Showing papers by "Zdenek P. Bazant published in 2001"
01 Jan 2001
141 citations
TL;DR: In this article, a new thermodynamic framework for the microplane model is proposed, where a free energy potential is defined at the micro-plane level, such that its integral over all orientations gives the standard macroscopic free energy.
124 citations
TL;DR: In this paper, a simplified approximate analysis of the overall collapse of the World Trade Center towers is presented, and it is shown that if prolonged heating causes the majority of columns of a single floor to lose their load-carrying capacity, the whole tower is doomed.
Abstract: Simplified approximate analysis of the overall collapse of the World Trade Center towers is presented. It is shown that if prolonged heating causes the majority of columns of a single floor to lose their load-carrying capacity, the whole tower is doomed.
118 citations
01 Jan 2001
TL;DR: In this article, the authors presented a simplified approximate analysis of the overall collapse of the towers of World Trade Center in New York on September 11, 2001, showing that if prolonged heating caused the majority of columns of a single floor to lose their load carrying capacity, the whole tower was doomed.
Abstract: This paper presents a simplified approximate analysis of the overall collapse of the towers of World Trade Center in New York on September 11, 2001. The analysis shows that if prolonged heating caused the majority of columns of a single floor to lose their load carrying capacity, the whole tower was doomed. The structural resistance is found to be an order of magnitude less than necessary for survival, even though the most optimistic simplifying assumptions are introduced. The problems of tall buildings with a load-bearing R/C core are briefly pointed out.
103 citations
01 Jan 2001
TL;DR: In this article, the authors describe the recent efforts to combin eth eclassica lWeibul ltheor yo fstatistica lsiz eeffec tdu et al. with the recently developed energetic theory, and also survey various related problems such as the probability tail structure of the stochastic finite element methods, the random scatter in fracture testing, the role of fractal nature of cracks, the reliability provisions of design codes, and the lessons from past structural catastrophes.
Abstract: Progres si nstructura ldesig nrequire sprobabilisti cmodelin go fquasibrittle fracture ,whic hi stypica lo fconcrete ,fibe rcomposites ,rocks ,toughene dceramics ,se aic eand man y'hig htech 'materials .Th emos timportan tconsequenc eo fquasibrittl ebehavio ri sa deterministi c(energetic )siz eeffect ,th etheor yo fwhic hevolve dnea rth een do flas tcentury. After a review of the background, the present plenary lecture describes the recent efforts to combin eth eclassica lWeibul ltheor yo fstatistica lsiz eeffec tdu et oloca lstrengt hrandomness with the recently developed energetic theory, and also surveys various related problems, such as the probability tail structure of the stochastic finite element methods, the random scatter in fracture testing, the role of fractal nature of cracks, the reliability provisions of design codes, and the lessons from past structural catastrophes.
41 citations
TL;DR: In this article, the authors proposed a method to incorporate this size effect into the existing test standards, and focused particularly on ASTM Standards C 7894 and C 293-94, based on a recently established size effect formula that describes both the deterministic-energetic size effect caused by stress redistribution within the cross section due to finite size of the boundary layer of cracking at the tensile face of beam, and the classical Weibull-type statistical size effect due to the randomness of the local strength of material.
Abstract: Recently accumulated test data on the modulus of rupture, as well as analytical studies and numerical simulations, clearly indicate that the flexural strength of concrete, called the modulus of rupture, significantly decreases as the beam size increases. This paper proposes a method to incorporate this size effect into the existing test standards, and focuses particularly on ASTM Standards C 7894 and C 293-94. The proposed method is based on a recently established size effect formula that describes both the deterministic-energetic size effect caused by stress redistribution within the cross section due to finite size of the boundary layer of cracking at the tensile face of beam, and the classical Weibull-type statistical size effect due to the randomness of the local strength of material. Two alternatives of the test procedure are formulated. In the first alternative, beams of only one size are tested (as is recommended in the current standard), and the size effect on the mean modulus of rupture is approximately predicted on the basis of the average of existing information for all concretes. In the second alternative, beams of two sufficiently different sizes are tested. The latter is more tedious but gives a much better prediction of size effect for the concrete at hand; it allows for the estimation of size effect on not only the mean but also the coefficient of variation of the modulus of rupture (particularly, its decrease with increasing size). Numerical examples demonstrate the feasibility of the proposed approach.
39 citations
TL;DR: In this article, the size effect in concrete based on large-size asymptotic approximations of the cohesive crack model was analyzed, and it was shown that the nominal strength can be determined only for sizes above a certain lower bound, large enough to invalidate, at least for concrete, all the existing experimental methods based on size effect measurements, such as the Bažant or the general bilinear fit method of Planas, Guinea and Elices.
Abstract: Karihaloo recently published an analytical study of the size effect in concrete based on large-size asymptotic approximations of the cohesive crack model. From this analysis, he concluded that the nominal strength can be determined only for sizes above a certain lower bound, large enough to invalidate, at least for concrete, all the existing experimental methods based on size effect measurements, such as the size effect method of Bažant or the general bilinear fit method of Planas, Guinea and Elices. The purpose of this paper is to show that this conclusion is misleading, and to explain why.
13 citations
01 Jan 2001
TL;DR: In this article, a nonlocal generalization of Weibull theory is presented to predict the probability of failure of unnotched structures that reach the maximum load before a large crack forms, as is typical of the test of modulus of rupture.
Abstract: A nonlocal generalization of Weibull theory is presented to predict the probability of failure of unnotched structures that reach the maximum load before a large crack forms, as is typ- ical of the test of modulus of rupture. The probability of failure at a material point is assumed to be a power function of the average strain in the neighborhood of that point. For normal sizes, the deterministic theory is found to dominate the mean response and govern the size effect. But the probabilistic theory can provide the entire probability distribution. For extremely large beam sizes, the statistical size effect dominates and the mean prediction approaches asymptotically the classical Weibull size effect. This fundamental feature is discussed in relation to the existing stochastic finite element models. Comparison to the existing test data demonstrates a good agreement with the theory. As became clear in the early 1980's, the size effect on the nominal strength of quasibrittle structures is in most instances predominantly deterministic. It is caused by stress redistributions and energy release associated with either the growth of a large fracture process zone (FPZ) or a long stable crack (Bazant 1984, Bazant & Chen, 1997; Bazant & Planas 1998). Since the material properties represent a random field, some aspects of the size effect should nevertheless be probabilistic. Presenting a new combined energetic-probabilistic theory and exploring where the statistical aspect is important for the mean, variance and probability distribution is objective of this paper. A combined energetic-probabilistic theory, having the classical Weibull probabilistic theory of failure as one limit and the deterministic energetic theory as another limit, can be now developed on the basis of the available evidence. Since the Weibull theory (Weibull 1939), based on the weakest link model, deals with structures that fail before a large (macroscopic) crack can form, a nonlocal generalization of Weibull statistical theory may be developed to predict the probability of failure of unnotched structures that reach the maximum load before a large crack forms, as is typical of the test of modulus of rupture (flexural strength). The tail of the cumulative probability distribution of material failure at one point is assumed to be a power function (characterized by Weibull modulus and scaling parameter )o f the average inelastic (or damage) strain in a neighborhood the size of which is characterized by the material char- acteristic length. The averaging indirectly imposes spatial statistical correlation. The deterministic size effect is automatically exhibited as the limit case of such a formulation for .
4 citations