Simpson Gumpertz & Heger Simpson Gumpertz & Heger Consulting Engineers Consulting Engineers

Building Engineering Building Engineering 

 Infrastructure and Sp Infrastructure and Special Structures ecial Structures 

 C

C

Structural Response of Components

Structural Response of Components

and Global Models of WTC T

and Global Models of WTC T

to 

Aircraft Impact and Fire Aircraft Impact and Fire

Simpson Gumpertz & Heger Inc. Simpson Gumpertz & Heger Inc.

Waltham, MA 02453 Waltham, MA 02453

15 September 2005 15 September 2005
Objective and Approach Objective and Approach 

• Objective: Present the results of the finite e

Objective: Present the results of the finite e

performed for each of the WTC towers to d

performed for each of the WTC towers to d

structural response to aircraft impact dama

structural response to aircraft impact dama

subsequent fires. subsequent fires.

• Approach: For components, subsystems, a

Approach: For components, subsystems, a

 Identify probable failure modes and key structu Improve numerical efficiency in larger subsyste

analyses by developing reduced degree of freethat capture essential behavior and failure mod

 Guide and validate structural response using k
Method of Approach Method of Approach 

Components and C

Full Floor Subsystem E

Glob

Observed Damage

Impact Damage

Temperature

Failure Modes and Redu

Predicted Fire-Induced Damage 

Fire-Induced Damage:Disconnections and Pull-in Forces

Isolated 
Floors
Floor Truss with Concrete Sla

Floor Truss with Concrete Sla

288 in. 

span=713 in. 

y 

z 

X Y

40 in. 

4.35 in. 

29 in.

co

n

c

r

ete

slab 

top chord 

bearing angle 

bottom chord 

we

b

bo

w

eb diag

knuckle 
Temperature Temperature 

-Dependent Material Prop

Dependent Material Prop

• Steel

 Modulus of Elasticity Yield Strength Tensile Strength Coefficient of Thermal Expansion Creep εtot = εelastic + εplastic + εcreep + ε∆T

• Concrete Concrete

 Modulus of Elasticity Compressive Strength Tensile Strength Coefficient of Thermal Expansion

0 200 

0

0.20.40.60.8

1

Constr

Bolt St

Yield Strength Reduction Factor
Exterior Truss Seat Model Exterior Truss Seat Model
Truss Seat Failure Modes Truss Seat Failure Modes 

Possible failure sequence under horizontal load...

Bolt comes into bearing 

and shears off

Gusset plate fails
Break Element Model for Interior Truss Seat Break Element Model for Interior Truss Seat

Rigid beam

Bea

m element 

Beam element

Beam element(Out-of-plan)

2 n

3 n

n6

n5

n4

Rigid beam

n1

Break element No. 1: Capture walk-off supportB1[(2,3,UZ);(2,1,U

Y);(K,

∆0)]

n2 n3 n1

n3n2

Pz

Py

Break element No. 2:Capture seat vertical shear capacityB2[(1,3,UZ);(4,2,UZ);(K,∆0)]

Break element No. 4:Capture bolt shear capacityB4[(1,3,UY);(2,5,UY);(K,

∆0)]

Break element No. 3:Capture loss of horizontal resistance if seat fails verticallyB3[(2,3,UY);(4,2,UZ);(K,

∆0)]

n6 n5

n4 Beam element No. 1:

Make seat vertical shearcapacity temperaturedependent

Beam element No. 2: Make bolt shear capacitytemperature-dependent

Y

Z

Coordinate system

Rigid beam

Constraint equationsCoupling displacementD

OF of node 1 and 6 

Beam element(Out-of-plan)

Fix rotational D

OF

Seat model was use

d to make the 

connection between node 

n1, w

hich is

part of the seat and channel beam, and node 

n2, which part of the floor 

truss. The seat model consists of four break elements, two bea

m elements,

an

d six nodes

• Break 

Break 

the ele

the ele

stiffne

stiffne

failure 

failure 

• Break 

Break 

depen

depen
Knuckle Analysis Knuckle Analysis

Crush R

e

gion in Gray
Axial Stress in Truss Members Near the Inter

Axial Stress in Truss Members Near the Inte

Displacement magnification facto
Sagging Obser Sagging Observed in the Detailed Truss Mo

ved in the Detailed Truss Mo

MN

MX

-42.11

-37.357

-32.603

-27.849

-23.095

-18.342

-13.588

-8.834

-4.081

.67

Vertical displacement contour at 700  ̊

Buckling of web members

-100

-80-60-40-20

0

2040

0 100 200 30

Tempe

Total Horizontal Reaction Force 

(kip)

• After web members buckled, the After web members buckled, the 

truss pulled exterior columns in. truss pulled exterior columns in.

• The tension force ranged from 9 The tension force ranged from 9 

kip to 14 kip per column in this kip to 14 kip per column in this model.
Response of Reduced DOF Truss Model to Tem

Response of Reduced DOF Truss Model to Tem

Y X Z

M

Y X

Z

-40-35-30-25-20-15-10

-5

0

0 100 200 300 400 500 600 700

T

emperature ( ̊C)

Vertical Displacement (in)

Detailed Truss ModelSimplified Truss Model

-100

-80-60-40-20

0

2040

0 100 200 

Horizontal Reaction Force per Column 

(kip)

Detailed TrusSimplified Tru

Vertical displacement at midspan

Horizontal rea
Creep Effect on Vertical Displacement of Trus

Creep Effect on Vertical Displacement of Trus

1

MN

MX

X Y

Z

Simplified Truss Model at COL333 from Full Floor Model w/o Creep 

-25.523

-22.523 -19.522 -16.521 -13.521 -10.52 -7.52 -4.519 -1.519 1.482

MAR 29 2005

16:29:34

NODAL SOLUTIONSTEP=5SUB =12TIME=2400UZ (AVG)RSYS=0DMX =25.523SMN =-25.523SMX =1.482

1

MX

X YZ

Simplified Truss Model at COL333 f

-44.184

-39.117

-34.051

-28

NODAL SOLUTIONSTEP=5SUB =54TIME=2400UZ (AVG)RSYS=0DMX =44.221SMN =-44.184SMX =1.415

w/o Creep at 2,400 s

Max. = 25.5 in.

w/ Cr

Ma
Full Floor Model Full Floor Model 

1

APR 19 2004

20:40:22

ELEMENTSTYPE NUM

Bridging Truss

Knuckle

Knuckle

Primary truss to bridging trussbottom chord connection

Primary truss to bridging trusstop chord connection

Diagonal bucklingand weld fracture

Primary Truss 1 APR 19 2004

20:40:22

ELEMENTSTYPE NUM

Bridging Truss

Knuckle

Knuckle

Primary truss to bridging trussbottom chord connection

Primary truss to bridging trusstop chord connection

Diagonal bucklingand weld fracture

Primary Truss

Componen

• Knuck• Truss • Truss/

Subsystem 

• Concr• Prima• Bridgin• Transf• Strap • Interio• Spand• Core b
Finite Element Model of Full F

Finite Element Model of Full F

X Y

Z

TYPE NUM

X Y

Z

X

Y

Z

exterior column

spandrel

bridging truss

long-span primary truss

concrete slab

core beam
WTC 1 Floor 98 WTC 1 Floor 98 

- Temperatures at 50 

Temperatures at 50 

1

X Y

Z

0

100

200

300

ELEMENTSTEMPERATURESTMIN=24.41TMAX=920.169

1

X Y

Z

0

100

200

300

400

500

600

700

800

900

950

SEP 18 2004

17:26:41

ELEMENTSTEMPERATURESTMIN=20TMAX=924.418

N 

 ̊C 

Concrete Slab Temperatures Stee
Break Elements in Full Floor Models Break Elements in Full Floor Model

1

X

Y

Z

WTC2 FL83 

ELEMENTSSEC NUM

• Truss web diagonals Truss web diagonals 

–

buckling and weld failure buckling and weld failure 

• Gusset plates Gusset plates 

- fracture fracture

• Truss seat bolt Truss seat bolt 

- shear off shear off

• Truss seat Truss seat 

- tension, shear, tension, shear, 

and walk and walk-off failures off failures

• Primary/bridging truss Primary/bridging truss connection connection 

- failure failure

• Primary long Primary long-span/transfer span/transfer truss connection truss connection 

- failure failure

• Studs at slab Studs at slab-spandrel spandrel connections connections 

– failure Strap failure Strap anchors anchors 

- weld failure weld failure
WTC 1 Floor 98 WTC 1 Floor 98 - Vertical Displacement at 

Vertical Displacement at 

1

MN

MX

X Y

Z

WTC1 FL98 - Maximum Damage Case Te

-49.045

-43.13

-37.215

-31

NODAL SOLUTIONSTEP=15SUB =18TIME=6000UZ (AVG)RSYS=0DMX =49.136SMN =-49.045SMX =4.187

1

MN

MX

X Y

Z

WTC1 FL98 - Maximum Damage Case Temperature at 6000 sec 

-49.045

-43.113

-37.181

-31.249

-25.318

-19.386

-13.454

-7.522

-1.59

4.341

OCT 29 2004

09:46:42

NODAL SOLUTIONSTEP=15SUB =18TIME=6000UZ (AVG)RSYS=0DMX =49.136SMN =-49.045SMX =4.341

N

Floor/wall disconnection

Max displacement = 49.0 in.

5x displacement magnification 
WTC 1 Floor 96 WTC 1 Floor 96 – Effect of Firepr

Effect of Firepr

1

X Y

Z

0

100

200

300

400

500

600

700

800

900

950

SEP 15 2004

20:21:51

ELEMENTSTEMPERATURESTMIN=29.539TMAX=902.356

1

MN

MX

X Y

Z

WTC1 FL96 - Maximum Damage Case Tem

-22.431

-19.594

-16.756

-13.

NODAL SOLUTIONSTEP=11SUB =8TIME=6000UZ (AVG)RSYS=0DMX =22.529SMN =-22.431SMX =3.108

N 

Area of fireproofing damage

• Maximum temperature of steel me Maximum temperature of steel members with fireproofing reac

mbers with fireproofing reac

• Maximum temperature of steel me Maximum temperature of steel members without fireproofing mbers without fireproofing e

reached 800 reached 800  ̊C.

Temperature of steel membersat 100 min

Vertical disp(5x displace
Exterior Walls Exterior Walls
One 

-Story Exterior Column Mode

Story Exterior Column Mode

2 in. pushdown at room temperature

2 
Axial Load Deflection of Exterior Colum

Axial Load Deflection of Exterior Colum

0

175350525700875

10501225

0.

0

0.5 1.

0 1.5 2.

0

Vertical Displacemen

t (in)

Axial Load (kips)

Ela

stic local buckling load for 1-story

high colum

n at RT =1004 Ki

p

Axial yield load of column at RT =1177 Kip

Gravity load demand

Elastic local b

uckling load at 700C = 682 Kip

Axial yiel

d load of colu

m

n at 7

0

0

C = 444 Kip
10 ft

52 in.

40 in. 

40 in. 

12 ft

Prefabricated panel

Column splice 

Spandrelsplice

Floor 99Floor 98Floor 97Floor 96Floor 95Floor 94Floor 93Floor 92Floor 91

A A

COL158 

COL157 

COL156 

COL155 

COL154 

COL153 

COL152 

COL151 

COL150 Exterior Wall M

Exterior Wall M

Subsystem Mode

• Columns• Spandrels• Column splic• Spandrel spl
Exterior Wall Load Cases Exterior Wall Load Cases 

Y 

Vertical

Loads

• All floors connected All floors connected 

• Two floors disconnected Two floors disconnected

• Three floors disconnected Three floors disconnected

• Three floors disconnected Three floors disconnected 

with pull with pull

-in forces in forces

• Three floors disconnected Three floors disconnected 

with push down forces. with push down forces. 
Large Inelastic Buckling of Spandr

Large Inelastic Buckling of Spandr

and Partial Separation at Connectio

and Partial Separation at Connectio

Add 14 Tear 94

50x disp
Instability of Exterior Wall subject

Instability of Exterior Wall subject

to Horizontal Pull to Horizontal Pull

-in Forces at Three 

in Forces at Three 

1

10X displacement magnification
Simpson Gumpertz & Heger Simpson Gumpertz & Heger Consulting Engineers Consulting Engineers

Building Engineering Building Engineering 

 Infrastructure and Sp Infrastructure and Special Structures ecial Structures 

 C

C

Global Analysis of WTC 1 and W

Global Analysis of WTC 1 and W
Global Models Global Models 

• ANSYS models were developed for nonlinear ANSYS models were developed for nonlinear large deflection analysis of the towers. large deflection analysis of the towers.

• WTC 1: Truncated below Floor 91 with WTC 1: Truncated below Floor 91 with 

vertical springs for stiffness of floors below. vertical springs for stiffness of floors below.

• WTC 2: Truncated below Floor 77 with vertical WTC 2: Truncated below Floor 77 with vertical 

springs for stiffness of floors below and springs for stiffness of floors below and superelement above Floor 86. superelement above Floor 86.

1

X Y

Z

WTC1 - Severe Temp at 6000s w/5ki

-6.499

-5.757

-5.015

-

NODAL SOLUTIONSTEP=33SUB =1437TIME=150UZ (AVG)RSYS=0DMX =42.979SMN =-6.499SMX =.177856

WTC 1

• Tower Model Features Tower Model Features

 Columns included creep and inelastic buckling.  Spandrels were axially released to prevent local plate buckling, wit

shear stiffness.

 Office floors modeled as a membrane capable of transferring in-pla

and exterior wall.

 Core slab and beams with moment connection were modeled simu

and bending stiffness for load transfer between columns. 

 Core beams without moment connections were not modeled. Cor

beams was modeled to match the in-plane stiffness of the co
Global Models Global Models 

• Core and exterior columns had temperature Core and exterior columns had temperature- dependent pr dependent properties

 Thermal expansion Plasticity  Creep

• Gravity Loads Gravity Loads 

 Self-weight plus 8 psf superimposed 

dead

 Live (25% of design live load) Weight of antenna (750 kip) at the top of 

WTC 1 

• Thermal Loads Thermal Loads 

 Temperatures at 10 min intervals

1

M

X Y

Z

WTC2 Reduced Model At 2540s 

-11.25

-10

-8.75

-7.5

NODAL SOLUTIONSTEP=17SUB =523TIME=63.523UZ (AVG)RSYS=0DMX =61.911SMN =-11.096

• Floors

 Full floor models were not included in global models du

limitations

 Effects of the floor disconnections and inward pull force

were included
WTC 1 South Wall

Fire-Induced Dam

Induced Dam

• Disconnection 

Disconnection 

wall at truss se

wall at truss se

• Pull-in forces a

in forces a

connections du

connections du

caused inward 

caused inward 

walls

Analysis Analysis 

Locations of disconnections between the Locations of disconnections between the sagging floors a sagging floors and exterior walls nd exterior walls

x 

Bow-in areas of exterior wall system in areas of exterior wall system x 

Magnitude of inw gnitude of inward bow - Magnitude of hor gnitude of horizontal pull izontal pull-in force in force x 
Estimation of Magnitude of Estimation of Magnitude of Pull

-in Forces in Global Model in Forces in Global Model

• Analyze structural response of global model wit

Analyze structural response of global model wit

• Impose floor disconnections and in Impose floor disconnections and inward pull for

ward pull for

isolated wall models (South face of WTC 1; Eas

isolated wall models (South face of WTC 1; Eas

• Compare results with observed inward bowing. Compare results with observed inward bowing.

• Adjust magnitude of inward bowing forces to ma

Adjust magnitude of inward bowing forces to ma

WTC 

(East Face of F

(East Face of F

Time Interval Time Interval 

(s)

0 

– 1,800 

1,800 

– 2,540 

WTC 1 

(South Face of Floors 95 to 99) (South Face of Floors 95 to 99)

Time Interval Time Interval 

(s)

Inward Pull Inward Pull 

(kip)

0 

– 4,800 

0

4,800 

– 6,000

5

* Pull forces applied to 
Important Factors in Global Analy

Important Factors in Global Analy

• Aircraft damage Aircraft damage 

→ Load redistributi

Load redistributi

• Thermal expansion Thermal expansion 

→ Load redistrib

Load redistrib

• Creep of steel in high temperature Creep of steel in high temperature 

→

Displacement increase, column axia

Displacement increase, column axia

and load redistribution and load redistribution 

• Thermal weakening/softening of stee

Thermal weakening/softening of stee

in high temperature in high temperature

 Loss of strength 

→ Component fa

redistribution

 Loss of stiffness 

→ Buckling and 

redistribution
Results from Global Analysis o

Results from Global Analysis o
Vertical Displacement of Exterior W

Vertical Displacement of Exterior W

of WTC 2 (Floor 77 to Floor 86) of WTC 2 (Floor 77 to Floor 86)

Before Aircraft Impact A

1

MN

MX

X Y

Z

WTC2 Reduced Model At BfrImp

-11.25

-10

-8.75

-7.5

-6.25

-5

-3.75

-2.5

-1.25

0

MAR 2 2005

10:51:30

NODAL SOLUTIONSTEP=1SUB =1TIME=.100E-02UZ (AVG)RSYS=0DMX =3.032SMN =-2.971SMX =-2.142

1

X Y

Z

WTC2 Reduced Model At 2540s

-11.25

-10

-8.75

-7.

NODAL SOLUTIONSTEP=17SUB =523TIME=63.523UZ (AVG)RSYS=0DMX =61.911SMN =-11.096

Min = -3.0 in Max = -2.1 in Min = -11 in 

N

(Downward displacement is negative
Vertical Displacement of Co

Vertical Displacement of Co

of WTC 2 (Floor 77 to Floor 8

of WTC 2 (Floor 77 to Floor 8

Before Aircraft Impact 

1

MX

X Y

Z

WTC2 Reduced Model At 2540s

-13.05

-11.6

-10.15

-8.

NODAL SOLUTIONSTEP=17SUB =523TIME=63.523UZ (AVG)RSYS=0DMX =13.576SMN =-12.982

1

MN

MX

X Y

Z

WTC2 Reduced Model At AftrImp 

-13.05

-11.6

-10.15

-8.7

-7.25

-5.8

-4.35 -2.9 -1.45 0

MAR 2 2005

10:36:08

NODAL SOLUTIONSTEP=1SUB =68TIME=.001UZ (AVG)RSYS=0DMX =10.229SMN =-10.052

N

Min = -10 in Max = 0.0 in Min = -13 in 

(Downward displacement is negative
Out-of-Plane Displacement of Plane Displacement of East Wall of WTC 2 East Wall of WTC 2

View from 

359 

7781

85

Min = -4.0 in 

33

359 301 2

7781

85

0

15304560

0 10 20 30 40 50

Time, min

Maximum out-of-plane displacement

in east wall, in

Critical displacement
Variation of Vertical Displaceme

Variation of Vertical Displaceme

at Floor 86 of WTC 2 at Floor 86 of WTC 2

Before Impact A

N

~3.0 in

~4.0 in

~

3.0 i

n

~3.0 in

N

~3.0 in

~4.0 in

~

3.0 i

n

~3.0 in

~11 in

~10 in

~4.5 i

n

~2.5 in 

13 in 12 in 1

N

Like

to

w

e

~11 in

~10 in

~4.5 i

n

~2.5 in 

13 in 12 in 1

N

Like

to

w

e

(Downward displacement is positive)
Tilt Above Floor 86 of WTC 2 Tilt Above Floor 86 of WTC 2 at 43 min (Total Displacements) at 43 min (Total Displacements)

20X Magnification

1

MN

MX

X

Y Z

 WTC-2 Severe Case Temperature Analysis 

3.298

5.332

7.366

9.399

11.433

13.467

15.5 17.5

NODAL SOLUTIONSTEP=7SUB =1TIME=.007USUM (AVG)RSYS=0DMX =21.601SMN =3.298SMX =21.601

Un
Elastic + Plastic Strain in Columns Elastic + Plastic Strain in Columns 

Maximum between Floor 78 and Floor 84 o

Maximum between Floor 78 and Floor 84 o

Af

1001

501 508

1008

N

~0.04

~0.0

5

~0.04

~0.05

~0.05

1001

501 508

1008

N

~0.04

~0.0

5

~0.04

~0.05

~0.05

Before Impact

1001

501 

9

.60

~0.34

~0.10

~0.0

~0

1001

501 

9

.60

~0.34

~0.10

~0.0

~0

Compression is taken as positive.Strain values are in %.
Elastic + Plastic Strain in Column

Elastic + Plastic Strain in Column

Maximum between Floor 78 and Floor 84 o

Maximum between Floor 78 and Floor 84 

At 40 min

0.9

1001

501 508

1008

N

0.9

1001

501 508

1008

N

A

1001

501 

~0.09

~0.7

~0.8

0

~0.40

~0.30

~1.0

1001

501 

~0.09

~0.7

~0.8

0

~0.40

~0.30

~1.0

Compression is taken as positive.Strain values are in %.
Elastic + Plastic + Creep Strain in Colu

Elastic + Plastic + Creep Strain in Colu

Maximum between Floor 78 and Floor 84 o

Maximum between Floor 78 and Floor 84 o

1001

501 

~0.0

9

~3

~0.8

0

~0.4

0

~0.3

0

~2.3

1001

501 

~0.0

9

~3

~0.8

0

~0.4

0

~0.3

0

~2.3

1001

501 50

8

1008

N

0.50

0.09

0.04

0.90

1.3

0.60

0.35

0.11

0.04

0.70

1001

501 50

8

1008

N

0.50

0.09

0.04

0.90

1.3

0.60

0.35

0.11

0.04

0.70

At 20 min

Compression is taken as positive.Strain values are in %.
WTC 2 Hat Truss WTC 2 Hat Truss 

• Hat truss was part of the Hat truss was part of the 

superelement superelement

• Hat truss members and Hat truss members and 

connections were checked for connections were checked for failure failure

• Analysis found that: Analysis found that: 

 Failure of several column splices 

in the southeast corner of the core occurred due to impact

 Additional column splices failed 

and an outrigger buckled due to subsequent fires

 Such failures did not 

propagate and reduce the load on the overstressed outrigger.

1

X

Y

Z

 WTC-2 Severe Case Temperature Analys

ELEMENTSTYPE NUM

N

E

D

J

I

G

F

K

H

218 - 217

229

23

- 228 2 - 231

243 - 242

329 - 330 - 331

310 - 311

150 
WTC 2 Global Analysis Resul

WTC 2 Global Analysis Resul

After Aircraft Impact After Aircraft Impact

• WTC 2 was stable after impact and had considerable reserve capac WTC 2 was stable after impact and had considerable reserve capacity.

• Severed columns in the southeast corner of the core caused the c Severed columns in the southeast corner of the core caused the core to le

ore to le

tendency of the core to lean was resi tendency of the core to lean was resisted by floors and exterior sted by floors and exterior walls.

• After impact, core loads decreased by 6%, east wall loads increa After impact, core loads decreased by 6%, east wall loads increased by 24

sed by 24

decreased by 10%. decreased by 10%.

Effects of Fires and Effects of Fires and Damaged Fireproofing Damaged Fireproofing

• Thermal expansion of the core columns caused core loads to incre Thermal expansion of the core columns caused core loads to increase unt

ase unt

exceeded thermal strains and t exceeded thermal strains and the columns short he columns shortened and unloaded. ened and unloaded.

• Loads were transferred between the exterior wall and the core pr Loads were transferred between the exterior wall and the core primarily thr

arily thr

• The floors sagged and pulled inward on the east wall shortly aft The floors sagged and pulled inward on the east wall shortly after impact. 

er impact. 

due to the persi due to the persistence of the fires on the east si stence of the fires on the east side of the towe de of the tower. 

• The east wall bowed inward 10 in. approxi The east wall bowed inward 10 in. approxi

mately 20 min after imp y 20 min after impact. The 

act. The 

collapse. collapse.

• Loads were transferred between exteri Loads were transferred between exterior walls through the spandr or walls through the spandrels.

Collapse Collapse Initiation Initiation

• When the east wall buckl When the east wall buckled, the loads were transferred to the we ed, the loads were transferred to the weakened c

akened c

• The building section above the impact area tilted to the southea The building section above the impact area tilted to the southeast.
Results from Global Analysis o

Results from Global Analysis o
Vertical Displacement of Vertical Displacement of Exterior Walls of WTC 1 Exterior Walls of WTC 1 1

X Y

Z

WTC1 - Severe Temp at 6000s w/5kip pul

-6.499

-5.757

-5.015

-4.273

NODAL SOLUTIONSTEP=33SUB =1437TIME=150UZ (AVG)RSYS=0DMX =42.979SMN =-6.499SMX =.177856

At 1

Before Impact

1

MN

MX

X Y

Z

WTC1 - Gravity before Impact w/o Const 

-3.285

-2.92

-2.555

-2.19

-1.825

-1.46

-1.095

-.730004

-.365002

0

MAR 16 2005

09:59:08

NODAL SOLUTIONSTEP=1SUB =2TIME=.100E-02UZ (AVG)RSYS=0DMX =3.286SMN =-3.285

Max. = 3.3 i

n. N

FL93FL95FL97FL99

Max. = 6.5 i

n.

1

MN

MX

Y X Z

WTC1 - Severe Temp at 6000s w/5kip pul

-6.499

-5.757

-5.015

-4.273

NODAL SOLUTIONSTEP=33SUB =1437TIME=150UZ (AVG)RSYS=0DMX =42.979SMN =-6.499SMX =.177856

N 

(Downward displacement is negative)
Vertical Displacement of Vertical Displacement of Core of WTC 1 Core of WTC 1 At 10

1

X Y

Z

WTC1 - Severe Temp at 6000s w/5kip pul

-8.571

-7.616

-6.661

-5.706

NODAL SOLUTIONSTEP=33SUB =1437TIME=150UZ (AVG)RSYS=0DMX =27.32SMN =-8.571SMX =.022969

Before Impact 

1

MN

MX

X Y

Z

WTC1 - Gravity before Impact w/o Const 

-4.246

-3.775

-3.303

-2.831

-2.359

-1.887

-1.415

-.943626

-.471813

0

FEB 14 2005

09:51:34

NODAL SOLUTIONSTEP=1SUB =2TIME=.100E-02UZ (AVG)RSYS=0DMX =4.247SMN =-4.246

N

FL9

3

FL9

5

FL9

7

FL9

9

Max. = 4.2 i

n.

Max. = 8.6 i

n.

1

MX

Y X Z

WTC1 - Severe Temp at 6000s w/5kip pul

-8.571

-7.616

-6.661

-5.706

NODAL SOLUTIONSTEP=33SUB =1437TIME=150UZ (AVG)RSYS=0DMX =27.32SMN =-8.571SMX =.022969

N

(Downward displacement is negative)
WTC 1 South Wall Out WTC 1 South Wall Out-of-Plane Displac

Plane Displac

A

1

M

Y X

Z

WTC1 Severe Temp at 6000s w/5kip pul

-

.701059

4.135

8.972

13.8

NODAL SOLUTIONSTEP=33SUB =1437TIME=150UY (AVG)RSYS=0DMX =42.979SMN =-.701059SMX =42.826

COL359

05

1015202530354045

80 85 90 95 100

Time (min)

Maximum Inward Bowing (in)

Looking from th

Inward displacement is 
Elastic + Plastic Strain in Columns Elastic + Plastic Strain in Columns Maximum between Floor 93 and Floor 99

0.57

Col501 

Col1001 

0.57

Col501 

Col1001 

Col501 

Col1001 

Col501 

Col1001 

A

Maximum between Floor 93 and Floor 99

N

Maximum strain is given in %.Compression is taken as positive.

Elastic + Plastic Strain

0.07

Col501 Col508

Col1001 Col1008

Elastic + Plastic Strain

0.07

Col501 Col508

Col1001 Col1008

Before Impact
Col501 

Col1001 

Col501 

Col1001 

Col501 

Col1001 

Col501 

Col1001 

Elastic + Plastic + Creep Strain in Columns Elastic + Plastic + Creep Strain in Columns

Maximum between Floor 93 and Floor 99 Maximum between Floor 93 and Floor 99

N

Maximum strain is given in %.Compression is taken as positive.

Severed or Heavily DamagedElastic + Plastic + Creep Strain

1.39

Col501 Col508

Col1001 Col1008

Severed or Heavily DamagedElastic + Plastic + Creep Strain

1.39

Col501 Col508

Col1001 Col1008

At 10 min
WTC 1 Hat Truss WTC 1 Hat Truss 

• Analysis found no failure of hat tr Analysis found no failure of hat truss members or supporting 

uss members or supporting 

1

MN

MX

X Y

Z

WTC1 Severe Temp at 6000s w/5kip pull - Hat Truss 

-.351E+07

-.292E+07

-.233E+07

-.174E+07

-.114E+07

-553893

36667

627226

ELEMENT SOLUTIONSTEP=33SUB =1437TIME=150SMIS1TOPDMX =6.782SMN =-.351E+07SMX =.181E+07

Axial force in hat truss at 100 min
WTC 1 Global Analysis Results WTC 1 Global Analysis Results 

After Aircraft Impact After Aircraft Impact

• WTC 1 was stable after impact and had considerable reserve capac WTC 1 was stable after impact and had considerable reserve capacity.

• Severed core columns in the north Severed core columns in the north side of the core caused it to side of the core caused it to lean slig

lean slig

• After impact, core loads increased by 1%, east and wall loads in After impact, core loads increased by 1%, east and wall loads increased 

crease

south walls decreased by 7%. south walls decreased by 7%.

Effects of Fires and Effects of Fires and Damaged Fireproofing Damaged Fireproofing

• Thermal expansion of the core columns caused core loads to incre Thermal expansion of the core columns caused core loads to increase 

ase 

exceeded thermal strains and t exceeded thermal strains and the columns short he columns shortened and unloaded. ened and unloaded.

• Loads were transferred between the exterior wall and the core pr Loads were transferred between the exterior wall and the core primarily 

arily 

• Fires progressing from the north to the south si Fires progressing from the north to the south side of the tower de of the tower caused t

caused t

on the south wall approxi on the south wall approximately 80 mi ely 80 min after impact. n after impact. 

• The south wall bowed inward, reachi The south wall bowed inward, reaching approxi ng approximately 55 in. of in ately 55 in. of inward d

ward d

collapse. collapse.

• Loads were transferred between exteri Loads were transferred between exterior walls through the spandr or walls through the spandrels.

Collapse Collapse Initiation Initiation

• When the south wall buckled, the loads were transferred to the w When the south wall buckled, the loads were transferred to the weaken

eaken

walls.

• The building section above the impact area tilted to the south. The building section above the impact area tilted to the south.