structural members behaviour -...

PraguePrague, , CzechCzech RepublicRepublic, 30, 30--31 31 MarchMarch 20072007

Structural Members Behaviour

COST Action C26Urban habitat constructions under catastrophic events

WG1- Fire resistanceCollected contributions

Nuno Lopes, Paulo Vila RealNuno Lopes, Paulo Vila RealUniversityUniversity ofof Aveiro, PortugalAveiro, Portugal

Nuno LopesNuno LopesB. B. UppfeldtUppfeldtTheThe SwedenSweden InstituteInstitute ofof SteelSteelConstructionConstruction, , SwedenSweden

M. VeljkovicM. VeljkovicLuleLuleåå UniversityUniversity ofof TechnologyTechnology, , SwedenSweden

JeanJean--Marc FranssenMarc FranssenUniversityUniversity ofof LiegeLiege, , BelgiumBelgium

Luís SilvaLuís SilvaUniversityUniversity ofof Coimbra, PortugalCoimbra, Portugal

Viktor GribniakViktor Gribniak, Darius Ba, Darius Baččinskas, Gintaris inskas, Gintaris KaklauskasKaklauskasVilnius Vilnius GediminasGediminas Technical University, Technical University, LithuaniaLithuania

E. Nigro, G. E. Nigro, G. CefarelliCefarelliDepartment of Structural Engineering, University of Naples Department of Structural Engineering, University of Naples ““Federico IIFederico II””, Italy, Italy

ContentsContents

Stainless steel structural elements in case of fireStainless steel structural elements in case of fire

ClassClass 4 4 stainlessstainless steelsteel box box columnscolumns inin firefire

Contributions from four papers:

NonNon--linear modelling of reinforced concrete beams linear modelling of reinforced concrete beams subjected to firesubjected to fire

Some remarks on the simplified design methods for steel and Some remarks on the simplified design methods for steel and concrete composite beamsconcrete composite beams

Class 4 Stainless Steel Box Columns in Fire

B. UppfeldtThe Swedish Institute of Steel Construction, Stockholm, Sweden

M. VeljkovicLuleå University of Technology, Sweden

A study of stainless steel cold-rolled box columns at elevatedtemperatures is presented, which is a part of an on-going RFCS project”Stainless Steel in Fire”.

Experimental results of six, class 4, stub columns at elevatedtemperature, were used to evaluate the FE model.

The FE analysis obtained shows that the critical temperature was closelypredicted.

A parametric study was the basis to check the quality of prediction of a newly proposed improvement for design rules of class 4 cross-sectionsin fire according to Part1-4 and Part 1-2 of EC3 (stainless steel and firedesign part respectively).

IntroductionIntroduction

Four cold rolled stainless steel stub columns, λ < 0.1, with cross-sectionclass 4 were tested at the ambient temperature, Ala-Outinen (2005). Fourstrain-gauges were used to measure stresses at mid column.

The geometry of the columns and local imperfections were measured. Thematerial used in the columns was EN 1.4301. Fully restrained ends wereachieved in experiments.

Six unprotected columns were tested at elevated temperatures. The testset-up was equivalent to the ambient temperature tests.

The temperatures were measured with twelve chromel-alumelthermocouples and the axial deformation was measured using transducers.

The transient procedure was applied, meaning that the axial load was keptconstant and the furnace temperature was raised in a controlled way, at therate of 10°C/min.

ExperimentsExperiments

ElementsA general-purpose shell element, called S4R, within Abaqus/Standard wasused.

FEFE--ModelModel

ImperfectionsThe two types of geometrical imperfections that have to be considered are, global imperfections and local imperfections.For the modelling of the tested stub columns the measured local imperfections were used and no global imperfections were introduced.

MaterialIt is well established that the mechanicalproperties of stainless steel are stronglyinfluenced by the level of cold-work.

FEFE--ModelModel

Residual stressesNo residual stresses were introduced in the modelling of the testedcolumns.

Validation

It is concluded that the FE-model predicts the failure temperatures withgood accuracy for all tests but specimen No. 4 and the general conclusionis that the model is reliable for parametric study.

DevelopmentDevelopment ofof improvedimproved design design modelmodelfor for classclass 4 4 crosscross--sectionssections

Comparison between experiments at the elevated temperature and resultsobtained from FEA indicates that

- assumptions made for the influence of the material properties inthe corners are realistic;

- assumptions for the shape and level of the local buckling, b/200, and global imperfections, L/1000, are consistent with assumptionsestablished at ambient temperature.

In this work it was made an test that showned that it is possible to use unprotected stainless steel columns and fulfil requirement for resistance, R30.

Design recommendations for class 4 cross sections made of austeniticstainless steel presented are coherent with part1-2 and part1-4 of EC3.

The proposed design model is an improvement compared to the design model on EN 1993-1-2.

ConclusionsConclusions

Stainless steel structural elements in case of fire

Nuno LopesUniversity of Aveiro, Portugal

Paulo Vila RealUniversity of Aveiro, Portugal

Luis SilvaUniversity of Coimbra, Portugal

Jean-Marc FranssenUniversity of Liege, Belgium

IntroductionIntroduction

The part 1-4 of Eurocode 3 (EC 3) “Supplementary rules for stainless steels” gives design rules for stainless steel structural elements at room temperature and only mentions its fire resistance by doing reference to the fire part of EC 3 (EN 1993-1-2).

Carbon and stainless steel exhibit different stress-strain relationships.

This study was made using the program SAFIR that has been adapted, according to the material properties defined in prEN 1993-1-4 and EN 1993-1-2, to model the behaviour of stainless steel structures.

In this work the accuracy and safety of the currently prescribed columnand beam-column formulae are evaluated.

Case studyCase study

Axially loaded column with:Welded cross-sections: equivalent HEA 200 and HEB 280 sections of

the stainless steel grades 1.4301 and 1.4401The temperatures chosen were 400, 500, 600 and 700 ºC

Beam-columns with combined axial compression and uni-axial major and minor uniform moment with:

Welded equivalent to a HEA 200 cross-sections of the stainless steel grade 1.4301

The temperature chosen was 600 ºC

For both types of elementsBuckling around the strong and around the weak axisA lateral geometric imperfection was considered given byAn initial rotation around the beam axis with a maximum value of

l/1000 radians at mid span was also consideredIt were adopted residual stresses

yf/2354.1=α

1122≤

−+=

θθθ λβφφχ fi

⎥⎦⎤

⎢⎣⎡ ++=

21

21

θθθ λβλαφ

5.1=βfiM

yfiRdbfi AfN,

,,,1

γχ θ= yf/23565.0=α

EC3

New Proposal

MemberMember stabilitystabilityColumnColumn bucklingbuckling atat highhigh temperaturestemperatures

Column HEA200 - zz

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

N/Nfi,θ,Rd

EN 1993-1-2New proposalSafir-400(ºC)Safir-500(ºC)Safir-600(ºC)Safir-700(ºC)

θλ

Column HEA200 - yy

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

N/Nfi,θ,Rd

EN 1993-1-2New proposalSafir-400(ºC)Safir-500(ºC)Safir-600(ºC)Safir-700(ºC)

θλ

HE 200A grade 1.4301

MemberMember stabilitystabilityColumnColumn bucklingbuckling atat highhigh temperaturestemperatures

The new proposal is more safe

1

,

,,

,,

,,,

, ≤+

fiM

yipl

Edfiii

Rdfiib

Edfi

fW

Mk

NN

γθ

31

,,,

, ≤−=

fiM

yyfii

Edfiii f

Ak

Nk

γχ

μ

θ

( ) 8.029.044.032.1 ,,, ≤−+−= yMyyMy βλβμ θ

( )1.1with

8.029.044.052

,

,,,

≤

≤−+−=

θ

θ

λ

βλβμ

z

zMzzMz

EC 3 proposal “EN1993-1-2”

With the new proposal for columns “EN1993-1-2NP”

Beam columnsBeam columns

EC 3 proposal for stainless steel interaction curves at room temperature adapted for fire situation “prEN1993-1-4fi”

With the new proposal for columns “prEN1993-1-4fiNP”

Without the minimum limiting value of 1.2 for ki “prEN1993-1-4fiNP+NK”

1

1,

,

,,≤+

M

yipl

Edii

Rdib

Edf

W

Mk

NN

γ

( )

iRdb

Edi

iRdb

Edii

NN

k

NN

k

,,

,,

22.12.1but

5.020.1

+≤≤

−+= λ


EC 3 proposal for carbon steel interaction curves at room temperature adapted for fire situation and for stainless steel

Two alternative proposals were adopted for the carbon steel interaction formulae at room temperature. Here a same approach was adopted using the expressions for stainless steel columns with the interaction formulae from Part 1.1 of EC3 “Method 1fi” and “Method 2fi”

With the new proposal for columns “Method1fiNP” and “Method2fiNP”


600 ºC

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1M/Mfi,Rd

N/Nfi,Rd SAFIR

EN 1993-1-2

EN 1993-1-2 NP

600 ºC

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1M/Mfi,Rd

N/Nfi,Rd SAFIR

EN 1993-1-2

EN 1993-1-2 NP

prEN 1993-1-4 fi

prEN 1993-1-4 fi NP

prEN 1993-1-4 fi NP+NK

600 ºC

0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1M/Mfi,Rd

N/Nfi,Rd SAFIREN 1993-1-2EN 1993-1-2 NPMethod 1 fiMethod 1 fi NPMethod 2 fiMethod 2 fi NP

N+Mybuckling around the y-y-axisL=3000mm;

=0.360θλ ,y

ParametricParametric StudyStudy

600 ºC

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1M/Mfi,Rd

N/Nfi,Rd SAFIR

EN 1993-1-2

EN 1993-1-2 NP

600 ºC

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1M/Mfi,Rd

N/Nfi,Rd SAFIR

EN 1993-1-2

EN 1993-1-2 NP

prEN 1993-1-4 fi

prEN 1993-1-4 fi NP

prEN 1993-1-4 fi NP+NK

600 ºC

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1M/Mfi,Rd

N/Nfi,Rd SAFIR

EN 1993-1-2

EN 1993-1-2 NP

Method 1 fi

Method 1 fi NP

Method 2 fi

Method 2 fi NP

N+Mzbuckling around the z-z-axisL=3000mm;

=0.584θλ ,z

ParametricParametric StudyStudy

It is shown that the new proposal for the design buckling resistance of stainless steel compression members at high temperatures is in good agreement with the numerical results obtained with the program SAFIR, in opposition to the results obtained with the formulae of the Part 1-2 of EC 3, which are not on the safe side.

For beam-columns with bending in the strong axis and buckling around the yy-axis, the curves obtained with the new proposal for columns shows a better approximation to the numerical results. The method that approximates more closely the real behaviour of stainless steel beam-columns under fire conditions is “EN 1993-1-2 NP”. However, for the case of bending around the weak axis there is not a curve that provides a good approximation to the numerical results, which means that new interaction factors should be developed. Nevertheless “EN 1993-1-2 NP” still remains the best method.

The results presented in the paper show that EC 3 formulae for the evaluation of the fire resistance of columns and beam-columns need to be improved.

ConclusionsConclusions

Non-linear modelling of reinforced concrete beams subjected to fire

Viktor GribniakVilnius Gediminas Technical University, Lithuania

Darius BačinskasVilnius Gediminas Technical University, Lithuania

Gintaris KaklauskasVilnius Gediminas Technical University, Lithuania

((Shi, X., Tan, T.Shi, X., Tan, T.--H., Tan, K.H., Tan, K.--H., Guo, Z.H., Guo, Z. ))

Experimental specimensExperimental specimens

Test loadTest load--deflection Diagramsdeflection Diagrams

((Shi, X., Tan, T.Shi, X., Tan, T.--H., Tan, K.H., Tan, K.--H., Guo, Z.H., Guo, Z. ))

MSC.MARC MSC.MARC –– MSC.MSC.SoftwareSoftware CoCo..

Finite element modelFinite element model

TEMPERATURE DISTRIBUTION IN THE SECTIONTEMPERATURE DISTRIBUTION IN THE SECTION

400 400 °°CC 600 600 °°CC

Results of numerical analysisResults of numerical analysis

COMPARISON OFCOMPARISON OF CALCULATEDCALCULATED ANDAND TESTTEST TEMPERATURESTEMPERATURES


Tested

Calculated

COMPARISON OFCOMPARISON OF CALCULATEDCALCULATED ANDAND TESTTEST DEFLECTIONSDEFLECTIONS


Tested

Calculated

Comparison of the experimental and modelling results has shown Comparison of the experimental and modelling results has shown that that MSC.MARC has MSC.MARC has satisfactorilysatisfactorily captured the captured the loadload--deflection behaviourdeflection behaviour of of the beamsthe beams

Concluding remarksConcluding remarks

Developing a simplified Developing a simplified layerlayer (grid) (grid) modelmodel for nonfor non--linear thermolinear thermo--mechanical analysis of reinforced concrete membersmechanical analysis of reinforced concrete members

Verification of the Verification of the layerlayer modelmodel using commercial FE softwareusing commercial FE software ((DIANADIANA, , ATENAATENA, , MSC.MARCMSC.MARC))

Objectives of future researchObjectives of future research

E. NigroDepartment of Structural Engineering, University of Naples “Federico II”, Italy

G. CefarelliDepartment of Structural Engineering, University of Naples “Federico II”, Italy

Some Remarks on the Simplified Design Methods for Steel and

Concrete Composite Beams

It is shown the It is shown the comparisoncomparison of resistance between of resistance between steel beam, composite beam steel beam, composite beam and composite beam with partial concrete encasementand composite beam with partial concrete encasement. .

The following features affecting the resistance of the compositeThe following features affecting the resistance of the composite beam with partial beam with partial concrete encasement are firstly investigated: influence of the concrete encasement are firstly investigated: influence of the beam dimensionsbeam dimensionsand and effectiveness of the reinforcing barseffectiveness of the reinforcing bars in concrete encasement.in concrete encasement.

Moreover, it is shown a Moreover, it is shown a comparison comparison between the general between the general numerical approachnumerical approachand the simplified method proposed in and the simplified method proposed in EN 1994EN 1994--11--22 for evaluating the sagging for evaluating the sagging moment resistance of the composite beam with partial concrete enmoment resistance of the composite beam with partial concrete encasement. casement.

Finally, it is Finally, it is proposed a simplified plastic methodproposed a simplified plastic method for evaluating the sagging for evaluating the sagging moment resistance of the composite beam with partial concrete enmoment resistance of the composite beam with partial concrete encasement in fire casement in fire conditions.conditions.

The present paper recalls the main characteristics of a general The present paper recalls the main characteristics of a general numerical approach numerical approach to assess the ultimate bearing capacity of steel and concrete coto assess the ultimate bearing capacity of steel and concrete composite beams in fire mposite beams in fire conditions. The conditions. The behaviourbehaviour of the composite beams during a of the composite beams during a standard fire exposurestandard fire exposureis investigated. is investigated.

AbstractAbstract

( ) δ≤− estNN int

The procedure for evaluating the momentThe procedure for evaluating the moment--curvature diagram, for each time of fire curvature diagram, for each time of fire exposure, is based on the following steps:exposure, is based on the following steps:

Iterations varying the average strain Iterations varying the average strain εεmedmed of the section need up to satisfying the of the section need up to satisfying the longitudinal equilibrium equation within a suitable error:longitudinal equilibrium equation within a suitable error:

Then the bending moment Then the bending moment MMjj corresponding to the assigned curvature corresponding to the assigned curvature χχjj may be may be determined.determined.

The finite elements technique must be used;The finite elements technique must be used;The external axial force NThe external axial force Nextext (N(Nextext = 0 in pure = 0 in pure bending) and the distribution of the temperatures bending) and the distribution of the temperatures Ti(tTi(t) within the section, related to the assigned ) within the section, related to the assigned exposure time t, are known and fixed for each exposure time t, are known and fixed for each momentmoment--curvature diagram (Mcurvature diagram (M--c ; Next ; t);c ; Next ; t);For an assigned curvature For an assigned curvature χχjj , a tentative value for the average strain , a tentative value for the average strain εεmedmed of the of the crosscross--section is initially assumed and the corresponding distributionssection is initially assumed and the corresponding distributions of strain of strain eieiand stress and stress σσii = = σσ((εεii) within the section are determined on the basis of the ) within the section are determined on the basis of the temperaturetemperature--dependent stressdependent stress--strain laws;strain laws;The internal axial force The internal axial force NNintint is then evaluated starting from the stress distribution;is then evaluated starting from the stress distribution;

)( ii f εσ = ∑ ⋅=i

iiAN σint

G

>0

<0

med

y=0

c,i

a,i

Description of an accurate procedure to assess Description of an accurate procedure to assess bearing capacity of composite beamsbearing capacity of composite beams

Comparison between various types of beamsComparison between various types of beams

0

50

100

150

200

250

0 20 40 60 80 100 120

time (min)

sagg

ing

mom

ent r

esis

tanc

e (k

N*m

)

Non composite beam

0,000

0,200

0,400

0,600

0,800

1,000

1,200

0 20 40 60 80 100 120

time (min)

load

ratio

Non composite beam

The comparison in resistance field The comparison in resistance field shows the better shows the better behaviourbehaviour of of composite members; however, in composite members; however, in load ratio field, the composite load ratio field, the composite beam without concrete beam without concrete encasement shows a similar encasement shows a similar behaviourbehaviour to nonto non--composite composite beam. This is due to, both in the beam. This is due to, both in the composite beam without concrete composite beam without concrete encasement and nonencasement and non--composite composite beam, the beam, the moment capacity moment capacity depends on depends on loss of strength of loss of strength of metallic partmetallic part exposed to fire. In exposed to fire. In the case of composite beam with the case of composite beam with partial concrete encasement, it is partial concrete encasement, it is shown a quite better behaviour, shown a quite better behaviour, thanks to lower temperature thanks to lower temperature values in the steel beam.values in the steel beam.

Effectiveness of the reinforcing barsEffectiveness of the reinforcing bars

0

50

100

150

200

250

300

350

400

450

0 20 40 60 80 100 120 140 160 180

time (min)

(kN

*m)

level 1

level 2

without reinforcing bars

Sagg

ing

mom

ent

resi

stan

ce

It is clear how tIt is clear how the he reinforcement to level 1 reinforcement to level 1 provides a better provides a better performance in ambient performance in ambient condition, but it provides condition, but it provides a worth performance in a worth performance in fire condition, compared fire condition, compared to the case of to the case of reinforcement placed to reinforcement placed to level 2.level 2.

level 2

level 1

Proposed simplified plastic methodProposed simplified plastic method

concrete concrete slabslab;;upper flange of steel beam;upper flange of steel beam;upper half of the web steel beam;upper half of the web steel beam;bottom half of the web steel beam;bottom half of the web steel beam;bottom flange of the steel beam.bottom flange of the steel beam.

The crossThe cross--section of the beam is divided in section of the beam is divided in 5 main parts5 main parts::

Moreover, the flanges are further divided in 3 parts.Moreover, the flanges are further divided in 3 parts.

A A uniform temperatureuniform temperature, equal to , equal to average temperature of the same average temperature of the same part, is assigned to each of this parts. part, is assigned to each of this parts. The average temperature is The average temperature is evaluated from the thermal analysis.evaluated from the thermal analysis.

Concrete with temperatures in Concrete with temperatures in excess of 500excess of 500°°C is assumed not to C is assumed not to contribute to the load bearing contribute to the load bearing capacity of the member, whilst the capacity of the member, whilst the residual concrete crossresidual concrete cross--section section retains its initial values of strength.retains its initial values of strength.

A 2

A 3

A 4 b

A 1 a

A 1 b

A 1 c

A 4 a

A 4 c

timemin KN*m KN*m

0 208,33 208,279 1,0015 205,35 208,279 1,0130 139,31 130,256 0,9360 73,75 73,313 0,9990 31,69 31,406 0,99

120 16,79 16,856 1,00150 9,98 10,024 1,00180 7,16 7,510 1,05

Ultimate Resistant Moment - general procedure -

Ultimate Resistant Moment - proposed simplified moment - Msimpl/Mgen

Thank you for your attention

structural members behaviour -...

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