Fire-Induced Progressive Collapse Analyses of High-Rise Towers
D. Isobe1, H. Yokota2 and L. T. T. Thanh3
1

University of Tsukuba, JapanSuzuki Motor Co., Japan
3
Graduate School, University of Tsukuba, Japan
2Abstract
Isobe and his collaborators are seeking for the true cause of the total collapse of the WTC
towers back in 2001 by conducting several numerical simulations, including the full model
aircraft impact analysis of the WTC tower. Isobe suggested in the past papers that the springback phenomenon due to rapid unloading caused by aircraft impact possibly have destructed
member joints in the core structure, which might have caused the towers to become brittle andunstable. However, it does not give answers to the total collapse of WTC tower 7, whichcollapsed, reportedly, only by fire. In this study, the investigation is made from a different
point of view and the influence of fire and heat is taken into account. The main objective of
this study is to conduct some fire-induced collapse analyses to investigate how fire patterns,
structural weakness of member joints, and outrigger trusses on roof tops give influence on thecollapse behaviors of high-rise towers. The analytical results obtained using the ASI-Gauss
finite element code show a clear difference between each fire pattern, between the models withstrong and weak member-joint strengths, and between the models with and without theoutrigger trusses. In general, the strongly designed models withstand the total collapse,
whereas the weak models initiate their collapse when the temperature reaches to the highest,and ends, eventually in a total collapse. The models with outrigger trusses tend to withstandlonger in time by catenary action only if their load paths are protected.
Keywords: progressive collapse, high-rise towers, 9/11, ASI-Gauss technique, finite elementanalysis.

______________________________________
Daigoro Isobe
University of Tsukuba
1-1-1 Tennodai, Tsukuba-shiIbaraki, 305-8573
Japan
Email: isobe@kz.tsukuba.ac.jp
Tel: +81-29-853-6191

1.0 Introduction
Isobe and his collaborators are seeking for the true cause of the total collapse of the WTC towers
back in 2001 by conducting several numerical simulations. Isobe and Sasaki [1] first performed thefull model aircraft impact analysis of the WTC tower and suggested regarding the obtained resultsthat the spring-back phenomenon due to rapid unloading caused by aircraft impact possibly havedestructed member joints in the core structure, which might have caused the towers to become
brittle and unstable. However, it does not give answers to the total collapse of WTC tower 7,
which collapsed, reportedly, only by fire. In this study, the investigation is made from a different
point of view and the influence of fire and heat is taken into account. The main objective of thisstudy is to conduct some fire-induced collapse analyses to investigate how fire patterns, structural
weakness of member joints, and outrigger trusses on roof tops give influence on the collapse
behaviors of high-rise towers. The analyses are carried out using the ASI-Gauss finite element
code which provides higher computational efficiency than the conventional code. It can also copewith dynamic behavior with strong nonlinearities including phenomena such as member fracture.
A general outline of the ASI-Gauss technique is described and several numerical simulations on
the fire-induced progressive collapse behaviors of high-rise towers are discussed in this paper.

Figure 1. Linear Timoshenko beam element and its physical equivalent.

2.0 Numerical Methods
2.1 ASI-Gauss TechniqueIn this paper, the numerical analyses are carried out using a finite element code based upon theASI-Gauss technique [1,2] with the linear Timoshenko beam elements. Figure 1 shows a linear
Timoshenko beam element and its physical equivalence to the RBSM. As shown in the figure, therelationship between the locations of the numerical integration point and the stress evaluation point
where a plastic hinge is formed is expressed as [3]:r = Äs(1)Here, s is the location of the numerical integration point and r is the location where stresses andstrains are evaluated. s and r are nondimensional quantities that take values between -1 and 1.
In the ASI-Gauss technique, the numerical integration point is shifted adaptively according to Eq.
(1) when a fully plastic section is formed within an element, to form a plastic hinge exactly at thatsection. By doing so, the plastic behavior of the element is simulated appropriately, and theconverged solution is achieved with minimum number of elements per member. When the plastic
hinge is unloaded, the corresponding numerical integration point is shifted back to its normalposition. Here, the normal position means the location where the numerical integration point isplaced when the element acts elastically. Two consecutive elements forming a member are
considered as a subset, as shown in Fig. 2, and the numerical integration points of an elastically
deformed member are placed such that the stress evaluation points coincide with the Gaussian
integration points of the member. This means that stresses and strains are evaluated at theGaussian integration points of elastically deformed members. Gaussian integration points are
optimal for two-point integration and the accuracy of bending deformation is mathematicallyguaranteed [4]. The scheme takes advantage of two-point integration while using one-point
integration in actual calculations. More details on the code can be found in previously publishedpapers [1,2].
Member-101/√31-1 -1

sg 0 r g

1-1/√3r g 0 sg

1Element

Element
Numerical integration pointsg = 1 - (2/√3)

Stress evaluation point

rg = -1 + (2/√3)

Figure 2. Locations of numerical integration and stress evaluation points.
2.2 Consideration of Member Joint Strength and Fracture
We define the joint strength ratio CM which indicates the ratio of member joint strength against themember strength itself. The value is directly used in the function as follows, to explicitly express
the weakness of member joint strength:f=íMx
CM Mx0ì2+íMyCM My0

ì2+íNN0ì2Ä 1 = fy Ä 1 = 0(2)Here, fy is the yield function, and Mx , My and N are the bending moments around the x- and y-axes
and axial force, respectively. Those with the subscript 0 are values that result in a fully plastic

section in an element when they act on a cross section independently. The ratio value CM isassumed on the basis of the fact that the member joint strengths of typical core columns in theWTC towers were about 20 to 30 % of those of the members [5]. The values used in this paper are
CM =1.0 for strong member-joint model and CM = 0.3 for weak member-joint model.
Structurally discontinuous problems also become easily handled using the ASI-Gauss technique byshifting the numerical integration point of the linear Timoshenko beam element to an appropriate
position and by releasing the resultant forces in the element simultaneously. Here, the fracture
condition of member joints are considered by examining the strain values in a member, as follows:ååååååååìíå îx ååå çxz ååå çyz åèzååÄ1 ï 0 or å îy åÄ1 ï 0 orååÄ1 ï 0åå
Ä1 ï 0 or å
Ä1 ï 0 or ååîf x ååîf y åèf z
çf xz åçf yz å(3)where κx, κy, εz, γxｚ, and γyｚ are the bending strains around the x- and y-axes, the axial tensile
strain and the shear strains for the x- and y-axes, respectively. The critical values for these strains
are indicated by the subscript f. We used the critical strain values that are actually obtained fromsome experiments on member joints concerning high strength joint bolts [6]. Elemental contact isconsidered in the code by introducing gap elements between pairs of elements determined to be incontact by geometrical relations.

(a) Elastic modulus(b) Yield strengthFigure 3. Strength reduction curves of steel due to elevated temperatures.
2.3 Consideration of Strength Reduction due to Elevated Temperature
Thermal stress effect is applied to the above mentioned finite element code. The reduction curvesof elastic modulus and yield strength of steel due to elevated temperatures [7], as shown in Figs.
3(a) and 3(b), are also adopted. The elastic modulus of the raw columns without thermal insulationis reduced to 60 % of the original value, and the yield strength to 10 % of the original strength, at
700 ℃, which is a natural temperature in normal fire. We assumed the temperature to rise up to700 ℃ in 7 minutes as shown in Fig. 4. A time increment control is also applied to reduce
calculation time in the seamless analysis from static to dynamic phenomena.

1000

Temperature [℃]8006004002000200

400600800
Duration Time [s]1000

Figure 4. Assumed time history of temperature.

3.0 Numerical Model
The numerical model used in the fire-induced collapse analyses is a 25-story 3-span tower asshown in Fig. 5. An outrigger truss system is placed on the roof top of the model and the influenceof the system against structural vulnerability of the tower is verified in the analyses. The tower ismodeled with 2056 linear Timoshenko beam elements and contains 1488 nodes and 8928 degreesof freedom. For example, the sectional sizes of the columns used on the 1st floor are □430×430×13×13. We provided two cases of member joint strengths as mentioned; strong type (CM= 1.0) and weak type (CM = 0.3), each with and without outrigger truss system, and assumed two
fire patterns; middle three blocks and outer three blocks from 17th to 19th floors as shown in Fig. 5.
Outrigger truss system

100m

Front view

Upper view

18m

18m
Floor size
Figure 5. 25-story 3-span tower model.

Middle three blocks/
17th to 19th floors

Outer three blocks/
17th to 19th floors

Fire patterns

4.0 Numerical Results
Two of the numerical results are shown in Figs. 6 and 7. Both are performed with the weak
member-joint type (CM = 0.3) with outrigger truss systems placed on the roof tops. Figure 6 shows
the result with the middle three blocks on fire and Fig. 7 with the outer three blocks on fire,respectively. Both cases initiate to collapse in different times and continue to collapse
progressively in different modes. The collapse initiation time in the former case is longer than in
the latter case and the upper structure drops vertically to the ground. The collapse initiation time isshort in the latter case and the upper structure slants to the right where the blocks are on fire.

846s

848s

850s

852s

854s

866s

Figure 6. Collapse mode (CM = 0.3, with outrigger truss system, middle three blocks on fire).

698s

700s

702s

704s

706s

720s

Figure 7. Collapse mode (CM = 0.3, with outrigger truss system, outer three blocks on fire).
Table 1 shows the sum of all the results. Strong member-joint models did not collapse regardlessof the arrangement of outrigger truss systems or the fire patterns. The effect of outrigger truss
systems can be observed in the collapse initiation times of the weak member-joint models. Whenthe middle three blocks are on fire, the model with an outrigger truss system initiates its collapse
earlier than the model without it. The load paths to/from the outrigger truss system are completelyintercepted and the system behaves only as an extra mass. The good effect becomes evident when
the outer blocks are on fire. The model tends to withstand longer in time by the catenary action of
the system. It may well be said that the former case with middle three blocks on fire is stable, andthe collapse initiation time tends to delay since the fire pattern is symmetric. However, theoutrigger truss system has reverse effect in this case (151s shortening the initiation time) since theload paths are not protected. The latter case with outer three blocks on fire is comparatively
unstable than the former case, and the collapse initiation time tends to shorten since the fire pattern
is asymmetric. However, the outrigger truss system helps largely to delay the collapse initiation
time (121s delayed in time), since the load paths are partially protected in this case.
Table 1: Influences of member-joint strengths, fire patterns and outrigger truss systems
CMC M =0.3

C M =1.0

Fire patterns
Middle three blocks/
17th to 19th floors
Outer three blocks/
17th to 19th floors
Middle three blocks/
17th to 19th floors
Outer three blocks/
17th to 19th floors

Outrigger truss systems
None
Yes
None
Yes
None
Yes
None
Yes

Collapse initiation time [s]
997
846
577
698－－－－

5.0 Conclusion
The numerical results shown in this paper indicate that the member-joint strengths and fire patterns
give large influences on collapse behaviors of high-rise buildings. Moreover, the outrigger truss
systems on roof tops tend to help elongating the collapse initiation time, only if the load paths
to/from the systems are protected.

6.0 References
1. Isobe, D. and Sasaki, Z., “Aircraft Impact Analyses of the World Trade Center Towers,” CDROM Proceedings of the 1st International Workshop on Performance, Protection, andStrengthening of Structures under Extreme Loading (PROTECT2007), Whistler, Canada, 2007.
2. Kyaw, M.L. and Isobe, D. 2007. “Finite element code for impact collapse problems of framedstructures,” Int. J. Numer. Methods Eng., 69(12): 2538-2563.
3. Toi, Y. 1991. “Shifted Integration Technique in One-Dimensional Plastic Collapse Analysis
Using Linear and Cubic Finite Elements,” Int. J. Numer. Methods Eng., 31: 1537-1552.
4. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P., “Numerical recipes in
FORTRAN: The art of scientific computing,” New York: Cambridge University Press, 1992.
5. ASCE/FEMA, “World Trade Center Building Performance Study: Data Collection, Preliminary
Observation and Recommendations,” 2002.
6. Hirashima, T., Hamada, N., Ozaki, F., Ave, T. and Uesugi, H. 2007. “Experimental Study on
Shear Deformation Behavior of High Strength Bolts at Elevated Temperature,” J. Struct. Constr.
Eng., AIJ, 621: 175-180, in Japanese.
7. NIST NCSTAR 1, “Federal Building and Fire Safety Investigation of the World Trade Center
Disaster: Final Report on the Collapse of the World Trade Center Towers,” National Institute ofStandards and Technology (NIST), 2005.