Shear strength of concrete members without transverse reinforcement: A mechanical approach to consistently account for size and strain effects

Many theories and empirical formulae have been proposed to estimate the shear strength of reinforced concrete members without transverse reinforcement. It can be noted that these approaches differ not only in the resulting design expressions, but also on the governing parameters and on the interpretation of the failure mechanisms and governing shear-transfer actions. Also, no general consensus is yet available on the role that size and strain effects exhibit on the shear strength and how should they be accounted. This paper reviews the various potential shear-transfer actions in reinforced concrete beams with rectangular cross-section and discusses on their role, governing parameters and the influences that the size and level of deformation may exhibit on them. This is performed by means of an analytical integration of the stresses developed at the critical shear crack and accounting for the member kinematics. The results according to this analysis are discussed, leading to a number of conclusions. Finally, the resulting shear strength criteria are compared and related to the Critical Shear Crack Theory. This comparison shows the latter to be physically consistent, accounting for the governing mechanical parameters and leading to a smooth transition between limit analysis and Linear Elastic Fracture Mechanics in agreement to the size-effect law provided by Bazant et al.

Influence of Fatigue Loading in Shear Failures of Reinforced Concrete Members without Transverse Reinforcement

Miguel Fernández Ruiz, Juan Manuel Gallego Martín, Francisco Manuel Maciel Natário, Aurelio Muttoni

Shear fatigue of reinforced concrete members without transverse reinforcement has been observed to be potentially governing for the strength of some structural members subjected to large live loads of repetitive nature (as traffic, wind or wave actions). Although extensive experimental programmes have been performed in the past and a rational approach to the problem can be performed on the basis of Fracture Mechanics, most design codes still ground shear fatigue design on empirical equations fitted on the basis of existing data. These empirical formulas show inconsistency amongst them and some neglect potentially relevant parameters as the ratio of maximum and minimum fatigue load levels. In this paper, a consistent design approach is presented, by using the principles of Fracture Mechanics applied to quasi-brittle materials in combination with the Critical Shear Crack Theory. This approach leads to a simple, yet sound and rational, design equation incorporating the different influences of fatigue actions (minimum and maximum load levels) and shear strength (size and strain effects, material and geometrical properties). The accuracy of the design expression is checked against available test data in terms of Wöhler (S-N) and Goodman diagrams, showing consistent agreement to experimental evidence. In addition, the estimate of the number of cycles until failure is shown to be significantly more accurate and with lower scatter than current empirical shear fatigue formulations of Eurocode 2 or fib-Model Code 2010.

Journal of Advanced Concrete Technology2015

Tragverhalten und Bemessung von Holz-Glas-Verbundträgern unter Berücksichtigung der Eigenspannungen im Glas

Klaus Kreher

The construction principles of "Timber-Glass-Composite-Girders" demand practical and theoretical research to ensure reliable designs. Toward this objective the mathematical description of load-bearing and the non-rigid bond is the subject of this work, i.e. to define the contributing parameters for the design of these girders. The non-rigid-bond of the adhesive joint is of great importance because of its influence on the load-bearing of the system as a whole. The loading of girders is dominated by permanent forces thus leading to the obligation of knowing the long-term behaviour of the system and its components. The definition of the characteristic values, taking into account the long-term load-bearing, is an intrinsic part of this investigation. It can be shown that the load-bearing of the girders depends on the fracture of the glass panes. The properties of glass-fractures are a function of the residual internal prestresses due to the heat-strengthening of the panes. The load-bearing, particularly the post-cracked behaviour, changes with respect to the intensity of these internal prestresses. The timber is able to reinforce the cracked glass, leading to a ductile load-bearing behaviour as in the girders, with a dependency upon the size of the remaining fractures. A model based on the differential equations of the non-rigid bond is defined in order to calculate the loading-peaks of the adhesive joint and the material loading itself. The characteristic values of the non-rigid bond, such as the number and distances between cracks and the load introducing length, were evaluated in tests on composite slabs and small scale girders. The existing calculation models which take into account non-rigid bonding were modified to adapt the influence of the width and thickness of the adhesive joint. In order to calculate the stressing of the material the existing calculation models were adapted to calculate the post-cracked situation. The load-bearing behaviour of glass-panes bent with respect to its strong neutral axis needs other safety-considerations than panes, bent off their plane. It is shown that the existing safety considerations subject to the use of glass can not easily be adapted onto the composite girders. The bending with respect to the strong neutral axis and the reinforcement of the glass of the timber demands a different hypothesis to adapt the fractural mechanical analysis and to establish a safe limit conception. This is part of the performed research of this document. The following descriptions present briefly the obtained results: Depending on the quality of the glass (residual stresses due to heat-strengthening, e.g. annealed glass, heat-strengthened glass, fully tempered glass), the ductility and the mode of failure of the girders does change. As a result of its failure mode, annealed glass without internal prestresses offers the highest remaining load-carrying potential after the first crack has appeared. This ductility and thus the structural safety, diminishes with an increasing degree of internal prestressing due to thermal treatment. Heat-strengthened glass (with various degrees of prestressing, various residual stresses) shows a decrease in remaining load-carrying capacity with an increasing degree of prestressing until it fails in a brittle mode as fully toughened glass does. This has to be well considered in respect to safety considerations. Girders with panes made of glass having internal residual stresses due to heat strengthening below 50N/mm2 are considered to collapse ductily, residual stresses bigger than 50N/mm2 cause brittle failure. The effective stiffness of the girders decreases under permanent loads in function of the bondage. Both, timber and adhesive take part in this decrease; the influence of both of the involved materials has been defined. Since the design of conventional glass constructions which uses the concept of principle stresses cannot be adapted, unidirectional shear stresses had to be determined for the shear strength of glass, which is defined as 25N/mm2 for annealed glass. The characteristic values of the adhesive to define the non-rigid bonds have been determined, likewise the influence of the width and thickness of the adhesive joint. The load introducing length, the distances between cracks and the number of cracks are defined with tests on composite slabs. A model to describe the theoretical bond with the defined parameters based on the differential equations was developed. This model allows the calculation of the material stressing at the load introduction and on both sides of a crack. To calculate the stressing of glass and timber existing calculation models which take into account non-rigid bonding were modified to adapt the influence of the width and thickness of the adhesive joint. In order to calculate the stressing of the material the existing calculation models were adapted to calculate the post-cracked situation. The safety factors for the influences of the glass surface, environmental conditions, load duration and the parameters of fracture mechanical analysis as developed as they are known for semi-probabilistic safety concepts for glass constructions cannot easily be adopted. The bending with respect to the strong neutral axis demands a different hypothesis in order to adapt the fractural mechanical analysis and to develop the safety parameters. For the reliable design of timber-glass-composite-girders a contribution to the appropriate use of probabilistic, semi-probabilistic and deterministic safety concepts are given. A realised construction (Hotel "Palafitte" in Monruz (NE)) shows an example and the experience made in designing girders.

EPFL2004

Shear strength of members without transverse reinforcement as function of critical shear crack width

Miguel Fernández Ruiz, Aurelio Muttoni

This paper investigates the shear strength of beams and one-way slabs without stirrups based on the opening of a critical shear crack. The shear-carrying mechanisms after the development of this crack are investigated. On this basis, a rational model is developed to estimate the shear strength of members without shear reinforcement. The proposed model is based on an estimate of the crack width in the critical shear region, taking also into account the roughness of the crack and the compressive strength of concrete. The proposed model is shown to properly describe a large set of available test data. A simplified method adopted by the Swiss code for structural concrete (SIA 262) is also introduced. Comparisons with other codes of practice are finally presented, with a highlight on the main differences between them.

ACI Structural Journal2008

Tragverhalten und Bemessung von Holz-Glas-Verbundträgern unter Berücksichtigung der Eigenspannungen im Glas

Klaus Kreher

EPFL2004