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 fire-induced collapse analyses are carried out on a high-rise tower
model, as shown in Fig. 1, which presents an important role in an investigation
of the true cause of the total collapse of the WTC towers. An outrigger
truss system is placed on the roof top of the model, and the influence
of the system against structural vulnerability of the tower is verified
in the analysis. The tower is modeled with 9,360 linear Timoshenko beam
elements and contains
6,644 nodes and 39,600 degrees of freedom. For example, the sectional sizes of
the columns used on the 1^{st}
floor are □-700×28. We
set the member joint strength ratio *C _{M}* to vary from 0.1 to
0.6. We applied three fire patterns; middle three rows to outer three rows,
from the 21

Fig. 1 Analyzed model

Fig. 2 Assumed
fire patterns (21F~24F)

Fig. 3 Collapse
mode (*C _{M}_{ }*= 0.3, fire pattern A)

Fig. 4 Collapse
mode (*C _{M}_{ }*= 0.3, fire pattern B)

Fig. 5 Collapse
mode (*C _{M}_{ }*= 0.3, fire pattern C)

Figures 3, 4, 5 show the collapse modes of the tower exposed to each fire
pattern when the member joint strength ratio *C _{M}* was set to 0.3 and the axial force ratio was set to 0.33 with the regular-strength outrigger truss system (the structural strength was similar to the beams on the 1st floor) placed on the roof. In all of the cases, a total collapse was inevitable and the results clearly show the effect of the weak member joints and the effect of the strength reduction due to the elevated temperatures. As shown in the figures, the shock wave propagates through the columns and moves faster than the falling motion of the upper structure, which destroys the member joints as it moves towards the ground level. The fire patterns do not seem to affect the overall collapse behavior; however, the slant angles at the collapse initiation phase are different, and the collapse initiation time is shorter if the fire pattern is asymmetrical. The collapse initiation time depends on the strength and the number of outrigger trusses that support the load paths near structural deficiencies. In general, the models with outrigger truss systems withstand for a longer time due to catenary action under the condition that the load paths are protected.

**Related papers (Books):**

D. Isobe: Redudancy and Robustness in Architectural and Structural Design, Applied Mechanics Series 12, Architectural Institute of Japan, ISBN:978-4-8189-0611-2, pp. 84-98, 2013.

D. Isobe: Progressive Collapse Analysis of Structures: Numerical Codes and Applications, Elsevier, eBook ISBN:9780128130421, Paperback ISBN:9780128129753, 2017. ElsevierD. Isobe, Solving problems in structural dynamics using beam elements: From collapse behaviors of buildings to torque cancelling of robots, Maruzen, ISBN:978-4-621-30544-7, 2020. Maruzen Amazon

**Related papers (Journals):**

Y.Toi and D.Isobe: Adaptively Shifted Integration Technique in the Finite Element Collapse Analysis of Framed Structures, Journal of the Society of Naval Architects of Japan, Vol.171, (1992), pp.309-317, in Japanese. DOI: 10.2534/jjasnaoe1968.1992.309

Y.Toi and D.Isobe: Adaptively Shifted Integration Technique for Finite Element Collapse Analysis of Framed Structures, International Journal for Numerical Methods in Engineering, Vol.36, (1993), pp.2323-2339. DOI: 10.1002/nme.1620361402

Y.Toi and D.Isobe: Finite Element Analysis of Buckling Collapse Behaviors of Framed Structures by Using Adaptively Shifted Integration Technique, Journal of the Society of Naval Architects of Japan, Vol.174, (1993), pp.469-477, in Japanese. DOI: 10.2534/jjasnaoe1968.1993.174_469

Y.Toi and D.Isobe: Finite Element Analysis of Dynamic Collapse Behaviors of Framed Structures by the Adaptively Shifted Integration Technique, Journal of the Society of Naval Architects of Japan, Vol.175, (1994), pp.299-306, in Japanese. DOI: 10.2534/jjasnaoe1968.1994.299

Y.Toi and D.Isobe: Finite Element Analysis of Quasi-Static and Dynamic Collapse Behaviors of Framed Structures by the Adaptively Shifted Integration Technique, Computers and Structures, Vol.58, No.5, (1996), pp.947-955. DOI: 10.1016/0045-7949(95)00195-M

D.Isobe and Y.Toi: Finite Element Analysis of Dynamic Collapse Behaviors of Brittle Framed Structures by the Adaptively Shifted Integration Technique, Journal of the Society of Naval Architects of Japan, Vol.180, (1996), pp.471-478, in Japanese. DOI: 10.2534/jjasnaoe1968.1996.180_471

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. DOI: 10.1016/S0045-7949(99)00122-4

D. Isobe and L. T. T. Thanh: Verification on Collapse Behaviors of High-Rise Buildings under Fire Using Numerical Approach, Journal of Structural and Construction Engineering, AIJ, Vol. 76, No. 667, (2011), pp.1659-1664, in Japanese. DOI: 10.3130/aijs.76.1659

D. Isobe, L. T. T. Thanh and Z. Sasaki: Numerical Simulations on the Collapse Behaviors of High-Rise Towers, International Journal of Protective Structures, Vol. 3, No. 1, (2012), pp.1-19. DOI: 10.1260/2041-4196.3.1.1

K. Oi and D. Isobe: Collapse Risk Prediction of Buildings on Fire Using Key Element Index, Journal of Structural and Construction Engineering, AIJ, Vol. 82, No. 738, (2017), pp.1213-1220, in Japanese. DOI: 10.3130/aijs.82.1213

K. Azuma and D. Isobe: Risk Prediction of Progressive Collapse Using Evaluation Index for Structural Strengths of Buildings, Journal of Structural and Construction Engineering, AIJ, Vol. 83, No. 744, (2018), pp.253-263, in Japanese. DOI: 10.3130/aijs.83.253

M. M. Javidan, H. Kang, D. Isobe and J. Kim: Computationally Efficient Framework for Probabilistic Collapse Analysis of Structures under Extreme Actions, Engineering Structures, Vol. 172, (2018), pp. 440-452. DOI: 10.1016/j.engstruct.2018.06.022

**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

D. Isobe:An adaptive finite element code for impact and collapse analyses of buildings, Abstracts of the 2nd International Workshops on Advances in Computational Mechanics (IWACOM-II), (2010), Yokohama, Japan. abstract

D. Isobe: Structural Collapse Analyses of Buildings Using an Adaptive Finite Element Code, Abstracts of the 4th Korea-Japan COSEIK-JSCES Workshop on Computational Engineering, (2010), Fukuoka, Japan. abstract

D. Isobe, L. T. T. Thanh, T. Katsu and Y. Arakaki, Recent Applications of ASI-Gauss FE Code in Structural Collapse Problems of Large-Scale Framed Structures, Proceedings of the 9th World Congress on Computational Mechanics and 4th Asian Pacific Congress on Computational Mechanics (WCCM/APCOM2010), (2010), Sydney, Australia. abstract

L. T. T. Thanh and D. Isobe, Numerical Investigations on Effects of Structural Parameters in Fire-Induced Collapse Behaviors of High-Rise Buildings, Proceedings of the 9th World Congress on Computational Mechanics and 4th Asian Pacific Congress on Computational Mechanics (WCCM/APCOM2010), (2010), Sydney, Australia. abstract

L. T. T. Thanh and D. Isobe: Investigation on Fire-Induced Collapse Initiation Times of High-Rise Buildings with Outrigger Truss Systems, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2010 B-1, (2010), pp.285-286, in Japanese. abstract

L. T. T. Thanh and D. Isobe: Verification on Collapse Initiation Times of High-Rise Buildings by Fire-Induced Collapse Analysis, Proceedings of the 23th JSME Computational Mechanics Conference, No.10-2, (2010), pp.424-425, in Japanese. abstract

D. Isobe and L. T. T. Thanh: Effects of Outrigger Truss Systems on Collapse Initiation Times of High-Rise Towers Exposed to Fire, Applied Mechanics and Materials (Selected, peer reviewed papers of the 3rd International Workshop on Performance, Pretection and Strengthening of Structures under Extreme Loading (PROTECT2011)), (2011), Vol. 82, pp.344-349, Lugano, Switzerland. abstract

D. Isobe: A Collapse Analysis Code and Its Recent Applications, Abstracts of the 1st Spain - Japan Workshop on Computational Mechanics, (2012), Barcelona, Spain.abstract

N. Yokemura, J. Suzuki and D. Isobe: Study on Scattered Area of Non-Structural Elements of Steel Construction Buildings under Fire, CD-ROM Proceedings of the Conference on Computational Engineering and Science, Vol.18, (2013), in Japanese. abstract

N. Yokemura, J. Suzuki and D. Isobe: Numerical Study on Scattered Area of Non-Bearing Walls under Fire, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2013, (2013), pp. 71-72, in Japanese. abstract

J. Suzuki, N. Yokemura and D. Isobe: Damage Estimation of Steel Frame Buildings under Fire Using Collapse Analysis, Extended Abstracts of the 1st International Conference on Computational Engineering and Science for Safety and Environmental Problems (COMPSAFE2014), (2014), pp. 436-439, Sendai, Japan. abstract

K. Oi and D. Isobe: Collapse Risk Prediction of Buildings under Fire Using Key Element Index, CD-ROM Proceedings of the Conference on Computational Engineering and Science, Vol.20, (2015), in Japanese. abstract

K. Oi and D. Isobe: Collapse Risk Prediction of Buildings under Fire Using Key Element Index, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2015, (2015), pp. 293-294, in Japanese. abstract

K. Oi and D. Isobe: Relevance of Key Element Index and Damage Extent of Buildings under Fire, Proceedings of the 28th JSME Computational Mechanics Conference, No.15-19, (2015), in Japanese. abstract

K. Azuma and D. Isobe: Relationship between Design Strength of Buildings and the Risk of Occurrence of Progressive Collapse, CD-ROM Proceedings of the Conference on Computational Engineering and Science, Vol.21, (2016), in Japanese.abstract

D. Isobe: A Finite Element Approach to Analyze Large-Scale Collapse Behaviors of Buildings and Motion Behaviors of Non-Structural Components, Semi Plenary Lecture, Proceedings of the 12th World Congress on Computational Mechanics (WCCM XII), (2016), Seoul, Korea. abstract

D. Isobe: Large-Scale Collapse Analyses of Buildings and Motion Analyses of Non-Structural Components within Them, Thematic Plenary Lecture, Abstracts of the International Conference on Computational Methods (ICCM2016), (2016), Berkeley, CA, USA. abstract

K. Oi and D. Isobe: Risk Prediction of Collapse for Buildings under Fire

K. Azuma and D. Isobe: Relationship between the Risk of Occurrence of Progressive Collapse and Overload Ratio of Buildings, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2016, (2016), pp. 357-358, in Japanese. abstract

K. Oi and D. Isobe: Relevance of Key Element Index and Collapse Risk of Buildings under Fire, Proceedings of the 29th JSME Computational Mechanics Conference, No.16-4, (2016), in Japanese. abstract

K. Azuma and D. Isobe: Relationship between Key Element Index and the Risk of Progressive Collapse, CD-ROM Proceedings of the Conference on Computational Engineering and Science, Vol.22, (2017), in Japanese.abstract

D. Isobe, K. Oi and K. Azuma: Risk Estimation for Progressive Collapse of Buildings, Keynote Lecture, 12th International Conference on Shock & Impact Loads on Structures (SILOS2017), 15-16 June 2017, Singapore. abstract

K. Azuma and D. Isobe: Relationship between the Risk of Occurrence of Progressive Collapse and Key Element Index of Buildings, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2017, (2017), pp. 269-270, in Japanese. abstract

K. Azuma and D. Isobe: Relationship between Risk of Progressive Collapse and Evaluation Index for Structural Strengths of Buildings, Proceedings of the 30th JSME Computational Mechanics Conference, No.17-4, (2017), in Japanese. abstract

K. Azuma and D. Isobe: Risk Estimation for Progressive Collapse of Buildings Using Key Element Index, Abstracts of the 2nd International Conference on Computational Engineering and Science for Safety and Environmental Problems (COMPSAFE2017), (2017), Chengdu, China. abstract

D. Isobe and K. Azuma: Progressive Collapse Analysis of Buildings and Its Risk Estimation Using Key Element Index, Proceedings of the 13th World Congress on Computational Mechanics (WCCM XIII), (2018), New York, USA. abstract

D. Isobe: Development of a Collapse Analysis Code of Buildings and Its Applications, Proceedings of the Mechanical Engineering Congress, 2018 Japan, JSME, No.18-1, (2018), in Japanese. abstract

D. Isobe: Solving problems in structural dynamics using beam elements: From collapse behaviors of buildings to torque cancelling of robots, Plenary Lecture, Abstracts of the 11th International Conference on Computational Methods (ICCM2020), (2020), Virtual Conference. abstract

T. Tago and D. Isobe: Numerical Evaluation on Collapse Behavior of Prefabricated Scaffolds under Wind Loads, CD-ROM Proceedings of the Conference on Computational Engineering and Science, Vol.26, (2021), in Japanese.abstract

S. Chiba and D. Isobe: Numerical Investigation on Progressive Collapse of Rack Systems in Warehouse, CD-ROM Proceedings of the Conference on Computational Engineering and Science, Vol.26, (2021), in Japanese.abstract

S. Chiba and D. Isobe: Numerical Investigation on Methods for Suppressing the Collapse of Pallet Rack Systems, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2021, (2021), pp. 277-278, in Japanese. abstract

T. Tago and D. Isobe: Evaluation on the Collapse Behavior of Prefabricated Scaffolds due to the Difference in Attachment Positions of Wall Ties, Summaries of Technical Papers of Annual Meeting Architectural Institute of Japan 2021, (2021), pp. 735-736, in Japanese. abstract

D. Isobe: Beam elements and their applications in various fields of structural dynamics, Plenary Lecture, the 28th International Conference on Computational & Experimental Engineering and Sciences (ICCES2022), (2022), Virtual Conference. abstract

K. Itakura and D. Isobe: Collapse Risk Evaluation of Buildings due to Large-Scale Fire Spread, Proceedings of the Conference on Computational Engineering and Science, Vol.27, (2022), in Japanese.abstract

T. Tago and D. Isobe: One-Way FSI Analysis of Prefabricated Scaffolds under Wind Loads, Proceedings of the Conference on Computational Engineering and Science, Vol.27, (2022), in Japanese.abstract

D. Isobe and S. Chiba: Progressive Collapse Analysis of Heavily Loaded Pallet Rack Systems Subjected under Impact Loads, Proceedings of the 15th World Congress on Computational Mechanics (WCCM XV), (2022), Yokohama, Japan, Virtual Congress. abstract

J. Zhu and D. Isobe: Numerical Investigation on the Collapse of the Champlain Towers South in Florida, Proceedings of the 35th JSME Computational Mechanics Conference, (2022), in Japanese. abstract