Fire-Induced Progressive Collapse Analyses of High-Rise Towers

D. Isobe: Numerical Simulations for Investigation on True Cause of the Total Collapse of the WTC Towers, Proceedings of International Symposium on Structures under Earthquake, Impact, and Blast Loading 2008 (IB'08), (2008), pp. 157-164, Osaka, Japan.

Some analyses of fire-induced collapse are carried out on a 25-story 3-span tower as shown in Fig. 1 to determine the effect of the strength reduction due to elevated temperatures. We used a model with two cases of column thickness; thick type (□-600×600×18×18 at the 1^st floor) and thin type (□-430×430×13×13 at the 1^st floor), two cases of member joint strengths; strong type (C_M=1.0) and weak type (C_M=0.2), and three cases of fire patterns; 17^th ~ 19^th floors with 3 blocks (symmetry), 4 blocks (asymmetry) and 9 blocks (all floor) on fire. The joint strength ratio C_M indicates the ratio of member joint strength against the member strength itself. The value is directly used in the yield function as follows, to explicitly express the influence of member joint strength:

　　　　　　　　　　　　　　　　　　　　　　　(1)

Fig. 1 Analyzed model

The ratio value is assumed on the basis of the fact that the member joint strengths of typical core columns were about 20 to 30 % of those of the members in the WTC towers [ASCE/FEMA, 2002]. Here, the fracture condition of member joints are considered by examining bending strains, axial tensile strain and shear strains in a member, as follows:

　　　 　　　　　　　　 (2)

where γ_xｚ, γ_yｚ, γ_fxｚ, γ_fyｚare the shear strains for the x- and y-axes and the critical values for the strains, respectively. The critical strain values used here are the values actually obtained from some experiments concerning the high strength joint bolts [Hirashima et al, 2007]. Curves showing the reduced elastic modulus and yield strength of steel due to elevated temperatures [NIST NCSTAR1, 2005], as shown in Figs. 2(a) and 2(b), are adopted. The elastic modulus of the columns with no thermal insulation is 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 to 700 ℃ in 7 minutes as shown in Fig. 3. Also, we applied a time increment control to enable continuous calculation from static to dynamic phenomena.

Fig. 2 Strength reduction curves of steel due to elevated temperatures

Fig. 3 Assumed time history of temperature

Two of the numerical results are shown in Figs. 4 and 5. Both are performed with the thin-column type model. Figure 4 shows the result with 3-floors 4-blocks on fire and Fig. 5 with 3-floors 9-blocks on fire, each performed on strong-member-joint type (C_M=1.0) and weak-member-joint type (C_M=0.2). We can clearly see the difference in collapse modes between the two models in both figures. The strong-member-joint models initiate to collapse once they buckle at the floors that are on fire, but withstand to collapse any further by redistributing the stresses in the towers. The weak-member-joint models, on the other hand, fail to stop the progression of collapse and end in a total destruction. Table 1 shows the sum of all the results. It can be concluded that the possibility of total collapse becomes high, in spite of thickness of the columns, when the joint strength ratio is low. Fire patterns do have influence on the possibility of collapse. Multi-floor and asymmetric fire patterns may increase the possibility of collapse. And furthermore, the collapse speeds were much slower than the free-fall or saturated speed in these cases, which does not explain the high-speed collapse of the WTC towers.

Fig. 4 Fire-induced collapse analysis with 3F-4 blocks fire pattern (thin column model)

　
Fig. 5 Fire-induced collapse analysis with 3F-9 blocks fire pattern (thin column model)

Table 1 Collapse modes occurred in the fire-induced collapse analyses

The numerical results shown above might indicate that the highly-rapid total collapse of the WTC towers was caused not only by the buckling and strength reduction of members due to elevated temperatures, but by the original weakness of the member joints and the destruction of those during the collision of the aircraft (see here). Further investigations by performing full-model fire-induced collapse analyses of the WTC towers are scheduled.

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D.Isobe and Y.Toi: Analysis of Structurally Discontinuous Reinforced Concrete Building Frames Using the ASI Technique, Computers and Structures, Vol.76, No.4, (2000), pp.471-481. abstract

Related papers (Proceedings):

K.Shimizu and D.Isobe: Collapse Analysis of Framed Structures Considering Strength Reduction Caused By Fire, Proceedings of the 17th JSME Computational Mechanics Conference, No.04-40, (2004), pp.501-502, in Japanese. abstract

K.Imanishi and D.Isobe: Progressive Collapse Analyses of Framed Structures by Using ASI-Gauss Technique, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2005 B-1, (2005), pp.329-330, in Japanese. abstract

K.Imanishi and D.Isobe: Progressive Collapse Analyses of Framed Structures by Using ASI-Gauss Technique, Proceedings of the 18th JSME Computational Mechanics Conference, No.05-2, (2005), pp.325-326, in Japanese. abstract

T. Omuro and and D. Isobe: Collapse Analysis of Framed Structures Considering Strength Reduction Caused By Fire, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2006 B-1, (2006), pp.271-272, in Japanese. abstract

K. Imanishi and and D. Isobe: Progressive Collapse Analyses of Framed Structures Considering Member Joint Factor, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2006 B-1, (2006), pp.273-274, in Japanese. abstract

T. Omuro and D. Isobe: On Fire-induced Collapse Behavior of Buildings, Proceedings of the 19th JSME Computational Mechanics Conference, No.06-9, (2006), pp.251-252, in Japanese. abstract

K. Imanishi and D. Isobe: Effect of Member Joint Strength in Progressive Collapse Phenomenon, Proceedings of the 19th JSME Computational Mechanics Conference, No.06-9, (2006), pp.253-254, in Japanese. abstract

T. Omuro and D. Isobe: Influence of Earthquakeproof Structural Strength on Fire-Induced Collapse Behavior of Buildings, Proceedings of the 20th JSME Computational Mechanics Conference, No.07-36, (2007), pp.295-296, in Japanese. abstract

D. Isobe and T. Omuro: Fire-Induced Collapse Analysis of Framed Structures Using ASI-Gauss Technique, Proceedings of the Conference on Computational Engineering and Science, Vol.13, No.1, (2008), pp.129-130, in Japanese. abstract

D. Isobe: An Adaptive Finite Element Code Using Linear Timoshenko Beam Elements and Its Applications, CD-ROM Proceedings of 6 th International Conference on Computation of Shell and Spatial Structures IASS-IACM2008, (2008), Ithaca, New York USA. abstract

D. Isobe: Investigation on the Cause of Total Collapse of WTC Towers using ASI-Gauss Dynamic Collapse Analysis Code, Proceedings of the 57th National Congress of Theoretical and Applied Mechanics, (2008), pp.247-248, in Japanese. abstract

D. Isobe and T. Omuro: Fire-Induced Collapse Analyses of High-Rise Towers using ASI-Gauss technique, Abstracts of the 8th World Congress on Computational Mechanics, (2008), Venice, Italy. abstract

H. Yokota and D. Isobe: Progressive Collapse Analyses of Framed Structures Considering Elevated Temperature due to Fire, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2008 B-1, (2008), pp.393-394, in Japanese. abstract

D. Isobe: Numerical Simulations for Investigation on True Cause of the Total Collapse of the WTC Towers, Proceedings of International Symposium on Structures under Earthquake, Impact, and Blast Loading 2008 (IB'08), (2008), pp. 157-164, Osaka, Japan. abstract

H. Yokota and D. Isobe: Fire-Induced Collapse Analysis of Miniature WTC Models using ASI-Gauss Technique, Proceedings of the 21th JSME Computational Mechanics Conference, No.08-33, (2008), pp.61-62, in Japanese. abstract

L. T. T. Thanh and D. Isobe: Fire-Induced Collapse Analysis of Buildings with Eartuquake-Resistant Design, Proceedings of the Conference on Computational Engineering and Science, Vol.14, No.1, (2009), pp.329-332, in Japanese. abstract

D. Isobe, H. Yokota and L. T. T. Thanh: Fire-Induced Progressive Collapse Analyses of High-Rise Towers, CD-ROM Proceedings of the 2nd International Workshop on Performance, Protection, and Strengthening of Structures under Extreme Loading (PROTECT2009), (2009), Hayama, Japan. abstract

L. T. T. Thanh and D. Isobe: Effect of Outrigger System on Fire-Induced CollapseBehaviors of High-Rise Buildings, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2009 B-1, (2009), pp.275-276, in Japanese. abstract

L. T. T. Thanh and D. Isobe: Influence of Outrigger Truss System on Fire-Induced Collapse Behavior of High-Rise Buildings, Proceedings of the 22th JSME Computational Mechanics Conference, No.09-21, (2009), pp.151-152, in Japanese. abstract

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