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

April 22nd, 2008 Agenda Applied Element Method as a Practical Tool for Progressive Collapse Analysis of Structures April 22nd, 2008 8am PDT (Los Angeles) / 11am EDT (New York) / 4pm BST (London)

Welcome & Introduction (Overview of NAFEMS Activities) Matthew Ladzinski, NAFEMS North America Applied Element Method as a Practical Tool for Progressive Collapse Analysis of Structures Dr. Hatem TagelTagel--Din,Din, Applied Science International, LLC Q&A Session PPlanel Closing

Ladzinski Tagel-Din www.nafems.org THE INTERNATIONAL ASSOCIATION FOR THE ENGINEERING ANALYSIS COMMUNITY

An Overview of NAFEMS NA Activities

Matthew Ladzinski NAFEMS North American Representative

www.nafems.org Planned Activities in North America ¾Webinars New topic each month! Verification & Validation (V&V): Quantifying Prediction Uncertainty and Demonstrating Simulation Credibility (May 15) Managing FEA in the Design Process (June) Recent webinars: AUTOSIM: The Future of Simulation in the Automotive Industry A Common Sense Approach to Stress Analysis and Finite Element Modeling The Interfacing of FEA with Press ure Vessel Design Codes (CCOPPS Project) Multiphysics Simulation using Directly Coupled-Field Element Technology Methods and Technology for the Analysis of Composite Materials Simulation Process Management Simulation-supported Decision Making (Stochastics) Simulation Driven Design (SDD) Findings

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www.nafems.org Applied Element Method as a Practical Tool for Progressive Collapse Analysis of Structures

Hatem Tagel-Din Applied Science International, LLC Contents

• Definition of Progressive Collapse • Problem Statement • Why AEM? • AEM Theory • Modeling Advantages of AEM compared to FEM • AliAdtAnalysis Advantages of fAEM AEM compare dtFEMd 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 Î to reduce the potential for progressive collapse through:

1) Redundancy for ensuring alternative load paths 2) Structural Continuity and Ductility 3) Capability of resisting load reversals 4) Capability of resisting shear failure Definition of Progressive Collapse GSA Code: Analysis

Remove a vertical supporting element from the location being considered (first floor on ly ) an d con duc t a sttitatic or d ynami c anal ysi s fthtfor the struct ure.

Exterior consideration Interior consideration Definition of Progressive Collapse GSA Code: Analysis

1) Maximum Allowable Collapse Area: Problem Statement

• Given: – Structural full geometry – Full reinforcement detailing – Material properties – Threat type (B omb , car colli s ion, fire, element removal.) • Questions: – Will the structural collapse or not? – Is it partial or total collapse? – Which part will fail and how? – What is the footprint of the collapsed structures? – What are the effects of falling debris on adjacent structures? Why AEM? Why AEM? Methods for Structural Analysis

• Finite Element Method (FEM) • Boundary Element Method (BEM) • Finite Difference Method • Discrete Element Method (DEM) • Discontinuous Deformation Analysis (DDA) • Truss Method and Lattice Method • Strut and Tie Method • Spring Network Method • Finit e S ecti on M eth od • Rigid Body and Spring Method (RBSM) • Mesh-Free Methods Why AEM? FEM/DEM Comparison

Collapse History MM MM

Cracking, Yield, Buckling, Post- Element Debris falling as Linear Collision Crushing Buckling Separation Rigid Bodies ced FE ified FE nn ll Adva Simp Continuum Discrete

FEM Can not be Automated

Accurate Problems with Static analysis and continuum materials Reliable DEM Not reliable Why AEM? Analysis of Oklahoma City Building Using Advanced FEM Why AEM? Advantages of AEM compared to FEM

• Analysis Advantages – Ana lys is i s as si mpl e as th e si mplifi ed FEM and as accurat e as th e advanced FEM. – Output includes stresses, strain and internal force diagrams – Automatic yield and cut of reinforcement bars – Automatic element separation and contact detection – Automatic plastic hinge formation – Au toma tic el ement colli si on • Modeling Advantages – Physical elements – MhMuch eas ier meshi ng – Easier modeling of reinforcement bars – Realistic and Easier modeling for Steel Structures Why AEM?

Complexity, Accuracy, Time and Qualifications of User tions ns uu oo

Progressive Collapse Analysis e Soluti near Sol ll ii

Engineering Judgment, Uncertainty and Construction Cost Simp hly Nonl gg

FEM Hi Simplified FEM Gap Advanced FEM Performance Based Design Not verified

AEM Why AEM? Analysis of Oklahoma City Building Using AEM Why AEM? Analysis of Oklahoma City Building Using AEM AEM Theoretical Background Element Discretization

Material Springs

The continuum is discretized into elements connected together with nonlinear sppgrings that rep resent the material behavior

The springs represent axial deformations as well as shear deformations AEM Theoretical Background Connectivityy( (Matrix Sp ring s)

Volume Element 1 Element 2 Z Y represented by springs x

Element 1 Element 1 Element 1

Normal Springs Shear Springs x-z Shear Springs y-z AEM Theoretical Background Connectivityy( (Reinforcement S prin gs )

Z Y Element 1 Element 2 Reinforcing bar x

Element 1 Element 1 Element 1

Normal Sppgrings Shear Sppgrings x-z Shear Sppgrings y-z AEM Theoretical Background Connectivityy( (Steel Sections )

2 ways for modeling a steel section

Implicit Steel section Explicit Steel section

Steel Elements Vacuum cells AEM Theoretical Background Connectivityy( (Matrix S prin gs )

Steel Springs AEM Theoretical Background Connectivityy( (Matrix S prin gs )

Steel Springs

concrete

Concrete Sppgrings AEM Theoretical Background Masonryyg Walls Modeling

Mortar

Brick

Mortar

Concrete AEM Theoretical Background Masonryyg Walls Modeling

Brick Sppgrings

Mortar Springs Concrete Springs AEM Theoretical Background Degrees of Freedom

Normal Normal

Shear x-z Shear x-z Shear x-y

Shear x-y Normal

Translation Rotation AEM Theoretical Background Assembly of Overall Stiffness Matrix

12 x 12 stiffness matrix

Elements directly affect each other

OllStiffMtiOverall Stiffness Matrix AEM Theoretical Background Equation of Motion

[]M {}Δ&y&i + []Ci {}Δy& i + []Ki {Δyi }= {ΔFi } Incremental Equation of Motion

requested Step-by-step integration (Newmark-beta) method Acceleration {}{}Δy& i = &y&i Δt + γ Δ&y&i Δ {}t yoo(t +Δt) 1 2 2 i {Δyi }= {y& i }Δt + {&y&i }Δt + β{Δ&y&i }Δt 2

Δt

Time ti ti +θ Δt AEM Theoretical Background Material Models ((Concrete under axial stresses)

Tension Fully path-dependent model for concrete Compression (Okamura and Maekawa, 1991) AEM Theoretical Background Material Models ((Concrete under Shear Stresses)

Before Cracking After Cracking

Friction and interlocking AEM Theoretical Background Material Models ((Steel under axial stresses)

Tension Fully path-dependent model for reinforcement Compression (Ristic et al, 1986) AEM Theoretical Background z Material Models ((Cracking Criteria)

τxz σx τyz τxy σy y zy τyx τ

τzx σz x z

τxz σx τyz σy τxy y τyx τzy τzx σz Plane of major x principal stress AEM Theoretical Background Cut of Rebar

VonVon--MissesMisses Criteria applied for Ultimate Strength Bar resists only Normal and shear forces No Flexural rigidity at the time-time-beingbeing

V N

FilFailure envel ope

2 2 2 ⎛ N ⎞ ⎛ V ⎞ ⎛ M ⎞ ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ = 1 ⎝ NP ⎠ ⎝ VP ⎠ ⎝ MP ⎠ AEM Theoretical Background Types of Contact

Corner-Ground Type Edge-Edge Type Corner-Face Type AEM Theoretical Background Collision Springs

Falli ng Element

Normal and shear springs are created

Shear spring in y Shear spring in X Normal Spring AEM Theoretical Background FEM/AEM Comparison

FEM AEM Full nodal compatibility

DDfeforma tions ins ide e lemen ts DfDeforma tions ou tidtside e lemen ts

Deformations in surface springs AEM Theoretical Background FEM/AEM Comparison

FEM AEM

8 nodes x 3 DOF Î 24 DOF/ Element 6 DOF/ Element AEM Theoretical Background FEM/AEM Comparison

16 17 18 19 20 9 10 11 12 9 10 11 12

11 12 13 14 15 5 6 7 8 5 6 7 8

6 7 8 9 10 1 2 3 4 1 2 3 4

1 2 3 4 5 FEM AEM Elements compatible at nodes Elements are connected through (moves together there) their faces For example Node 13 connects For example elements 6,7,10,11 Elements 6,7,10,11 are not compatible in deformations Deformations are inside the Deformations are localized at the eltlements faces of the elements AEM Theoretical Background FEM/AEM Comparison

FEM AEM

No Connectivity Connectivity included AEM Theoretical Background FEM/AEM Comparison (Transition Elements)

FEM AEM

There should be transition There is no need for the transition elements between large elements elements between large elements and small elements and small elements Modeling Advantages of AEM compared to FEM Modeling Advantages of AEM compared to FEM Easy Element Connectivity

Easy Mesh Generation Modeling Advantages of AEM compared to FEM Easy Element Connectivity

FEM AEM

Auto meshing of elements connectivity

Difficult meshing and For Compatibility Merge Nodes of Slab and Column Modeling Advantages of AEM compared to FEM Easy Element Connectivity

Concrete Slblab

Girder

W in do w Fra me olumnolumn CC Brick Wall

G lass Window Modeling Advantages of AEM compared to FEM Easy Element Connectivity

FEM AEM

Difficult meshing Between wide Connection of andthid thin el ement s Elements Through Interfaces Modeling Advantages of AEM compared to FEM Easy Modeling of Steel Structures Modeling Advantages of AEM compared to FEM No Need for Gap Elements

AEM Shell Elements Solid Elements

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

In AEM, link between a column and a footing is automatically defined at Springs Modeling Advantages of AEM compared to FEM Easy Modeling of Reinforcement Details Analysis Advantages of AEM compared to FEM Analysis Advantages of AEM compared to FEM Analysis Iterations using Simplified FEM

Remove a vertical support

CdtConduct a s ttidtatic or dynam ic ana lilysis

No DCR exceeded in any member? yes The member is DCR exceeded yes based upon shear considered a failed member force ? Failed members No should be removed from the yes Flexural DCR ratio model, and all Place a hinge at exceeded in a dead and live the member’s end member end ? loads associated with failed No members should At inserted hinge , apply be redistributed to equal-but-opposite Flexural DCR values the other members in adjacent bays moments whose for both ends of a yes The member is magnitude should equal member, as well as considered a the expected flexural span itself, are failed member strength exceeded ?

No

Calculate collapsed area End Analysis Advantages of AEM compared to FEM No Need for Analysis Iterations using AEM

Remove a vertical support

Conduct a dynamic analysis

Calculate collapsed area End Analysis Advantages of AEM compared to FEM Manual Formation of Plastic Hinges using Simplified FEM

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

2-Both Moment-curvature and Moment-rotation relations in such a case should be estimated by the user before analysis 3-The user should be a qualified engineer

Predefined Plastic Hinges Moment-Curvature Analysis Advantages of AEM compared to FEM Automatic 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.

Plastic hinge at maximum +ve moment

Plastic hinge at maximum -ve Plastic hinge at maximum -ve moment moment

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 cells.

3-Preprocessing time in SAP is longer than ELS. Post processing time is equal in SAP and ELS. Analysis Advantages of AEM compared to FEM Automatic Formation of Plastic Hinges Analysis Advantages of AEM compared to FEM Automatic Formation of Plastic Hinges Analysis Advantages of AEM compared to FEM Comparison between Progressive Collapse Analysis using AEM and FEM

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

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

(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 Î Time consuming and not accurate

(4) In AEM, Plastic hinge formation, failure and collapse of members is automated Î Advantage of AEM Analysis Advantages of AEM compared to FEM Localization of Failed Areas

Cracking and Mechanisms Progressive Collision and Plastic Hinges Formation and collapse of Progressive Formation Elements Failure Elements collapse of Parts of Structures

Automatic prediction in one analysis Analysis Advantages of AEM compared to FEM Effects of Reinforcement Bars

0 0 0.5 1 1.5 OClOne Column removed -5 Bottom RFT= 82% of LEFEM design

-10

n (cm) 76% oo -15 71% No collapse 63% -20 Floor Deflecti 50% -25 Collapsing 44% & Non-continuous Bottom RFT -30 Time (Seconds)

Amount of additional RFT Strengthened Girders (calculated as a percentage of RFT (above collapsed columns) based upon elastic analysis after element removal) Analysis Advantages of AEM compared to FEM Internal Force Diagrams Through Integration of Stresses Analysis Advantages of AEM compared to FEM Internal Force Diagrams Through Integration of Stresses Analysis Advantages of AEM compared to FEM Damage assessments due to column removal

P P.6 Q R

Highly 6 6 cracked zones 7 7

Case (1)

8 8 Case (2)

8.3 8.3 Case (3)

9 9

P P.6 Q R

Collapse of Column Q-6 Analysis Advantages of AEM compared to FEM Damage assessments due to two column removal

P P.6 Q R

6 6

7 7

Case (1)

8 8 Case (2)

8.3 8.3 Case (3)

9 9

P P.6 Q R

Collapse of Columns Q-6 and R-6 Analysis Advantages of AEM compared to FEM Damage assessments due to column removal

11270 11270

2074 2074 847847847847 847 847 847 847 33333333 33333333 3728 3728 3728 3728 3728 3728 3728 3728 10822 10822 11063 11063 4481 4481 5160 5160 5160 5160 5160 5160 5160 5160

12269 12269 Bending Moment Just After Column Collapse Analysis Advantages of AEM compared to FEM Visual Damage Assessments Analysis Advantages of AEM compared to FEM Visual Damage/Non -Structural Components Analysis Advantages of AEM compared to FEM Visual Damage/Automatic Contact Detection

Earthquake Direction Verification Examples Verification Examples Charlotte Coliseum, North Carolina

Demolition Scenario Verification Examples Charlotte Coliseum, North Carolina

AEM Model Verification Examples Charlotte Coliseum, North Carolina

1 2 3 4 Verification Examples Charlotte Coliseum, North Carolina Verification Examples Sheraton Hotel, Raleigh North Carolina

Layout Verification Examples Sheraton Hotel, Raleigh North Carolina

AEM Model Verification Examples Sheraton Hotel, Raleigh North Carolina

1 2 3 Verification Examples Sheraton Hotel, Raleigh North Carolina Verification Examples Stubbs Tower, Savannah, Georgia

ELS Model Verification Examples Stubbs Tower, Savannah, Georgia The removed components are shown in red Level (1) at 0.10 sec Level (1) at 1.1 sec

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

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

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 Verification Examples Stubbs Tower, Savannah, Georgia

(1) (3)

(2) (4) Verification Examples Stubbs Tower, Savannah, Georgia Verification Examples Briquetting Structure, Australia Verification Examples Briquetting Structure, Australia Verification Examples Briquetting Structure, Australia

(1) (2) (3)

(4) (5) (6) Verification Examples Briquetting Structure, Australia

200

150

orce (tons) orce 100 FF

50

0 0 5 10 15 20 25 30 Verification Example of Steel Structures Hot rolled steel beam under flexure

35

30

25

20

15 Load (Ton)

10

FEM 5 FEM ELS2

0 0123456 Displacement (cm) AEM Stress contours Verification Example of Steel Structures Concrete-Filled Tube Girder under Four-Point Loading m

mm Box (120*120 * 3384).84) 120

120mm

50mm 250mm 500mm 250mm 50mm Verification Example of Steel Structures Concrete-Filled Tube Girder under Four-Point Loading

3500

3000

2500 ) mm 2000

1500 oment (kN.c MM

1000 EXPeriment 500 ELS

0 0 0.5 1 1.5 2 2.5 3 Deflection (cm) Verification Example of Steel Structures Steel Composite Beam under Four-Point Loading

610mm 1118mm

64mm 64mm

150mm 150mm Shear stud 20 mm W16* 6 Shear stud 20 mm W16* 6

B1 B2

L/3 L/3 L/3

L= 2.44m Verification Example of Steel Structures Steel Composite Beam under Four-Point Loading (B1)

35000

30000

25000

20000 d (kg) aa

Lo 15000

10000

5000 EXP ELS

0 00.511.522.533.5 Deflection (cm) Verification Example of Steel Structures Steel Composite Beam under Four-Point Loading (B2)

40000

35000

30000

25000

(kg) 20000 Load Load 15000

10000

5000 EXP ELS

0 00.511.522.533.544.55 Deflection (cm) Verification Example of Steel Structures Hybrid Steel Girder with Longitudinal and Transverse Stiffeners

50 mm

7000 mm

LoogtudaSteesngitudinal Stiffeners 4.50 mm 900 mm Transverse Stiffeners 15 mm 200 mm Verification Example of Steel Structures Hybrid Steel Girder with Longitudinal and Transverse Stiffeners

1200

Deflection Pattern obtained by ELS (elevation). 1000

800 Deflection Pattern obtained by ELS (plan) 600 plied load (KN) load plied

Ap 400

200 ELS Expe

0 0 204060801 Deflection (mm)

LtLateral lt torsi onal lb buckli ng ob served di in th e experi ment THE INTERNATIONAL ASSOCIATION FOR THE ENGINEERING ANALYSIS COMMUNITY

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