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Reply #205: No, it is you who does not understand Bazant's calculations. [View All]

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eomer Donating Member (1000+ posts) Send PM | Profile | Ignore Wed Nov-11-09 10:31 PM
Response to Reply #202
205. No, it is you who does not understand Bazant's calculations.
Edited on Wed Nov-11-09 10:35 PM by eomer
Bazant makes it quite clear that he treats Part C as though it is a rigid block. A rigid block transfers all of its kinetic energy at once when it collides with another object.

Here is one place where Bazant makes that clear (emphasis mine):
3. Localization of Energy Dissipation into Crushing Front:
In the discussers opinion: the hypothesis that the energy
is dissipated at the crushing front implies that the blocks in
Fig. 2 may be treated as rigid, i.e., the deformations of the
blocks away from the crushing front may be neglected. This
is a fundamental misunderstanding. Of course, blocks C and
A are not rigid and elastic waves do propagate into them. But
the wave velocity, given by {formula omitted} where Et=tangential
modulus of steel in the loaded columns and p=mass density,
tends to zero as soon as the plastic or fracturing response is
triggered, because in that case, Et→0. Therefore, as explained
in courses on stress waves, no wave attaining the
material strength can penetrate beyond the crushing (or plastic
) front. Only harmless elastic waves can. Propagation of
the crushing front is not a wave-propagation phenomenon.
Destruction of many stories at the rate corresponding to the
elastic wave speed, which would appear as simultaneous, is
impossible. This is why the collapse is called progressive.
Blocks C and A can, of course, deform. Yet, contrary to
the discussers claim, they may be treated in calculations as
rigid because their elastic deformations are about 1,000 times
smaller than the deformations at the crushing front.

Bazant takes credit in his calculations for 100% of the kinetic energy being applied against Part A at the instant that Part C collides with it. That is what "rigid" means.

Bazant's justification for treating the blocks as rigid might be valid if it weren't for the fact of crush-up of Part C. Given crush-up, the rigid assumption is completely invalidated.

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