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World Trade Center Collapse-Some Examples of Mechanics

World Trade Center Collapse-Some Examples of Mechanics. J. W. Eischen. Precision Engineering Center Lunch Seminar Nov. 8, 2002. Reference. Why Did the World Trade Center Collapse?- Simple Analysis, Prof. Z. P. Bazant and Y. Zhou, Mechanics Magazine, Oct. 2001.

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World Trade Center Collapse-Some Examples of Mechanics

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  1. World Trade Center Collapse-Some Examples of Mechanics J. W. Eischen Precision Engineering Center Lunch Seminar Nov. 8, 2002

  2. Reference • Why Did the World Trade Center Collapse?- Simple Analysis, Prof. Z. P. Bazant and Y. Zhou, Mechanics Magazine, Oct. 2001. • Some simple mechanics to explain impact effect and collapse mechanism • We will look at aircraft impact, dynamic loading, energy considerations, and timing

  3. Aircraft Impact • Conservation of momentum • m767=179,000kg, v767=550km/hr • MWTC=Meq=141x106kg (44% total) • m767v767=MWTCvWTC » vWTC=0.7km/hr=0.19m/s • Impact on equivalent cantilever • T1=14s, Meq=141x106kg • dmax= vWTCT1/2p » dmax =0.4m

  4. Aircraft Impact • Maximum deflection within design limits (wind loads), only local damage expected • Building was designed for 707 impact, weight only about 15% less than 767 • Building was adequately designed for impact • Fire damage was critical • B-25 impact on Empire State building in 1945 caused fire contained to two floors, columns are much heavier in this older building

  5. Upper Structure Collapse

  6. Upper Structure Collapse • Failure process after initial trigger is very complex • Upper part of South Tower tilted initially • Distribution of impact forces on floors below is complex • A simple calculation follows that shows it was impossible for the structure to survive

  7. Upper Structure Collapse • Impact analysis (ignores wave propagation and energy dissipation) • C=71GN/m, h=3.7m, m=58x106kg »

  8. Upper Structure Collapse • Estimate of energy dissipation in columns due to rotation of plastic hinges is only 12% of gravitational potential even if columns were cold • Dynamic loading on columns exceeded capacity by at least an order of magnitude (SF probably 1.6-2) • Dynamic loading is even worse if based on wave propagation analysis

  9. Upper Structure Collapse

  10. Rotation of Upper Part of South Tower • Rotational dynamics

  11. Rotation of Upper Part of South Tower • Horizontal shear resistance of columns is overwhelmed by dynamic reaction force from tilting • Fmax/Fp exceeds one when q 2.8deg. • Pivoting would have caused failures below and then the motion was predominately vertical

  12. Free-Fall Analysis • Particle motion vertical direction • htop=416m, hpile=25m »tfall=8.93sec • Matches observations exactly, confirms lack of energy dissipation in slowing collapse

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