by Heiwa on Mon Nov 09, 2009 10:10 pm
Mr Beck writes:
II. BAZANT-SEFFEN MODEL OF PROGRESSIVE COLLAPSE
The model was proposed by Bazant and Verdure (Bazant and Verdure, 2006), and then further
developed by Seffen (Seffen, 2008). Under the term progressive collapse the authors assume the
motion of the top section through the stationary building under the following conditions. First,
there is a transfer of mass from the stationary building to the moving top section, which is a
function of a travel distance. Second, the stationary building resists the motion of the top section
through the, so called, crushing force Fc.
The above also clarifies the mistaken assumptions of Bazant/Seffen.
Evidently no transfer of mass from the stationary building, part A, to the moving top section, part C, can take place under any circumstances in a collision. Elements in contact between parts A and C may fail but they will either be attached to A or C or be completely detached from the A or C. It is not possible that a broken element of part A suddenly becomes associated with part C or that a completely detached element (from either A or C) is being accelerated by part C to the latters velocity and then becomes attached to it. Thus the total mass of all elements in part C should remain the same or be reduced due to ejections after impact. What you would expect after impact is that part C suffers serious local failures and is the arrested on top of A - also locally damaged.
Evidently at/after impact part C applies forces on part A, but A applies exactly the same forces on C. Completely detached elements will evidently apply forces on both C and A unless ejected out of way. A major component of the active forces, apart from forces producing elastic and inelastic deformations in elements of A and C, is evidently friction between displaced elements in both C and A now in contact with each other. Both Bazant and Seffen ignores the latter.
Equation (1) therefore does not describe the motion of the upper part C.