443
Test 7 624 416 567
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
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across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
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Fig 4 Tested beams 1 to 7
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎4
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A simply supported beam with two equal concentrated point
loads applied symmetrically was chosen for the test see Fig 3 The
central part of the beam (between the point loads) subjected to
uniform bending moment was the only heated part The tempera-
ture affects the plate slenderness as described above and shown in
Fig 2b The two temperatures selected for the tests were decided
to represent the most signi1047297cant change of the slenderness for the
same section These were namely 450 1C and 650 1C
Seven tests vary in the cross-sections length of the middle
and side span and temperature Table 1 present the used
Table 2
Tested sectionsmdashlateral torsional buckling
Test number Dimensions [mm] Classi1047297cation Non-dimensional slenderness
Test 5 (450 1C) hfrac14460 WebmdashClass 4
bfrac14150 λp frac14 107 λLT frac14 091
t f frac145 FlangemdashClass 4
t wfrac144 λp frac14 096 λLTθ frac14 086
Test 6 (450 1C) hfrac14460 WebmdashClass 4 λLT frac14 092
bfrac14150 λp frac14 101 λLTθ frac14 088
t f frac147 FlangemdashClass 4
t wfrac144 λp frac14 069
Test 7 Tapered beam (650 1C) h Afrac14460 Endmdashsection A-B WebmdashClass 4
hBfrac14620 λpethATHORN frac14 107
bfrac14150 λpethBTHORN frac14 152
t f frac147 FlangemdashClass 4
t wfrac144 λpethABTHORN frac14 096
Fig 5 Simple bending test setup (upper) and lateral torsional buckling test setup (lower)
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cross-sections which were fabricated by one side 1047297llet welding
Fig 4 summarises the tested beams dimensions and used steel
plates S1ndashS7 for which the material properties are given later
(Table 5) In case of the simple bending two cross-sections of
constant height were tested for each temperature In these tests
the lateral movement of the beam was prevented at smalldistances so the failure mode was not affected by lateral torsional
buckling The length of the middle part was approximately
1500 mm (after heating) Each section was tested at temperatures
450 1C and 650 1C The other three tests were designed to fail with
major contribution of lateral torsional buckling and the lateral
restrains were at larger distances Two of the tests were performed
on beams of constant section height One test was made on a
tapered beam where the height of the web varied linearly from
one end to another The length of the middle part (between the
load points) of the beams was approximately 2800 mm (after
heating) Free rotation and transverse de1047298ection was allowed
between load points The section rotation was also allowed at
the supports The temperature for each section is detailed in
Tables 1 and 2
All tests were controlled by displacement (vertical de1047298ection)
which was estimated as 45 mm per minute for simple bending
tests Final de1047298ection at midspan was 70 mm For beams subjected
Fig 6 Lateral restraints
Fig 7 Simple bending test supports (a) pinned (b) roller
Fig 8 Lateral restraints at the end of the tested beams (simple bending and LTB)
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to lateral torsional buckling deformation increase was estimated
as 35 mm per minute and the 1047297nal de1047298ection was 50 mm The
load was introduced via a distributing beam at the edges of the
heated part (middle span) The load was applied by means of one
hydraulic jack of 650 kN capacity All the tests were performed on
steady state it means that the beams were 1047297rst heated and then
the load was applied until failure
The additional test equipment was designed as universal for
the experiments It respected boundary conditions based on the
numerical analyses and is described below Test setup for both
types of the tests is illustrated in Fig 5 It consisted of lateral
restraints supports and the load distributing beam At the location
of the load application (at the edge of the heated part) the top and
the bottom 1047298ange were laterally restrained by two vertical CHS
80 56 supported transversally by diagonal members Bolts above
and below the tested pro1047297le section interconnected these two
vertical pro1047297les The lateral restraints are depicted in Fig 6
For all tests the beams were supported at the ends under the
lower 1047298ange In the case of simple bending tests both supports
were pinned (free rotation in the direction of the strong axis) One
of the supports was designed as a rolling bearing (set of horizontal
rods) and allowed free horizontal displacement in the longitudinal
direction (beam axismdashroller) Other displacements and rotations
were restricted see Fig 7 The restriction of lateral displacementand lateral rotation was ensured by couple of vertical pro1047297les (UPE
100) see Fig 8 The horizontal recti1047297cation of the vertical pro1047297les
was allowed to 1047297t to both tested section widths
In the case of the lateral torsional buckling tests the end
supports were considered just by one point support It was made
using a high-resistance steel sphere bearing placed between two
steel plates Both end supports allowed free torsion of the end
cross-section around the sphere bearing One restrained the
displacement in all directions (pinned) The second allowed also
free horizontal displacement in the direction along the beam axis
(roller) The prevented transverse displacement in at the supports
was found to have very little effect on the beam resistance and was
much easier to reach in the test Fig 9 shows both pinned and
roller supports of the beam
Fig 9 Lateral torsional buckling test supports (a) pinned (b) roller
Fig 10 Manual measurement
Fig 11 Simple bending testsmdashpoints of the measurement (the web and the upper
1047298ange)
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21 Measurement of the initial geometric imperfections
Before the experiment after placing the beam on the support
the initial geometry of the specimens was established using the
two methods namely manual measurements and laser scanningThe 1047297rst methodmdashmanual measurement consists of amplitude
measurement for global and local imperfection Amplitude of
global imperfection was measured as a deviation from a string
spanned between the stiffeners (load application points) For
measurements of local imperfection amplitude a special device
set with a centesimal displacement meter was used see Fig 10
The length of device set was chosen according to the half sine
wave length corresponding to the local buckling shape for each
beam calculated in ABAQUS The investigation was made in
compression zone of the beams only Figs 11 and 12 show the
position of the measurements The local imperfection amplitudes
of the web and 1047298ange for beam test 1 to 4 are in Figs 13ndash16 and in
Figs 17 and 18 for the beam test 5 to 7 For these the side of the
1047298ange with higher imperfection amplitude is shown Table 3
summarises the maximum amplitude of the local and global
imperfection along each beam
The second method of imperfection measurement (see Fig 19)
was the laser scanning method It is still comparatively new
technology (1047297rst instrument were used about 15 years ago) andit is very effective for measuring of complex surface topography
Therefore it was used as control method to measure the global
and local initial imperfections All tested beams were scanned
before testing Scanning resolution was set to average grid
5 5 mm on the beam surface The result were plotted as set of
longitudinal and transverse sections trough the tested beams
which adequately describes each beams geometrical properties
Eight standpoints were used to reach maximum covering of the
beam surface It took about 5 min to carry out one standpoint
Surphaser 25HSX with IR_X con1047297guration (the second most
accurate con1047297guration) was used in all cases It is the most
accurate polar laser scanning system on the market The most
important speci1047297cation of the scanner are measurement speed up
to 12 million points per second 1047297eld of view panoramic accuracy
Fig 14 Distribution of the imperfection amplitude along the beammdashTest 2
Fig 12 Lateral torsional buckling testsmdashpoints of the measurement (the web and the upper 1047298ange)
Fig 13 Distribution of the imperfection amplitude along the beammdashTest 1
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better than 05 mm (absolute) at 5 m noise 01 mm at 3 m
measurement range 04ndash30 m Scanner 3D data from eight stand-
points was transformed to unique coordinate system using sphe-
rical control points in the Leica Cyclone software Then the beam
part from point cloud was cut out and 3D model in the form of
triangular mesh was created in the software Geomagic Studio see
Fig 20 The last step was generation of cross and horizontal
sections in 5 cm intervals see Fig 21 Detailed information about
scanning of these beams can be found in [11] In comparison of
both methods laser scanning and manual measurement found
the imperfection amplitudes very similar see Fig 22
22 Heating of specimens
There is not much experimental work on the behaviour of Class
4 beams at elevated temperature but similar experiments using the
same type of heating equipment were made on the lateral-torsional
buckling of Class 1 section beams in 2003 [12] and in 2005 [13] For
the described tests Mannings 70 kV A heat power units with
6 channels were used to heat the specimens see Fig 23 This unit
provides a 60 V supply for powering various types of low voltage
heating elements It consists of an air natural 3 phase transformer
switching is by contactors The output channels are controlled by
means of energy regulators and the temperature controllers Each
channel has its own automanual switch so any combination of
channels can be operated either auto or manual
Cable connection of 70 kV A consists of 6 triple cable sets and
4-way splitter cables can accommodate total of 24 1047298exible ceramic
heating pads attached Maximum connected load for the 70 kV A
unit is 648 kW In order to be able to heat two different beams of
the experimental tests universal size of the ceramic pads was
used 305 165 mm Ceramic heating elements are constructed
from nickel-chrome core wire and nickel cold tail wire which is
electrically insulated by interlocking high grade sintered alumina
ceramic beads The construction allows the heating element to be
1047298exible and provides high heat transfer ef 1047297ciency The heating
pads are able to reach a maximum temperature of 1200 1C
working temperature capability is 1050 1C at a heating rate
10 1Cmin
In the 1047297rst step the pads were put on the rod rack in order to
maintain the position of the heating elements on the web On the
bottom 1047298ange the pads were 1047297xed with steel wire On the top
1047298ange the pads were 1047297xed with adhesive tape only They were
placed on the outer surface of the 1047298anges For the web they were
attached from one side only where the side was alternated along
the beam length (Fig 24)
Two types of material were used for the beams insulation First
the space between the 1047298anges and the outer surface of the 1047298anges
was insulated by standard mineral wool (ROCKWOOL Airrock HD)
The wool was 1047297xed on the beam with steel wires Second themiddle span was wrapped by super wool insulation material see
Fig 25
Seventeen thermocouples were used for the temperature
measurement Eleven of them were placed in the middle span
and six were placed in the side spans for monitoring of the
temperature in not-heated section For lateral torsional buckling
test where the middle span was longer twenty thermocouples
were used in the middle span and four in the side spans The
thermocouples were distributed on the beam according to the
position of ceramic pads as shown and numbered in Fig 24 Beam
temperatures were recorded from the beginning of heating to the
end of the experiment The average measured temperatures
during the loading can be found in Table 4 for each part of the
beam separately The temperature of the bottom 1047298ange was lower
Table 3
Local and global geometric imperfection amplitudes
Test number Imperfection amplitude [mm]
Local-web Local-1047298ange Global
Test 1 4 77 120 ndash
Test 2 1 34 198 ndash
Test 3 2 36 192 ndash
Test 4 1 60 067 ndash Test 5 736 227 25
Test 6 58 069 15
Test 7 759 213 15
Fig 15 Distribution of the imperfection amplitude along the beammdashTest 3
Fig 16 Distribution of the imperfection amplitude along the beammdashTest 4
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as result of worse contact between beam and ceramic pads The
sets of four heating pads were controlled by one thermocouple
The displacements were measured by potentiometers For the
simple bending test two potentiometers were used for measure-
ment of the vertical displacement in the locations of load applica-
tion and one at the mid span For the lateral torsional bending test
two potentiometers were place in the locations of load application
as in the previous case Vertical (VD) and horizontal (HD) de1047298ec-
tion of the bottom 1047298ange centre and section rotation (R) of the
beam at mid-span were calculated from measurement of four
potentiometers Two measured vertical de1047298ection and two hor-
izontal one for two points of the section (see Fig 26)
Fig 17 Local imperfection amplitude along the webmdashlateral torsional buckling Test 5 to 7
Fig 18 Local imperfection amplitude along the upper 1047298angemdashlateral torsional buckling Test 5 to 7
Fig 19 Laser scanner
Fig 20 Beam triangular mesh model
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23 Material properties
For possible model validation material properties for each part
of the welded section were measured at ambient temperature and
at elevated temperature namely 450 1C and 650 1C The tensile
coupon tests were carried out in accordance with EN ISO 6892-1
[14] to determine the basic engineering stress-strain response of
the material The measured values of yield strength for each plate
as were de1047297ne in Fig 4 and temperature are presented in Table 5
3 Numerical analyses and its comparison with experiments
The tests were replicated by means of the 1047297nite element
method program ABAQUS [10] The ABAQUS code is general
software and allows a complete solution for a large range of
problems including the analysis of structures under 1047297re Static
calculation was used in this case The same models as for
preliminary numerical simulation were used The beam was
meshed using quadrilateral conventional shell elements (namely
type S4) Conventional shell elements discretize a body by de1047297ning
the geometry at a reference surface In this case the thickness is
de1047297ned through the section property de1047297nition Conventional
shell elements have 3 displacement and 3 rotational degrees of
freedom per node Element type S4 is a fully integrated general-
purpose 1047297nite-membrane-strain shell element The element has
four integration points per element
All experimental data have been used for validation of thenumerical model Both local and global (if any) geometrical
imperfections were introduced into the geometrically and materi-
ally nonlinear analysis
The material law was de1047297ned by elasticndashplastic nonlinear
stressndashstrain diagram where enough data points were used The
true material stressndashstrain relationship was calculated from the
static engineering strassndashstrain curves obtained from the coupon
tests at room temperature The reductions of material properties
as well as the material nonlinearity were taken from the EC3 12
[4] as only two levels of elevated temperature were tested and
mostly con1047297rmed the established reduction factors The measured
average temperatures from each heated part of the beams were
introduced to the model Adjacent parts of the beam and stiffeners
were modelled as in room temperature (20 1C)
Fig 21 Cross and horizontal beam sections
Fig 22 Comparison between manual measurement and laser scanning for web
of beam
Fig 23 Mannings heat power units
Table 4
Temperature during the tests
Test number Average temperature [1C]
Upper 1047298ange Bottom 1047298ange Web
Test 1 444 469 458
Test 2 654 636 649
Test 3 481 425 431
Test 4 661 631 641
Test 5 457 354 444
Test 6 481 369 443
Test 7 624 416 567
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
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across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
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A simply supported beam with two equal concentrated point
loads applied symmetrically was chosen for the test see Fig 3 The
central part of the beam (between the point loads) subjected to
uniform bending moment was the only heated part The tempera-
ture affects the plate slenderness as described above and shown in
Fig 2b The two temperatures selected for the tests were decided
to represent the most signi1047297cant change of the slenderness for the
same section These were namely 450 1C and 650 1C
Seven tests vary in the cross-sections length of the middle
and side span and temperature Table 1 present the used
Table 2
Tested sectionsmdashlateral torsional buckling
Test number Dimensions [mm] Classi1047297cation Non-dimensional slenderness
Test 5 (450 1C) hfrac14460 WebmdashClass 4
bfrac14150 λp frac14 107 λLT frac14 091
t f frac145 FlangemdashClass 4
t wfrac144 λp frac14 096 λLTθ frac14 086
Test 6 (450 1C) hfrac14460 WebmdashClass 4 λLT frac14 092
bfrac14150 λp frac14 101 λLTθ frac14 088
t f frac147 FlangemdashClass 4
t wfrac144 λp frac14 069
Test 7 Tapered beam (650 1C) h Afrac14460 Endmdashsection A-B WebmdashClass 4
hBfrac14620 λpethATHORN frac14 107
bfrac14150 λpethBTHORN frac14 152
t f frac147 FlangemdashClass 4
t wfrac144 λpethABTHORN frac14 096
Fig 5 Simple bending test setup (upper) and lateral torsional buckling test setup (lower)
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cross-sections which were fabricated by one side 1047297llet welding
Fig 4 summarises the tested beams dimensions and used steel
plates S1ndashS7 for which the material properties are given later
(Table 5) In case of the simple bending two cross-sections of
constant height were tested for each temperature In these tests
the lateral movement of the beam was prevented at smalldistances so the failure mode was not affected by lateral torsional
buckling The length of the middle part was approximately
1500 mm (after heating) Each section was tested at temperatures
450 1C and 650 1C The other three tests were designed to fail with
major contribution of lateral torsional buckling and the lateral
restrains were at larger distances Two of the tests were performed
on beams of constant section height One test was made on a
tapered beam where the height of the web varied linearly from
one end to another The length of the middle part (between the
load points) of the beams was approximately 2800 mm (after
heating) Free rotation and transverse de1047298ection was allowed
between load points The section rotation was also allowed at
the supports The temperature for each section is detailed in
Tables 1 and 2
All tests were controlled by displacement (vertical de1047298ection)
which was estimated as 45 mm per minute for simple bending
tests Final de1047298ection at midspan was 70 mm For beams subjected
Fig 6 Lateral restraints
Fig 7 Simple bending test supports (a) pinned (b) roller
Fig 8 Lateral restraints at the end of the tested beams (simple bending and LTB)
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to lateral torsional buckling deformation increase was estimated
as 35 mm per minute and the 1047297nal de1047298ection was 50 mm The
load was introduced via a distributing beam at the edges of the
heated part (middle span) The load was applied by means of one
hydraulic jack of 650 kN capacity All the tests were performed on
steady state it means that the beams were 1047297rst heated and then
the load was applied until failure
The additional test equipment was designed as universal for
the experiments It respected boundary conditions based on the
numerical analyses and is described below Test setup for both
types of the tests is illustrated in Fig 5 It consisted of lateral
restraints supports and the load distributing beam At the location
of the load application (at the edge of the heated part) the top and
the bottom 1047298ange were laterally restrained by two vertical CHS
80 56 supported transversally by diagonal members Bolts above
and below the tested pro1047297le section interconnected these two
vertical pro1047297les The lateral restraints are depicted in Fig 6
For all tests the beams were supported at the ends under the
lower 1047298ange In the case of simple bending tests both supports
were pinned (free rotation in the direction of the strong axis) One
of the supports was designed as a rolling bearing (set of horizontal
rods) and allowed free horizontal displacement in the longitudinal
direction (beam axismdashroller) Other displacements and rotations
were restricted see Fig 7 The restriction of lateral displacementand lateral rotation was ensured by couple of vertical pro1047297les (UPE
100) see Fig 8 The horizontal recti1047297cation of the vertical pro1047297les
was allowed to 1047297t to both tested section widths
In the case of the lateral torsional buckling tests the end
supports were considered just by one point support It was made
using a high-resistance steel sphere bearing placed between two
steel plates Both end supports allowed free torsion of the end
cross-section around the sphere bearing One restrained the
displacement in all directions (pinned) The second allowed also
free horizontal displacement in the direction along the beam axis
(roller) The prevented transverse displacement in at the supports
was found to have very little effect on the beam resistance and was
much easier to reach in the test Fig 9 shows both pinned and
roller supports of the beam
Fig 9 Lateral torsional buckling test supports (a) pinned (b) roller
Fig 10 Manual measurement
Fig 11 Simple bending testsmdashpoints of the measurement (the web and the upper
1047298ange)
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21 Measurement of the initial geometric imperfections
Before the experiment after placing the beam on the support
the initial geometry of the specimens was established using the
two methods namely manual measurements and laser scanningThe 1047297rst methodmdashmanual measurement consists of amplitude
measurement for global and local imperfection Amplitude of
global imperfection was measured as a deviation from a string
spanned between the stiffeners (load application points) For
measurements of local imperfection amplitude a special device
set with a centesimal displacement meter was used see Fig 10
The length of device set was chosen according to the half sine
wave length corresponding to the local buckling shape for each
beam calculated in ABAQUS The investigation was made in
compression zone of the beams only Figs 11 and 12 show the
position of the measurements The local imperfection amplitudes
of the web and 1047298ange for beam test 1 to 4 are in Figs 13ndash16 and in
Figs 17 and 18 for the beam test 5 to 7 For these the side of the
1047298ange with higher imperfection amplitude is shown Table 3
summarises the maximum amplitude of the local and global
imperfection along each beam
The second method of imperfection measurement (see Fig 19)
was the laser scanning method It is still comparatively new
technology (1047297rst instrument were used about 15 years ago) andit is very effective for measuring of complex surface topography
Therefore it was used as control method to measure the global
and local initial imperfections All tested beams were scanned
before testing Scanning resolution was set to average grid
5 5 mm on the beam surface The result were plotted as set of
longitudinal and transverse sections trough the tested beams
which adequately describes each beams geometrical properties
Eight standpoints were used to reach maximum covering of the
beam surface It took about 5 min to carry out one standpoint
Surphaser 25HSX with IR_X con1047297guration (the second most
accurate con1047297guration) was used in all cases It is the most
accurate polar laser scanning system on the market The most
important speci1047297cation of the scanner are measurement speed up
to 12 million points per second 1047297eld of view panoramic accuracy
Fig 14 Distribution of the imperfection amplitude along the beammdashTest 2
Fig 12 Lateral torsional buckling testsmdashpoints of the measurement (the web and the upper 1047298ange)
Fig 13 Distribution of the imperfection amplitude along the beammdashTest 1
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better than 05 mm (absolute) at 5 m noise 01 mm at 3 m
measurement range 04ndash30 m Scanner 3D data from eight stand-
points was transformed to unique coordinate system using sphe-
rical control points in the Leica Cyclone software Then the beam
part from point cloud was cut out and 3D model in the form of
triangular mesh was created in the software Geomagic Studio see
Fig 20 The last step was generation of cross and horizontal
sections in 5 cm intervals see Fig 21 Detailed information about
scanning of these beams can be found in [11] In comparison of
both methods laser scanning and manual measurement found
the imperfection amplitudes very similar see Fig 22
22 Heating of specimens
There is not much experimental work on the behaviour of Class
4 beams at elevated temperature but similar experiments using the
same type of heating equipment were made on the lateral-torsional
buckling of Class 1 section beams in 2003 [12] and in 2005 [13] For
the described tests Mannings 70 kV A heat power units with
6 channels were used to heat the specimens see Fig 23 This unit
provides a 60 V supply for powering various types of low voltage
heating elements It consists of an air natural 3 phase transformer
switching is by contactors The output channels are controlled by
means of energy regulators and the temperature controllers Each
channel has its own automanual switch so any combination of
channels can be operated either auto or manual
Cable connection of 70 kV A consists of 6 triple cable sets and
4-way splitter cables can accommodate total of 24 1047298exible ceramic
heating pads attached Maximum connected load for the 70 kV A
unit is 648 kW In order to be able to heat two different beams of
the experimental tests universal size of the ceramic pads was
used 305 165 mm Ceramic heating elements are constructed
from nickel-chrome core wire and nickel cold tail wire which is
electrically insulated by interlocking high grade sintered alumina
ceramic beads The construction allows the heating element to be
1047298exible and provides high heat transfer ef 1047297ciency The heating
pads are able to reach a maximum temperature of 1200 1C
working temperature capability is 1050 1C at a heating rate
10 1Cmin
In the 1047297rst step the pads were put on the rod rack in order to
maintain the position of the heating elements on the web On the
bottom 1047298ange the pads were 1047297xed with steel wire On the top
1047298ange the pads were 1047297xed with adhesive tape only They were
placed on the outer surface of the 1047298anges For the web they were
attached from one side only where the side was alternated along
the beam length (Fig 24)
Two types of material were used for the beams insulation First
the space between the 1047298anges and the outer surface of the 1047298anges
was insulated by standard mineral wool (ROCKWOOL Airrock HD)
The wool was 1047297xed on the beam with steel wires Second themiddle span was wrapped by super wool insulation material see
Fig 25
Seventeen thermocouples were used for the temperature
measurement Eleven of them were placed in the middle span
and six were placed in the side spans for monitoring of the
temperature in not-heated section For lateral torsional buckling
test where the middle span was longer twenty thermocouples
were used in the middle span and four in the side spans The
thermocouples were distributed on the beam according to the
position of ceramic pads as shown and numbered in Fig 24 Beam
temperatures were recorded from the beginning of heating to the
end of the experiment The average measured temperatures
during the loading can be found in Table 4 for each part of the
beam separately The temperature of the bottom 1047298ange was lower
Table 3
Local and global geometric imperfection amplitudes
Test number Imperfection amplitude [mm]
Local-web Local-1047298ange Global
Test 1 4 77 120 ndash
Test 2 1 34 198 ndash
Test 3 2 36 192 ndash
Test 4 1 60 067 ndash Test 5 736 227 25
Test 6 58 069 15
Test 7 759 213 15
Fig 15 Distribution of the imperfection amplitude along the beammdashTest 3
Fig 16 Distribution of the imperfection amplitude along the beammdashTest 4
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as result of worse contact between beam and ceramic pads The
sets of four heating pads were controlled by one thermocouple
The displacements were measured by potentiometers For the
simple bending test two potentiometers were used for measure-
ment of the vertical displacement in the locations of load applica-
tion and one at the mid span For the lateral torsional bending test
two potentiometers were place in the locations of load application
as in the previous case Vertical (VD) and horizontal (HD) de1047298ec-
tion of the bottom 1047298ange centre and section rotation (R) of the
beam at mid-span were calculated from measurement of four
potentiometers Two measured vertical de1047298ection and two hor-
izontal one for two points of the section (see Fig 26)
Fig 17 Local imperfection amplitude along the webmdashlateral torsional buckling Test 5 to 7
Fig 18 Local imperfection amplitude along the upper 1047298angemdashlateral torsional buckling Test 5 to 7
Fig 19 Laser scanner
Fig 20 Beam triangular mesh model
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23 Material properties
For possible model validation material properties for each part
of the welded section were measured at ambient temperature and
at elevated temperature namely 450 1C and 650 1C The tensile
coupon tests were carried out in accordance with EN ISO 6892-1
[14] to determine the basic engineering stress-strain response of
the material The measured values of yield strength for each plate
as were de1047297ne in Fig 4 and temperature are presented in Table 5
3 Numerical analyses and its comparison with experiments
The tests were replicated by means of the 1047297nite element
method program ABAQUS [10] The ABAQUS code is general
software and allows a complete solution for a large range of
problems including the analysis of structures under 1047297re Static
calculation was used in this case The same models as for
preliminary numerical simulation were used The beam was
meshed using quadrilateral conventional shell elements (namely
type S4) Conventional shell elements discretize a body by de1047297ning
the geometry at a reference surface In this case the thickness is
de1047297ned through the section property de1047297nition Conventional
shell elements have 3 displacement and 3 rotational degrees of
freedom per node Element type S4 is a fully integrated general-
purpose 1047297nite-membrane-strain shell element The element has
four integration points per element
All experimental data have been used for validation of thenumerical model Both local and global (if any) geometrical
imperfections were introduced into the geometrically and materi-
ally nonlinear analysis
The material law was de1047297ned by elasticndashplastic nonlinear
stressndashstrain diagram where enough data points were used The
true material stressndashstrain relationship was calculated from the
static engineering strassndashstrain curves obtained from the coupon
tests at room temperature The reductions of material properties
as well as the material nonlinearity were taken from the EC3 12
[4] as only two levels of elevated temperature were tested and
mostly con1047297rmed the established reduction factors The measured
average temperatures from each heated part of the beams were
introduced to the model Adjacent parts of the beam and stiffeners
were modelled as in room temperature (20 1C)
Fig 21 Cross and horizontal beam sections
Fig 22 Comparison between manual measurement and laser scanning for web
of beam
Fig 23 Mannings heat power units
Table 4
Temperature during the tests
Test number Average temperature [1C]
Upper 1047298ange Bottom 1047298ange Web
Test 1 444 469 458
Test 2 654 636 649
Test 3 481 425 431
Test 4 661 631 641
Test 5 457 354 444
Test 6 481 369 443
Test 7 624 416 567
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
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across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
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cross-sections which were fabricated by one side 1047297llet welding
Fig 4 summarises the tested beams dimensions and used steel
plates S1ndashS7 for which the material properties are given later
(Table 5) In case of the simple bending two cross-sections of
constant height were tested for each temperature In these tests
the lateral movement of the beam was prevented at smalldistances so the failure mode was not affected by lateral torsional
buckling The length of the middle part was approximately
1500 mm (after heating) Each section was tested at temperatures
450 1C and 650 1C The other three tests were designed to fail with
major contribution of lateral torsional buckling and the lateral
restrains were at larger distances Two of the tests were performed
on beams of constant section height One test was made on a
tapered beam where the height of the web varied linearly from
one end to another The length of the middle part (between the
load points) of the beams was approximately 2800 mm (after
heating) Free rotation and transverse de1047298ection was allowed
between load points The section rotation was also allowed at
the supports The temperature for each section is detailed in
Tables 1 and 2
All tests were controlled by displacement (vertical de1047298ection)
which was estimated as 45 mm per minute for simple bending
tests Final de1047298ection at midspan was 70 mm For beams subjected
Fig 6 Lateral restraints
Fig 7 Simple bending test supports (a) pinned (b) roller
Fig 8 Lateral restraints at the end of the tested beams (simple bending and LTB)
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to lateral torsional buckling deformation increase was estimated
as 35 mm per minute and the 1047297nal de1047298ection was 50 mm The
load was introduced via a distributing beam at the edges of the
heated part (middle span) The load was applied by means of one
hydraulic jack of 650 kN capacity All the tests were performed on
steady state it means that the beams were 1047297rst heated and then
the load was applied until failure
The additional test equipment was designed as universal for
the experiments It respected boundary conditions based on the
numerical analyses and is described below Test setup for both
types of the tests is illustrated in Fig 5 It consisted of lateral
restraints supports and the load distributing beam At the location
of the load application (at the edge of the heated part) the top and
the bottom 1047298ange were laterally restrained by two vertical CHS
80 56 supported transversally by diagonal members Bolts above
and below the tested pro1047297le section interconnected these two
vertical pro1047297les The lateral restraints are depicted in Fig 6
For all tests the beams were supported at the ends under the
lower 1047298ange In the case of simple bending tests both supports
were pinned (free rotation in the direction of the strong axis) One
of the supports was designed as a rolling bearing (set of horizontal
rods) and allowed free horizontal displacement in the longitudinal
direction (beam axismdashroller) Other displacements and rotations
were restricted see Fig 7 The restriction of lateral displacementand lateral rotation was ensured by couple of vertical pro1047297les (UPE
100) see Fig 8 The horizontal recti1047297cation of the vertical pro1047297les
was allowed to 1047297t to both tested section widths
In the case of the lateral torsional buckling tests the end
supports were considered just by one point support It was made
using a high-resistance steel sphere bearing placed between two
steel plates Both end supports allowed free torsion of the end
cross-section around the sphere bearing One restrained the
displacement in all directions (pinned) The second allowed also
free horizontal displacement in the direction along the beam axis
(roller) The prevented transverse displacement in at the supports
was found to have very little effect on the beam resistance and was
much easier to reach in the test Fig 9 shows both pinned and
roller supports of the beam
Fig 9 Lateral torsional buckling test supports (a) pinned (b) roller
Fig 10 Manual measurement
Fig 11 Simple bending testsmdashpoints of the measurement (the web and the upper
1047298ange)
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21 Measurement of the initial geometric imperfections
Before the experiment after placing the beam on the support
the initial geometry of the specimens was established using the
two methods namely manual measurements and laser scanningThe 1047297rst methodmdashmanual measurement consists of amplitude
measurement for global and local imperfection Amplitude of
global imperfection was measured as a deviation from a string
spanned between the stiffeners (load application points) For
measurements of local imperfection amplitude a special device
set with a centesimal displacement meter was used see Fig 10
The length of device set was chosen according to the half sine
wave length corresponding to the local buckling shape for each
beam calculated in ABAQUS The investigation was made in
compression zone of the beams only Figs 11 and 12 show the
position of the measurements The local imperfection amplitudes
of the web and 1047298ange for beam test 1 to 4 are in Figs 13ndash16 and in
Figs 17 and 18 for the beam test 5 to 7 For these the side of the
1047298ange with higher imperfection amplitude is shown Table 3
summarises the maximum amplitude of the local and global
imperfection along each beam
The second method of imperfection measurement (see Fig 19)
was the laser scanning method It is still comparatively new
technology (1047297rst instrument were used about 15 years ago) andit is very effective for measuring of complex surface topography
Therefore it was used as control method to measure the global
and local initial imperfections All tested beams were scanned
before testing Scanning resolution was set to average grid
5 5 mm on the beam surface The result were plotted as set of
longitudinal and transverse sections trough the tested beams
which adequately describes each beams geometrical properties
Eight standpoints were used to reach maximum covering of the
beam surface It took about 5 min to carry out one standpoint
Surphaser 25HSX with IR_X con1047297guration (the second most
accurate con1047297guration) was used in all cases It is the most
accurate polar laser scanning system on the market The most
important speci1047297cation of the scanner are measurement speed up
to 12 million points per second 1047297eld of view panoramic accuracy
Fig 14 Distribution of the imperfection amplitude along the beammdashTest 2
Fig 12 Lateral torsional buckling testsmdashpoints of the measurement (the web and the upper 1047298ange)
Fig 13 Distribution of the imperfection amplitude along the beammdashTest 1
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better than 05 mm (absolute) at 5 m noise 01 mm at 3 m
measurement range 04ndash30 m Scanner 3D data from eight stand-
points was transformed to unique coordinate system using sphe-
rical control points in the Leica Cyclone software Then the beam
part from point cloud was cut out and 3D model in the form of
triangular mesh was created in the software Geomagic Studio see
Fig 20 The last step was generation of cross and horizontal
sections in 5 cm intervals see Fig 21 Detailed information about
scanning of these beams can be found in [11] In comparison of
both methods laser scanning and manual measurement found
the imperfection amplitudes very similar see Fig 22
22 Heating of specimens
There is not much experimental work on the behaviour of Class
4 beams at elevated temperature but similar experiments using the
same type of heating equipment were made on the lateral-torsional
buckling of Class 1 section beams in 2003 [12] and in 2005 [13] For
the described tests Mannings 70 kV A heat power units with
6 channels were used to heat the specimens see Fig 23 This unit
provides a 60 V supply for powering various types of low voltage
heating elements It consists of an air natural 3 phase transformer
switching is by contactors The output channels are controlled by
means of energy regulators and the temperature controllers Each
channel has its own automanual switch so any combination of
channels can be operated either auto or manual
Cable connection of 70 kV A consists of 6 triple cable sets and
4-way splitter cables can accommodate total of 24 1047298exible ceramic
heating pads attached Maximum connected load for the 70 kV A
unit is 648 kW In order to be able to heat two different beams of
the experimental tests universal size of the ceramic pads was
used 305 165 mm Ceramic heating elements are constructed
from nickel-chrome core wire and nickel cold tail wire which is
electrically insulated by interlocking high grade sintered alumina
ceramic beads The construction allows the heating element to be
1047298exible and provides high heat transfer ef 1047297ciency The heating
pads are able to reach a maximum temperature of 1200 1C
working temperature capability is 1050 1C at a heating rate
10 1Cmin
In the 1047297rst step the pads were put on the rod rack in order to
maintain the position of the heating elements on the web On the
bottom 1047298ange the pads were 1047297xed with steel wire On the top
1047298ange the pads were 1047297xed with adhesive tape only They were
placed on the outer surface of the 1047298anges For the web they were
attached from one side only where the side was alternated along
the beam length (Fig 24)
Two types of material were used for the beams insulation First
the space between the 1047298anges and the outer surface of the 1047298anges
was insulated by standard mineral wool (ROCKWOOL Airrock HD)
The wool was 1047297xed on the beam with steel wires Second themiddle span was wrapped by super wool insulation material see
Fig 25
Seventeen thermocouples were used for the temperature
measurement Eleven of them were placed in the middle span
and six were placed in the side spans for monitoring of the
temperature in not-heated section For lateral torsional buckling
test where the middle span was longer twenty thermocouples
were used in the middle span and four in the side spans The
thermocouples were distributed on the beam according to the
position of ceramic pads as shown and numbered in Fig 24 Beam
temperatures were recorded from the beginning of heating to the
end of the experiment The average measured temperatures
during the loading can be found in Table 4 for each part of the
beam separately The temperature of the bottom 1047298ange was lower
Table 3
Local and global geometric imperfection amplitudes
Test number Imperfection amplitude [mm]
Local-web Local-1047298ange Global
Test 1 4 77 120 ndash
Test 2 1 34 198 ndash
Test 3 2 36 192 ndash
Test 4 1 60 067 ndash Test 5 736 227 25
Test 6 58 069 15
Test 7 759 213 15
Fig 15 Distribution of the imperfection amplitude along the beammdashTest 3
Fig 16 Distribution of the imperfection amplitude along the beammdashTest 4
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as result of worse contact between beam and ceramic pads The
sets of four heating pads were controlled by one thermocouple
The displacements were measured by potentiometers For the
simple bending test two potentiometers were used for measure-
ment of the vertical displacement in the locations of load applica-
tion and one at the mid span For the lateral torsional bending test
two potentiometers were place in the locations of load application
as in the previous case Vertical (VD) and horizontal (HD) de1047298ec-
tion of the bottom 1047298ange centre and section rotation (R) of the
beam at mid-span were calculated from measurement of four
potentiometers Two measured vertical de1047298ection and two hor-
izontal one for two points of the section (see Fig 26)
Fig 17 Local imperfection amplitude along the webmdashlateral torsional buckling Test 5 to 7
Fig 18 Local imperfection amplitude along the upper 1047298angemdashlateral torsional buckling Test 5 to 7
Fig 19 Laser scanner
Fig 20 Beam triangular mesh model
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23 Material properties
For possible model validation material properties for each part
of the welded section were measured at ambient temperature and
at elevated temperature namely 450 1C and 650 1C The tensile
coupon tests were carried out in accordance with EN ISO 6892-1
[14] to determine the basic engineering stress-strain response of
the material The measured values of yield strength for each plate
as were de1047297ne in Fig 4 and temperature are presented in Table 5
3 Numerical analyses and its comparison with experiments
The tests were replicated by means of the 1047297nite element
method program ABAQUS [10] The ABAQUS code is general
software and allows a complete solution for a large range of
problems including the analysis of structures under 1047297re Static
calculation was used in this case The same models as for
preliminary numerical simulation were used The beam was
meshed using quadrilateral conventional shell elements (namely
type S4) Conventional shell elements discretize a body by de1047297ning
the geometry at a reference surface In this case the thickness is
de1047297ned through the section property de1047297nition Conventional
shell elements have 3 displacement and 3 rotational degrees of
freedom per node Element type S4 is a fully integrated general-
purpose 1047297nite-membrane-strain shell element The element has
four integration points per element
All experimental data have been used for validation of thenumerical model Both local and global (if any) geometrical
imperfections were introduced into the geometrically and materi-
ally nonlinear analysis
The material law was de1047297ned by elasticndashplastic nonlinear
stressndashstrain diagram where enough data points were used The
true material stressndashstrain relationship was calculated from the
static engineering strassndashstrain curves obtained from the coupon
tests at room temperature The reductions of material properties
as well as the material nonlinearity were taken from the EC3 12
[4] as only two levels of elevated temperature were tested and
mostly con1047297rmed the established reduction factors The measured
average temperatures from each heated part of the beams were
introduced to the model Adjacent parts of the beam and stiffeners
were modelled as in room temperature (20 1C)
Fig 21 Cross and horizontal beam sections
Fig 22 Comparison between manual measurement and laser scanning for web
of beam
Fig 23 Mannings heat power units
Table 4
Temperature during the tests
Test number Average temperature [1C]
Upper 1047298ange Bottom 1047298ange Web
Test 1 444 469 458
Test 2 654 636 649
Test 3 481 425 431
Test 4 661 631 641
Test 5 457 354 444
Test 6 481 369 443
Test 7 624 416 567
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
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across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
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to lateral torsional buckling deformation increase was estimated
as 35 mm per minute and the 1047297nal de1047298ection was 50 mm The
load was introduced via a distributing beam at the edges of the
heated part (middle span) The load was applied by means of one
hydraulic jack of 650 kN capacity All the tests were performed on
steady state it means that the beams were 1047297rst heated and then
the load was applied until failure
The additional test equipment was designed as universal for
the experiments It respected boundary conditions based on the
numerical analyses and is described below Test setup for both
types of the tests is illustrated in Fig 5 It consisted of lateral
restraints supports and the load distributing beam At the location
of the load application (at the edge of the heated part) the top and
the bottom 1047298ange were laterally restrained by two vertical CHS
80 56 supported transversally by diagonal members Bolts above
and below the tested pro1047297le section interconnected these two
vertical pro1047297les The lateral restraints are depicted in Fig 6
For all tests the beams were supported at the ends under the
lower 1047298ange In the case of simple bending tests both supports
were pinned (free rotation in the direction of the strong axis) One
of the supports was designed as a rolling bearing (set of horizontal
rods) and allowed free horizontal displacement in the longitudinal
direction (beam axismdashroller) Other displacements and rotations
were restricted see Fig 7 The restriction of lateral displacementand lateral rotation was ensured by couple of vertical pro1047297les (UPE
100) see Fig 8 The horizontal recti1047297cation of the vertical pro1047297les
was allowed to 1047297t to both tested section widths
In the case of the lateral torsional buckling tests the end
supports were considered just by one point support It was made
using a high-resistance steel sphere bearing placed between two
steel plates Both end supports allowed free torsion of the end
cross-section around the sphere bearing One restrained the
displacement in all directions (pinned) The second allowed also
free horizontal displacement in the direction along the beam axis
(roller) The prevented transverse displacement in at the supports
was found to have very little effect on the beam resistance and was
much easier to reach in the test Fig 9 shows both pinned and
roller supports of the beam
Fig 9 Lateral torsional buckling test supports (a) pinned (b) roller
Fig 10 Manual measurement
Fig 11 Simple bending testsmdashpoints of the measurement (the web and the upper
1047298ange)
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21 Measurement of the initial geometric imperfections
Before the experiment after placing the beam on the support
the initial geometry of the specimens was established using the
two methods namely manual measurements and laser scanningThe 1047297rst methodmdashmanual measurement consists of amplitude
measurement for global and local imperfection Amplitude of
global imperfection was measured as a deviation from a string
spanned between the stiffeners (load application points) For
measurements of local imperfection amplitude a special device
set with a centesimal displacement meter was used see Fig 10
The length of device set was chosen according to the half sine
wave length corresponding to the local buckling shape for each
beam calculated in ABAQUS The investigation was made in
compression zone of the beams only Figs 11 and 12 show the
position of the measurements The local imperfection amplitudes
of the web and 1047298ange for beam test 1 to 4 are in Figs 13ndash16 and in
Figs 17 and 18 for the beam test 5 to 7 For these the side of the
1047298ange with higher imperfection amplitude is shown Table 3
summarises the maximum amplitude of the local and global
imperfection along each beam
The second method of imperfection measurement (see Fig 19)
was the laser scanning method It is still comparatively new
technology (1047297rst instrument were used about 15 years ago) andit is very effective for measuring of complex surface topography
Therefore it was used as control method to measure the global
and local initial imperfections All tested beams were scanned
before testing Scanning resolution was set to average grid
5 5 mm on the beam surface The result were plotted as set of
longitudinal and transverse sections trough the tested beams
which adequately describes each beams geometrical properties
Eight standpoints were used to reach maximum covering of the
beam surface It took about 5 min to carry out one standpoint
Surphaser 25HSX with IR_X con1047297guration (the second most
accurate con1047297guration) was used in all cases It is the most
accurate polar laser scanning system on the market The most
important speci1047297cation of the scanner are measurement speed up
to 12 million points per second 1047297eld of view panoramic accuracy
Fig 14 Distribution of the imperfection amplitude along the beammdashTest 2
Fig 12 Lateral torsional buckling testsmdashpoints of the measurement (the web and the upper 1047298ange)
Fig 13 Distribution of the imperfection amplitude along the beammdashTest 1
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better than 05 mm (absolute) at 5 m noise 01 mm at 3 m
measurement range 04ndash30 m Scanner 3D data from eight stand-
points was transformed to unique coordinate system using sphe-
rical control points in the Leica Cyclone software Then the beam
part from point cloud was cut out and 3D model in the form of
triangular mesh was created in the software Geomagic Studio see
Fig 20 The last step was generation of cross and horizontal
sections in 5 cm intervals see Fig 21 Detailed information about
scanning of these beams can be found in [11] In comparison of
both methods laser scanning and manual measurement found
the imperfection amplitudes very similar see Fig 22
22 Heating of specimens
There is not much experimental work on the behaviour of Class
4 beams at elevated temperature but similar experiments using the
same type of heating equipment were made on the lateral-torsional
buckling of Class 1 section beams in 2003 [12] and in 2005 [13] For
the described tests Mannings 70 kV A heat power units with
6 channels were used to heat the specimens see Fig 23 This unit
provides a 60 V supply for powering various types of low voltage
heating elements It consists of an air natural 3 phase transformer
switching is by contactors The output channels are controlled by
means of energy regulators and the temperature controllers Each
channel has its own automanual switch so any combination of
channels can be operated either auto or manual
Cable connection of 70 kV A consists of 6 triple cable sets and
4-way splitter cables can accommodate total of 24 1047298exible ceramic
heating pads attached Maximum connected load for the 70 kV A
unit is 648 kW In order to be able to heat two different beams of
the experimental tests universal size of the ceramic pads was
used 305 165 mm Ceramic heating elements are constructed
from nickel-chrome core wire and nickel cold tail wire which is
electrically insulated by interlocking high grade sintered alumina
ceramic beads The construction allows the heating element to be
1047298exible and provides high heat transfer ef 1047297ciency The heating
pads are able to reach a maximum temperature of 1200 1C
working temperature capability is 1050 1C at a heating rate
10 1Cmin
In the 1047297rst step the pads were put on the rod rack in order to
maintain the position of the heating elements on the web On the
bottom 1047298ange the pads were 1047297xed with steel wire On the top
1047298ange the pads were 1047297xed with adhesive tape only They were
placed on the outer surface of the 1047298anges For the web they were
attached from one side only where the side was alternated along
the beam length (Fig 24)
Two types of material were used for the beams insulation First
the space between the 1047298anges and the outer surface of the 1047298anges
was insulated by standard mineral wool (ROCKWOOL Airrock HD)
The wool was 1047297xed on the beam with steel wires Second themiddle span was wrapped by super wool insulation material see
Fig 25
Seventeen thermocouples were used for the temperature
measurement Eleven of them were placed in the middle span
and six were placed in the side spans for monitoring of the
temperature in not-heated section For lateral torsional buckling
test where the middle span was longer twenty thermocouples
were used in the middle span and four in the side spans The
thermocouples were distributed on the beam according to the
position of ceramic pads as shown and numbered in Fig 24 Beam
temperatures were recorded from the beginning of heating to the
end of the experiment The average measured temperatures
during the loading can be found in Table 4 for each part of the
beam separately The temperature of the bottom 1047298ange was lower
Table 3
Local and global geometric imperfection amplitudes
Test number Imperfection amplitude [mm]
Local-web Local-1047298ange Global
Test 1 4 77 120 ndash
Test 2 1 34 198 ndash
Test 3 2 36 192 ndash
Test 4 1 60 067 ndash Test 5 736 227 25
Test 6 58 069 15
Test 7 759 213 15
Fig 15 Distribution of the imperfection amplitude along the beammdashTest 3
Fig 16 Distribution of the imperfection amplitude along the beammdashTest 4
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as result of worse contact between beam and ceramic pads The
sets of four heating pads were controlled by one thermocouple
The displacements were measured by potentiometers For the
simple bending test two potentiometers were used for measure-
ment of the vertical displacement in the locations of load applica-
tion and one at the mid span For the lateral torsional bending test
two potentiometers were place in the locations of load application
as in the previous case Vertical (VD) and horizontal (HD) de1047298ec-
tion of the bottom 1047298ange centre and section rotation (R) of the
beam at mid-span were calculated from measurement of four
potentiometers Two measured vertical de1047298ection and two hor-
izontal one for two points of the section (see Fig 26)
Fig 17 Local imperfection amplitude along the webmdashlateral torsional buckling Test 5 to 7
Fig 18 Local imperfection amplitude along the upper 1047298angemdashlateral torsional buckling Test 5 to 7
Fig 19 Laser scanner
Fig 20 Beam triangular mesh model
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23 Material properties
For possible model validation material properties for each part
of the welded section were measured at ambient temperature and
at elevated temperature namely 450 1C and 650 1C The tensile
coupon tests were carried out in accordance with EN ISO 6892-1
[14] to determine the basic engineering stress-strain response of
the material The measured values of yield strength for each plate
as were de1047297ne in Fig 4 and temperature are presented in Table 5
3 Numerical analyses and its comparison with experiments
The tests were replicated by means of the 1047297nite element
method program ABAQUS [10] The ABAQUS code is general
software and allows a complete solution for a large range of
problems including the analysis of structures under 1047297re Static
calculation was used in this case The same models as for
preliminary numerical simulation were used The beam was
meshed using quadrilateral conventional shell elements (namely
type S4) Conventional shell elements discretize a body by de1047297ning
the geometry at a reference surface In this case the thickness is
de1047297ned through the section property de1047297nition Conventional
shell elements have 3 displacement and 3 rotational degrees of
freedom per node Element type S4 is a fully integrated general-
purpose 1047297nite-membrane-strain shell element The element has
four integration points per element
All experimental data have been used for validation of thenumerical model Both local and global (if any) geometrical
imperfections were introduced into the geometrically and materi-
ally nonlinear analysis
The material law was de1047297ned by elasticndashplastic nonlinear
stressndashstrain diagram where enough data points were used The
true material stressndashstrain relationship was calculated from the
static engineering strassndashstrain curves obtained from the coupon
tests at room temperature The reductions of material properties
as well as the material nonlinearity were taken from the EC3 12
[4] as only two levels of elevated temperature were tested and
mostly con1047297rmed the established reduction factors The measured
average temperatures from each heated part of the beams were
introduced to the model Adjacent parts of the beam and stiffeners
were modelled as in room temperature (20 1C)
Fig 21 Cross and horizontal beam sections
Fig 22 Comparison between manual measurement and laser scanning for web
of beam
Fig 23 Mannings heat power units
Table 4
Temperature during the tests
Test number Average temperature [1C]
Upper 1047298ange Bottom 1047298ange Web
Test 1 444 469 458
Test 2 654 636 649
Test 3 481 425 431
Test 4 661 631 641
Test 5 457 354 444
Test 6 481 369 443
Test 7 624 416 567
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
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across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
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21 Measurement of the initial geometric imperfections
Before the experiment after placing the beam on the support
the initial geometry of the specimens was established using the
two methods namely manual measurements and laser scanningThe 1047297rst methodmdashmanual measurement consists of amplitude
measurement for global and local imperfection Amplitude of
global imperfection was measured as a deviation from a string
spanned between the stiffeners (load application points) For
measurements of local imperfection amplitude a special device
set with a centesimal displacement meter was used see Fig 10
The length of device set was chosen according to the half sine
wave length corresponding to the local buckling shape for each
beam calculated in ABAQUS The investigation was made in
compression zone of the beams only Figs 11 and 12 show the
position of the measurements The local imperfection amplitudes
of the web and 1047298ange for beam test 1 to 4 are in Figs 13ndash16 and in
Figs 17 and 18 for the beam test 5 to 7 For these the side of the
1047298ange with higher imperfection amplitude is shown Table 3
summarises the maximum amplitude of the local and global
imperfection along each beam
The second method of imperfection measurement (see Fig 19)
was the laser scanning method It is still comparatively new
technology (1047297rst instrument were used about 15 years ago) andit is very effective for measuring of complex surface topography
Therefore it was used as control method to measure the global
and local initial imperfections All tested beams were scanned
before testing Scanning resolution was set to average grid
5 5 mm on the beam surface The result were plotted as set of
longitudinal and transverse sections trough the tested beams
which adequately describes each beams geometrical properties
Eight standpoints were used to reach maximum covering of the
beam surface It took about 5 min to carry out one standpoint
Surphaser 25HSX with IR_X con1047297guration (the second most
accurate con1047297guration) was used in all cases It is the most
accurate polar laser scanning system on the market The most
important speci1047297cation of the scanner are measurement speed up
to 12 million points per second 1047297eld of view panoramic accuracy
Fig 14 Distribution of the imperfection amplitude along the beammdashTest 2
Fig 12 Lateral torsional buckling testsmdashpoints of the measurement (the web and the upper 1047298ange)
Fig 13 Distribution of the imperfection amplitude along the beammdashTest 1
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎8
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better than 05 mm (absolute) at 5 m noise 01 mm at 3 m
measurement range 04ndash30 m Scanner 3D data from eight stand-
points was transformed to unique coordinate system using sphe-
rical control points in the Leica Cyclone software Then the beam
part from point cloud was cut out and 3D model in the form of
triangular mesh was created in the software Geomagic Studio see
Fig 20 The last step was generation of cross and horizontal
sections in 5 cm intervals see Fig 21 Detailed information about
scanning of these beams can be found in [11] In comparison of
both methods laser scanning and manual measurement found
the imperfection amplitudes very similar see Fig 22
22 Heating of specimens
There is not much experimental work on the behaviour of Class
4 beams at elevated temperature but similar experiments using the
same type of heating equipment were made on the lateral-torsional
buckling of Class 1 section beams in 2003 [12] and in 2005 [13] For
the described tests Mannings 70 kV A heat power units with
6 channels were used to heat the specimens see Fig 23 This unit
provides a 60 V supply for powering various types of low voltage
heating elements It consists of an air natural 3 phase transformer
switching is by contactors The output channels are controlled by
means of energy regulators and the temperature controllers Each
channel has its own automanual switch so any combination of
channels can be operated either auto or manual
Cable connection of 70 kV A consists of 6 triple cable sets and
4-way splitter cables can accommodate total of 24 1047298exible ceramic
heating pads attached Maximum connected load for the 70 kV A
unit is 648 kW In order to be able to heat two different beams of
the experimental tests universal size of the ceramic pads was
used 305 165 mm Ceramic heating elements are constructed
from nickel-chrome core wire and nickel cold tail wire which is
electrically insulated by interlocking high grade sintered alumina
ceramic beads The construction allows the heating element to be
1047298exible and provides high heat transfer ef 1047297ciency The heating
pads are able to reach a maximum temperature of 1200 1C
working temperature capability is 1050 1C at a heating rate
10 1Cmin
In the 1047297rst step the pads were put on the rod rack in order to
maintain the position of the heating elements on the web On the
bottom 1047298ange the pads were 1047297xed with steel wire On the top
1047298ange the pads were 1047297xed with adhesive tape only They were
placed on the outer surface of the 1047298anges For the web they were
attached from one side only where the side was alternated along
the beam length (Fig 24)
Two types of material were used for the beams insulation First
the space between the 1047298anges and the outer surface of the 1047298anges
was insulated by standard mineral wool (ROCKWOOL Airrock HD)
The wool was 1047297xed on the beam with steel wires Second themiddle span was wrapped by super wool insulation material see
Fig 25
Seventeen thermocouples were used for the temperature
measurement Eleven of them were placed in the middle span
and six were placed in the side spans for monitoring of the
temperature in not-heated section For lateral torsional buckling
test where the middle span was longer twenty thermocouples
were used in the middle span and four in the side spans The
thermocouples were distributed on the beam according to the
position of ceramic pads as shown and numbered in Fig 24 Beam
temperatures were recorded from the beginning of heating to the
end of the experiment The average measured temperatures
during the loading can be found in Table 4 for each part of the
beam separately The temperature of the bottom 1047298ange was lower
Table 3
Local and global geometric imperfection amplitudes
Test number Imperfection amplitude [mm]
Local-web Local-1047298ange Global
Test 1 4 77 120 ndash
Test 2 1 34 198 ndash
Test 3 2 36 192 ndash
Test 4 1 60 067 ndash Test 5 736 227 25
Test 6 58 069 15
Test 7 759 213 15
Fig 15 Distribution of the imperfection amplitude along the beammdashTest 3
Fig 16 Distribution of the imperfection amplitude along the beammdashTest 4
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as result of worse contact between beam and ceramic pads The
sets of four heating pads were controlled by one thermocouple
The displacements were measured by potentiometers For the
simple bending test two potentiometers were used for measure-
ment of the vertical displacement in the locations of load applica-
tion and one at the mid span For the lateral torsional bending test
two potentiometers were place in the locations of load application
as in the previous case Vertical (VD) and horizontal (HD) de1047298ec-
tion of the bottom 1047298ange centre and section rotation (R) of the
beam at mid-span were calculated from measurement of four
potentiometers Two measured vertical de1047298ection and two hor-
izontal one for two points of the section (see Fig 26)
Fig 17 Local imperfection amplitude along the webmdashlateral torsional buckling Test 5 to 7
Fig 18 Local imperfection amplitude along the upper 1047298angemdashlateral torsional buckling Test 5 to 7
Fig 19 Laser scanner
Fig 20 Beam triangular mesh model
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23 Material properties
For possible model validation material properties for each part
of the welded section were measured at ambient temperature and
at elevated temperature namely 450 1C and 650 1C The tensile
coupon tests were carried out in accordance with EN ISO 6892-1
[14] to determine the basic engineering stress-strain response of
the material The measured values of yield strength for each plate
as were de1047297ne in Fig 4 and temperature are presented in Table 5
3 Numerical analyses and its comparison with experiments
The tests were replicated by means of the 1047297nite element
method program ABAQUS [10] The ABAQUS code is general
software and allows a complete solution for a large range of
problems including the analysis of structures under 1047297re Static
calculation was used in this case The same models as for
preliminary numerical simulation were used The beam was
meshed using quadrilateral conventional shell elements (namely
type S4) Conventional shell elements discretize a body by de1047297ning
the geometry at a reference surface In this case the thickness is
de1047297ned through the section property de1047297nition Conventional
shell elements have 3 displacement and 3 rotational degrees of
freedom per node Element type S4 is a fully integrated general-
purpose 1047297nite-membrane-strain shell element The element has
four integration points per element
All experimental data have been used for validation of thenumerical model Both local and global (if any) geometrical
imperfections were introduced into the geometrically and materi-
ally nonlinear analysis
The material law was de1047297ned by elasticndashplastic nonlinear
stressndashstrain diagram where enough data points were used The
true material stressndashstrain relationship was calculated from the
static engineering strassndashstrain curves obtained from the coupon
tests at room temperature The reductions of material properties
as well as the material nonlinearity were taken from the EC3 12
[4] as only two levels of elevated temperature were tested and
mostly con1047297rmed the established reduction factors The measured
average temperatures from each heated part of the beams were
introduced to the model Adjacent parts of the beam and stiffeners
were modelled as in room temperature (20 1C)
Fig 21 Cross and horizontal beam sections
Fig 22 Comparison between manual measurement and laser scanning for web
of beam
Fig 23 Mannings heat power units
Table 4
Temperature during the tests
Test number Average temperature [1C]
Upper 1047298ange Bottom 1047298ange Web
Test 1 444 469 458
Test 2 654 636 649
Test 3 481 425 431
Test 4 661 631 641
Test 5 457 354 444
Test 6 481 369 443
Test 7 624 416 567
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
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across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 13
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 15
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎16
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
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better than 05 mm (absolute) at 5 m noise 01 mm at 3 m
measurement range 04ndash30 m Scanner 3D data from eight stand-
points was transformed to unique coordinate system using sphe-
rical control points in the Leica Cyclone software Then the beam
part from point cloud was cut out and 3D model in the form of
triangular mesh was created in the software Geomagic Studio see
Fig 20 The last step was generation of cross and horizontal
sections in 5 cm intervals see Fig 21 Detailed information about
scanning of these beams can be found in [11] In comparison of
both methods laser scanning and manual measurement found
the imperfection amplitudes very similar see Fig 22
22 Heating of specimens
There is not much experimental work on the behaviour of Class
4 beams at elevated temperature but similar experiments using the
same type of heating equipment were made on the lateral-torsional
buckling of Class 1 section beams in 2003 [12] and in 2005 [13] For
the described tests Mannings 70 kV A heat power units with
6 channels were used to heat the specimens see Fig 23 This unit
provides a 60 V supply for powering various types of low voltage
heating elements It consists of an air natural 3 phase transformer
switching is by contactors The output channels are controlled by
means of energy regulators and the temperature controllers Each
channel has its own automanual switch so any combination of
channels can be operated either auto or manual
Cable connection of 70 kV A consists of 6 triple cable sets and
4-way splitter cables can accommodate total of 24 1047298exible ceramic
heating pads attached Maximum connected load for the 70 kV A
unit is 648 kW In order to be able to heat two different beams of
the experimental tests universal size of the ceramic pads was
used 305 165 mm Ceramic heating elements are constructed
from nickel-chrome core wire and nickel cold tail wire which is
electrically insulated by interlocking high grade sintered alumina
ceramic beads The construction allows the heating element to be
1047298exible and provides high heat transfer ef 1047297ciency The heating
pads are able to reach a maximum temperature of 1200 1C
working temperature capability is 1050 1C at a heating rate
10 1Cmin
In the 1047297rst step the pads were put on the rod rack in order to
maintain the position of the heating elements on the web On the
bottom 1047298ange the pads were 1047297xed with steel wire On the top
1047298ange the pads were 1047297xed with adhesive tape only They were
placed on the outer surface of the 1047298anges For the web they were
attached from one side only where the side was alternated along
the beam length (Fig 24)
Two types of material were used for the beams insulation First
the space between the 1047298anges and the outer surface of the 1047298anges
was insulated by standard mineral wool (ROCKWOOL Airrock HD)
The wool was 1047297xed on the beam with steel wires Second themiddle span was wrapped by super wool insulation material see
Fig 25
Seventeen thermocouples were used for the temperature
measurement Eleven of them were placed in the middle span
and six were placed in the side spans for monitoring of the
temperature in not-heated section For lateral torsional buckling
test where the middle span was longer twenty thermocouples
were used in the middle span and four in the side spans The
thermocouples were distributed on the beam according to the
position of ceramic pads as shown and numbered in Fig 24 Beam
temperatures were recorded from the beginning of heating to the
end of the experiment The average measured temperatures
during the loading can be found in Table 4 for each part of the
beam separately The temperature of the bottom 1047298ange was lower
Table 3
Local and global geometric imperfection amplitudes
Test number Imperfection amplitude [mm]
Local-web Local-1047298ange Global
Test 1 4 77 120 ndash
Test 2 1 34 198 ndash
Test 3 2 36 192 ndash
Test 4 1 60 067 ndash Test 5 736 227 25
Test 6 58 069 15
Test 7 759 213 15
Fig 15 Distribution of the imperfection amplitude along the beammdashTest 3
Fig 16 Distribution of the imperfection amplitude along the beammdashTest 4
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as result of worse contact between beam and ceramic pads The
sets of four heating pads were controlled by one thermocouple
The displacements were measured by potentiometers For the
simple bending test two potentiometers were used for measure-
ment of the vertical displacement in the locations of load applica-
tion and one at the mid span For the lateral torsional bending test
two potentiometers were place in the locations of load application
as in the previous case Vertical (VD) and horizontal (HD) de1047298ec-
tion of the bottom 1047298ange centre and section rotation (R) of the
beam at mid-span were calculated from measurement of four
potentiometers Two measured vertical de1047298ection and two hor-
izontal one for two points of the section (see Fig 26)
Fig 17 Local imperfection amplitude along the webmdashlateral torsional buckling Test 5 to 7
Fig 18 Local imperfection amplitude along the upper 1047298angemdashlateral torsional buckling Test 5 to 7
Fig 19 Laser scanner
Fig 20 Beam triangular mesh model
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23 Material properties
For possible model validation material properties for each part
of the welded section were measured at ambient temperature and
at elevated temperature namely 450 1C and 650 1C The tensile
coupon tests were carried out in accordance with EN ISO 6892-1
[14] to determine the basic engineering stress-strain response of
the material The measured values of yield strength for each plate
as were de1047297ne in Fig 4 and temperature are presented in Table 5
3 Numerical analyses and its comparison with experiments
The tests were replicated by means of the 1047297nite element
method program ABAQUS [10] The ABAQUS code is general
software and allows a complete solution for a large range of
problems including the analysis of structures under 1047297re Static
calculation was used in this case The same models as for
preliminary numerical simulation were used The beam was
meshed using quadrilateral conventional shell elements (namely
type S4) Conventional shell elements discretize a body by de1047297ning
the geometry at a reference surface In this case the thickness is
de1047297ned through the section property de1047297nition Conventional
shell elements have 3 displacement and 3 rotational degrees of
freedom per node Element type S4 is a fully integrated general-
purpose 1047297nite-membrane-strain shell element The element has
four integration points per element
All experimental data have been used for validation of thenumerical model Both local and global (if any) geometrical
imperfections were introduced into the geometrically and materi-
ally nonlinear analysis
The material law was de1047297ned by elasticndashplastic nonlinear
stressndashstrain diagram where enough data points were used The
true material stressndashstrain relationship was calculated from the
static engineering strassndashstrain curves obtained from the coupon
tests at room temperature The reductions of material properties
as well as the material nonlinearity were taken from the EC3 12
[4] as only two levels of elevated temperature were tested and
mostly con1047297rmed the established reduction factors The measured
average temperatures from each heated part of the beams were
introduced to the model Adjacent parts of the beam and stiffeners
were modelled as in room temperature (20 1C)
Fig 21 Cross and horizontal beam sections
Fig 22 Comparison between manual measurement and laser scanning for web
of beam
Fig 23 Mannings heat power units
Table 4
Temperature during the tests
Test number Average temperature [1C]
Upper 1047298ange Bottom 1047298ange Web
Test 1 444 469 458
Test 2 654 636 649
Test 3 481 425 431
Test 4 661 631 641
Test 5 457 354 444
Test 6 481 369 443
Test 7 624 416 567
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎12
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7172019 Check This Paper for Experiment and Numerical Model Validation
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across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 13
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎14
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 15
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎16
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
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as result of worse contact between beam and ceramic pads The
sets of four heating pads were controlled by one thermocouple
The displacements were measured by potentiometers For the
simple bending test two potentiometers were used for measure-
ment of the vertical displacement in the locations of load applica-
tion and one at the mid span For the lateral torsional bending test
two potentiometers were place in the locations of load application
as in the previous case Vertical (VD) and horizontal (HD) de1047298ec-
tion of the bottom 1047298ange centre and section rotation (R) of the
beam at mid-span were calculated from measurement of four
potentiometers Two measured vertical de1047298ection and two hor-
izontal one for two points of the section (see Fig 26)
Fig 17 Local imperfection amplitude along the webmdashlateral torsional buckling Test 5 to 7
Fig 18 Local imperfection amplitude along the upper 1047298angemdashlateral torsional buckling Test 5 to 7
Fig 19 Laser scanner
Fig 20 Beam triangular mesh model
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎10
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23 Material properties
For possible model validation material properties for each part
of the welded section were measured at ambient temperature and
at elevated temperature namely 450 1C and 650 1C The tensile
coupon tests were carried out in accordance with EN ISO 6892-1
[14] to determine the basic engineering stress-strain response of
the material The measured values of yield strength for each plate
as were de1047297ne in Fig 4 and temperature are presented in Table 5
3 Numerical analyses and its comparison with experiments
The tests were replicated by means of the 1047297nite element
method program ABAQUS [10] The ABAQUS code is general
software and allows a complete solution for a large range of
problems including the analysis of structures under 1047297re Static
calculation was used in this case The same models as for
preliminary numerical simulation were used The beam was
meshed using quadrilateral conventional shell elements (namely
type S4) Conventional shell elements discretize a body by de1047297ning
the geometry at a reference surface In this case the thickness is
de1047297ned through the section property de1047297nition Conventional
shell elements have 3 displacement and 3 rotational degrees of
freedom per node Element type S4 is a fully integrated general-
purpose 1047297nite-membrane-strain shell element The element has
four integration points per element
All experimental data have been used for validation of thenumerical model Both local and global (if any) geometrical
imperfections were introduced into the geometrically and materi-
ally nonlinear analysis
The material law was de1047297ned by elasticndashplastic nonlinear
stressndashstrain diagram where enough data points were used The
true material stressndashstrain relationship was calculated from the
static engineering strassndashstrain curves obtained from the coupon
tests at room temperature The reductions of material properties
as well as the material nonlinearity were taken from the EC3 12
[4] as only two levels of elevated temperature were tested and
mostly con1047297rmed the established reduction factors The measured
average temperatures from each heated part of the beams were
introduced to the model Adjacent parts of the beam and stiffeners
were modelled as in room temperature (20 1C)
Fig 21 Cross and horizontal beam sections
Fig 22 Comparison between manual measurement and laser scanning for web
of beam
Fig 23 Mannings heat power units
Table 4
Temperature during the tests
Test number Average temperature [1C]
Upper 1047298ange Bottom 1047298ange Web
Test 1 444 469 458
Test 2 654 636 649
Test 3 481 425 431
Test 4 661 631 641
Test 5 457 354 444
Test 6 481 369 443
Test 7 624 416 567
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 11
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎12
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across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 13
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎14
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 15
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎16
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
7172019 Check This Paper for Experiment and Numerical Model Validation
httpslidepdfcomreaderfullcheck-this-paper-for-experiment-and-numerical-model-validation 1117
23 Material properties
For possible model validation material properties for each part
of the welded section were measured at ambient temperature and
at elevated temperature namely 450 1C and 650 1C The tensile
coupon tests were carried out in accordance with EN ISO 6892-1
[14] to determine the basic engineering stress-strain response of
the material The measured values of yield strength for each plate
as were de1047297ne in Fig 4 and temperature are presented in Table 5
3 Numerical analyses and its comparison with experiments
The tests were replicated by means of the 1047297nite element
method program ABAQUS [10] The ABAQUS code is general
software and allows a complete solution for a large range of
problems including the analysis of structures under 1047297re Static
calculation was used in this case The same models as for
preliminary numerical simulation were used The beam was
meshed using quadrilateral conventional shell elements (namely
type S4) Conventional shell elements discretize a body by de1047297ning
the geometry at a reference surface In this case the thickness is
de1047297ned through the section property de1047297nition Conventional
shell elements have 3 displacement and 3 rotational degrees of
freedom per node Element type S4 is a fully integrated general-
purpose 1047297nite-membrane-strain shell element The element has
four integration points per element
All experimental data have been used for validation of thenumerical model Both local and global (if any) geometrical
imperfections were introduced into the geometrically and materi-
ally nonlinear analysis
The material law was de1047297ned by elasticndashplastic nonlinear
stressndashstrain diagram where enough data points were used The
true material stressndashstrain relationship was calculated from the
static engineering strassndashstrain curves obtained from the coupon
tests at room temperature The reductions of material properties
as well as the material nonlinearity were taken from the EC3 12
[4] as only two levels of elevated temperature were tested and
mostly con1047297rmed the established reduction factors The measured
average temperatures from each heated part of the beams were
introduced to the model Adjacent parts of the beam and stiffeners
were modelled as in room temperature (20 1C)
Fig 21 Cross and horizontal beam sections
Fig 22 Comparison between manual measurement and laser scanning for web
of beam
Fig 23 Mannings heat power units
Table 4
Temperature during the tests
Test number Average temperature [1C]
Upper 1047298ange Bottom 1047298ange Web
Test 1 444 469 458
Test 2 654 636 649
Test 3 481 425 431
Test 4 661 631 641
Test 5 457 354 444
Test 6 481 369 443
Test 7 624 416 567
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 11
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7172019 Check This Paper for Experiment and Numerical Model Validation
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎12
Please cite this article as Prachar M et al Experiments of Class 4 open section beams at elevated temperature Thin-Walled Structures(2015) httpdxdoiorg101016jtws201504025i
7172019 Check This Paper for Experiment and Numerical Model Validation
httpslidepdfcomreaderfullcheck-this-paper-for-experiment-and-numerical-model-validation 1317
across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 13
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎14
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 15
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎16
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
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The numerical models were loaded by displacements The steel
thermal expansion was not modelled directly but the middle
spans were set as 1500 mm resp 2800 mm (expected length after
the thermal expansion) The measured values of the steel mechan-
ical properties (yield strength and modulus of elasticity) and the
measured temperatures were adopted in the models All experi-
mental data were used for the numerical model validation
Generally the residual stresses have a negligible in1047298uence on
the sectional resistance [15] at elevated temperature For beams
subjected to lateral torsional buckling the in1047298uence was found to
be notable It was more than 4 decrease of the resistance for the
tested beams if generalised residual stress patterns (published also
in [15]) were used However the residual stresses were not
measured for the tested beams and newer investigated for the
speci1047297c fabrication method (one side 1047297llet weld) which is believed
to lead to a lower stress levels due to the lower heat input by
welding No residual stresses were therefore considered in the
validation
31 Simple bending tests
For each model of the beam web was formed by 200 elements
along the length and by 16 elements along the height of the cross-
section Upper and lower 1047298anges were modelled by 6 elements
Fig 25 Isolation of the beam
Fig 24 Layout of 1047298exible ceramic pads and thermocouples (numbered)
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎12
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across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 13
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎14
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7172019 Check This Paper for Experiment and Numerical Model Validation
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 15
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎16
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
7172019 Check This Paper for Experiment and Numerical Model Validation
httpslidepdfcomreaderfullcheck-this-paper-for-experiment-and-numerical-model-validation 1317
across the width of the cross-section The structural mesh and
boundary conditions are shown in Fig 27 The mesh coarseness
was established by a sensitivity study Initial imperfections were
modelled by the actual measured imperfections of the beams The
individual curves describing the shape imperfections (see from
Figs13ndash16) were replaced by a sinusoidal function for simpli1047297ca-
tion with the maximum amplitude taken from Table 3
In the next table and 1047297gures the results obtained in the 1047297re
tests are compared to the results obtained by the numericalsimulations The load corresponds to the total force imposed on
the two load application points The shown displacement corre-
sponds to the vertical displacement at the bottom 1047298ange at mid
span Failure mode of the tests and the numerical model is also
compared in the 1047297gures (Figs 28 and 29) They show the deformed
shape of the central heated part of the beam for Test 1 and Test 2
Figs 30 and 31 for Test 3 and Test 4 Comparison of loadndash
de1047298ection curves are depicted in Figs 32 and 33
32 Lateral torsional buckling tests
A similar mesh geometry was used as for the previous model
But 20 elements for web height and 4 elements per 100 mm of the
beam length were used The mesh and boundary conditions are
shown in Fig 34
Initial global and local geometric imperfections were included
to the model by means of the elastic buckling eigenmodes Two
imperfection shapes were considered the beam 1047297rst local buck-
ling mode and 1047297rst global buckling mode (LTB) shapes see Fig 35
The imperfection amplitudes were based on the initial geometry
measurements
In test below the experimental results are compared with the
numerical results Figs 36ndash38 show the beams after tests (Test 5 to
7) As can be observed from Fig 39 the obtained failure shapes
were very close to numerical prediction Comparison of loadndash
de1047298ection curves are in Fig 40
Fig 26 Measurement of vertical displacement (VD) horizontal displacement (HD)
and section rotation (R) at beam midspan
Table 5
Steel plates yield strength (S355)
Part S1 S2 S3 S4 S5 S6
Upper yield stress R eH [MPa] 430 394 388 376 385 435
Lower yield stress R eL [MPa] 424 392 384 361 435 408
Yield stress R 02 at 450 1C [MPa] 349 260 271 ndash 260 272
Yield stress R 20 at 450 1C [MPa] 399 310 328 ndash 318 330
Yield stress R 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash
Yield stress R 20 at 650 1C [MPa] 126 84 118 ndash 108 ndash
Fig 27 Loading and boundary conditions for the simple bending test model
Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 13
Please cite this article as Prachar M et al Experiments of Class 4 open section beams at elevated temperature Thin-Walled Structures(2015) httpdxdoiorg101016jtws201504025i
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎14
Please cite this article as Prachar M et al Experiments of Class 4 open section beams at elevated temperature Thin-Walled Structures(2015) httpdxdoiorg101016jtws201504025i
7172019 Check This Paper for Experiment and Numerical Model Validation
httpslidepdfcomreaderfullcheck-this-paper-for-experiment-and-numerical-model-validation 1517
slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 15
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7172019 Check This Paper for Experiment and Numerical Model Validation
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎16
7172019 Check This Paper for Experiment and Numerical Model Validation
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
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4 Discussion of the results
Numerical simulations exhibit similar behaviour as the beams
during the experiment As seen in Table 6 and Fig 41 the
difference between the resistance calculated by ABAQUS and
obtained from the test is less than 3 for the simple bending test
Whereas the results obtained for the beams subjected to the
lateral torsional buckling shows bigger difference (15 in average)
This demonstrates the dif 1047297culties of lateral torsional buckling
tests which are highlighted by the elevated temperature
A problem with lateral restraints occurred during Test 5 The
experimental curve of load displacement relationship is not
smooth and the force is unnaturally increasing see Fig 40 Besides
that the experimentally obtained initial stiffness is different from
the numerical curves mainly in Test 5 and 7
Overall the approximations are reasonable considering the
nature of the different parameters involved in the presented tests
as for instance the heating process The numerical model was able
to predict the behaviour (load capacity and failure mode) of beams
observed in the tests
5 Conclusions
The paper presents experiments and numerical modelling of
seven steel beams at elevated temperature All beams were of
Fig 30 Failure modemdashTest 3 (a) numerical simulation (b) experiment
Fig 29 Failure modemdashTest 2 (a) numerical simulation (b) experiment Fig 31 Failure modemdashTest 4 (a) numerical simulation (b) experiment
Fig 32 Loadndashde1047298ection diagram for Test 1 (left) and 2 (right)
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎14
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slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 15
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎16
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
7172019 Check This Paper for Experiment and Numerical Model Validation
httpslidepdfcomreaderfullcheck-this-paper-for-experiment-and-numerical-model-validation 1517
slender Class 4 open I-section fabricated by welding Four beams
were tested by simple bending and additional three with in1047298uence
of the lateral torsional buckling The elevated temperature was
induced by heat power units and the tests were carried out in
Fig 33 Load-de1047298ection diagram for Test 3 and 4
Fig 34 Loading and boundary conditions for the lateral torsional buckling
test model
Fig 35 Beams buckling modes shape (a) local (b) global
Fig 36 Test 5mdashbeam after the test
Fig 37 Test 6mdashbeam after the test
Fig 38 Test 7mdashbeam after the test
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 15
Please cite this article as Prachar M et al Experiments of Class 4 open section beams at elevated temperature Thin-Walled Structures(2015) httpdxdoiorg101016jtws201504025i
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎16
7172019 Check This Paper for Experiment and Numerical Model Validation
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standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
7172019 Check This Paper for Experiment and Numerical Model Validation
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Fig 39 Failure mode carried by (a) ABAQUS analysis (b) experiment
Fig 40 Loadndashdisplacement diagram for the lateral torsional buckling tests experimental and numerical
Table 6
Summary of tests results vs numerical results
Test Cross-section
h w x t w bf x t f
Load capacity [kN] Difference between the
experiment and FEM []
Experiment FEM
1 656 4 250 12 63782 64052 042
2 656 4 250 12 23061 23699 269
3 830 5 300 8 48468 49801 268
4 830 5 300 8 20122 19591 264
5 450 4 150 5 13459 1072 2 556
6 446 4150 7 18905 15184 2405
7 (610ndash450)
4ndash150 5
7096 7411 425
Fig 41 Comparison of test results with numerical results
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎16
7172019 Check This Paper for Experiment and Numerical Model Validation
httpslidepdfcomreaderfullcheck-this-paper-for-experiment-and-numerical-model-validation 1717
standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17
7172019 Check This Paper for Experiment and Numerical Model Validation
httpslidepdfcomreaderfullcheck-this-paper-for-experiment-and-numerical-model-validation 1717
standard laboratory conditions For all tests the necessary char-
acteristics were measured Namely the initial geometric imperfec-
tions and material properties at both room and elevated
temperature
The results of the numerical models were compared to the tests
and found reasonably close especially for the simple bending
tests Therefore the numerical model may be used for possible
calculation of beam load-capacity or further parametric study
Acknowledgement
The presented research was supported by the RFCS research
project FIDESC4 - Fire Design of Steel Members (Grant Agreement
Number RFSR-CT-2011-00030) with Welded or Hot-rolled Class 4
Cross-sections
References
[1] Renaud C Zhao B Investigation of simple calculation method in EN 1993-1-2for buckling of hot rolled Class 4 steel members exposed to 1047297re In Structuresin 1047297re proceedings of the fourth international conference Aveiro Portugal2006 pp 199ndash211
[2] CEN European Committee for Standardisation EN 1993-1-1 Eurocode 3mdash
design of steel structures Part 1ndash1 General rules and rules for buildings CENBrussels 2005
[3] CEN European Committee for Standardisation EN 1993-1-5 Eurocode 3design of steel structuresmdashPart 1ndash5 Plated structural elements BrusselsBelgium 2005
[4] CEN European Committee for Standardisation EN 1993-1-2 Eurocode3-design of steel structures-Part 1ndash2 general rules structural 1047297re design2005
[5] CEN European Committee for Standardisation EN 1993-1-3 Eurocode 3 ndash
design of steel structures ndash Part 1ndash3 general rules ndash supplementary rules forcold-formed members and sheeting 2006
[6] Marques L Simotildees da Silva L Rebelo C Application of the general method forthe evaluation of the stability resistance of non-uniform members InProceedings of ICASS Hong Kong 16ndash18 December 2009
[7] Couto C Vila Real PMM Ferreira J Lopes N Numerical validation of theGeneral Method for structural 1047297re design of web-tapered beams In EURO-
STEEL 2014mdashseventh European conference on steel and composite structuresNaples Italy September 2014
[8] Marques L Simotildees da Silva L Greiner R Rebelo C Taras A Development of aconsistent design procedure for lateral-torsional buckling of tapered beams
J Construct Steel Res 201389213ndash35[9] Braham M Hanikenne D Lateral buckling of web tapered beams an original
design method confronted with a computer simulation J Construct Steel Res19932723ndash36
[10] Hibbitt Karlsson amp Sorensen ABAQUS Analysis userrsquos manual Volumes IndashIVversion 610 Inc Providence RI USA 2010
[11] Kremen T Koska B Determination of the initial shape and the deformation of the steel beams with high accuracy during the stress tests using laser scanningtechnology In Thirteenth international multidisciplinary scienti1047297c geoconfer-ence and EXPO Albena Bulgaria 2013 pp 601ndash608
[12] Vila Real PMM Piloto PAG Franssen JM A new proposal of a simple model forthe lateral-torsional buckling of unrestrained steel I-beams in case of 1047297reexperimental and numerical validation J Construct Steel Res 200359179ndash99
[13] Mesquita L Piloto P Vaz M Vila Real P Experimental and numerical research
on the critical temperature of laterally unrestrained steel I beams J ConstructSteel Res 2005611435ndash46[14] EN ISO 6892-1 International Standard Metallic materials ndash tensile testing ndash
Part 1 Method of test at room temperature Switzerland 2009[15] Couto C Vila Real P Lopes N Zhao B Effective width method to account for
the local buckling of steel thin plates at elevated temperatures Thin-WalledStruct 201484134ndash49
M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 17