Showing papers by "Zdenek P. Bazant published in 2007"
TL;DR: In this article, a dynamic one-dimensional continuum model of progressive collapse is developed, in which two phases are distinguished by a nonlinear second-order differential equation for the propagation of the crushing front of a compacted block of accreting mass.
Abstract: Progressive collapse is a failure mode of great concern for tall buildings, and is also typical of building demolitions. The most infamous paradigm is the collapse of the World Trade Center towers. After reviewing the mechanics of their collapse, the motion during the crushing of one floor (or group of floors) and its energetics are analyzed, and a dynamic one-dimensional continuum model of progressive collapse is developed. Rather than using classical homogenization, it is found more effective to characterize the continuum by an energetically equivalent snap-through. The collapse, in which two phases—crush-down followed by crush-up—must be distinguished, is described in each phase by a nonlinear second-order differential equation for the propagation of the crushing front of a compacted block of accreting mass. Expressions for consistent energy potentials are formulated and an exact analytical solution of a special case is given. It is shown that progressive collapse will be triggered if the total (intern...
170 citations
23 Apr 2007
TL;DR: In this article, a rational determination of safety factors of quasibrittle structures, taking into account their size and shape, is presented. But the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully WeibULL pdf at large sizes.
Abstract: The objective of this paper1 is a rational determination of safety factors of quasibrittle structures, taking into account their size and shape. To this end, it is necessary to establish the probability density distribution function (pdf) of the structural strength. For perfectly ductile and perfectly brittle materials, the proper pdf’s of the nominal strength of structure are known to be Gaussian and Weibullian, respectively, and are invariable with structure size and geometry. However, for quasibrittle materials, many of which came recently to the forefront of attention, the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully Weibull pdf at large sizes. This recent result is reviewed, and then mathematically extended in two ways: 1) to a mathematical description of structural lifetime as a function of applied (time-invariable) nominal stress, and 2) to a mathematical description of ∗McCormick Institute Professor and W.P. Murphy Professor of Civil Engineering and Materials Science, Northwestern University, 2145 Sheridan Road, CEE/A135, Evanston, Illinois 60208; z-bazant@northwestern.edu. Authorized republication, with minor modifications, of a paper that was presented at the 48th AIAA/ASME/ASCE/AHS/ASE Structures, Structural Dynamics and Materials Conference in Honolulu, Hawaii, and appeared in the CD of conference proceedings, American Institute of Aeronautics and Astronautics, pp. 1–15.
3 citations