This article attempts to review the progress achieved in the understanding of scaling and size ef­ fect in the failure of structures. Particular emphasis is placed on quasi brittle materials for which the size etTect is important and complicated. After reflections on the long history of size effect studies, attention is focused on three main types of size effects, namely the statistical size effect due to randomness of strength, the energy release size effect, and the possible size effect due to fractality of fracture or microcracks. Definitive conclusions on the applicability of these theories are drawn. Subsequently, the article discusses the application of the known size effect law for the measurement of material fracture properties, and the modeling of the size effect by the cohesive crack model, non local finite element models and discrete element models. Extensions to com­ pression failure and to the rate-dependent material behavior are also outlined. The damage con­ stitutive law needed for describing a microcracked material in the fracture process zone is dis­ cussed. Various applications to quasibrittle materials, including concrete, sea ice, fiber compos­ ites, rocks and ceramics are presented. There are 377 references included in this article.

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Scaling of Structural Failure

The article attempts a broad review of the problem of size effect or scaling of failure, which has recently come to the forefront of attention because of its importance for concrete and geotechnical engineering, geomechanics, arctic ice engineering, as well as for designing large load-bearing parts made of advanced ceramics and composites, e.g. for aircraft or ships. First, the main results of Weibull statistical theory of random strength are briefly summarized, and its applicability and limitations described. In this theory as well as plasticity, elasticity with a strength limit, and linear elastic fracture mechanics (LEFM), the size effect is a simple power law, because no characteristic size or length is present. Attention is then focused on the deterministic size effect in quasibrittle materials which, because of the existence of a nonnegligible material length characterizing the size of the fracture process zone, represents the bridging between the simple power-law size effects of plasticity and of LEFM. The energetic theory of quasibrittle size effect in the bridging region is explained, and then a host of recent refinements, extensions and ramifications are discussed. Comments on other types of size effect, including that which might be associated with the fractal geometry of fracture, are also made. The historical development of the size-effect theories is outlined, and the recent trends of research are emphasized.

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Size effect on structural strength: a review

It is not correct to state that the collapse of the Wilkins Air Force Base depot building occurred without warning. The structure was known to be extensively cracked in shear well before the collapse, and it is the discusser’s understanding that some beams in the building were already being braced with shoring consisting of various wooden poles. The observer was in fact looking for additional trouble at the time of the collapse, although it must be argued that the fact that the failure occurred while he was present was coincidence. The record of cracking for the particular design at Wilkins was so bad that a revised design had already been prepared and was used in some similar buildings. The January 1957 issue of the ACI Journal had several articles dealing with the failure and with the repairs to other structures of the same group that had not failed but that were showing significant shear cracking.

Recent Approaches to Shear Design of Structural Concrete

This paper presents a review of research on shear strength of reinforced concrete members without stirrups (shear reinforcement). A database of 1849 available experimental results from over the past 60 years is examined and these results are compared to predictions from current North American shear design procedures. Special attention is paid to the behavior of beams ranging from short span deep beams to members controlled by flexure. The findings from the review indicate that using the current ACI shear provisions to decide where shear reinforcement is required can be unconservative for members with larger effective depths, or higher stresses in the longitudinal reinforcement. Improvements to the ACI Code are proposed to mitigate these weaknesses. The AASHTO-LRFD and Canadian CSA sectional and strut-and-tie provisions are found to provide a more uniform level of safety for all member types. The results from this review can allow engineers to identify members in their own structure where a more conservative shear design procedure is appropriate.

Where is Shear Reinforcement Required? Review of Research Results and Design Procedures

The EURO-C conference series (Split 1984, Zell am See 1990, Innsbruck 1994, Badgastein 1998, St Johann im Pongau 2003, Mayrhofen 2006, Schladming 2010, St Anton am Alberg 2014) brings together researchers and practising engineers concerned with theoretical, algorithmic and validation aspects associated with computational simulations of concrete and

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Norbert Lehwalter

Papers

Size effects in short beams loaded in shear