Aircraft Impact 

Analysis of the 

WTC Towers 

NIST Symposium 

September 14, 2005 
Silicon Valley Office (SVO) 

2 

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 
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 
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

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Floor: 

84

85

78

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Floors 81 & 82, Side 300 

Floors 78-81, Side 400 
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WTC Tower Model Parameters 
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 
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)] 

Fine Brick Element Model Coarse Shell 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 

Connection: Merged Spandrels Spandrels Plates 
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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) 

Coarse

Mesh 

(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
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 
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: 

Fn 

1 

(X1 , Y1 , Z1 

n n n ) 

F

2 

m 

F

2 

m-1 

F

2 

m-2 

F

2 

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 
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 
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: