National Institute of Standards and Techno

Technology Administration

U.S. Department of Commerce

NIST Response to the World Trade Center Di

Federal Building and Fire Safety Investiga

of 

the World Trade Center Disaster

Part IIA – Collapse Analysis

April 5, 2005
Analysis of Probable Collapse Sequence Analysis of Probable Collapse Sequence

NIST developed and used a series of rigorous and comprehensidetermine the probable collapse sequence for the WTC towers, fimpact to collapse initiation. The approach:

 Combined mathematical modeling, well-established statistical and proba

analysis methods, laboratory experiments, and analysis of visual and phevidence—significantly advancing the current state-of-the-art and telimits of current computational capabilities.

 Analyzed the complete sequence of events from aircraft impact to the sp

ignited multi-floor fires, thermal weakening of structural components, and progression of local structural failures that ultimately initiated collapse of 

 Allowed for evaluation and comparison of possible collapse sequences b

different damage states, fire paths, and structural load redistribution path

 Accounted for variations in models, input parameters, analyses, and obs

 Required use of advanced strategies for managing computational de

unprecedented analysis complexity and sophistication; adequately 

physics of phenomena essential to determining the probable collap
Critical Analysis Inter Critical Analysis Inter

-Dependencies Dependencies

Collapse Seq

Reference 

Structural 

Models 

SAP 2000 

SAP to ANSYS 

Conversion

SAP to LS-DYNA 

Conversion

Compartment Damage

Debris and Fuel 

Distribution

Fireproofing

Damage

Structural 

Damage

Gas Temperat

Time-Historie

(FSI)

Structural

Temperature T

Histories

Resolution1-4 in.10-6 s

Aircraft Impact 

Damage Analysis

LS-DYNA

Fire Dynam

Analysis (FD

Thermal Ana

ANSYS v.8

Structural Res

and Failure An

ANSYS v.8

Time scale: 10 orders of magnitudeLength scale: 5 orders of magnitude

Baseline Performance Analysis
Structural, Fire, and Thermal Analysis M

Structural, Fire, and Thermal Analysis M

• NIST simulated highly-complex structural failures and fires at the component, subsys

system levels to determine the probable collapse sequences. The models include:

• Reference structural model of a typical truss-framed floor of the WTC towers with o

elements and 166,000 degrees of freedom. 

• Reference structural model of a typical beam-framed floor of WTC towers with over 

and 35,000 degrees of freedom.

• Reference global model of WTC 1 structure with over 80,000 elements and 218,000 

freedom (with 17 flexible and other rigid diaphragm floors).

• Reference global model of WTC 2 structure with over 78,000 elements and 200,000 

freedom. 

• Structural model of a typical turbofan engine of the Boeing 767-200ER aircraft with 

60,000 elements and 100,000 nodes.

• Structural model of the Boeing 767-200ER aircraft, including engines, airframe, land

tanks, passenger cabin, and cargo bay, with over 700,000 elements and 740,000 nod

• Structural model of the WTC structure for the aircraft impact damage analysis wi

elements and 1,300,000 nodes.

• Computational fluid dynamics model of the fires and thermal environments that en

floors and 1,200,000 cells in WTC 1 and 6 floors and 900,000 cells in WTC 2. 

• Fire-structure interface model that maps the thermal environment onto and within t

model, comprising 500,000 floor elements and 300,000 column nodes per building flo

• The first four models described above were used to evaluate the baseline performanc

towers under design gravity and wind loads. They also served as reference models f

aircraft impact damage and response of the thermally-insulated WTC structures to sub
High Fidelity Aircraft Model High Fidelity Aircraft Model
High Fidelity Aircraft Models High Fidelity Aircraft Models
Wheel 

Pressu

Front SparBulkhead

Main Landing GearWheel Well

Center Wing

Rear SparBulkhead
Preliminary Aircraft Impact Damage Ana

Preliminary Aircraft Impact Damage Ana

 The impact of the exterior 

wall by an empty wing segment produces significant damage to the perimeter columns, not necessarily complete failure.

 The impact of a fuel-filled 

wing section results in extensive damage to the exterior wall panel, including complete failure of the perimeter columns.
Preliminary Aircraft Impact Damage Ana

Preliminary Aircraft Impact Damage Ana

 Engine impact against an 

exterior wall panel results in a penetration of the exterior wall and failure of impacted perimeter columns.

 The residual velocity and mass 

of the engine after penetration is sufficient to fail a core column in the event of a direct impact
Aircraft Engine Impacting Column Floor Aircraft Engine Impacting Column Floor 

Subsystem Subsystem
Engine Impact on WTC Tower Subsyste

Engine Impact on WTC Tower Subsyste
Effect of Engine Impact Location Effect of Engine Impact Location
WTC 1 Tower Model for Aircraft Impact A

WTC 1 Tower Model for Aircraft Impact A
WTC 2 Tower Model for Aircraft Impact A

WTC 2 Tower Model for Aircraft Impact A
AA 11 (WTC 1) Aircraft Impact Initial Conditions AA 11 (WTC 1) Aircraft Impact Initial Conditions

Aircraft Roll (left wing down) 20.7o 

6.2o 

Vertical Approach Angle (downward)

4.3o 

Lateral Approach Angle (clockwise)Speed Error Estimate (mph) + 30 / - 50

± 51

± 34

Best Estimate Speed (mph) 470 500 429 466 

NIST 

Simplified MIT Analysis Hart- FEMA Weidlinger

UAL 175 (WTC 2) Aircraft Impact Initial Conditions UAL 175 (WTC 2) Aircraft Impact Initial Conditions

Aircraft Roll (left wing down) 30.1o 

2.7o 0o

Vertical Approach Angle (downward)

11.7o 15o 

Lateral Approach Angle (clockwise)Speed Error Estimate (mph)

± 38

± 18

Best Estimate Speed (mph) 590 550 503 545 

NIST 

Simplified MIT Analysis Hart- FEMA Weidlinger
WTC 1 Severe Case WTC 1 Severe Case
WTC 1 Severe Case WTC 1 Severe Case
WTC 1 Aircraft Impact WTC 1 Aircraft Impact

T = 0.0 s T = 0.1 s

T = 0.2 s T = 0.5 s
T = 0.0 s 

T = 0.2 s 

WTC 2 Severe Case WTC 2 Severe Case
WTC 2 Severe Case WTC 2 Severe Case
WTC 2 Aircraft Impact WTC 2 Aircraft Impact

T = 0.2 s T = 0.5 

T = 0.0 s T = 0.1 s
T = 0.2 s 

T = 0.0 s 

Enhancements added by NIST.

Broken 

Column Longitu

Panel JuObscure
Validation of Aircraft Impact Model Pred

Validation of Aircraft Impact Model Pred

With Observations for WTC 1 With Observations for WTC 1
Validation of Aircraft Impact Model Pred

Validation of Aircraft Impact Model Pred

With Observations for WTC 2 With Observations for WTC 2
Initial Fire and Smoke Simulations: Fall 

Initial Fire and Smoke Simulations: Fall 
WTC Fire Model Validation Experiments 

Prediction of steel temperatures through fireproofing

Assess the effect of i

damage to ceiling tile 

Multiple workstation bur

validation of fire model p

Single workstation burn tests for input to fire dynamics simulator

WTC Phase 1, Test 2, West Aspirated T

Time (

0 200 400 600 

Temperature (C)

0

100200300400500600
Burn test video... Burn test video...
Multiple Workstation Burn Multiple Workstation Burn

23 ft

4ft 4 ft

TC tree

3 ft

1 ft 

5 ft

8.5 ft 20 "

equidistant openings Platform to ceiling 11 

 9 ft8.5 ftPLATFORM 2PLATFORM 1

PLATFORM 3

B 1

B 2
Multiple Workstation Burn and Simulatio

Multiple Workstation Burn and Simulatio

Large Fire Burn FDS S
Multiple Workstation Burn Results Multiple Workstation Burn Results

Excellent agreementNoise is from turbulence, b

model and the experim

Early HRR falloff in predict

small underestimate of mass

Provisional finding: FDS ca

with confidence to recrWTC fire event
Reconstru

Reconstru

of the WT

of the WT
Upper Layer Temperatures (WTC 1, Floo

Severe Case
Collection and Analysis of Photographic 

Collection and Analysis of Photographic 

Video Images Video Images

• Visual database contains:

• Well in excess of 7,000 

photographs taken by more than 185 photographers

• 150 hours of videotape from 

major media outlets and more than 20 individuals

• From the analysis of the visual 

images to date, NIST has identified significant events for WTC 1 and 2 related to aircraft impact, fire development, and building damage

• NIST has developed detailed 

mappings for the fire, smoke, and the condition of windows at several specific times for each WTC tower; work is nearing completion for WTC 7
Structural Analysis: Aircraft Damage, Th

Structural Analysis: Aircraft Damage, Th

Response, Local Failures, Collapse Initi

Response, Local Failures, Collapse Initi

• Structural response analysis posed unprecedented challenges:

• Captured complex physical mechanisms and structural state

from prior analyses.

• Captured additional physical complexities and structural state

from progression of local failures at component, connection, system levels that ultimately initiated global building collapse

• Overcame computational demands associated with integratio

complexities, analysis of highly nonlinear temperature-depenunstable mechanisms, and model size limitations.

• Adopted rigorous approach with cascading complexity to adequa

physics of phenomena essential to determining the probable coll

sequence with advanced strategies for managing computational 

• Conducted extensive and methodical sensitivity analyses at 

connection, sub-system, and system levels to identify and mmost influential physical mechanisms and associated failure 
Structural Analysis Progression Structural Analysis Progression

Component Analyses Knuckle Truss seat connections Single truss and 

concrete slab

 Full floor Column splice 

connection

 Single story column Nine story column Nine story-nine column 

exterior wall panel

Subsystem Analyses WTC 1

• Isolated Core• South Exterior Face• Floors 93 to 99

 WTC 2

• Isolated Core• East Exterior Face• Floors 79 to 83

Glob WT WT

Detailed nonlinear analyses to determine component behaviors and failure mechanisms

Nonlinear analyses with component simplifications and failure mechanism simplifications to determine major subsystem behavior and sequential failure mechanisms.

Nonlindetermbehavsequemecha
Structural Analysis: Connection Models Structural Analysis: Connection Models

• Knuckle shear connector

 Truss web members protruded above the top chord in the form of a “knuc

embedded in the concrete slab to develop composite action

 Failure modes between the concrete slab and steel knuckle for longitudin

transverse shear transfer capacity were evaluated:

• Knuckle to concrete interface was modeled as unbonded and fully bonde

• Nonlinear concrete behavior included concrete crushing

 Analysis results were validated against test results Knuckle capacity based on steel and concrete properties at elevated tem

• Perimeter column splice

 Perimeter columns were connected with a four bolt splice in the upper sto

• Bolt pretension was found to play a minor role in bolt stiffness and was no

 Failure modes of the bolts were evaluated:

• Tensile failure due to rotation or tension at column splices • Shear failure was not modeled as it was not a likely failure mode in the ex
Shear Knuckle Analysis Shear Knuckle Analysis

Crush Region in Gray
Column Splice Analysis Column Splice Analysis

Outside

Inside Face

11”

14”

Spandrel (at floor locations)

Bolts (at splice)

Column Cross Section

Not to Scale
Structural Analysis: Connection Models 

Structural Analysis: Connection Models 

• Truss-to-column connections (interior and exterior)

 Connection capacities were designed for at least 2 percent of column de Exterior truss connections had a welded gusset plate at the top chord an

the truss seat, with the gusset plate and truss seat welded to the spandre

 Interior truss connections had two bolts at the truss seat, with the truss se

a floor support beam at the edge of the core.

 Horizontal and vertical temperature-dependent capacities and failure seq

computed for 12 truss seat configurations.

 Failure modes included:

• Failure of groove weld between the gusset plate and the spandrel

• Failure of fillet weld between the gusset plate and truss top chord

• Failure of fillet weld at the truss seat-to-spandrel connection

• Tensile failure of the gusset plate• Bolt shear, bearing and tear-out failures

• Truss walking off the seat support
Truss Seat Connections Truss Seat Connections

Stand-off plates -

Seat angle

5/8 in. diameter bolt

Truss top chord

Gusset plate

Strut

Column/spandrel

Bearing angle

Channel beam

Vertical plate stiffener

Truss top chord

Strut

Bearing angle

5/8 in. dia. bolt

Exterior Seat Interior Seat
Horizontal Tensile Force Resistance of Exterio

Horizontal Tensile Force Resistance of Exterio

182

156

67

32

20C 400C 600C 700C

100 115

42

20

20C 400C 600C 700C

134 120

62

31

20C 400C 600C 700C

104 93

49

25

20C 400C 600C 700C

1411, E61

5210, E51C 

1411, E62 

5110, E52A 

1411, E61 

5110, E52B 

1411, E62 

5210, E51C 

1411, E61 

1411 

1411 

1411 

1411 

1411 

1411 

1411 

1411 

1411 

1511 

1411 

1411 

1311 

1311 

1313 

1013 1212 1212 1212 1611 1111 1111 1111 1111 1111 1111 1111 

22, E2

23, E1 

23, E2 

23, E1 

23 

23 

23 

23 

23 

22 

22 

21 

21 

20 

20 226A, 

17 17 17 17 17 15 15 

#1311, #1411, and #1511

#1013

#1212#1611#1111

For all interior seats 

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134 120

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20C 400C 600C 700C

#1313

182

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67

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20C 400C 600C 700C

182

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20C 40

Original drawing used with permission of PANYNJ
Vertical Force Resistance of Exterior Seats Vertical Force Resistance of Exterior Seats

207

184

90

41

20C 400C 600C 700C

5210, E51C

1411, E62 

5110, E52A 

1411, E61 

5110, E52B 

1411, E62 

5210, E51C 

1411, E61 

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1411 

1411 

1411 

1411 

1411 

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1411 

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1013 1212 1212 1212 1611 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111, E63 5210, E51C 1111, E64 5210, E51B 1111, E63 5210, E51A 1611, E65 5110 E53

23, E1 

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20 

20 226A, 

17 17 17 17 17 15 15 15 15, E4 17, E4 17, E3 17, E4 226A, E3 

#1411 #1511 #1311 

#1013 and #1313

#1212#1611

#1111

#20 #226A #15 and #17

#21 

#22 and #23 

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20C 400C 600C 700C

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20C 400C 600C 700C

Original drawing used with permission 
Structural Analysis: Floor Sub Structural Analysis: Floor Sub

-System M

System M

• Single truss with tributary slab section 

Detailed model to determine the response of a truss section to uniformly increasing temp

• Large deflections and inelastic buckling• Temperature-dependent steel material properties – thermal expansion, plasticity, creep, mod

strength

• Temperature-dependent concrete material properties – thermal expansion, nonlinear tensile 

strengths, and modulus

• Failure of welds, knuckles, truss seat connections, and studs on the steel straps and on the 

• Composite floor sub-system

Detailed model to determine the response of a full floor to representative thermal loads in 

towers; included:

• Simplified truss model, validated against the single truss model results• Primary and bridging trusses, deck support angles, spandrels, moment-connected core floor 

concrete floor slab

• Restraint was provided by exterior and core columns which extended one floor above and be

• Large deflections and inelastic buckling • Temperature-dependent steel material properties – creep was not included

• Temperature-dependent concrete material properties – bilinear tensile and compressive stre• Failure of connection between primary and bridging trusses; connection between long-span 
Truss Section Model Truss Section Model

Exterior End of Truss Core End of Truss

Structural Analysis: Floor Sub Structural Analysis: Floor Sub

-System Mo

System M

• Impact of floor dropping onto the floor below

 Analysis examined whether the impact of falling floor sections would severely dama

 Conditions modeled included 

• full truss section dropping to the floor below • one end of a truss section dropping to the floor below

 Dynamic response was calculated using conservation of energy and momentum prin

loss of kinetic energy during truss deformation

 Estimated floor response at room and elevated temperatures (truss seat capacity as 

temperature was included):

• All truss seats have sufficient capacity to support the weight of two floors for tempera• No truss seat failures expected for gravity plus impact loads for temperatures up to 40• At 400 oC, the interior side of the truss may walk off the interior seat after impact• At 700 oC, the failure of impacted interior or exterior seats is expected• If the impacted truss deforms to an extent that it loses composite action with large sa

it will not restrain the exterior column against transverse movement or instability
Schematic of Full Truss or Partial Truss 

Schematic of Full Truss or Partial Truss 

and Diagonal Crushing at Impact and Diagonal Crushing at Impact 

Before impact

After impact

L/4

Before impact

After impact

Schematic of full truss drop Schematic of partial truss dro

Before impact

After impact

L/4

Before impact

After impact

Schematic of full truss drop Schematic of partial truss dro
Structural Analysis: Column Sub Structural Analysis: Column Sub

-System 

System 

• Single-story exterior column

Model was evaluated for:

• Temperature-dependent steel material properties – thermal expansion, plasticity, creep, mo

strength

• Local buckling and plastic hinge formation under axial load • Post buckling strength

• Single 9-story exterior column

Model integrated behavior of single-story column and added column and spandrel splice

• Temperature dependent steel material properties - creep not included 

• Column splices (bolt shear and tensile failures and friction between butt plates)• Thermal gradients (linear through column cross section)• Column stability (effect of floor disconnection or inward pull)

Pushdown analysis was used to determine reserve capacity

• Exterior wall sub-system (3x3 panel section; 9 columns wide, 9 sto

Model integrated behavior of 9-story column to evaluate column panel behavior; include

• Spandrel temperature gradients over their depth• Spandrel splice failure 

Analysis results include:

• Spandrel splices may partially separate or spandrels may buckle at elevated temperatures 

do not affect column stability

• Instability of exterior wall columns may occur when at least three adjacent floors are discon

restrain the columns
Exterior Wall Model Exterior Wall Model

1

Y XZ

SWALL-02 

APR 

0

ELEMENTSSEC NUMUROTACEL

Floor 91

150 158

Floor 99

Y

Z

X
Structural Analysis: Exterior Wall Sub Structural Analysis: Exterior Wall Sub

-S

Model

 Models included: South face of WTC 1 (floors 89 to 106) and East face of WTC 2 (floor

on photographic evidence of column bowing

 Model features included:

• Equivalent springs at the base of the wall model to represent the floors below

• Removal of aircraft-damaged components• Post-impact column axial forces from global model • Gravity (dead/service) loads at each floor level from global model• Temperature histories applied at 10 min intervals with linear ramping between time interva• Failed truss seat connections removed at start of time interval during which failure occurre

 Floor disconnections were applied at wall-to-floor connections; they were based upon 

subsystem analysis and observations.

 Inward pull forces were applied at wall-to-floor connections; they were based upon the 

analysis and adjusted (in magnitude and extent) such that the wall subsystem results m

observed inward bowing.

 At the end of the thermal loading (6000 s for WTC 1, 3600 s for WTC 2), the gravity loa

from the global model

• Axial column forces were corrected for load redistribution from the core and other exterior • Corrective forces were applied at columns on the floors immediately above the fire region 

and WTC 2 floor 84)

 A pushdown analysis at the end of the thermal loading was conducted to determine res
Structural Analysis: Core Sub Structural Analysis: Core Sub

-System M

System M

 Models extended from below the impact and fire zones to the highest floor below the hat 

• WTC 1: floors 89 to 106• WTC 2: floors 73 to 106

 Model features included:

• Core columns, moment-connected floor beams, and concrete slab• Equivalent springs at the base of the core columns represented the structure below the mode• Removal of aircraft damaged components • Large deflections and inelastic buckling• Temperature-dependent steel material properties – thermal expansion, plasticity, creep, modu

strength

• Temperature-dependent concrete material properties – thermal expansion, bilinear tensile and 

strengths and modulus

• Post-impact column axial forces from global model were applied at floor 106• Gravity (dead/service live) loads from global model applied at each floor level• Temperature histories applied at 10 min intervals with linear ramping between time intervals

 Analyses determined core stability and deformations under impact conditions and therma

• WTC 1 core was stable under base case impact damage with severe thermal loads• WTC 1 core was not stable under base case impact damage and base case thermal loads an

northeast; the core model was restrained in horizontal directions at floors above the impact zo

through the thermal loads

• WTC 2 core was not stable for either base case or severe impact damage conditions and tilte

in both cases; the core model was restrained in horizontal directions at all floors to represent provided by the perimeter wall

• WTC 1 and WTC 2 cores did not converge under severe impact damage; no thermal loads we

 A pushdown analysis at the end of the thermal loading determined reserve capacity
Structural Analysis: Global System Mod

Structural Analysis: Global System Mod

• Global analysis without creep and plastic buckling of columns

 These models provided analysis results more quickly than the global models with creep 

buckling and provided initial insight into sub-system interactions under impact damage 

 Models extended from below the impact and fire zones to the roof level at floor 110 for 

to 110) and WTC 2 (floors 73 to 110).

 Model features included:

• Equivalent springs at the base of the core columns to represent the structure below the mo

• Removal of aircraft damaged components • Large deflection and temperature-dependent column properties – thermal expansion, plas

yield strength

• Equivalent linear-elastic floor slabs that model composite floor systems in tenant areas• Equivalent linear-elastic core floor slabs and moment connected core beams

• Hat truss members• WTC time temperature histories applied at 10 min intervals with linear ramping between tim

 Staged analysis simulated the effects of construction sequence as follow:

• Stage 1: apply dead loads up to and including floor 106• Stage 2: add members above floor 106 (including hat truss) and additional dead loads• Stage 3: add 25% service live loads• Stage 4: remove components severed by aircraft impact• Stage 5 onwards: thermal loads at 10 minute intervals with linear temperature ramp durin
Structural Analysis: Global System Mod

Structural Analysis: Global System Mod

• Global analysis with creep and plastic buckling of columns

 These models provided complete analysis results and insight into s

interactions leading to the probable collapse sequence.

 Models extended from below the impact and fire zones (floor 91 fo

floor 77 for WTC 2) to the roof level

 Additional model features included:

• Plastic buckling and temperature dependent plasticity and creep• Use of super-elements in WTC 2 for the section of the building abov

remained essentially elastic in previous analyses; any hat truss nonwas not captured 

• 3D thin-walled beam (BEAM24) was substituted for 3D linear finite 

(BEAM188) to improve column buckling behavior under thermal loa

• Effects of construction sequence not included

 7 % to 15% increase in axial forces for exterior columns 10% decrease in axial forces for core columns

 Hat truss outriggers yield strength was increased to compen

increased loads with construction sequencing

• Gravity loads were applied following removal of aircraft damaged co

prior to thermal loading
Structural Analysis: Global System Mod

Structural Analysis: Global System Mod

 Additional model features included (contd.):

• Equivalent linear-elastic floor slabs that model composite floor 

tenant areas 

• Removal of thermal expansion from the spandrels and equiva

the tenant area to avoid local buckling that affected convergenlittle influence on global collapse initiation.

• Floor thermal forces estimated from single truss with slab sect

and adjusted to match observations using wall subsystem modimposed as forces at columns.

• Floor thermally-induced disconnections estimated from full floo

disconnections due to aircraft impact damage (adjusted to maobserved damage) and thermal effects imposed at failed conn

Web site Web site http:// http://wtc.nist.gov wtc.nist.gov

Email to Email to wtc@nist.gov wtc@nist.gov

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WTC Technical Information Repository, Stop 8

Technical Information Repository, Stop 8

100 Bureau Drive, Gaithersburg, MD 20899 Bureau Drive, Gaithersburg, MD 20899-86
Background Slides Background Slides
WTC 1 Severe Case WTC 1 Severe Case
WTC 2 Severe Case WTC 2 Severe Case