aircraft impact analysis of the wtc towers
TRANSCRIPT
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Aircraft Impact Analysis of the WTC Towers
NIST Symposium September 14, 2005
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Aircraft Impact Analyses Introduction
Material Constitutive Modeling
Component Analyses
Subassembly Analyses
Global Analyses
Material Testing
Observables
Very Fine (~0.01 in)
Coarse (~1-10 in.)
Very Fine (~1 inch)
Coarse (~100 feet)
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Aircraft Impact Analyses Objectives Perform aircraft impact analyses to
obtain: 1. Structural damage to the WTC towers
produced by aircraft impacts. 2. Estimates of jet fuel distribution. 3. Estimates of debris distribution. 4. Environment for fireproofing removal. 5. Analysis of uncertainties in results.
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Aircraft Impact Analyses Outline Part 1 Material Constitutive and Failure Modeling
Part 2 WTC Tower Model Development
Part 3 Aircraft Data Collection & Model Development
Part 4 Component Impact Analyses
Part 5 Subassembly Impact Analysis
Part 6 Analysis of Aircraft Impact Conditions
Part 7 Component/Subassembly Uncertainty Analyses
Part 8 Global Impact Analyses
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Part 1 Material Modeling Tower steel constitutive modeling Aircraft material models Concrete material models Weld and connection failure models
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Steel Constitutive Model Piecewise Linear Plasticity
Model Yield stress dependence:
strain rate plastic strain
Strain rate effects Cowper & Symonds rate
effects model used. High-rate data provided
by NIST.
Models validated against NIST material test data.
Yield Stress Variation with Effective Plastic Strain
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Material Model Validation ASTM-A370 Tensile Specimen Model
Grip Test Sample
Fine Mesh
Analysis of Material Testing Used to Validate the Constitutive Models
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ASTM-370 Tensile Test Analysis Fine Mesh: 0.3 mm spacing
Plastic Strain
Analysis of a Material Test Including Necking and Failure
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Material Model Validation ASTM-A370 75 ksi Tensile Test Comparison
Procedure: Develop true
stress-strain curve.
Simulate material testing.
Validate the model against engineering test data.
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Validated True Stress-Strain Curves
Constitutive Model Input for Mechanical Behavior
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Mesh Refinement Effects Tensile Test for 75ksi Steel
Coarse Shell Element Mesh
Fine Mesh Necking Behavior
Coarse Mesh Necking Behavior
Mesh Effects on the Failure Strain
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Strain Rate Effects Cowper and Symonds Model
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True Stress-Strain Curves Aircraft Aluminum Alloys
Developed From Open Source Data
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Lightweight Concrete Model Pseudo-tensor model selected for this program:
Good for low-confinement modeling. Tabular rate effects modeling - fit to data in literature sources. Damage with softening and various failure/erosion options.
Pseudo-tensor model was calibrated using a simulation of an unconfined compression specimen.
Unloaded 2% Displacement
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Weld Zone Modeling
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Exterior Column Bolt Modeling
Strength of the bolted connections is important for damage analyses.
Detailed models of the bolts not feasible beyond component level analyses
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Exterior Column Bolt Modeling
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Part 2 WTC Tower Model Development
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Automatic Model Generation Excel Visual Basic Tool Reads LERA database for
dimensions Capabilities:
Exterior wall generation. single panel subassembly global
Core Column Generation Automatically inserts
bolts and boundary butt plates.
Controls mesh refinement for different regions
Approach selected to reduce the potential for model errors.
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Exterior Panel Auto Generation Panel Type 300-307
300 panel model shown
Panel Type 400-401
400 panel model shown
Parameterized models developed for panel types. Parameters automatically extracted from database.
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WTC 1 Impact Face Model
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Spandrel Splice Connections
Placement of Splice Connections
Connection Details
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Tower Model Development Core Columns: Floors 95-97
42 ksi columns: shown as orange
36 ksi columns: shown as purple 50 ksi columns: shown as red
Dimensions and Materials Extracted from the Database
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Tower Model Development Connections are weak points
for lateral impacts. Wide Flange to Wide Flange
Splice. Connection made with tied
interface between splice plates and column ends.
Splice Plates
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Tower Model Development Box Column to Wide Flange Splice
Connection made with tied interface between column cap on BC and column end of WF
Column Cap/Splice Plate
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Tower Model Development Core Floor Structure for 96th Floor
With Floor Slab Without Floor Slab
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Tower Model Development: Core Connection Details
Perimeter Beams Connected with Splice Plates
Splice Plates at Column Connections
Node-to-Surface Tied Interface at Floor Beam Connections
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Tower Model Development: Core
With Floor Slabs
Floor 94
Floor 95
Floor 96
Floor 97
Floor 98
Note: Different Colors Correspond to Different Material Assignments
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Tower Model Development: Truss Floor
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Tower Model Development: 96th floor of WTC 1
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Tower Model Development: 96th floor of WTC 1 including interior contents
96th Floor Used as a Representative Floor Plan
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Tower Model Development: 96th floor of WTC 1 including interior contents
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Tower Model Development: 96th floor of WTC 1 including interior contents
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WTC 1 Global Tower Model
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WTC 2 Global Tower Model
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WTC 2 Global Tower Model Exterior Removed
Detailed floor sections placed only where needed, farfield model elsewhere:
83
81
82
80
79
Floor:
84 85
78 77
Floors 81 & 82, Side 300
Floors 78-81, Side 400
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WTC Tower Model Parameters
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Part 3 767 Model Development
Data collection for the 767-200ER Development of aircraft model Fuel Distribution Analysis
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Aircraft Model Development: Boeing 767-200ER
Commercially Available Geometry Models
Airline Data
Open Literature Data Sources
Aircraft structural information collected from various sources.
Remaining data was obtained from measurements on 767.
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Digimation Surface Model Surface Model
(CAD geometry overlaid) Tail Modified to match
CAD Drawings (www.boeing.com)
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Aircraft Inspection: Main Landing Gear
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Aircraft Inspection: Ultrasonic thickness measurement of landing gear components
Main landing gear beam
measurement locations
Nose gear measurement
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Aircraft Inspection: Control Surfaces and Control Linkage
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Passenger and Cargo Data From United and American Airlines
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Engine Modeling: PW4000 Materials Received from Pratt & Whitney:
PW4000 94 Inch Fan Secondary Flow and Lubrication Systems (CTC29748.20001020)
The Jet Engine (S14345) PW4000/B747/767/
External Components Left Side (J38249)
PW4000/B747/767/ External Components Right Side (J38249)
PW4000 Engine Build Groups (ref. W058)
PW4000 94-Inch Fan Engine (S12049)
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Engine Model
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Boeing 767-200ER Aircraft Model
Finite Element Model of the Boeing 767-200ER.
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Fuselage Structure and Wing Integration
Wheel Well Pressure Deck
Wheel Well Bulkhead
Front Spar Bulkhead
Main Landing Gear Wheel Well
Center Wing
Rear Spar Bulkhead
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Aircraft Model Internal Structure and Non-Structural Components
Floor Structure and Seats
Main Landing Gear Beam
Cargo Containers
Engine Strut
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Boeing 767-200ER with Estimated Wing Deflection at Time of Impact
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Fuel Tank Capacities and Locations
Fuel was located in the Main Fuel Tanks only at the time of impact. (United and American Airlines Correspondence)
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Fuel Tank Capacity and Fuel Distribution
Wing Buttock Line
(WBL) 6°
Tank capacity to Baffle Rib 18 is approximately the same volume as the fuel onboard at the time of impact.
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Boeing 767-200ER with Fuel Load at Time of Impact
Baffle Rib 18
Baffle Rib 5
Dry Bay
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Boeing 767-200ER Aircraft Model Parameters
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Part 4 Component Impact Analyses Exterior columns, core columns, and floor
assembly components.
Engine and wing section impactors.
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Component Level Analyses Primary objective is to develop the simulation
techniques required for the global analysis of the aircraft impacts into the WTC towers. Develop reduced FE models appropriate for high fidelity global
impact analyses.
Primary Component Simulations: An exterior column impacted by an aircraft engine. An interior column impacted by an aircraft engine. An exterior column impacted by an aircraft wing segment. An exterior column impacted by an aircraft wing filled with fuel.
Additional Component Simulations: Floor system with concrete slab obliquely impacted by an engine. Bolted column and spandrel connections.
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Preliminary Component Analyses Detailed brick element column model. Shell elements for wing and fuel tank
section. Fuel effects included.
Lagrangian fuel model.
Failure modes of column analyzed. Model uses first estimate of material
properties 60 ksi yield Bilinear E-P column 42 ksi yield Bilinear E-P spandrel 30% failure strain
Fringes of Effective Plastic
Strain.
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Preliminary Component Analysis Failure modes of column analyzed.
Shear failures of front plate. Subsequent shear failure of back plate.
Fringes of Effective Plastic
Strain.
Fuel overloads column welds Subsequent analyses have no fuel for
more subtle column response.
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Component: External Column Response Comparison [Displaying Contours of Resultant Displacement (m)]
Coarse Shell Element Model Fine Brick Element Model
Left View at 35 ms
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Core Box Column Impact Model Comparison
[Displaying Contours of Resultant Displacement (m)]
Left View at 35 ms
Coarse Shell Element Model
Fine Brick Element Model
Modeling Considerations Column 801B, 77-80 Modeled Impactor: Wing section with
fuel Standard Fuel density 250 m/s impact
(est. WTC 2 impact speed) Impact on flange side
WTC-B impact scenario for 801B
BC treated by fixing ends of long column
V = 250 m/s
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Engine & Exterior Wall Three Panels Wide Spandrel Centered Impact
Initial Configuration Impact Response at 40 ms Impact Response at 80 ms
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Engine & Exterior Wall
Spandrel Centered Impact
Impact Response at 80 ms
Between Spandrel Impact
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Spandrel Splice Plate Model
t = 75 ms
Plastic Strain
Merged Spandrels Spandrels Plates Connection:
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Engine & Exterior Wall
Comparison of Various Engine Impact Conditions
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Engine Impact Analysis
Combined Engine Impact Analysis – Exterior and Core Columns
Initial Configuration Impact Response at 90 ms
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Engine Impact Analysis
Combined Engine Impact Analysis – Exterior and Core Columns
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Wing Segment Component Analysis Two Exterior Panels
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Wing Segment Component Analysis Two Exterior Panels
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Wing Segment Component Analysis
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Empty Wing Section Impact 442 mph
Initial Configuration Impact Response at 40 ms
Coarse Shell Element Wing Section Model
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Wing Segment Component Analysis Coarse Mesh
(Front)
CoarseMesh (Back)
Fine Mesh
(Front)
Fine Mesh (Back)
Effective Plastic Strain
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Treatment of Aircraft Fuel Fluid Structure Interaction (FSI) is difficult to
model with traditional computational methods and requires special analysis techniques.
FSI approach needs to capture: Primary inertial affects of fuel impacting structural
members. Secondary fuel dispersion.
3 Options for this program: Arbitrary Lagrangian-Eularian (ALE). Smoothed Particle Hydrodynamics (SPH). Lagrangian analysis with erosion (traditional approach).
Cannot solve fuel motions after initial impact.
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Fuel Analysis Methodologies ALE - Eulerian treatment of fuel with Lagrangian structural
components. Fluid motion represented with Euler equations (inviscid
Navier-Stokes). Appropriate methodology for analysis of continuous
fluid dynamics. Large meshes are required for ALE fuel modeling.
Longer run times are required. SPH - Mesh-Free model of fuel with Lagrangian structural
components. Smaller mesh is required: shorter run time. SPH well suited for debris cloud calculations.
Neither methodology includes physics of droplet formation, wetting of structures, or fuel combustion.
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Wing Segment with ALE Fuel V = 500 mph
AVI
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Wing Segment with SPH Fuel V = 500 mph
AVI
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Wing Segment with Fuel Comparison V = 500 mph
SPH ALE
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Part 5 Subassembly Impact Analyses
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Tower Subassembly Model
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Subassembly Engine Impact
Initial Configuration
Impact Response at 0.25 s
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Subassembly Engine Impact
Engine deceleration produced by the interaction with: Exterior wall Truss floor Internal contents Core Column
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Subassembly Engine Impact
Impact Configuration
3 ksi concrete damage
4 ksi concrete damage
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Subassembly Wing Impact
Initial Configuration
Impact Response at 0.10 s
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Subassembly Impact Analyses
Comparison of Engine and Fuel Momentum Transfer
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Part 6 Analysis of Aircraft Impact Conditions
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Definitions of the Aircraft Impact Parameters
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Analysis of Aircraft Impact Conditions Video footage of the aircraft impacts were first used to
assess the impact conditions Two videos of WTC 1 Seven videos of WTC 2.
A complex video analysis technique was first applied to generate initial estimates of orientation and location.
Estimates from the video analysis were refined using the visible damage on the impact face of the towers.
Aircraft speed was determined using a simplified video analysis.
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Analysis of Aircraft Impact Conditions
Complex Motion Analysis Methodology:
Location of the object along the vector not
known.
Step 1:
n F1 (X1 , Y1 , Z1 ) n n n
F2 m
F2 m-1
F2 m-2
F2 m+1
Camera No. 2
Camera No. 1
Intersect vector from one camera with data from a second camera.
Step 2:
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Analysis of Aircraft Impact Conditions
Simplified Motion Analysis Methodology:
Image 1 Image 2
Image 3
d34
L3
L4
Image 4
Speed = (Actual plane length)(Image Rate) (L3+L4)/2
(d34)
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Refinement of the Aircraft Impact Orientation and Location Damage pattern on the external panels was used
to determine the impact location, orientation and trajectory within the bounds of the video analysis.
Impact locations for the engines, wing tips and and tip of the vertical stabilizer is most clearly seen in the impact damage.
Relative locations of wing, engine, and tail strike place constraints on possible combinations of orientation and trajectory.
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Schematic of Impact Damage – WTC 1
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WTC 1 – Baseline Impact conditions vertical angle = 10.6, lateral angle = 0
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Schematic of Impact Damage – WTC 2
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WTC 2 Impact Conditions vertical angle = 6, lateral angle = 13
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Aircraft Impact Conditions
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Part 6 Uncertainty Analyses Component Uncertainty Analyses Subassembly Uncertainty Analyses
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Component-Level Uncertainty Analyses
Engine-Core Column
Wing Segment – Exterior Panel
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Parameter Variation Engine – Core Column
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Experimental Design Engine – Core Column
Fractional Factorial 213-9 Experimental Design
Measures of Core Column Damage
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Parameter Variation Wing Segment – Exterior Panel
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Main Effects Plot Wing Segment – Exterior Panel
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Engine-Subassembly Uncertainty Analysis
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Significant Modeling Parameters for the Global Impact Analysis
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Part 7 Global Impact Analyses
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Global Impact Analyses
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Global Impact Analyses WTC 1 WTC 2
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Global Impact – WTC 1
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Global Impact – WTC 1
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Global Impact – WTC 2
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Global Impact – WTC 1
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Aircraft Breakup and Momentum Loss – WTC 1
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WTC 1 Core Column Damage
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WTC 1 Floor Slab Damage
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WTC 1 Fuel/Debris Distribution
(Floor slab removed from view)
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WTC 1 Fuel/Debris Distribution Floor 94
Initial impact configuration
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WTC 1 Fuel/Debris Distribution Floor 94
Calculated impact response
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WTC 1 Fuel/Debris Distribution Floor 94
Calculated impact response (fuel removed)
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WTC 1 Fuel/Debris Distribution Floor 94
Calculated aircraft debris
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Impact Damage on the Tower Exterior Impact Face
WTC 2
Schematic of actual damage
Calculated damage
WTC 1
Schematic of actual damage
Calculated damage
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Input Parameters for Additional WTC 1 Global Impact Analyses
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Calculated WTC 1 Core Damage
Calculated less severe impact damage Calculated more severe impact damage
Calculated base case impact damage
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WTC 1 Exterior Damage Comparison
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Input Parameters for Additional WTC 2 Global Impact Analyses
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Calculated Core Impact Damage to WTC 2
Calculated less severe impact damage Calculated more severe impact damage
Calculated base case impact damage
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Exterior Wall Damage Comparison for WTC 2
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Summary Component, subassembly and global aircraft impact
analyses were performed on WTC 1 and WTC 2.
Global impact damage comparisons with available observable evidence was good.
Predictions of damage to the tower core columns: