TITLE:
A Contribution to Analysis of Collapse of High-Rise Building Inspired by the Collapses of WTC1 and WTC2: Derivation of Simple Formulas for Collapse Upper Speed and Acceleration
AUTHORS:
Ivan Němec, Miroslav Trcala, Jiří Vala, Adéla Vaněčková
KEYWORDS:
Progressive Collapse, WTC, High-Rise Building, Equation of Motion, Upper Limit Acceleration, 9/11
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.12,
December
27,
2018
ABSTRACT: The paper is a contribution to the
technical discussion concerning the collapses of the WTC buildings. It returns
to the problem of the dynamics of the collapses; it does not concern the reason
why the buildings started collapsing, but investigates the dynamics of the
collapse itself. It works with the same assumptions as the official NIST report [1], i.e. that the falling mass
hits the motionless mass beneath; the supporting
columns loose stability and the mass of the pertinent floor starts to fall
together with the falling mass. The aim was to derive the theoretical upper
limit of the speed of the collapse, supposing that influence of the columns
which resist the fall, is neglected. The differential equation of the fall was
obtained using two independent laws of mechanics, with the identical result.
Its solution can be found from a very simple explicit formula. The theoretical
upper limit acceleration of the fall obtained by such formula is one third of
the gravitational acceleration, which is faster than it was observed in the
case of the collapses of WTC1 and WTC2. This leads to the conclusion that the
mechanism of the collapse must be different from the assumed and the falling mass must not hit the motionless mass bellow it,
but rather a mass which had started to fall before the impact of the falling
mass occurred.