marian a. gizejowski leslaw kwasniewski wael … kwasniewski wael salah faculty of ... buckling...

COST Action TU0601 Robustness of Structures : Timisoara Meeting 29-30 September 2008

Robustness of continuous steelRobustness of continuous steel--concrete composite beams ofconcrete composite beams ofRobustness of continuous steelRobustness of continuous steel concrete composite beams of concrete composite beams of slender slender plainplain webbed and cellular open webbed sectionwebbed and cellular open webbed sectionss

Marian A. GIZEJOWSKI

Leslaw KWASNIEWSKI

Wael SALAH

Faculty of Civil Engineering

W U i i f T h lWarsaw University of Technology


Outline of the presentationOutline of the presentation

• Introductory remarks and objectivesIntroductory remarks and objectives

• Slender section castellated composite beams

• Results of experimental investigations

P d t FE i l ti ith f ABAQUS• Proposed computer FE simulations with use of ABAQUS

• Comparison of results from simulations and experimentsp p

• Final remarks


Basic restrained instability modes of composite beamsBasic restrained instability modes of composite beamsBasic restrained instability modes of composite beams Basic restrained instability modes of composite beams in hogging moment regionsin hogging moment regions

Local bucklingLocal buckling

Torsional-distortionaldistortional

buckling Lateral-distortional buckling Lateral-torsional-g Lateral torsional

distortional buckling


LoadLoad--deflection curves of slender section composite beams deflection curves of slender section composite beams f f pf f pwith different regions of the bending moment diagramwith different regions of the bending moment diagram

Composite beam with the sagging moment regionsagging moment region

Composite beam with the hogging moment region


CContinuous or semiontinuous or semi--continuous continuous castellated castellated steelsteel--concreteconcreteccompositeomposite beams in multibeams in multi--story buildingsstory buildings


Castellation processCastellation process

Castellation process for I-rolled section

h ≈ 1.5 dh ≈ 1.5 d

Built up section with web openingsBuilt-up section with web openings


Advantages of using castellated sections in modernAdvantages of using castellated sections in modernAdvantages of using castellated sections in modern Advantages of using castellated sections in modern structuresstructures

• Steel castellated beams are lighter than conventionalSteel castellated beams are lighter than conventional plain webbed shapes.

• Greater flexural stiffness of the castellated beams allows f ti fl ibl fl l th t f f i t ifor creating flexible floor plans that are free of interior columns.

• The web openings are used to pass the services allowing p g p gto minimize the floor depth.


Disadvantages of using castellated sections inDisadvantages of using castellated sections inDisadvantages of using castellated sections in Disadvantages of using castellated sections in composite beamscomposite beams

• More severe conditions for restrained distortional instabilityyof both the web and the bottom flange in the negativebending moment regions than in the case of plain webbedbeams.

• Lower shear force resistance of the steel part of thecomposite section.


St t f th t d h bj tiState-of-the-art and research objective

Previous conducted researchesA review has been made of research work carried out to date onthe effect of openings on the behaviour of thin-walled compositebeams Research as foc sed on simpl s pported compositebeams. Research was focused on simply supported compositebeams with web openings.

Current study objective

This study aims to widen the knowledge of the behaviour of thin-walled composite beams for the behaviour in the negative momentwalled composite beams for the behaviour in the negative momentregion.


Arrangement of beams for testing and computerArrangement of beams for testing and computerArrangement of beams for testing and computer Arrangement of beams for testing and computer simulationssimulations

100

R168

R168

R168

R168

480 long specimen

with circular web openingsopenings

100

160,

5

480

long specimen with hexagonal web openings



100

298

480

1

long specimen with square web openingsweb openings

R ti L dReaction Load1058 1058

A

short specimen pwith circular web openings

100 1058 100264 529 26511581158

A



Reaction LoadA Load1058 1058

A

100 1052 100264

298

529 265100 1052 100264

11581158

529 265

A

short specimen with hexagonal web openings

short specimen with square web openings



5252510

0

Section (A A)Section (A-A)

Experimental investigationsExperimental investigationsSteel grades: S355 and S420Steel grades: S355 and S420Steel grades: S355 and S420Steel grades: S355 and S420


Test rig setupTest rig setup

Composite beam with circular web openings

C it b ithComposite beam with hexagonal web openings

Composite beam withComposite beam with rectangular web openings


Displacement control program designed for theDisplacement control program designed for theDisplacement control program designed for the Displacement control program designed for the experimental investigationsexperimental investigations

Displacement control program for the tested long specimens

Displacement control program for the tested short specimens


Beam deformation at the level of maximum loadBeam deformation at the level of maximum loadBeam deformation at the level of maximum loadBeam deformation at the level of maximum loadLong span specimen with circular web openingsLong span specimen with circular web openings

Distortional d f ti

Vertical displacementsdeformations

Concrete slab cracks


Beam deformation at the end of the testBeam deformation at the end of the testBeam deformation at the end of the testBeam deformation at the end of the testLong span specimen with circular web openingsLong span specimen with circular web openings

Vertical displacements Distortional deformations

Concrete slabConcrete slab cracks


Beam deformation at the level of maximum loadBeam deformation at the level of maximum loadBeam deformation at the level of maximum loadBeam deformation at the level of maximum loadShort span specimen with circular web openingsShort span specimen with circular web openings

Di t ti lVertical displacements Distortional deformations


Vertical displacements


Beam deformation at the end of the testBeam deformation at the end of the testBeam deformation at the end of the testBeam deformation at the end of the testShort span specimen with circular web openingsShort span specimen with circular web openings

Di t ti lVertical displacements Distortional deformations


Vertical displacements

Finite Element Analysis usingFinite Element Analysis usingFinite Element Analysis using Finite Element Analysis using ABAQUSABAQUSQQ


Finite Element modeling techniqueFinite Element modeling techniqueShell elements

S4RMaterials

Shell elements

Beam elementB31

Steel materialPerfect and imperfect steel models with

S4R5isotropic strain hardening

Concrete materialSmeared cracks model

Elements used in theAnalysis types Elements used in the developed FE model

Analysis types

Perturbation elastic buckling analysis

Riks post-yielding, post-buckling and post-cracking analysis


Geometric imperfection pattern for long span beamGeometric imperfection pattern for long span beam

First positive mode shape of the long specimen with circular web openings


Geometric imperfection patterns for short span beamGeometric imperfection patterns for short span beam

First positive mode shape Second positive mode shape Third positive mode shape

Combined mode shapes for the short beam specimen with circular web openings


FE calibration analysisFE calibration analysis

1. Nominal and measured web plate thickness.

2. Imperfection amplitude(s) for the first (the first several) bucklingmode shape(s) to be applied as initial geometric imperfectionp ( ) pp g ppattern.

3 Material imperfection parameter (n)3. Material imperfection parameter (n).

4. Concrete tension softening parameter εcr


Effect of nominal vs. measured web thickness forEffect of nominal vs. measured web thickness forEffect of nominal vs. measured web thickness for Effect of nominal vs. measured web thickness for idealized perfect material modelidealized perfect material model

80

6070

30

4050

tw=3.8 mmt =4 0 mm

test

10

2030 tw=4.0 mm

0

0 50 100 150 200Di l t ( )Displacement (mm)


Effect of geometric imperfections for long span Effect of geometric imperfections for long span beam and for idealized perfect material modelbeam and for idealized perfect material model

L ll l i bLong-span cellular composite beam


Material imperfections captured by using anMaterial imperfections captured by using anMaterial imperfections captured by using an Material imperfections captured by using an equivalent stressequivalent stress--strain diagramstrain diagram

nn

stRy

n

EfE

/1

,

11−

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

++⎟

⎠⎞

⎜⎝⎛=

εεσ

ststyRy Eff ε−=,

ff

⎦⎣

stu

yust

ffE

εε −

−=

J. MURZEWSKI, Random load carrying capacity of rod structures. PWN, Series: Engineering Studies, W 1976 [i P li h]Warszawa 1976 [in Polish].


Calibration of material behavior parameters forCalibration of material behavior parameters forCalibration of material behavior parameters for Calibration of material behavior parameters for the the nominal web thicknessnominal web thickness


Calibration of material behavior parameters forCalibration of material behavior parameters forCalibration of material behavior parameters for Calibration of material behavior parameters for the measured web thicknessthe measured web thickness

kN)

50

60

70

n=4n=∞

C4S355tw=3.8mm, cr=0.001

lied

load

(k

30

40

50

n=2

App

l

10

20 n=1

test

00 50 100 150 200

Displacement (mm)


Comparison between test data and FE results forComparison between test data and FE results forComparison between test data and FE results for Comparison between test data and FE results for long span beamlong span beam

Deformed shape of specimen C4S355 at the end of the test

Deformed shape of specimen C4S355 at the end of the FE analysis


Long span beam final comparison for calibratedLong span beam final comparison for calibratedLong span beam final comparison for calibrated Long span beam final comparison for calibrated material behavior parameters material behavior parameters

load

(kN

)A

pplie

d l

Comparison between test data and Comparison between test data and FE results for specimen C4S355 FE results for specimen C4S420


Comparison between test data and FE results forComparison between test data and FE results forComparison between test data and FE results for Comparison between test data and FE results for short span beamshort span beam

Deformed shape of specimen C2S355 at the end of the test

Deformed shape of specimen C2S355 at the end of the FE analysis


Short span beam final comparison for calibratedShort span beam final comparison for calibratedShort span beam final comparison for calibrated Short span beam final comparison for calibrated material behavior parameters material behavior parameters

N)

100

ed lo

ad (k

N

60

80

load

(kN

)

App

lie

20

40

App

lied

testFE

00 20 40 60 80 100 120 140

Di l t ( )

Comparison between test data and Comparison between test data and

Displacement (mm)

Comparison between test data and FE results for specimen C2S355

pFE results for specimen C2S420


C l iC l iConclusionsConclusions

The behaviour of statically indeterminate castellated compositeb i l th th t f i l t d b Abeams is more complex than that of simply supported beams. Acastellated composite beam may be subjected to different instabilityeffects in the negative moment regions where the bottom

i fl f th b i t i dcompression flange of the beam is unrestrained.

The experimental tests indicate that the shape of the web opening hasthe significant effect on both, the ultimate load and the stiffnessdegradation up to and beyond the limit point on the equilibrium path.



Within the same opening shape, there is no visible effect of steeld S355 d S420 h b h i f b h l d i lgrades S355 and S420 on the behavior of both, slender section long

span and short span composite beam specimens.

For slender welded steel sections, it is important to include thel f d b thi k d th ff t f id laverage value of measured web thickness and the effect of residual

stresses, e.g. by using an equivalent stress-strain diagram dependentupon the material imperfection factor n, as it has been proposedh iherein.



The calibration exercise shows that the maximum amplitude ofgeometric imperfections may be taken as equal to the nominal webthickness material imperfection factor should be taken as n=2 and thethickness, material imperfection factor should be taken as n 2 and theconcrete zero-tension strain εcr as 0.1 and 0.01 for two differentconcrete properties used for long and short span beams, respectively.

Both experimental investigations and the Finite Element modelingshow that the unrestrained bottom flange of long span beams areforced to distort laterally whereas the short span beams becomedistorted only torsionally.

Both distortional buckling modes, lateral and torsional for the long and short span beams respectively, are precisely captured in the numerical FE simulations with respect to the deformation patterns and the localFE simulations with respect to the deformation patterns and the local values of the deformed shape amplitudes.


Future researchFuture researchFuture researchFuture researchFE calibration vs. FE calibration vs. hierarchical validationhierarchical validation

1. Concrete tension softening parameter εcrg p cr- experimental bending test on concrete beams/plates

2 M t i l i f ti t ( )2. Material imperfection parameter (n).- laboratory coupon tension and bending tests (steel)

3. Nominal and measured web plate thickness (+ 2)- experimental bending test on rectangular steel plates

4. Geometrical imperfections (+ 2 and 3)- experimental bending test on castellated beams without concrete

Th k f ki dThank you for your kind tt tiattention

marian a. gizejowski leslaw kwasniewski wael … kwasniewski wael salah faculty of ... buckling...

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