Energy Estimates of Progressive Floor Collapses and the World Trade Center Catastrophe

The Simple Collapse Model of Ba\v{z}ant and Zhou is evaluated for a progressive floor collapse of a tall building. A sequence of energy estimates indexed by the collapsing floors is derived. Each of the estimates gives a sufficient condition to arrest the collapse at a given floor. The first estimate of this sequence has been stated by Ba\v{z}ant and Zhou and has been repeatedly cited later on. However, this estimate is not optimal in the sense that the following estimates give a weaker condition to arrest the collapse.