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Stress fields and strut-and-tie models are widely used for design and assessment of structural concrete members. Although they are often used in the same manner for both purposes, developing suitable stress fields and strut-and-tie models for the design of a new structure or for assessment of the strength of an existing one should not necessarily be performed following the same approach. For design, simple load-carrying models in equilibrium with the external actions can be considered. From the various possibilities, those leading to better behavior at serviceability limit state and to simple reinforcement layouts should be selected (or a combination of them). For the assessment of existing structures, however, avoiding unnecessary strengthening (or minimizing it) should be the objective. Thus, simple stress fields or strut-and-tie models are to be iteratively refined whenever the calculated strength of the member is insufficient with respect to the design actions. This can be done by accounting for kinematic considerations to calculate the higher possible strength of the member accounting for its actual geometry and available reinforcement (allowing to calculate the exact solution according to limit analysis). In this paper, the differences between the two approaches for design and assessment are clarified and explained on the basis of some examples. A number of strategies are comprehensibly presented to obtain suitable stress fields and strut-and-tie models in both cases. The results of exact solutions according to limit analysis (developed using elastic-plastic stress fields) are finally compared to 150 tests of the literature showing the consistency and generality of the presented approaches. [ABSTRACT FROM AUTHOR]

The material characterization of steel fibre-reinforced concrete (SFRC), which is required for its implementation in design codes, should be based on nominal properties that describe its post-cracking strength in tension. In the case of brittle and quasi-brittle materials, such as concrete, the tensile parameters are often derived indirectly. However, for materials with more ductility, such as SFRC, there is conjecture as to whether or not an indirect measure may be used to establish the stress versus crack opening displacement relationship, such as the use of a three- or four-point prism test combined with an inverse analysis. In this paper a simple and efficient inverse analysis technique is developed and shown to compare well with data obtained from direct tension tests. Furthermore, the methodology proposed by the fib Model Code for Concrete Structures 2010 has been investigated and recommendations made to improve its accuracy. [ABSTRACT FROM AUTHOR]

This paper outlines the theoretical background to the punching shear provisions implemented in the fib Model Code for Concrete Structures 2010 and presents a practical example of their application. The aim is to explain the mechanical model that forms the basis for the punching design equations, to justify the relevance of the provisions and to show their suitability for the design and assessment of structures. [ABSTRACT FROM AUTHOR]

This paper examines the evidence for the one-way shear model developed for the fib Model Code for Concrete Structures 2010 and provides examples of its application. For the design and analysis for shear, for members with and without shear reinforcement, the fib Model Code 2010 procedures have been developed from physical-mechanical models that are based on observed behaviour at the meso-scale level; they represent a significant advance over previous standardized empirical methods. In addition, an approach referred to as 'level of approximation' (LoA) is incorporated where advanced models are simplified in a consistent and conservative way such that the designer can select the effort needed to justify their design. To illustrate the practical use of the models and the LoA approach, two examples are presented. The first is a deck slab of a cut-and-cover tunnel where design and possible refinements are discussed for a given configuration. The second is a prestressed concrete bridge girder, which is considered for the cases of design and for the analysis of an existing structure. [ABSTRACT FROM AUTHOR]

Reinforced concrete flat slabs are a common structural system for cast-in-place concrete slabs. Failures in punching shear near the column regions are typically governing at ultimate. In case no punching shear or integrity reinforcement is placed, failures in punching develop normally in a brittle manner with almost no warning signs. Furthermore, the residual strength after punching is, in general, significantly lower than the punching load. Thus, punching of a single column of a flat slab overloads adjacent columns and can potentially lead to their failure on punching, thus triggering the progressive collapse of the structure. Over the past decades, several collapses have been reported due to punching shear failures, resulting in human casualties and extensive damage. Other than placing conventional punching shear reinforcement, the deformation capacity and residual strength after punching can also be enhanced by placing integrity reinforcement to avoid progressive collapses of flat slabs. This paper presents the main results of an extensive experimental campaign performed at the Ecole Polytechnique Fédérale de Lausanne (EPFL) on the role of integrity reinforcement by means of 20 slabs with dimensions of 1500x1500x 125 mm (~5ftx 5 ftx 5 in.) and various integrity reinforcement layouts. The performance and robustness of the various solutions is investigated to obtain physical explanations and a consistent design model for the load-carrying mechanisms and strength after punching failures. [ABSTRACT FROM AUTHOR]

Shear in one-way reinforced concrete (RC) members is transferred in cracked concrete members by a number of actions such as aggregate interlock, residual tensile stresses, dowelling action, inclination of compression chord and transverse reinforcement (if available). The amount of shear transferred by each action is significantly influenced by the cracking pattern (shape of shear cracks) and by the kinematics at failure (opening and sliding of the cracks). In this paper, the activation of the various shear-transfer actions is investigated for one-way RC members. This is done by using a set of detailed measurements on the cracking pattern and actual kinematics at failure recorded on a number of specimens (beams) with a very low amount of transverse reinforcement. The amount of shear transferred by each action is estimated on the basis of available physical models and compared for the various specimens. The results show rather good predictions in terms of strength by following this approach. Consistent explanations of the shear transferred by each action are provided. [ABSTRACT FROM AUTHOR]

This paper presents the results of an extensive experimental campaign on 16 flat-slab specimens with and without punching shear reinforcement. The tests aimed to investigate the influence of a set of mechanical and geometrical parameters on the punching shear strength and deformation capacity of flat slabs supported by interior columns. All specimens had the same plan dimensions of 3.0 x 3.0 m (9.84 x 9.84 ft). The investigated parameters were the column size (ranging between 130 and 520 mm [approximately 5 and 20 in.]), the slab thickness (ranging between 250 and 400 mm [approximately 10 and 16 in.]), the shear reinforcement system (studs and stirrups), and the amount of punching shear reinforcement. Systematic measurements (such as the load, the rotations of the slab, the vertical displacements, the change in slab thickness, concrete strains, and strains in the shear reinforcement) allow for an understanding of the behavior of the slab specimens, the activation of the shear reinforcement, and the strains developed in the shear-critical region at failure. Finally, the test results were investigated and compared with reference to design codes (ACI 318-08 and EC2) and the mechanical model of the critical shear crack theory (CSCT), obtaining a number of conclusions on their suitability. [ABSTRACT FROM AUTHOR]

The shear resistance of elements without stirrups has mainly been investigated by test setups involving simply supported beams of constant thickness subjected to one- or two-point loading, and most of the formulas included in codes have been adjusted using this experimental background. It is a fact, however , that most design situations involve constant or triangular distributed loading (such as retaining walls or footings) on tapered members. Furthermore, there seems to be few shear tests involving cantilever structures subjected to distributed loading. These structures, which are common in everyday practice, fail in shear near the clamped end, where the shear forces and bending moments are maximum (contrary to simply supported beams of tests, where shear failures under distributed loading develop near the support region for large shear forces but limited bending moments). In this paper, a specific testing program undertaken at the Polytechnic University of Madrid (UPM), Madrid, Spain, in close collaboration with Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, is presented. It was aimed at investigating the inluence of load distribution and tapered beam geometrics on the shear strength. The experimental program consists of eight slender beams without stirrups. Four specimens had a constant depth, whereas the others had variable depths (maximum depth of 600 mm [23.6 in.]). Each specimen was tested twice: one side was tested irst under point loading, and then (after repairing) the other side was tested under either uniform loading or triangular loading. The setup allowed direct comparisons between point and distributed loading. The experimental results showed a significant influence of the type of loading and of tapered geometries on the shear strength. On the basis of these results, and using the fundamentals of the critical shear crack theory, a consistent physical explanation of the observed failure modes and differences in shear strength is provided. Also, comparisons to current design provisions (ACI 318-08 and EC2) are discussed. [ABSTRACT FROM AUTHOR]

The influence of shear on the rotation capacity of one-way slabs without shear reinforcement is investigated in this paper by means of an experimental study. The experimental program consisted of 11 slab strips 8400 mm (331 in.) long and 450 mm (17.7 in.) thick with a flexural reinforcement ratio of 0.79%. The rotation capacity was investigated for various values of the shear span and for two types of flexural reinforcement (hot-rolled and cold-worked bars). The specimens developed shear failures with and without yielding of the flexural reinforcement and one specimen failed in flexure with rupture of the tensile reinforcement. The results clearly show that the rotation capacity at failure is governed by shear. Based on the test results, and considering the principles of the critical shear-crack theory (CSCT), an analytical expression is proposed to estimate the rotation capacity of one-way members without transverse reinforcement accounting for shear. [ABSTRACT FROM AUTHOR]

A significant number of existing flat slabs currently require strengthening against punching shear for safety reasons (the increase of applied loads and deficiencies during design or construction) or to comply with more stringent code requirements. Available strengthening methods are, however, not completely satisfactory, or they cannot be applied in many cases (depending on the possibilities to enlarge column sizes or to intervene on the upper face of slabs). In this paper, an innovative system overcoming most of the previous difficulties is presented. It consists of inclined shear reinforcement installed within existing slabs by drilling holes only from the soffit of the slab and by bonding it with high-performance epoxy adhesive. The results of a test program on 12 full-size slabs 3.0 x 3.0 x 0.25 m (118 x 118 x 9.8 in.) show that such reinforcement is an efficient way to increase both the strength and deformation capacity of flat slabs. Finally, the design of the reinforcement based on the critical shear-crack theory (CSCT) is presented. [ABSTRACT FROM AUTHOR]

This paper investigates the structural behavior of reinforced concrete (RC) arch-shaped members without transverse reinforcement subjected to bending. Such members have typical applications in tunnels, cut-and-cover structures, shells, vaults, ducts, silos, tanks, and off-shore structures. Although such members are mostly subjected to axial forces, bending moments may also develop when the shape of the structure does not perfectly match the ideal funicular shape. In this case, when the intrados reinforcement is in tension, deviation forces developed by the reinforcement increase the splitting stresses originated by bond and can lead to spalling of the reinforcement cover. Such a failure mode is particularly brittle and dangerous, leading to a sudden loss of load-carrying capacity of the structure. In this paper, a series of six tests on 400 mm (15.7 in.) thick arch-shaped beams are presented. They are aimed at investigating spalling failures before and after yielding of the tensile reinforcement. These results, as well as others taken from the literature, were compared to an analytical model accounting for the interaction between bond and deviation forces, showing a good agreement and explaining the various failure modes observed. On that basis, a practical formula for the design of such members is proposed. [ABSTRACT FROM AUTHOR]

The traditional approach of codes of practice for estimating the punching strength of shear-reinforced flat slabs is based on the assumption that concrete carries a fraction of the applied load at ultimate while the rest of the load is carried by the shear reinforcement. Concrete contribution is usually estimated as a fraction of the punching strength of members without shear reinforcement. The ratio between the concrete contribution for members with and without shear reinforcement is usually assumed constant, independent of the amount of shear reinforcement, flexural reinforcement ratio, and bond conditions of the shear reinforcement. The limitations of such an approach are discussed in this paper and a new theoretical model, based on the critical shear crack theory, is presented to investigate the strength and ductility of shear-reinforced slabs. The proposed approach is based on a physical model and overcomes most limitations of current codes of practice. Its application to various punching shear reinforcement systems is also detailed in the paper and its results are compared to available test data. [ABSTRACT FROM AUTHOR]

The results of a test series on the punching behavior of slabs with varying flexural reinforcement ratios and without transverse reinforcement are presented. The aim of the tests was to investigate the behavior of slabs failing in punching shear with low reinforcement ratios. The size of the specimens and of the aggregate was also varied to investigate its effect on punching shear. Measurements at the concrete surface as well as through the thickness of the specimens allowed the observation of phenomena related to the development of the internal critical shear crack prior to punching. The results are compared with design codes and to the critical shear crack theory. From that comparison, it is shown that the formulation of ACI 318-08 can lead to less conservative estimates of the punching strength for thick slabs and for lower reinforcement ratios than in the test results. Satisfactory results are, on the other hand, obtained using Eurocode 2 and the critical shear crack theory. [ABSTRACT FROM AUTHOR]

A mechanical explanation of the phenomenon of punching shear in slabs without transverse reinforcement is presented on the basis of the opening of a critical shear crack. It leads to the formulation of a new failure criterion for punching shear based on the rotation of a slab. This criterion correctly describes punching shear failures observed in experimental testing, even in slabs with low reinforcement ratios. Its application requires the knowledge of the load-rotation relationship of the slab, for which a simple mechanical model is proposed. The resulting approach is shown to give better results than current design codes, with a very low coefficient of variation (COV). Parametric studies demonstrate that it correctly predicts several aspects of punching shear previously observed in testing as size effect (decreasing nominal shear strength with increasing size of the member). Accounting for the proposed failure criterion and load-rotation relationship of the slab, the punching shear strength of a flat slab is shown to depend on the span of the slab, rather than on its thickness as often proposed. [ABSTRACT FROM AUTHOR]

This paper investigates the load-carrying mechanisms and the strength of thin-webbed, post-tensioned beams failing by crushing of the web. The shear strength in these members is significantly reduced because of the state of cracking in the web and because of the disturbance in the flow of stresses introduced by the prestressing tendons. The interaction between both effects is investigated. To that end, the results of six full-scale tests performed on actual prestressed beams extracted from a girder bridge are presented. The results are analyzed and various approaches for the modeling of such members are investigated and compared. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Strut-and-tie models and stress fields are methods that can be used for the dimensioning and detailing of reinforced and prestressed concrete structures as well as for checking existing ones. This paper presents an innovative approach toward the automatic development of stress fields based on a nonlinear finite element analysis. Strut-and-tie models can also be easily developed from the resulting stress fields. Most of the difficulties of the existing methods for developing stress fields and strut-and-tie models based on elastic uncracked analyses are overcome. The application of the proposed approach to the dimensioning of structural members in practical cases is detailed and several comparisons with experimental results are discussed. [ABSTRACT FROM AUTHOR]

A series of 16 specimens of concrete web panels 23.6 x 23.6 x 4.9 in. (600 x 600 x 125 mm) was tested in compression to investigate the effect of the presence of various types of post-tensioning ducts on the strength of the shear-induced compression struts. Most panels were cast in the laboratory, but some were extracted from an actual bridge girder, which had been previously loaded, allowing investigation of the effect of web cracking on the ultimate strength. The presence of a duct in a web, whether injected or not, decreases the compressive strength of the panel This effect is most pronounced for non-injected ducts, but is also much larger for injected, plastic ducts than for injected steel ducts. The effect of web cracking further decreases the strength of web panels containing post-tensioning ducts, and this effect can be estimated using classical strength reduction formulas. [ABSTRACT FROM AUTHOR]

In the recent years, Digital Image Correlation (DIC) was applied with very promising results to monitor cracks in reinforced concrete structures. However, current DIC measurements present some limitations to characterize the existing crack (already present in the reference image) and for long-term monitoring due to the principles of the correlation algorithm. This paper presents two techniques to complement DIC in these two cases. The first one is based on direct detection using existing algorithms. The second one is based on the detection of markers fixed around the crack. Their relative position in different images is used to compute the crack displacement that occurred between the inspections. A conventional DIC set-up can be used for this technique. Simplified and refined methods are proposed to quantify the measurement uncertainty and to determine the number and position of markers. Both techniques are validated in laboratory conditions and in-situ in an existing concrete bridge. The combination of the two presented techniques with conventional DIC is promising and could be of interest for applications with complicated crack patterns where a detailed understanding of the crack kinematics is required. • A direct detection technique is validated to characterize existing cracks in reinforced concrete structures. • A marker-based technique is proposed for long term monitoring of cracks in existing concrete structures. • The techniques are validated in laboratory conditions and in an existing prestressed concrete bridge. • Limits of applicability and recommendations are provided for both techniques based on the performed validation tests. [ABSTRACT FROM AUTHOR]

An editorial is presented on progresses that allow advancements in the direction of general models for shear design and assessment of structural concrete members. According to the author, these progresses are grounded on scientific advances such as the digital image correlation that helps designers and scientists to track the development of cracking.