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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

Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎



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

M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎ ∎∎ndash∎∎∎2




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





NOTE Classi1047297cationmdashaccording to EN 1993-1-2

Plate slendernessmdashaccording to EN 1993-1-2 Annex E

M Prachar et al Thin-Walled Structures ∎ (∎∎∎∎) ∎∎∎ndash∎∎∎ 3




Fig 4 Tested beams 1 to 7





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 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 wfrac144 λpethABTHORN frac14 096

Fig 5 Simple bending test setup (upper) and lateral torsional buckling test setup (lower)





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)





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)





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)






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 4 1 60 067 ndash Test 5 736 227 25

Test 6 58 069 15

Test 7 759 213 15







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





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





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)





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 02 at 650 1C [MPa] 125 76 109 ndash 98 ndash


Fig 27 Loading and boundary conditions for the simple bending test model

Fig 28 Failure modemdashTest 1 (a) numerical simulation (b) experiment





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 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)





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 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




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




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






εθ frac14 085 235

f y

05

eth6THORN





εθ frac14


kyθ or kp02θ

s 235

f y

05

eth7THORN


























































Table 1
































Table 2







































Tables 1 and 2



















































1047298ange)



















































































10 1Cmin












Fig 25













Table 3







Test 4 1 60 067 ndash Test 5 736 227 25

Test 6 58 069 15

Test 7 759 213 15


































































of beam


Table 4




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






















validation































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References

























εθ frac14 085 235

f y

05

eth6THORN





εθ frac14


kyθ or kp02θ

s 235

f y

05

eth7THORN


























































Table 1
































Table 2







































Tables 1 and 2



















































1047298ange)



















































































10 1Cmin












Fig 25













Table 3







Test 4 1 60 067 ndash Test 5 736 227 25

Test 6 58 069 15

Test 7 759 213 15


































































of beam


Table 4




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






















validation































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References







































Table 2







































Tables 1 and 2



















































1047298ange)



















































































10 1Cmin












Fig 25













Table 3







Test 4 1 60 067 ndash Test 5 736 227 25

Test 6 58 069 15

Test 7 759 213 15


































































of beam


Table 4




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






















validation































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References


































Table 2







































Tables 1 and 2



















































1047298ange)



















































































10 1Cmin












Fig 25













Table 3







Test 4 1 60 067 ndash Test 5 736 227 25

Test 6 58 069 15

Test 7 759 213 15


































































of beam


Table 4




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






















validation































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References










































Tables 1 and 2



















































1047298ange)



















































































10 1Cmin












Fig 25













Table 3







Test 4 1 60 067 ndash Test 5 736 227 25

Test 6 58 069 15

Test 7 759 213 15


































































of beam


Table 4




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






















validation































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References
































































1047298ange)



















































































10 1Cmin












Fig 25













Table 3







Test 4 1 60 067 ndash Test 5 736 227 25

Test 6 58 069 15

Test 7 759 213 15


































































of beam


Table 4




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






















validation































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References






































































































10 1Cmin












Fig 25













Table 3







Test 4 1 60 067 ndash Test 5 736 227 25

Test 6 58 069 15

Test 7 759 213 15


































































of beam


Table 4




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






















validation































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References




























































10 1Cmin












Fig 25













Table 3







Test 4 1 60 067 ndash Test 5 736 227 25

Test 6 58 069 15

Test 7 759 213 15


































































of beam


Table 4




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






















validation































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References



















































































of beam


Table 4




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






















validation































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References































































of beam


Table 4




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






















validation































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References









































validation































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References












































shown in Fig 34






measurements








Table 5


































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References











































5 Conclusions
















test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References






























test model











Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References


























Table 6


Test Cross-section

h w x t w bf x t f



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








temperature





Acknowledgement




Cross-sections

References



























temperature





Acknowledgement




Cross-sections

References






















Check This Paper for Experiment and Numerical Model Validation

Documents

design of class

behaviour of class

experiments of class

structural design

open section beams

structuralre design

design formulas

existing design rules