Proceeding of ICCES’05, 1-10 December 2005, INDIA

Aircraft Impact Analysis of New York World Trade Center Tower
by Using the ASI-Gauss Technique
D. Isobe1 and K. M. Lynn2
Summary
In this paper, a newly developed ASI-Gauss technique is applied to an aircraft impact
analysis of New York World Trade Center Tower 2 (WTC2), to evaluate the structuralvulnerability and behavior of the aircraft, at the horrifying scene that occurred in 2001.
The ASI-Gauss technique is a modified version of the formerly developed AdaptivelyShifted Integration (ASI) technique for the linear Timoshenko beam element, which
computes highly accurate elasto-plastic solutions even with the minimum number ofelements per member. Algorithms considering member fracture and elemental contact arealso implemented. The analytical results such as damages of the tower and motion of theaircraft engines, showed good agreement with the observed data.
Introduction
The aircraft impact and progressive collapse of the World Trade Center (WTC)
towers, an unprecedented building disaster, pointed out that peculiar external loads andphenomena, which are not considered in building designs and about which little technicalinformation is available, can lead to the total collapse of buildings and the loss of many
lives. It may be impractical to adopt building codes that demand structural capabilities toresist such loads and phenomena. However, we should have in-depth technicalknowledge about them in order to minimize fatalities and structural damage. Due to thenature of the problem, finite element simulation with dynamic schemes and global
analytical models is considered to be an effective means of clarifying actual phenomena.
However, conducting dynamic analyses of full-model large-scale structures such as theWTC towers leads to high calculation cost, and it usually becomes a bottleneck. If theanalyzed phenomenon is a lengthy one, such as the fire-induced collapse of a large-scalestructure, the problem of calculation cost becomes more significant.
To fulfill the desire to reduce calculation costs, a new scheme called the ASI-Gausstechnique, which can effectively cope with strong nonlinearities and discontinuities
common in impact collapse problems, is developed. In this paper, the newly developed
ASI-Gauss technique is briefly explained, and it is compared with the former version ofthe technique, the Adaptively Shifted Integration (ASI) technique [1] for the linear
Timoshenko beam element. Algorithms considering member fracture and elemental
contact [2] are also implemented. An impact collapse analysis is conducted using a1
2

Department of Engineering Mechanics and Energy, University of Tsukuba, Ibaraki 305-8573, Japan
Ex-graduate student, University of Tsukuba, Ibaraki 305-8573, Japan

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detailed finite element model to simulate the aircraft impact with the World Trade Center
South Tower (WTC2), and the analytical results are compared with the observed data.
ASI-Gauss Technique
The main difference between the ASI and ASI-Gauss techniques lies in the positionof the numerical integration point in elastic range. In the ASI-Gauss technique, twoconsecutive elements forming a member are considered as a subset, and the numericalintegration points of an elastically deformed member are placed such that the stressevaluation points coincide with the Gaussian integration points of the member. Thismeans that stresses and strains are evaluated at the Gaussian integration points ofelastically deformed members. Gaussian integration points are known to be optimal fortwo-point integration and the accuracy of bending deformation is mathematicallyguaranteed. In this way, the ASI-Gauss technique takes advantage of two-point
integration while using one-point integration in actual calculations. Figure 1 shows thelocations of the numerical integrations points of elastically deformed elements in the ASIand ASI-Gauss techniques.
MemberMember

-1-1/2

0

1/2

1-1

10-1

011

Element 1

Element 2

Numerical integration point

Stress evaluation point-1/√3rg 0 sg
Element 101/√31-1sg 0 rg

1

Element 2sg = 1-(2/√3), rg = -1+(2/√3)(a) ASI technique(b) ASI-Gauss techniqueFig. 1 Locations of numerical integration and stress evaluation points in elastic range

An Elasto-plastic response analysis is performed to evaluate the convergency of theschemes. A load of 12 kN is applied to a space frame as shown in Fig.2. The
conventional scheme shows a very slow convergence and sixteen-element modeling isnecessary to obtain the converged solution. Although the ASI technique gives
comparatively better results than the conventional scheme, a difference in the vibration
mode can be observed in less-element modeling. On the other hand, the ASI-Gauss
technique shows a very fast convergence and nearly converged solutions are obtainedeven when the number of elements per member is two.

Proceeding of ICCES’05, 1-10 December 2005, INDIA

100

2 elements/member
4 elements/member
8 elements/member
16 elements/member
32 elements/member
64 elements/memberP,δ
80

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100

100
2 elements/member
4 elements/member
8 elements/member
16 elements/member

80

60

60

60

40

40

402020200.1

0.2

0.3

0.4

0.5

(a) Conventional scheme

0.1

0.2

0.3

0.4

(b) ASI technique

2 elements/member
4 elements/member
8 elements/member

80

0.5

0.1

0.2

0.3

0.4

0.5

(c) ASI-Gauss techniqueFig. 2 Elasto-plastic responses of space frame

Aircraft Impact Analysis of World Trade Center Tower 2An aircraft impact analysis of WTC2 is carried out by using the ASI-Gauss technique.
Figure 3 shows the analytical finite element model and the initial position of the aircraft.
The floors near the region of aircraft impact, 77th to 86th floor, are modeled with linear
Timoshenko beam elements. The number of elements per member is uniformly set to two.
The analytical model contains 54740 elements, 47267 nodes and 281880 degrees offreedom. The boundary conditions for the upper and lower ends are assumed to be
horizontal rollers. Two parameters used for fracture criterion, axial and bending strains,are set to 0.1 and 0.0003 respectively, for perimeter and core columns. The mean weight
per unit floor area is assumed to be 8.29 kN/m2. The initial gravity load is applied to allstructural members. A B767-200ER aircraft is also modeled with linear Timoshenko
North face

East face

West face(b) View from the south
South face(a) Aerial view(c) View from the west

Fig. 3 Analyzed model and initial position of aircraft

Proceeding of ICCES’05, 1-10 December 2005, INDIA

beam elements. The model consists of 4322 linear Timoshenko beam elements, 2970
nodes and 17820 degrees of freedom. The two-element modeling is also used. All
structural members of the aircraft are assumed to have box-shaped cross sections and thematerial properties of extra super duralumin. The total mass of the aircraft at the time ofimpact is assumed to be 142.5 t, which is the sum of the masses of the aircraft (112.5 t)
and the jet fuel (30 t). The mass of each engine is 19.315 t. The nose of the aircraft istilted 11.5 degrees to the east and 5 degrees downward, and its left wing is inclined
downward by 35 degrees. It is assumed to collide with the 81st floor of WTC2 with acruise speed of 590 mph (262 m/s) [3]. Newmark’s β method (δ=5/6, β= 4/9) [4], updatedLagrangian formulation and the conjugate gradient (CG) method is used in the analysis.
The analytical code is run on a personal computer (3.3 GHz P4 CPU and 2GB RAM),and the calculation takes approximately 23 hr for a physical time of 0.8 s.
Figure 4 shows how the aircraft cuts through the perimeter columns and spandrels on
the south face. Fractured elements are not plotted in the figures. Immediately after theimpact, shock waves travel up and down in the perimeter columns and back and forth in
the longitudinal members of the fuselage. The engines are detached from the aircraft soonafter the main wings crashed into the south face. Figure 5 shows the damages of theperimeter columns and spandrels on the south face. The result obtained from the analysis
is slightly larger than the observed one [3] especially near the lower and upper boundaries,
where horizontal rollers are assumed. Due to these boundary conditions, it is assumed(a) 0.04s(b) 0.08s(c) 0.12s(d) 0.16s
Fig. 4 Aircraft cutting through perimeter columns and spandrels on the south face(a) Analysis(b) Observed damage [3]Fig. 5 Damages on the south face1215

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that stresses are totally reflected from these boundaries, and the elements near them
became severely stressed.
Figure 6 shows how the aircraft debris moves through the building and to where it
causes damage. As shown in the figure, the right engine does not cause damage to thecore structure. It moves out from the northeast corner at 0.7 s (0.617 s after the impact).
The location from where the right engine moves out of the building is almost the same asthe observed data [3]. The core structure is mainly damaged by the left engine andfuselage. The debris of the fuselage moves out from the north face. The velocity of theleft engine is reduced more than that of the right one since the left one collides with themembers of the core structure. Figure 7 shows the velocity reduction curve of the rightengine, which is in very good agreement with the observed data [3]. The right engine
moves in the northeast direction after coming out of the building at a velocity
approximately of 53 m/s. Its traveled distance after moving out of the building iscalculated to be 368 m. The engine was reported to have been found at the corner of
Murray and Church Streets [3], which is approximately 443 m far from the building.
Therefore, the analytical result is in good agreement with the observed data if we takeinto account that the engine rolled over after reaching the ground.

(a) Before impact(b) 0.1 s(c) 0.2 s(d) 0.3 s(e) 0.4 s

Location of the left engine
Location of the right engine(f) 0.5 s(g) 0.6 s(h) 0.7 s

Fig. 6 Motion of aircraft debris during impactConclusion
In this paper, we briefly discussed on the newly proposed ASI-Gauss technique forthe linear Timoshenko beam element, which takes advantages of two-point integration

Proceeding of ICCES’05, 1-10 December 2005, INDIA

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Velocity of the right engine (m/s)

300
Analysis
Observation

200

10000.2
0.40.6Time after impact (s)Fig. 7 Velocity reduction curve of the right engine

while using one-point integration in actual calculations. The scheme is used to analyzedynamic collapse behavior of WTC2 subjected to aircraft impact, and the propagation ofshock waves resulting from the impact is confirmed. The damages of the tower andmotion of the aircraft engines are practically in good agreement with the observed data.
However, there still lie inconveniencies due to the usage of partial models. Therefore, afull-model analysis of WTC2 is scheduled to estimate the influence of shock waves
generated by the aircraft impact, against the progressive collapse of the tower thatoccurred 56 minutes after the impact.
Acknowledgement
This work is partially supported by Grant-in-Aid for Scientific Research
No.16206055, Japan Society for the Promotion of Science.
Reference
1 Toi, Y. and Isobe, D. (1993): “Adaptively Shifted Integration Technique for Finite
Element Collapse Analysis of Framed Structures”, International Journal for Numerical
Methods in Engineering, Vol. 36, pp. 2323-2339.
2 Isobe, D. and Tsuda, M. (2003): “Seismic Collapse Analysis of Reinforced Concrete
Framed Structures Using the Finite Element Method”, Earthquake Engineering andStructural Dynamics, Vol. 32, No. 13, pp. 2027-2046.
3 ASCE/FEMA (2002): World Trade Center building performance study: Datacollection, preliminary observation, and recommendations.
4 Bathe, K. J. (1996): Finite element procedures, Prentice Hall.