Fahim Sadek, Michael A. Riley, Emil S

William Fritz, and H.S. Lew

Building and Fire Research Labo

National Institute of Standards and Tec

U.S. Department of Commerce

fahim.sadek@nist.gov

Federal Building and Fire Safety Inves

of the World Trade Center Disast

Baseline Structural Performance a

Impact Damage Analysi

June 22, 2004
Disclaimer Disclaimer

Certain commercial entities, equipment, producare identified in this presentation in order to desprocedure or concept adequately or to trace the procedures and practices used. Such identificaintended to imply recommendation, endorsemeimplication that the entities, products, materialsare necessarily the best available for the purpo
Scope of Project Scope of Project

• Baseline Performance

 Develop reference structural models of the WTC  Establish baseline performance under design lo

(gravity + wind)

• Aircraft Impact Damage

 Simulate aircraft impacts into the towers to estim

damage to structural, mechanical, and architect

 Determine the response of towers immediately 

close to collapse were the buildings immediatelimpact?)
Summary (December 2, 2003) Summary (December 2, 2003)

 Completed the development of structural data

WTC towers. Final approval shortly.

 Completed the development of reference stru

the WTC towers. Models are under review.

 Baseline performance analysis will start upon 

reference models. Progress made in defining 

towers.

 Aircraft impact analysis: Progress made in de

aircraft model, component level analysis, and 

 Simplified stability analysis of the towers is on
Summary (June 22, 2004) Summary (June 22, 2004)

 Completed the development and review of structu

WTC towers. Databases have been approved by 

 Completed the development and review of referen

models of the WTC towers. Models have been app

 Estimates of wind loading on the towers completed 

by Skidmore, Owings & Merrill (SOM), a NIST conperformance analysis is nearing completion, review 

 Aircraft impact analysis: development of aircraft m

constitutive modeling, and component level analys

Subassembly analysis and global towers models acompletion. Global analysis and sensitivity analyse

 Preliminary stability analysis of the towers nearing 
Overview of Presentation Overview of Presentation

 Results of the review of the reference structu

towers

 NIST estimates of wind loading on the towers 

review by SOM

 Status of baseline performance analysis Status of aircraft impact analysis Preliminary stability analysis of the towers: m

results
Review of Reference Structural Mo

Review of Reference Structural Mo

SOM Third-party Review

 Consistency with original design

• Random checks

 Verification/validation of models

• Review assumptions and level of detail• Perform analyses using various loading conditions 

the models

NIST In-House Review

 Consistency with original design

• Models geometry / cross section properties• Material properties

 Verification/validation of models

• Review assumptions and level of detail• Perform analyses using various loading conditions 

the models
Floor Systems: Floor Systems: Floor 96 Floor 96-A Model
Floor Systems: Floor Systems: Floor 75 Floor 75-B Model
Tower Structural System FE Models Tower Structural System FE Models 

(Global Model) (Global Model)Models include:

Core columns Exterior panels

• Foundation to floor 7• Trees (transition from 3’-4 to 10’-0 col. 

spacing)

• Floor 9 to 106• Floor 107 to roof

Hat trussRigid floor diaphragmsFlexible floor diaphragms
 Reviews indicated minor discrepancies between the de

models and the original design documents.

 Modeling assumptions and level of detail in the models 

accurate and suitable for the purpose of the project.

 Identified two areas where the models need to be modi

• The effect of additional vertical stiffness of the exte

the presence of the spandrel beams

• Modeling of the connections of the floor slab to the 

typical beam-framed floor model, where this connecfixed while the connection should be modeled as pi

 The minor discrepancies and the areas identified for mo

reported to Leslie E. Robertson Associates (LERA), a N

implemented the changes and modified the models acc

 The reference structural models have been approved b

made available for other phases of the NIST investigati

Review of Reference Structural M

Review of Reference Structural M
Modeling of Exterior Panels Modeling of Exterior Panels

Detailed shell model of exterior panel E
NIST Estimates of Wind Loads on 

NIST Estimates of Wind Loads on 

 Objective: to provide estimates of wind-induced fo

on WTC 1 and WTC 2 towers, based on the state engineering.

 NIST estimates are based on assessment of resu

and extreme wind climatological estimates conducWilliams Davis and Irwin, Inc. (RWDI) and by CermPeterson, Inc. (CPP). NIST performed independeclimatological estimates, based on airport wind spfrom the National Climatic Data Center, NOAA, anwind speed database.

 NIST estimates of wind-induced forces and mome

on RWDI results, since no results for WTC 1 are aHowever, the estimates take into account a compaand CPP results for WTC 2. 
NIST Estimates of Wind Loads on 

NIST Estimates of Wind Loads on 

 Summary Comparison by Weidlinger Associ

and RWDI Estimates

Approximate maximum base moments induced by 

Standard wind loads 

 |

My| (lb-ft) 

RWDI 2 (Table 2a) 10.1e+9 

CPP (Upper Table, p. 21) 14.0e+9 

 Both RWDI and CPP results indicate that the 

moments occur for an angle of about 210 de
NIST Estimates of Wind Loads on 

NIST Estimates of Wind Loads on 

 Review of CPP Estimates:

• NIST estimated a 720-yr, 3-s peak gust speed of 99

interpolation between speeds for 202.5° and 225°).

• CPP estimated a 720-yr, 3-s peak gust speed of 117

• CPP results overestimated wind loads by about 39% 

[(99.8/117.5)

2=1/1.386].

(a) (b)

Estimates of wind speeds with various MRIs for: (a) 202.5°, 
NIST Estimates of Wind Loads on 

NIST Estimates of Wind Loads on 

 Review of CPP Estimates:

• CPP results should be modified to account for the

by-sector approach to integrate aerodynamic and climatological data. This approach is not fully reapoint of view.

• Using a rigorous probabilistic approach, NIST sho

sector-by-sector approach underestimates wind especified mean recurrence interval.

• NIST preliminary estimates, that would need to be 

research, indicate that the underestimation is abo

• Therefore, the overall reduction factor applied to t

effects to account for overestimated wind speed aresulting from the sector-by-sector approach shou20% (1.15/1.386

≈1/1.205). 
NIST Estimates of Wind Loads on 

NIST Estimates of Wind Loads on 

 Review of RWDI Estimates:

• A comparison of RWDI results with the correc

estimates indicates that the RWDI results undmoments by about 15%. 

• The underestimation is due largely to the inco

supported assumption that wind profiles in huflatter than in non-hurricane winds. RWDI, thestimated the ratio between responses to 88 98) and 80 mph (NYBC) wind speeds to be athan about (88/80)

2=1.21. 

• Also, it is not clear that RWDI’s use of the up

method (with hurricane wind speeds weighted to their squares) leads to unbiased estimatesjustification or references were provided for tprocedure.)
NIST Estimates of Wind Loads on 

NIST Estimates of Wind Loads on 

 Summary

• Wind loads consistent with ASCE 7-02 Stand

speeds can be estimated for both towers from via multiplication by 1.15. This factor is recombaseline analysis. However, it may be that thnumber is anywhere between, 1.10 and 1.20

• More elaborate calculations and/or tests wou

They should be reported in a transparent mareadily be scrutinized and might lead to more and precise results. However, in the absence detailed information, obtaining such results is now. 
NIST Estimates of Wind Loads on 

NIST Estimates of Wind Loads on 

 Third-party Review by SOM under contract f

• “NIST recommends a wind load that is betwe

and CPP estimates. The NIST recommended approximately 83% of the CPP estimates and RWDI estimates. SOM appreciates the need reconcile the disparate wind tunnel results. It engineering estimates must be done with less desired level of information. In the absence otesting and wind engineering done to NIST spNIST has taken a reasonable approach to appropriate values to be used in the WTC However, SOM is not able to independently cprecise values developed by NIST.”
Status of Baseline Performance A

Status of Baseline Performance A

• Conduct linear static, structural analyses of eac

towers to establish their baseline performance uloads:

 Load combination 1:

• Dead loads• Live loads used in the original design of the towers• Wind loads used in the original design of the towe

 Load combination 2:

• Dead loads• Live loads according to ASCE 7-02 Standard• Wind loads estimated by NIST based on the state 

engineering

• Analyses are nearing completion. In-house and 

to start shortly.
Floor 96 Floor 96-A: Long Span Trusses A: Long Span Trusses

D/C Ratios, AISC-ASD89

0.172 0.206 0.184 0.247 0.299 0.344 0.373 0.394 0.404 0.405 0.397 0.377 0.345 

0.430 0.588 0.669 0.785 0.881 0.935 0.971 0.981 0.965 0.935 0.868 

0.993 0.906 0.563 0.791 0.470 0.951 0.386 0.810 0.302 0. 622 0.218 0.444 0.127 0.254 0.044 0.079 0.107 0.060 0.285 0.146 0.484 0.236 0.666 0

Average Truss Diagonal D/C Ratio = 0.475Maximum Deflection: 

CDL= 0.75”SDL = 0.12”LL = 1.09”Total = 1.96”
Aircraft Impact Analysis: Outline Aircraft Impact Analysis: Outline

 Material Constitutive and Failure Modelin Aircraft Data Collection and Model Devel WTC Towers Model Development Component Impact Analyses Subassembly and Global Impact Analysis
Material Constitutive and Failure M

Material Constitutive and Failure M

 Develop constitutive and failure mo

data of recovered steel (Project 3)

• Detailed finite element analysis (FEA) of 

(validation) 

 Very fine to fine mesh resolution

• Analysis of local structural response

 Fine to medium mesh resolution

• Apply to analysis of tower structural comp

 Medium to coarse mesh resolution
Steel Constitutive Modeling Steel Constitutive Modeling

 Piecewise Linear Plasticity 

Model. 

• Yield Stress Dependence:

 Plastic Strain Strain rate

• Strain rate effects:

 Cowper and Symonds rate 

effects model based on test results from Project 3

Yield St

Effect
ASTM-A370 Tensile Specimen Mod

A370 Tensile Specimen Mod

Grip Test Sample

Fine 

Mesh

Coarse Mesh
Stress-Strain Behavior Strain Behavior

Constitutive Model True Stress (42 ksi WF Core Steel)

Core wide flange yield strength:

 42 ksi nominal 50 ksi actual

Development of the true stress-strain 

behavior.

Comparison of 

calculated (Fbehavior.

Updated mode

data.
Reinforced Concrete Modeling Reinforced Concrete Modeling

 Pseudo-Tensor Model:

• Appropriate for low-confinement modeling• Tabular rate effects modeling• Damage with softening and various failure/erosion o

 Pseudo-tensor model was calibrated using a simu

unconfined compression specimen.

Unloaded 2% Displacement
Aircraft Materials Modeling Aircraft Materials Modeling

 Open literature sources used to obtain mater

significant aircraft materials 

• Aerospace Structural Metals Handbook• MIL-HNBK-5F: Metallic Materials and Elemen

Vehicle Structures
Aircraft Data Collection and Model 

Aircraft Data Collection and Model 

• Aircraft Model Development: Boeing 767-200E

 Documentary aircraft structural information Data from measurements on 767 aircraft
Aircraft Model Components Aircraft Model Components
Aircraft Model Components Aircraft Model Components

Current 767 model statistics:

 740,000 Nodes 562,000 shell elements 70,000 brick elements
Wing - Leading Edge Structures Leading Edge Structures

Inbo

a

Outboard 

LE Ribs

and Slats 

Ma

Nose beam
Landing Gear Model Landing Gear Model

Main Gear
Fuselage Structure and Wing Integration Fuselage Structure and Wing Integration

Front SparBulkhead

Main Landing GearWheel Well

Center Wing

Rear SparBulkhead
Fuel Distribution Analysis Fuel Distribution Analysis

Wing Buttock

Line

(WBL) 6°

Tank capacity to Baffle Rib 18 is approximately the samfuel onboard at the time of impact.

UAL 175

Likely fuel level 

AA 11 First Estimate: 

• Assume all fuel has flowed inboard of 

outboard baffle rib (18)

• Assume an undeformed wing shape.• Use tank capacity for fuel location. 
WTC Tower Model Development WTC Tower Model Development

• Automated mesh generation 

developed for structural systems using the electronic structural database.

 Automated mesh generation for 

exterior walls and core structures

 Automatically inserts bolts, butt 

plates, and splices

 Controls mesh refinement for 

different regions
Exterior Panel Auto Generation Exterior Panel Auto Generation

Medium

panels

med-to-med

connection

(spliced)

coarse-to-med

connection

(spliced)

Spliced 

connection

Spandrel Splices
Global Model Development Global Model Development

Core Columns: Floors 95-97 

42 ksi columns: 

36 ksi colum

50 
Global Model Development Global Model Development

• Wide Flange to Wide 

Flange Splice

 Connection modeled 

with tied interface between splice plates and column ends

Splice Plates

Drawing used with permission from Port Authority of New York and New Jersey.
Global Tower Model: Truss Floor Global Tower Model: Truss Floor

Moderate Resolution Shell Based Model 

View from Above

Beam & Shells Elements 

for Truss Structure

Smeared Concrete & Metal 

Decking Shell Model
Global Tower Model: Core Global Tower Model: Core

Core Floor Structure for 96th Floor

With Floor Slab

Without Floor Slab

Spl

at 

Co

Node-toSurface Tied 

Interface at 

Floor Beam 

Connections
Global Tower Model: Core Global Tower Model: Core

With Floor Slabs

Floor 94

Floor 95Floor 96Floor 97Floor 98

Note: Different Colors Correspond to Different Material A
Global Tower Model Global Tower Model

WTC 1 Tower Model

 Core & Exterior 

Assembled

Floors 90-101

 Impact zone plus 

extra floors above and below

Note: Different Colors Correspond to Different Material Assignments
Component Level Analysis Component Level Analysis

 Exterior and interior column impacted by 

aircraft engine

 Exterior column impacted separately by:

• Segment of an aircraft wing• Model of aircraft fuel tanks filled with fuel

 Analyses include

• Highly-detailed finite element models considering 

possible dynamic plastic fracture criteria of materials

• Coarser finite element models similar to those 

used in the global analyses
Box Core Column Impact Box Core Column Impact

Fine Brick Mo

• Modeling Considerations

 Column 801B, floors 77-80 

modeled

 Impactor: wing section with 

fuel

• Standard fuel density• 560 mph impact• Impact on flange side 

 Boundary conditions: fixing 

ends of long column

V = 560 mph
Wide Flange Core Column Wide Flange Core Column

Fine Bric

• Modeling Considerations

 Column 503A, floors 95-98 

modeled

 Impactor: Wing section with 

fuel

• Double the fuel density to 

promote more damage

• 500 mph impact • Impact on flange side

 Boundary conditions: fixing 

ends of long column

V = 500 mph
Engine Impact on an Exterior Wall Engine Impact on an Exterior Wall

 Three panels wide Spandrel centered impact Impact speed 500 mph
Engine Impact on an Exterior Wall Engine Impact on an Exterior Wall

Spandrel Centered Impact Between S

∆V = 67 mph

∆V = 56 mph
Spandrel Splice Plate Model Spandrel Splice Plate Model

• Plates are connected to 

spandrels with spot weld tied nodes

 LS-DYNA tied interface type 

7

 Spot weld approximates 

bolted connection

• Material failure severs joint, 

not interface failure

• Two materials make up the 

plate (red & green)

 Identical material 

specification but different material #

• Done for contact stability Spot welded no
Spandrel Splice Plate Model Spandrel Splice Plate Model

t = 50 ms

Connection: Merged Spandrels Span

No Spandrel failure

∆V = 67 mph

∆V = 74 mph
Wing Segment Component Analysis Wing Segment Component Analysis

Rigid

Top 

Rigid Constraint

At Floor Locations
Treatment of Aircraft Fuel Treatment of Aircraft Fuel

• Fluid Structure Interaction (FSI) is difficult to 

traditional computational methods and requanalysis techniques.

• FSI approach needs to capture:

 Primary inertial effects of fuel impacting struc Secondary fuel dispersion

• 3 options for this analysis:

 Arbitrary Lagrangian-Eularian (ALE) Smoothed Particle Hydrodynamics (SPH) Lagrangian analysis with erosion (traditional 

• Cannot solve fuel motions after initial impact.
Fuel Analysis Methodologies Fuel Analysis Methodologies

• ALE - Eulerian treatment of fuel with Lagrang

components.

 Fluid motion represented with Euler equations 

Stokes). 

• Potential for very accurate analysis.

 Large meshes are required for ALE fuel mode

• Longer run times are required.

• SPH - Mesh-Free model of fuel with Lagrang

components.

 Smaller mesh is required: shorter run time. SPH well suited for debris cloud calculations.

• Less accurate fluid flow analysis.
Wing Segment without Fuel Wing Segment without Fuel 

V = 500 mph V = 500 mph
Wing Segment with Fuel (ALE) Wing Segment with Fuel (ALE)

V = 500 mph V = 500 mph
Wing Segment with SPH Fuel Wing Segment with SPH Fuel 

V = 500 mph V = 500 mph
Wing Segment with Fuel Comparis

Wing Segment with Fuel Comparis

V = 500 mph V = 500 mph

SPH 
Floor Section Analysis Floor Section Analysis

Fine Brick Element Floor Section 
Floor Section Analysis Floor Section Analysis

Fine Brick Element Floor Section 
Subassembly Modeling Subassembly Modeling

Spandrel Centered Impact

118

121

124

Engine Impact of WTC 1 at 96t
Subassembly Modeling Subassembly Modeling

Animation View 1: perspective from outside and to si
Global Analysis Global Analysis

885365 linear shells
Global Analysis Global Analysis

Side 100

Side 400

Partitions, workstations, and cubicles added throu
Global Analysis Global Analysis

Cu
Aircraft Impact into WTC 1 Aircraft Impact into WTC 1

North

Global impact analysis of WTC 1 and 2 is ongoing
• Objectives

 Examine the overall stability of the towers wh

removed

 Study the load redistribution mechanisms wh

are destroyed by aircraft impact

 Study the response of WTC 1 when columns 

the exterior walls and columns in the core araircraft impact, and columns in the exterior ato the subsequent fires, as observed in photovideos.

Preliminary Stability Analysis of th

Preliminary Stability Analysis of th
 Steel yield and ultimate 

strengths adjusted based on Project 3 results.

 Structure below the 84th floor 

of WTC 1 removed and represented by equivalent vertical springs.

 Gravity loads represent service 

conditions and are estimated from detailed floor models.

Reduced Global Model of WTC 1 Reduced Global Model of WTC 1
WTC Tower WTC Tower 

Model Loads Model Loads

• Applied Loads:

 Full dead load,

superimposed dead load (SDL),and antenna load.

 25% of design live load. 

• Loads varied with location.

 Large variation in core area.

• Loads based on reactions from detailed SAP200

 Typical floors (85 to 106) from model of WTC 1, flo Other floors (107 to 110 and roof) from tabulated d

to model of WTC 1 floor 96.
Staged Construction Staged Construction

• Used to eliminate unrealistic loads in hat truss region 

differences between core and exterior wall.

 Approximates the method used during constructi

differential vertical deformations.

• Three construction stages:

1. Floors below hat truss

• Floors up to 106• Dead load and SDL applied

2. Hat truss

• Floors 107 through roof• Dead load and SDL applied to new members

3. Remaining loads applied

• Live load on all members• Antenna load on roof
Eigenvalue Buckling Analysis Eigenvalue Buckling Analysis

 The linear stability analysis examines the stability 

tower under service loads through floor removal column lengths) in the absence of material nonline

 Results for intact WTC 1 (no damage, no reductio

• The tower was stable when 2 floors were remov• Two core columns buckled (704, 705) when 3 flo

but the tower maintained its overall stability.

• Two additional core columns buckled (601, 608) 

removed, but the tower maintained its overall sta

• Global instability of the tower occurred when 5 fl

 Assuming that all columns at the region of remove

temperature of 600oC (0.74E), the analysis indicatfour floors would induce global instability.
Redistribution of Forces within the 

Redistribution of Forces within the 

 When columns are severed in the core, the possible 

mechanisms include:

• load redistribution to neighboring core columns throug

• load redistribution to the hat truss through tensile load

columns, or

• a combination of both.

 A two-step approach was used:

• The 96th floor model was analyzed with severed core 

equivalent vertical springs, representing the combined above, and hat truss. The analysis estimated what po

be redistributed as forces in the springs to the hat trus

would be redistributed to neighboring columns through 

• The tensile capacities of the core column splices betw

and the hat trusses were estimated to determine if the calculated tensile loads.
Redistribution of Forces within the 

Redistribution of Forces within the 

 If 15 columns are assumed severed in the co

Floor 98 Floor 101 Floor 104 

Column Load Column Load Column Load 

Column 

Number kips (kN) 

Load to 

Capacit

y

Ratio kips (kN) 

Load to 

Capacit

y

Ratio kips (kN) 

Load to 

Capacit

Ratio 

503 109.3 (486) 0.21 273.2 (1215) 0.72 437.1 (1944) 1.15 504 82.8 (368) 0.22 207.0 (921) 0.54 331.2 (1473) 1.30 505 92.7 (412) 0.24 231.8 (1031) 0.61 370.9 (1650) 1.46 506 214.7 (955) 0.41 375.7 (1671) 0.98 536.7 (2387) 1.41 603 64.6 (287) 0.25 161.5 (718) 0.63 258.4 (1149) 1.02 604 57.5 (256) 0.23 143.8 (640) 0.57 230.1 (1024) 0.90 605 72.3 (321) 0.28 180.7 (804) 0.71 289.1 (1286) 1.14 606 138.7 (617) 0.55 242.8 (1080) 0.95 346.9 (1543) 1.36 703 39.1 (174) 0.15 97.8 (435) 0.38 156.5 (696) 0.61 704 20.1 (90) 0.08 50.4 (224) 0.20 80.6 (358) 0.32 705 27.3 (121) 0.11 68.2 (303) 0.27 109.1 (485) 0.43 706 27.2 (121) 0.11 68.0 (303) 0.27 108.9 (484) 0.43 803 24.8 (110) 0.10 62.0 (276) 0.24 99.2 (441) 0.39 804 36.2 (161) 0.14 90.4 (402) 0.36 144.7 (644) 0.57 805 18.9 (84) 0.07 47.1 (210) 0.19 75.4 (335) 0.30 
Redistribution of Forces within the 

Redistribution of Forces within the 

 If 8 columns are assumed severed in the cor

Floor 98 Floor 101 Floor 104 

Column Load Column Load Column Load 

Column 

Number kips (kN) 

L/C 

Ratio kips (kN) 

L/C 

Ratio kips (kN) 

L/

Ra

Loads with all column splices intact

504 34.7 (154) 0.09 138.9 (618) 0.36 243.1 (1081) 0.9505 79.5 (354) 0.21 198.8 (884) 0.52 318.1 (1415) 1.2604 21.3 (95) 0.08 85.2 (379) 0.33 149.1 (663) 0.5605 77.0 (343) 0.30 154.0 (685) 0.61 231.0 (1028) 0.9703 45.0 (200) 0.18 90.0 (400) 0.35 134.9 (600) 0.5704 3.6 (16) 0.01 14.3 (64) 0.06 25.1 (112) 0.706 21.0 (93) 0.08 36.7 (163) 0.14 52.4 (233) 0.2903 36.2 (161) 0.09 90.6 (403) 0.36 145.0 (645) 0.5
Redistribution of Forces within the 

Redistribution of Forces within the 

 If 15 core columns are assumed severed, the fl

above the failed columns induces tension in the

tension force increases as more floor loads are columns. At a certain floor level, the splice fails below the failed splices must redistribute their lneighboring undamaged columns.

 If only 8 core columns are assumed severed, th

the columns are smaller, due to the relatively la

floor. These forces may still fail the columns at extent to which severed core columns assist in via the hat truss without failing the splices is serelative magnitudes of the floor loads and splice 
Nonlinear Analysis Nonlinear Analysis

 Nonlinear response when an estimated pattern of 

columns and spandrels in the exterior wall, and cohas occurred. 

 A series of nonlinear, plastic hinges added to the h

members to capture their post-yield behavior.

 Representative aircraft impact damage stage:

• members in the north wall of WTC 1 that were visib• an exterior panel in the south face • 8 columns in the core were assumed severed

 Representative fire damage stage: 

• 24 columns on the south wall of WTC 1 between flo

assumed to have buckled and lost all load carrying 

evidence that indicates that columns in this area we

inward a few minutes before the tower collapsed.
Nonlinear Analysis Nonlinear Analysis

 Exterior damage

Aircraft impact damage

Fire damage

North Wall 
Nonlinear Analysis: Results Nonlinear Analysis: Results

 After aircraft impact, the tower maintained its 

highest stressed elements were the exterior c

damaged area on the north face of the tower

 The tower also maintained its stability after lo

south wall due to fire effects with some reservindicating that additional loss or weakening ocore, weakening of additional columns in the additional loss of floors is needed to collapse 

 More detailed models will account for local bu

and the failure and role of the floor system in loads; factors that are not considered in this a
Nonlinear Analysis: Results Nonlinear Analysis: Results

 Load vs. deformation in column 111 at floor 

west side of damage)

0

200400600800

10001200

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.4

Deformation (inches)

Axial Force (kips)

Construction StagesImpact DamageFire Damage
Nonlinear Analysis: Results Nonlinear Analysis: Results

 Load vs. deformation in column 332 at floor 

west side of damage)

0

200400600800

10001200

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.4

Deformation (inches)

Axial Force (kips)

Construction StagesImpact DamageFire Damage
Nonlinear Analysis: Results Nonlinear Analysis: Results

 Displacements and locations of plastic hinges in the no

walls of WTC 1 after impact and fire damage
Preliminary Findings Preliminary Findings

 A 500 mph engine impact against an exterior wall 

penetration of the exterior wall and failure of perimengine does not impact a floor slab, the majority oremains intact through the exterior wall penetratiovelocity of about 10% and 20%. The residual veloengine after penetration of the exterior wall are sucolumn in a direct impact condition. Interaction wibuilding contents, or a misaligned impact against tcould change this result . 

 A normal impact of the exterior wall by an empty w

produces significant damage to the exterior columcomplete failure. A fuel-filled wing section impact damage to the exterior wall, including complete facolumns. This is consistent with photographs shodamage to the towers due to impact.
Preliminary Findings, cont. Preliminary Findings, cont.

 At room temperature, global instability of the intac

five floors are removed from the tower model. At cof 600oC, the removal of four floors induces globa

 When 15 core columns are assumed severed, it is 

splices below the hat truss will fail due to the large 

columns. When only 8 core columns are assumed may fail; however, the results are not conclusive.

 The tower maintained its stability with the removal 

exterior walls and core columns representative of also after losing columns in the south wall due to freserve capacity left, indicating that additional weaother structural members is needed to collapse the