Applied Element Method as a Practical Tool for Progressive ...

Applied Element Method as a Practical Tool for Progressive

Collapse Analysis of Structuresp y

April 22nd, 2008

AgendaApplied Element Method as a Practical Tool forApplied Element Method as a Practical Tool for

Progressive Collapse Analysis of StructuresApril 22nd, 2008

8am PDT (Los Angeles) / 11am EDT (New York) / 4pm BST (London)

Welcome & Introduction (Overview of NAFEMS Activities)Welcome & Introduction (Overview of NAFEMS Activities)Matthew Ladzinski, NAFEMS North AmericaMatthew Ladzinski, NAFEMS North America

Applied Element Method as a Practical Tool for Applied Element Method as a Practical Tool for Progressive Collapse Analysis of StructuresProgressive Collapse Analysis of Structures

Dr. Hatem TagelDr. Hatem Tagel--Din, Applied Science International, LLCDin, Applied Science International, LLC

Q&A Session Q&A Session P lP lPanelPanel

ClosingClosing

www.nafems.orgwww.nafems.orgLadzinski Tagel-Din

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COMMUNITYCOMMUNITY

An Overview of NAFEMS NA Activities

Matthew LadzinskiMatthew LadzinskiNAFEMSNAFEMSNorth American RepresentativeNorth American Representative

www.nafems.orgwww.nafems.org

Planned Activities in North America

WebinarsNew topic each month!p

Verification & Validation (V&V): Quantifying Prediction Uncertainty and Demonstrating Simulation Credibility (May 15)Managing FEA in the Design Process (June)

Recent webinars:Recent webinars:AUTOSIM: The Future of Simulation in the Automotive IndustryA Common Sense Approach to Stress Analysis and Finite Element ModelingThe Interfacing of FEA ith Press re Vessel Design Codes (CCOPPSThe Interfacing of FEA with Pressure Vessel Design Codes (CCOPPS Project)Multiphysics Simulation using Directly Coupled-Field Element TechnologyMethods and Technology for the Analysis of Composite MaterialsMethods and Technology for the Analysis of Composite MaterialsSimulation Process ManagementSimulation-supported Decision Making (Stochastics)Simulation Driven Design (SDD) Findings


To register for upcoming webinars, or to view a past webinar, please visit: www.nafems.org/events/webinars


EventsPractical Stress Analysis & Finite ElementPractical Stress Analysis & Finite Element Methods with Bob Johnson

An opportunity to ensure that your organization gets maximum benefit from using FEAgThree-day Training CourseApril 30th – May 2nd, 2008 in Troy, MIOnly a two seats left! ywww.nafems.org/events



NAFEMS NA 2008 Regional SummitNAFEMS 2020 Vision of Engineering Analysis and Simulation

NAFEMS 2020 will bring together the leading visionaries, developers, and practitioners of CAE-related technologies and business processesGoal: Provide attendees with the best “food for thoughtGoal: Provide attendees with the best “food for thought and action” to deploy CAE over the next several yearsLocation: Embassy Suites Hotel & Convention Center,

Hampton VirginiaHampton, VirginiaDate: October 29-31, 2008

Call for Papers Now Open!Call for Papers Now Open!

For more information visit:


For more information, visit: www.nafems.org/nafems2020

Other NAFEMS Activities

NAFEMS Simulation Data Management Working Group (SDMWG) – name tbdg p ( )

www.nafems.org/tech/sdmwg

NAFEMS NA eNews UpdateMonthly newsletter containing information on upcoming NAFEMS NA activitiesCan be downloaded at: www.nafems.org/regional/north_america/enews


Applied Element Method as a Practical Tool for Progressive Collapse Analysis offor Progressive Collapse Analysis of

Structures

Hatem Tagel-DinApplied Science International, LLC

Contents

• Definition of Progressive Collapse • Problem Statement• Why AEM?• AEM Theory• Modeling Advantages of AEM compared to FEM

A l i Ad t f AEM d t FEM• Analysis Advantages of AEM compared to FEM• Practical Examples for Progressive Collapse Simulations

Definition of Progressive Collapse

“A collapse that is triggered by localized damage that can’t be contained and leads to a chain of failures resulting in a partial or total structural collapse, where the final damage is disproportionate to the local damage of the triggering event”

Definition of Progressive Collapse GSA Code: Guidance

GSA: Progressive Collapse Analysis and Design Guidelines for New Federal Office Buildings and Major Modernization Projects.

Objective to reduce the potential for progressive collapse through:

1) Redundancy for ensuring alternative load paths2) Structural Continuity and Ductility3) Capability of resisting load reversals4) Capability of resisting shear failure

Definition of Progressive Collapse GSA Code: Analysis

Remove a vertical supporting element from the location being considered (first fl l ) d d t t ti d i l i f th t t

y

floor only) and conduct a static or dynamic analysis for the structure.

Interior considerationExterior consideration

Definition of Progressive Collapse GSA Code: Analysis

1) Maximum Allowable Collapse Area:

y

Problem Statement

• Given:– Structural full geometryStructural full geometry– Full reinforcement detailing– Material properties

Th (B b lli i fi– Threat type (Bomb, car collision, fire, element removal.)

• Questions:– Will the structural collapse or not?– Is it partial or total collapse?– Which part will fail and how?Which part will fail and how?– What is the footprint of the collapsed

structures?What are the effects of falling debris on– What are the effects of falling debris on adjacent structures?

Why AEM?Why AEM?

Why AEM?Methods for Structural AnalysisMethods for Structural Analysis

• Finite Element Method (FEM)• Boundary Element Method (BEM)• Finite Difference Method• Discrete Element Method (DEM)• Discrete Element Method (DEM)• Discontinuous Deformation Analysis (DDA)• Truss Method and Lattice Method• Strut and Tie Method• Spring Network Method

Fi it S ti M th d• Finite Section Method• Rigid Body and Spring Method (RBSM)• Mesh-Free Methods

Why AEM?FEM/DEM Comparison

M M

Collapse History

FEM/DEM Comparison

lifie

d FE

M

nced

FEM

Linear Cracking, Yield, Crushing

Buckling, Post-Buckling

Debris falling as Rigid Bodies CollisionElement

Separation

Sim

pl

Adv

an

Continuum Discrete

Can not be

FEMAutomated

Problems with Static analysis and

Accurate

ycontinuum materials Reliable

Not reliableDEM

Why AEM?Analysis of Oklahoma City Building Using Advanced FEMAnalysis of Oklahoma City Building Using Advanced FEM

Why AEM?Advantages of AEM compared to FEMAdvantages of AEM compared to FEM

• Analysis AdvantagesA l i i i l th i lifi d FEM d t th– Analysis is as simple as the simplified FEM and as accurate as the advanced FEM.

– Output includes stresses, strain and internal force diagrams– Automatic yield and cut of reinforcement barsAutomatic yield and cut of reinforcement bars

– Automatic element separation and contact detection – Automatic plastic hinge formation

A t ti l t lli i– Automatic element collision• Modeling Advantages

– Physical elements

M h i hi– Much easier meshing– Easier modeling of reinforcement bars– Realistic and Easier modeling for Steel Structures

Why AEM?

Complexity, Accuracy, Time and Qualifications of User

ons

utio

ns

Progressive Collapse Analysis

le S

olut

io

inea

r Sol

u

Sim

pl

ghly

Non

li

Engineering Judgment, Uncertainty and Construction Cost

Hig

Advanced FEMFEM

GapSimplified FEM

Not verifiedPerformance Based Design

AEM

Not verifiedPerformance Based Design

AEM

Why AEM?Analysis of Oklahoma City Building Using AEMAnalysis of Oklahoma City Building Using AEM

Why AEM?Analysis of Oklahoma City Building Using AEMAnalysis of Oklahoma City Building Using AEM

AEM Theoretical Background Element Discretization

Material Springs

The continuum is discretized into elements connected together with nonlinear springs that represent the material behaviorp g p

The springs represent axial deformations as well as shear deformations

AEM Theoretical Background Connectivity (Matrix Springs)y ( p g )

Volume Volume represented by represented by springssprings

Element 1Element 1 Element 2Element 2YZ

x

Element 1Element 1El t 1El t 1 El t 1El t 1 Element 1Element 1Element 1Element 1 Element 1Element 1

Normal SpringsNormal Springs Shear Springs Shear Springs xx--zz Shear Springs Shear Springs yy--zz

AEM Theoretical Background Connectivity (Reinforcement Springs)y ( p g )

Element 1Element 1 Element 2Element 2YZ Reinforcing bar

xbar

Element 1Element 1Element 1Element 1 Element 1Element 1

Normal SpringsNormal Springs Shear Springs Shear Springs xx--zz Shear Springs Shear Springs yy--zzp gp g p gp g p gp g yy

AEM Theoretical Background Connectivity (Steel Sections)y ( )

2 ways for modeling a steel section

Implicit Steel section Explicit Steel sectionp p

Vacuum cellsSteel Elements

Vacuum cells

AEM Theoretical Background Connectivity (Matrix Springs)y ( p g )

Steel Springs

AEM Theoretical Background Connectivity (Matrix Springs)

Steel Springs

y ( p g )

concrete

Concrete Springsp g

AEM Theoretical Background Masonry Walls Modeling

MortarMortar

y g

BrickBrick

ConcreteConcrete

MortarMortar

AEM Theoretical Background Masonry Walls Modeling

Brick Springs

y g

p g

Concrete Springs

Mortar Springs

AEM Theoretical Background Degrees of Freedomg

Normal Normal

Shear x-z Shear x-zShear x-y

Shear x-y Normal

TranslationTranslation RotationRotation

AEM Theoretical Background Assembly of Overall Stiffness Matrix

12 12 x x 12 12 stiffness matrixstiffness matrix

y

Elements directly affect each otherElements directly affect each other

O ll Stiff M t iO ll Stiff M t iOverall Stiffness MatrixOverall Stiffness Matrix

AEM Theoretical Background Equation of Motion

[ ]{ } [ ]{ } [ ]{ } { }iiiiii FyKyCyM Δ=Δ+Δ+Δ &&& Incremental Equation of Motion

q

Step-by-step integration (Newmark-beta) method requestedrequested

Acceleration

yoo(ti+Δt){ } { } { }

{ } { } { } { } 221 tytytyy

tytyy

iiii

iii

ΔΔβ+Δ+Δ=Δ

ΔΔγ+Δ=Δ

&&&&&

&&&&&

Δt

{ } { } { } { }2

tytytyy iiii ΔΔβ+Δ+Δ=Δ

Timeti ti +θ Δt

AEM Theoretical BackgroundMaterial Models (Material Models (Concrete under axial stresses)

TensionTension CompressionCompressionFully path-dependent model for concrete(Okamura and Maekawa 1991)(Okamura and Maekawa, 1991)

AEM Theoretical BackgroundMaterial Models (Material Models (Concrete under Shear Stresses)

Before CrackingBefore Cracking After CrackingAfter Cracking

Friction and interlockingFriction and interlocking

AEM Theoretical BackgroundMaterial Models (Material Models (Steel under axial stresses)

TensionTension CompressionCompressionFully path-dependent model for reinforcementy(Ristic et al, 1986)

z

AEM Theoretical BackgroundMaterial Models (Material Models (Cracking Criteria)

τxzσx

τyz

yτzy

τxyy

τyx

σy

xτzx σz

y

z

τxy

τxz σxτyz

τzx σzτyx

yτzy

τxyσy

Plane of majorPlane of majorx

Plane of major Plane of major principal stressprincipal stress

AEM Theoretical BackgroundCut of RebarCut of Rebar

VonVon--Misses Criteria applied for Ultimate StrengthMisses Criteria applied for Ultimate StrengthBar resists only Normal and shear forcesBar resists only Normal and shear forcesNo Flexural rigidity at the timeNo Flexural rigidity at the time--beingbeing

NNVV

F il lFailure envelope

1222

⎟⎟⎞

⎜⎜⎛

+⎟⎟⎞

⎜⎜⎛

+⎟⎟⎞

⎜⎜⎛ MVN 1=⎟⎟

⎠⎜⎜⎝

+⎟⎟⎠

⎜⎜⎝

+⎟⎟⎠

⎜⎜⎝ PPP MVN

AEM Theoretical BackgroundTypes of ContactTypes of Contact

Corner-Face TypeEdge-Edge Type Corner-Ground Type

AEM Theoretical BackgroundCollision SpringsCollision Springs

F lliF lliFallingFallingElementElement

Normal and shear springs are createdNormal and shear springs are created

Shear spring in XShear spring in XShear spring in yShear spring in y Normal SpringNormal Spring

AEM Theoretical BackgroundFEM/AEM ComparisonFEM/AEM Comparison

FEMFEM AEMAEM

Full nodal compatibility

D f ti i id l tD f ti i id l t D f ti t id l tD f ti t id l tDeformations inside elementsDeformations inside elements Deformations outside elementsDeformations outside elements

Deformations in surface springsDeformations in surface springs


FEM AEM

8 nodes x 3 DOF 24 DOF/ Element 6 DOF/ Element


16 17 18 19 201211109 1211109

11 12 13 14 15

1211109

8765

1211109

8765

6 7 8 9 104321 4321

FEM AEM1 2 3 4 5

Elements compatible at nodes (moves together there)

Elements are connected through their faces(moves together there)

For example Node 13 connects Elements 6,7,10,11

Deformations are inside the l t

their facesFor example elements 6,7,10,11

are not compatible in deformationsDeformations are localized at the

elements faces of the elements


Connectivity includedNo Connectivity

FEM AEM

AEM Theoretical BackgroundFEM/AEM Comparison (Transition Elements)FEM/AEM Comparison (Transition Elements)

FEM AEM

There should be transition elements between large elements and small elements

There is no need for the transition elements between large elements and small elements

Modeling Advantages of AEM Modeling Advantages of AEM compared to FEMcompared to FEMcompared to FEMcompared to FEM

Modeling Advantages of AEM compared to FEMModeling Advantages of AEM compared to FEMEasy Element ConnectivityEasy Element Connectivity

Easy Mesh Generation

Modeling Advantages of AEM compared to FEMModeling Advantages of AEM compared to FEMEasy Element Connectivity

FEM AEM

Easy Element Connectivity

Auto meshing of elements connectivity

Difficult meshingand For CompatibilityCompatibility Merge Nodes of Slab and Column


Sl bSl b


Concrete SlabConcrete Slab

Girder

Wind

Girder

Wind

olum

n

Window Frame

olum

n

Window Frame

BrickWall

C BrickWall

C

Glass WindowGlass Window


FEM AEM


Difficult meshingBetween wide

d thi l tConnection of

and thin elements Elements Through Interfaces

Modeling Advantages of AEM compared to FEMModeling Advantages of AEM compared to FEMEasy Modeling of Steel StructuresEasy Modeling of Steel Structures

Modeling Advantages of AEM compared to FEMModeling Advantages of AEM compared to FEMNo Need for Gap ElementsNo Need for Gap Elements

AEMAEM Solid ElementsSolid ElementsShell ElementsShell Elements

In Simplified FEM link elements should be located and definedlocated and defined in the beginning.

In AEM, link between a column and a footing is automaticallyautomatically defined at Springs

Modeling Advantages of AEM compared to FEMModeling Advantages of AEM compared to FEMEasy Modeling of Reinforcement DetailsEasy Modeling of Reinforcement Details

Analysis Advantages of AEM Analysis Advantages of AEM compared to FEMcompared to FEMcompared to FEMcompared to FEM

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMAnalysis Iterations using Simplified FEM

C d t t ti d i l i

Remove a vertical support

Analysis Iterations using Simplified FEM

Conduct a static or dynamic analysis

DCR exceeded in any

member?yesyes

NoNo

DCR exceeded based upon shear

force ?

yesyes

Failed members should be removed from the

The member is considered a

failed member

NoNo

Flexural DCR ratio exceeded in a member end ?

model, and all dead and live loads associated with failed members should be redistributed to

Place a hinge at the member’s end

At inserted hinge apply

yesyes

NoNo

Flexural DCR values for both ends of a

member, as well as span itself, are

exceeded ?

the other members in adjacent bays

At inserted hinge, apply equal-but-opposite moments whose magnitude should equal the expected flexural strength

The member is considered a

failed member

yesyes

End

NoNo

Calculate collapsed area

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMNo Need for Analysis Iterations using AEM

Remove a vertical support

No Need for Analysis Iterations using AEM

Conduct a dynamic analysis

EndCalculate collapsed area

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMManual Formation of Plastic Hinges using Simplified FEM

1-In commercial FEM, usually explicit plastic hinges, in predefined locations, should be defined by the user in order to perform the nonlinear analysis.

Manual Formation of Plastic Hinges using Simplified FEM

y p y

2-Both Moment-curvature and Moment-rotation relations in such a case should be estimated by the user before analysis3 The user should be a qualified engineer3-The user should be a qualified engineer

Predefined Plastic HingesMoment-Curvature

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMAutomatic Formation of Plastic Hinges

1- The Nonlinear analysis is automatically considered in ELS. Location, number and all properties of plastic hinges in ELS are automatically determined by the ELS.

Automatic Formation of Plastic Hinges

Plastic hinge at maximum +ve moment

Plastic hinge at maximum -vemoment

Plastic hinge at maximum -vemoment

2- In FEM commercial software, fiber plastic hinges are used to overcome the disadvantage in (predefined moment-curvature), However definition of the Fiber hinge properties is difficult and needs large time to represent concrete and steel cellscells.

3-Preprocessing time in SAP is longer than ELS. Post processing time is equal in SAP and ELS.

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMAutomatic Formation of Plastic HingesAutomatic Formation of Plastic Hinges

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMAutomatic Formation of Plastic HingesAutomatic Formation of Plastic Hinges

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMComparison between Progressive Collapse Analysis using AEM and FEM

(1) In FEM analysis, no bar rupture available Not accurate

Comparison between Progressive Collapse Analysis using AEM and FEM

(2) In FEM analysis, no element separation and collision available Not accurate

(3) Since no progressive collapse can be simulated with FEM Iterative analysis is(3) Since no progressive collapse can be simulated with FEM, Iterative analysis is carried out in order to remove collapsed elements and to redistribute their loads to adjacent elements Time consuming and not accurate

(4) In AEM, Plastic hinge formation, failure and collapse of members is automated Advantage of AEM

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMLocalization of Failed Areas

Cracking and Plastic Hinges Formation

Mechanisms Formation and Elements Failure

Progressive collapse of Elements

Collision and Progressive collapse of Parts of Structures

Automatic prediction in one analysisAutomatic prediction in one analysis

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMEffects of Reinforcement Bars

00 0.5 1 1.5

O C l d

Effects of Reinforcement Bars

-10

-5

on (c

m)

Bottom RFT= 82% of LEFEM design

76%

One Column removed

-20

-15

Floo

r Def

lect

io

71%

63%

50%

No collapse

-30

-25

Time (Seconds)

50%

44% & Non-continuousBottom RFT

Collapsing

Time (Seconds)

Strengthened GirdersStrengthened Girders(above collapsed columns)(above collapsed columns)

Amount of additional RFT Amount of additional RFT (calculated as a percentage of RFT (calculated as a percentage of RFT based upon elastic analysis afterbased upon elastic analysis afterbased upon elastic analysis after based upon elastic analysis after element removal)element removal)

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMInternal Force Diagrams Through Integration of StressesInternal Force Diagrams Through Integration of Stresses

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMInternal Force Diagrams Through Integration of StressesInternal Force Diagrams Through Integration of Stresses

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMDamage assessments due to column removalDamage assessments due to column removal

Highly cracked zones

Highly cracked zones

P Q R

7 7

6 6

P.6

Case (1)

PP QQ RR

7 77 7

6 66 6

P.6P.6

Case (1)

8 8

8.3 8.3

9 9

Case (1)

Case (2)

Case (3)

8 88 8

8.3 8.38.3 8.3

9 99 9

Case (1)

Case (2)

Case (3)

P Q R

9 9

P.6PP QQ RR

9 99 9

P.6P.6

Collapse of Column Q-6

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMDamage assessments due to two column removalDamage assessments due to two column removal

P Q R

7 7

6 6

P.6

Case (1)

PP QQ RR

7 77 7

6 66 6

P.6P.6

Case (1)

8 8

8.3 8.3

9 9

Case (1)

Case (2)

Case (3)

8 88 8

8.3 8.38.3 8.3

9 99 9

Case (1)

Case (2)

Case (3)

P Q R

9 9

P.6PP QQ RR

9 99 9

P.6P.6

Collapse of Columns Q-6 and R-6

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMDamage assessments due to column removal

Damage assessments due to column removal

11270

3847 2074

11270

38472074

11270

3847 2074

11270

38472074

11270

3847 2074

11270

38472074

11270

3847 2074

11270

38472074

1082211063

5160

3

3728

4481

10822

5160

3

448111063

3728

1082211063

5160

3

3728

4481

10822

5160

3

448111063

3728

1082211063

5160

3

3728

4481

10822

5160

3

448111063

3728

1082211063

5160

3

3728

4481

10822

5160

3

448111063

3728

1226912269 1226912269 1226912269 1226912269

Bending Moment Just After Bending Moment Just After Column CollapseColumn Collapse

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMVisual Damage AssessmentsVisual Damage Assessments

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMVisual Damage/Non-Structural ComponentsVisual Damage/Non-Structural Components

Analysis Advantages of AEM compared to FEMAnalysis Advantages of AEM compared to FEMVisual Damage/Automatic Contact DetectionVisual Damage/Automatic Contact Detection

Earthquake Directionq

Verification ExamplesVerification Examples

Verification Examples Verification Examples Charlotte Coliseum, North Carolina

Demolition ScenarioDemolition Scenario


AEM ModelAEM Model


11 22 33 4411 22 33 44


Verification Examples Verification Examples Sheraton Hotel, Raleigh North Carolina

LayoutLayout


AEM ModelAEM Model


11 22 3311 22 33


Verification Examples Verification Examples Stubbs Tower, Savannah, Georgia

ELS ModelELS Model

The removedThe removed


Level (1) at 0.10 sec

The removed The removed components are components are shown in redshown in red

Level (1) at 1.1 sec

Level (1) at 1.43 secLevel (2) at 0.125 sec Level (1) at 2.60 sec

Level (3) at 0.15 sec Level (1) at 1.767 secLevel (1) at 2.27sec

Level (6) at0.175 sec Level (1) at 1.93 sec Level (1) at 2.28 sec

Level (1) at 0.767 sec Level (1) at 2.10 sec


(1) (3)

(2) (4)( ) ( )


Verification Examples Verification Examples Briquetting Structure, Australia



(1) (2) (3)

(4) (5) (6)


200

100

150

Forc

e (t

ons)

50

F

00 5 10 15 20 25 30

Verification Example of Steel StructuresVerification Example of Steel StructuresHot rolled steel beam under flexureHot rolled steel beam under flexure

25

30

35

15

20

25

Load

(Ton

)

FEMFEM 5

10

FEM ELS2

AEMAEM

00 1 2 3 4 5 6

Displacement (cm)

Stress contours

Verification Example of Steel StructuresVerification Example of Steel StructuresConcrete-Filled Tube Girder under Four-Point Loading

mm

Box (120*120*3 84)

120mm

120m Box (120 120 3.84)

50mm 250mm 250mm 50mm500mm

Verification Example of Steel StructuresVerification Example of Steel StructuresConcrete-Filled Tube Girder under Four-Point Loading

3000

3500

2500

3000

m)

1500

2000

Mom

ent (

kN.c

m

500

1000

M

EXPeriment

00 0.5 1 1.5 2 2.5 3

Deflection (cm)

ELS

Deflection (cm)

Verification Example of Steel StructuresVerification Example of Steel StructuresSteel Composite Beam under Four-Point Loading

610mm

64mm

1118mm

64mm

610mm

64mm

1118mm

64mm

W16* 6

64mm

W16* 6

64mm

Shear stud 20 mm Shear stud 20 mm 150mm 150mm

W16* 6

64mm

W16* 6

64mm

Shear stud 20 mm Shear stud 20 mm 150mm 150mm

B1 B2B1 B2

L/3 L/3 L/3

L= 2.44m

Verification Example of Steel StructuresVerification Example of Steel StructuresSteel Composite Beam under Four-Point Loading (B1)

30000

35000

20000

25000ad

(kg)

5000

10000

15000Loa

0

5000

0 0.5 1 1.5 2 2.5 3 3.5

Deflection (cm)

EXP ELS

Verification Example of Steel StructuresVerification Example of Steel StructuresSteel Composite Beam under Four-Point Loading (B2)

35000

40000

20000

25000

30000

(kg)

10000

15000

20000

Load

0

5000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deflection (cm)

EXP ELS

Verification Example of Steel StructuresVerification Example of Steel StructuresHybrid Steel Girder with Longitudinal and Transverse Stiffeners

50 mm

7000 mm

Longitudinal Stiffeners900 mm

200 mm

4.50 mm

15 mm

Transverse Stiffeners

o g tud a St e e s

Verification Example of Steel StructuresVerification Example of Steel StructuresHybrid Steel Girder with Longitudinal and Transverse Stiffeners

1000

1200

Deflection Pattern obtained by ELS (elevation).

600

800

plie

d lo

ad (K

N)

Deflection Pattern obtained by ELS (plan)

200

400Ap

ELSExpe

00 20 40 60 80 1

Deflection (mm)

L t l t i l b kli b d i th i tLateral torsional buckling observed in the experiment

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