Aircraft Impact Simulation of the WTC tower forInvestigation on True Cause of the Total Collapse

Tragedy of World Trade Center
2001.9.11○ Daigoro ISOBE
Zion SASAKI
Univ. of Tsukuba, Japan

Background・9/11 terrorist attack on the WTC towers caused an unprecedented tragedy in the history ofarchitecture
・Twin towers stood in flames caused by jet fuel until finally, both collapsed totally to the ground・Both towers collapsed at an unnaturally high speed
・Official statements given by FEMA in 2002 and NIST in 2005 stated that the main cause of thetotal collapse is the weakening of the core structures induced by the big fire…but, was it really the main cause of the total collapse?

Total collapse of the WTC 2

Statements in the official reports

World Trade Center Building Performance Study: Data Collection,
Preliminary Observations, and Recommendations, Federal
Emergency Management Agency (FEMA), 2002
“ …the fact that the structures were able to sustain this level of damage and remain standing foran extended period of time is remarkable and is the reason that most building occupants were able
to evacuate safely.”“…this heat (of burning jet fuel) induced additional stresses into the damaged structural frames
while simultaneously softening and weakening these frames. This additional loading and theresulting damage were sufficient to induce the collapse of both structures.”Statements in the official reports

Final Report on the Collapse of the World Trade Center Towers,
National Institute of Standards and Technology (NIST), 2005
“ …the WTC towers likely would not have collapsed under the combined effects of aircraft impact
damage and the extensive, multi-floor fires that were encountered on September 11, 2001, if thethermal insulation had not been widely dislodged or had been only minimally dislodged byaircraft impact.”“…NIST found no corroborating evidence for alternative hypotheses suggesting that the WTC
towers were brought down by controlled demolition using explosives planted prior to September
11, 2001. NIST also did not find any evidence that missiles were fired at or hit the towers.”

Some emerging queries
・Did the fire really spread to such awide range in the buildings to cause thetotal collapse?
・Was the heat high enough to reduce
the strengths of all the structuralmembers?
… not likely.

WTC 2 collapsing

Then, what was the real cause of the free-fall total collapse?
“The towers experienced an extreme dynamic load that noother high-rise building has ever experienced in history.”

Objectives
Perform some aircraft impact analyses of a full-model
WTC tower, to determine the possibility of the impact
itself acting as a fatal cause of the collapse

Numerical code must be highly accurate,less-memory-consuming, member
fracture and contact taken into accountMoment of impact

Applied a finite element code using the ASI-Gauss techniqueAdaptively Shifted Integration Technique
Relationship between the locations-10
θ1s1s1θ2

u1
u2
Linear Timoshenko beam element
θ1r1r

θ2

Numerical integration point shiftedu2u1Formation of fully plastic section

Precise location of plastic hinge expressed

Rigid Body Spring Model (RBSM)

In elastic range
Numerical integration point
Rotational and shear spring(Location of plastic hinge)

One integration point located at midpoint
Limitation of one-point integration(Location of stress evaluation point）

Accuracy fall in elastic solutionsASI-Gauss Technique
ASI technique-11-1/2

Member
01/2

Elastic range
1001-1 -1
Element 2
Element 1
s=0
r=0Improvement

ASI-Gauss technique
Member
0-1 -1/√31r g 0 sg
Element 1

Numerical integration point
Stress evaluation point-1 -1

1/√31sg 0 r g
1Element 2sg = 1 - (2/√3)
rg = -1 + (2/√3)

Place stress evaluation points of two consecutive elements
at Gaussian integration points

Optimal for two-point integration, accuracy mathematically guaranteedEstimation on ASI-Gauss TechniqueP,δ

Displacement δ (mm)

80

60

40

20

100

100P,δ

P,δ

2elem/member
4elem/member
8elem/member
16elem/member

80

60

40

200.1

0.2
0.3
Time (s)0.4

0.5

Conventional FEM

LLZ
Y
X

60

40

20

0.1

0.2
0.3
Time (s)0.4

ASI technique

0.5

0.1

0.2
0.3
Time (s)0.4

ASI-Gauss technique

Elasto-plastic response analysis of a space frameLP,δ

2elem/member
4elem/member
8elem/member

80
Displacement δ (mm)2elem/member
4elem/member
8elem/member
16elem/member
32elem/member
64elem/member

Displacement δ (mm)100

Achieved
high accuracy
in elastic
Time increment∆t = 0.05ms
range byStep
usingload
ASIP-Gauss= 12kNtechnique

0.5Member Fracture Algorithm
Shift to locate stress evaluation points
at Gaussian integration points

shift to opposite end

s=1
s=sg

Re-shift to midpoint

Stiffness reduced to zero

s=0
Fracture

Plastic hinge

Resultant forces
released

s=sg

s= 0

s=0

Node
(a) Elastic stage

Numerical integration point(b) Plastic stage(c) Member fracture

Locations of numerical integration points in each stage

Elemental Contact Algorithm
A1Bi1Collidingelement
Ec

Element
EiA2

Lie on the same planeOR
Nearly form a plane
ANDBi2A1(xc1,yc1,zc1), A2(xc2,yc2,zc2)
B1(xi1,yi1,zi1), B2(xi2,yi2,zi2)

Determination of contact

Bi1

Collidingelement
EcA1

A2
Element
Ei

Exist in a specific distance

Bi2

Gapelements

 4 gap elements connecting 2 elements after
determination of contact
 Gap elements automatically eliminatedafter certain time of contact
Connection of elements in contact

Initial velocity of aircraft = 262 m/s, mass = 142.5 t

Numerical Modeland AnalyticalConditions

Implicit scheme (Newmark’s β method)
Numerical damping (δ=5/6, β=4/9)
Updated Lagrangian Formulation
Conjugate Gradient solver
Strain rate effect on yield strength
Time increment = 0.2 ms (actual time 0.8 s)
ASI-Gauss techniqueCore beamCore column
Maindoubletruss
SpandrelTransverse
Perimeter
Diagonal
Intermediate truss
column brace member
supportangle

Analyzed model

Cross section of the WTC towers

Other Analytical Conditions
Yield condition

Mx, My : bending moments around the x- and y-axes, N : axial force,Mz : torsional moment, Mx0, My0, N, Mz0 : fully plastic values

Fracture condition

κx, κy : bending strains around the x- and y-axes,
εz : axial tensile strain,κfx, κfy, εfz : critical values

Typical WTC column joints, FEMA

Aircraft Impact Analysis of WTC2

Upper viewfy 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Global view

0.9 1.0

Aircraft Impact Analysis of WTC2
280●:Observed data [1]240Speed(m/s)
Speed

200
160
1208040A BCDEF000.1(a) Numerical result0.20.3
0.4
ElapsedElapsedtime
time(s)

0.5

0.6

0.7

Velocity curve of theright engine(b) Observed data (NIST)

Damages on
the south face

120

1F
11F
21F
31F
41F
51F
61F
71F
81F
91F
101F

100

60
40

軸力
[MN]

Axial force produced incore columns

80200-20-40-60-80① ②-100
0③

④

0.1

⑤⑥
0.2

0.3

0.4

0.5

0.4

0.5

0.4

0.5

0.4

0.5

0.6

0.7

0.6

0.7

0.6

0.7

0.6

0.7

時間[t]

120

1F
11F
21F
31F
41F
51F
61F
71F
81F
91F
101F

1008060軸力[MN]

40200-20-40-60-80① ②-1000③④0.1⑤⑥0.20.3
時間[t]

1201F
11F
21F
31F
41F
51F
61F
71F
81F
91F
101F

1008060

軸力[MN]

40200-20-40-60-80① ②-100
0③④0.1⑤⑥0.20.3
時間[t]

120

1F
11F
21F
31F
41F
51F
61F
71F
81F
91F
101F

1008060

軸力[MN]

40200-20-40-60-80① ②-1000③0.1④⑤⑥0.20.3
時間[t][Locations of core columns

Time histories of axial forces

What produced thegigantic tensile force?
Instant disconnections between the corecolumns and the main double trusses
during the impact is observed.
Distribution of fractured main double trusses
110
1009080

破断発生階層7060
504030
20
1000

0.1

0.2

0.3

0.4

0.5

0.6

時間[t]

Main double trusses disconnected from corecolumn No. 1001

0.7

“Spring-back theory”
ImpactFloor load

Fracture

Middle-classunloading

Large-classunloadingMain double truss

Core column

Disconnect-and-release chain reaction

A spring-back phenomenon of the core columns due to a very rapid
unloading is observed. The spring-back phenomenon is fatal enoughto produce gigantic tensile force to the columns. This might havetriggered some connections to become totally fractured, and thus,
eventually, have led to a total collapse of the towers.

“Spring-back theory”
1F
11F
21F
31F
41F
51F
61F
71F
81F
91F
101F

100

Axial force (MN)

80
60
40
200300200

Displacement (mm)120-20100011F
21F
31F
41F
51F
61F
71F
81F
91F
101F

-100-40-60-200-80-100-300

00.1

0.2

0.3

0.4

0.5

0.6

Elapsed time (s)Time histories of axial forces (core column No. 1001)

0.7

00.1

0.2

0.3
0.4
Elapsed time (s)

0.5

0.6

0.7

Axial displacement due to spring-back phenomena(core column No. 1001)

A spring-back phenomenon of the core columns due to a very rapid
unloading is observed. The spring-back phenomenon is fatal enoughto produce gigantic tensile force to the columns. This might havetriggered some connections to become totally fractured, and thus,
eventually, have led to a total collapse of the towers.

Conclusion

Spring-back phenomenon →fatal cause of the total collapse?

Future works
Re-investigate behaviors of member joints
Run parametric simulations

WTC１

WTC２