The author has had the good fortune to be active for the past four decades almost uninterruptedly as a designer, researcher, teacher, and standards-writer. Over this time, he has been observing a tendency for an increased degradation of the profession, with the segregation between education, research, and practice. It is the opinion of the author that each of these fields has been experiencing individual advances isolated from a holistic view of the profession, compromising the evolution and, consequently, the impact of civil engineers in society. Consequently, the profession is becoming less and less attractive for bright and motivated young people. It is the opinion of the author that such trend can only be inverted by placing more emphasis on the creative and intellectual components in each of the fields of education, research, and practice, as well as by bridging the gaps between them. These considerations are supported by personal experience which is shared in this article by presenting some instances of conceptual designs.
The anchorage of reinforcement in concrete is a complex phenomenon typically governed by several failure modes, including: pull-out failure, splitting, side spalling, edge wedge spalling, and corner spalling, depending on multiple factors. Extensive research has focused on the first four failure modes, however there is little detailed information in the literature regarding corner spalling. This paper presents an investigation aimed at better understanding the mechanical response and performance of anchorages in concrete corners. The investigation involves a series of inner-pressure tests performed with hydraulic inflator devices in cylindrical openings and pull-out tests on anchorages positioned near the corner. The effects of parameters commonly adopted in engineering practice are investigated, including concrete cover, casting position, confinement index, and anchorage length. Through detailed measurements, insights into the local and global behaviour, resistance, and failure mechanisms of corner anchorages are gained and thoroughly discussed. The results are further compared with the response of edge anchorages which failed due to wedge spalling, demonstrating that the effect of the casting position is less significant for corner anchorages than that for edge anchorages, as the inclined cracking plane caused by pressure does not align with sub-horizontal settlement cracks. Additionally, corner anchorages exhibit smaller resistances than edge anchorages with similar covers and lengths, due to limited stress redistribution capacity and more brittle behavior. On that basis, a mechanical model for calculating the corner spalling resistance is developed and validated, showing consistent agreement with the experimental results, which can be regarded as a step forward in the development of a unified mechanical model for anchorages that fail in different modes. This study underscores that Eurocode 2 (FprEN 1992-1-1:2023) tends to provide unconservative predictions for corner anchorages.
As the behavior and design of steel fiber reinforced concrete slabs subjected to punching still remain an area of concern, the present work aims to provide a further contribution to the knowledge on punching behavior of slabs without transverse reinforcement. The results of an experimental program on nine slab-column connections are presented with emphasis on the influence of size effect and steel fiber content. Experimental results show that fibers can significantly increase both strength and deformation capacity. In conclusion, the evaluation of the new Eurocode 2 (Annex L) against the specimens herein tested is presented and discussed. Thanks to the use of 2D Digital Image Correlation, tiltmeters as well as the analyses of slabs after cutting, several critical considerations were made.
Shear design and verification of bridge deck slabs subjected to concentrated loads (as those of wheels from traffic) is a topic subjected to scientific and engineering debate, where several questions remain open. Several design procedures have been proposed in the past to determine suitable values of the internal forces for design, such as the so-called load-spreading rule or considering a smoothing length for redistribution of the internal forces calculated based on linear elastic approaches. Despite these previous efforts, several instrumental aspects governing the response of bridge deck slabs still need to be clarified and subjected to scientific discussion. An important one relates to the location of the governing control section. Typically, for the case of cantilever bridge deck slabs, two control sections are checked: one close to the webs (acting as linear support) and another near the concentrated loads. While there is no debate about the shear check performed at the section close to the linear support (similar to a one-way slab response), how the check has to be done at the section close to the load introduction zone remains unclear (which can be interpreted as punching or as a one-way shear phenomenon). Another aspect under discussion is the determination of the internal forces considering the redistributions related to the non-linear behavior of the slab, avoiding too simplistic and overly conservative rules. To better understand the phenomenon and to lead to more comprehensive and consistent design approaches, the behavior of cantilever bridge deck slabs subjected to concentrated loads is thoroughly investigated in this paper. The study starts with several phenomenological observations on shear failures in cantilever bridge deck slabs obtained from previous experimental programs. Then, a refined analysis is presented considering a realistic out-of-plane shear response of reinforced concrete slabs. From these analyses, the internal forces can be evaluated in a sound manner accounting for a gradual reduction of the out-of-plane shear stiffness as a function of bending moments and shear forces. This new feature allows tracking the location of the potential shear-critical regions and examining the forces redistributions related to non-linear behavior. Unlike traditional approaches (like the “load-spreading rule” or smoothing lengths), the presented numerical analyses can consider shear failures at any location. The main findings from the physical observations and refined analysis are eventually used to propose a simple but phenomenologically consistent design methodology aimed at practical applications.
Estimating the stress of reinforcing bars and its variations in service conditions can be useful to determine the reserve capacity of structures or to assess the risk of fatigue in the reinforcement. This paper investigates the use crack width measurements to estimate the stress in the bars. In existing structures, crack width formulations can be used to estimate the stress in the reinforcement from crack width measurements, profiting from additional information that can be measured in-situ, such as the crack spacing. Recent experimental results show that the values of the mean bond stress typically considered in code formulations overestimate the actual bond stresses activated in cracked concrete specimens. This paper presents the results of an experimental program consisting of reinforced concrete ties and beams instrumented with Digital Image Correlation and fiber optical measurements. The results confirm the differences with typically assumed bond stresses. A formulation to estimate the bond stresses in service conditions is derived from the results of the numerical integration of a previously developed local bond-slip relationship. Their pertinence for the estimation of the stress in the reinforcement from the measured crack width is evaluated with satisfactory results for monotonic loading and for the maximum force in cyclic tests.
Bond between reinforcing bars and concrete plays a crucial role in the behaviour of reinforced concrete structures, often characterized by the bond stress-slip relationship. Numerous relationships exist in the literature, incorporating various parameters and calibrated with experimental databases. This results in a wide variety of analytical relationships and factors that are strongly affected by the experiments included in the database. In this paper, a thorough review of the literature is presented to identify the relevant parameters influencing the bond-slip relationship. On this basis, a bond-slip relationship for well-confined conditions is proposed combining analytical models for some aspects of the response and mechanical considerations to explain the considered factors. The results are compared with a database of 151 tests in well-confined conditions showing good agreement with the results. Additionally, expressions for other confinement conditions are proposed by adapting the model of the fib Model Code 2010 to provide a transition between the unconfined and the well-confined regimes.
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.
Many research efforts have so far been devoted to the topic of shear design of members without transverse reinforcement since the first development in structural concrete. This has allowed a number of significant advances in the understanding of the phenomenon, which is currently acknowledged to depend upon a number of shear-transfer actions in cracked concrete such as aggregate interlocking related to crack opening and sliding, the residual tensile strength of concrete after cracking, dowelling of the reinforcement and the inclination of the compression chord. In the last years, independent teams of researchers have confirmed this by means of detailed measurements on tests performed with Digital Image Correlation and by integrating constitutive laws governing the transfer of shear. In agreement to the observed physical reality, clear and scientifically based theories have been developed allowing researchers to reproduce the shear response in a realistic manner and to perform more accurate predictions on the strength of members. One of these theories, grounded on experimental facts and supported by mechanical modeling, is the Critical Shear Crack Theory (CSCT). In this paper, the fundamentals of the theory are reviewed, linking them to the experimental response of beams in shear. Based upon these fundamentals, a general physical -mechanical model is presented to implement the CSCT basic ideas. On the basis of these results, the aptness of defining a criterion to assess failures in shear is justified, which can be formulated in a simplified manner and is suitable for design. The aim of this criterion is to lead to consistent design expressions, sufficiently simple to be used in practice. It is particularly interesting that the mechanical basis of the model allows natural reproduction of physical phenomena, such as size and reinforcement strain effects, that can be assessed in an accurate manner considering the nonlinear response of a potentially cracked reinforced concrete member. This approach is consistent with the underlying physics and is significantly more general than approaches followed in the past, where empirical formulas were corrected with a size effect term to account for this phenomenon (imposing an effect on a formula which is not necessarily consistent or valid outside its ranges of calibration). Based on the evidence reviewed, this article replies in a scientific, detailed, and transparent manner to a number of criticisms by A. A. Donmez and Z. P. Bazant on the assumptions of the CSCT.
In typical reinforced concrete design, reinforcement is designed to carry axial forces, but it can also resist transversal forces by dowel action. This is usually neglected for simplicity's sake in the design phase, but it can be accounted for either explicitly in mechanical models or implicitly in empirical relationships. Furthermore, there are cases where the connection between various concrete elements explicitly depends on dowel action, as for example, in connections between precast elements or between two concrete parts cast at different times. On the other side, dowel action can have a negative impact on the fatigue resistance of reinforcing bars subjected to cyclic loading, because of the local stress concentrations near interfaces due to relative movements, either in sliding or in opening of cracks not perpendicular to the bar. For the assessment of the remaining capacity of existing structures, improved models of the behavior are needed, including realistic models of the behavior of concrete, steel and their interfaces. The aim of the present paper is to provide a contribution to a better understanding of dowel action by two test series. The first series focused on the behavior of the dowel: the concrete specimens with the embedded bars were placed in a custom-made test setup and subjected to monotonic or low stress-level cyclic actions with a longitudinal and a transversal crack opening component, up to developing the full plastic capacity of the dowel and rupture at the peak of catenary action. The measurement system included tracking the displacement field at the surface of the concrete and the strains in the dowel by optical fibers glued on its surface. The latter measurements allow to derive the internal forces in the reinforcing bar and deformed shape of the bar as well as the contact pressure between the bar and the surrounding concrete. The results show a strong dependency on the test variables: diameter of the bar, imposed crack kinematics and angle between the bar and the crack. The second test series looked more closely at the behavior of concrete underneath the bar, in the presence of a point load introduced at various locations into concrete through a reinforcing bar. A comparison of the test results with existing models shows a general good agreement and some aspects that deserve to be improved.
The use of steel fibre reinforced concrete (SFRC) is a well-known method for enhancing the punching and flexural resistances of flat slabs. The structural performance of SFRC elements depends significantly on the fibre distribution and orientation, which are typically unknown. One of the largest uncertainties regarding the performance and reliability of SFRC concerns the determination of its post-cracking mechanical properties in the real structural element, normally performed via standardised tests. However, due to differences in element sizes and casting procedures, and to the presence of rebars, the fibre spatial distribution and orientation in the standard specimens differ in general from those of the structural member. Several researchers have studied the correlation between the orientation of fibres and the mechanical performance of SFRC, yet tests were rarely carried out under representative conditions of the actual behaviour of the target structural member. The present paper analyses the spatial distribution and orientation of steel fibres in six SFRC flat slabs that were previously tested in concentric punching at the University of Brescia. The aim of this work is to analyse the fibre orientation and spatial distribution in structural elements. Cores were extracted from the specimens after the punching tests and scanned using micro-computed tomography (μ-CT) to reconstruct the fibre skeleton. The fibre arrangement was analysed focusing on the variation of the fibre spatial distribution and orientation through the slab thickness. A formulation to express the actual fibre dispersion in concrete is proposed, and effectiveness factors are defined to reflect the efficacy of fibres in punching shear and flexure, based on their location in the slab thickness. Pseudo-horizontal fibre orientations are found to be governing, with closer distributions to a 2D scenario for thicker slabs and higher fibre contents. Furthermore, the influence of flexural reinforcement on the fibre orientation has been observed to be significant. The observed fibre orientations are detrimental for the direct transfer of shear forces across cracks, but are favourable for enhancing the flexural capacity of the slab.
For the dimensioning and assessment of structures, it is common practice to compare action effects with sectional resistances. Extensive studies have been performed to quantify the model uncertainty on the resistance side. However, for statically indeterminate systems, the model uncertainty in the calculation of action effects has not been properly investigated yet. The aim of this article is to contribute in quantifying the model uncertainty in action effects and load bearing capacity calculations for reinforced concrete structures, accounting for the type of mechanical model used and for various failure modes. To collect a sufficient amount of data and perform statistical analyses, the experimental response of statically indeterminate systems is obtained with a simple and effective technique which allows using experimental results available in literature. Finally, on the basis of a parametric analysis and case studies, practical implications are discussed and recommendations are given concerning the implementation in the partial safety factor format.
Reinforcing bars in structural concrete are typically designed to carry axial forces. Nevertheless, due to their bending stiffness, the bars can also carry transverse forces, that are associated with the localized bending mechanism (dowel action) resulting from the relative displacements (or slip) wherever a crack interface or a discontinuity interface (between two concrete parts cast at different times) intercept the bar. Such localized bending induces stress concentrations in both the bars and the concrete. The relative displacement can occur at interfaces either perpendicular to the bar or inclined with respect to its axis. Thanks to steel ductility, the bending stresses in the bars due to dowel action do not impair the sectional capacity at the ultimate limit state. Fatigue verifications, however, require an accurate evaluation of these stresses under imposed transverse displacements or shear forces. As well known, dowel action can be described by means of the traditional unidimensional Winkler's model (beam on an elastic foundation), where the bearing stiffness of the concrete embedment is typically introduced through a couple of parameters, namely the bar diameter and the concrete strength in compression. The actual behavior of a dowel, however, is definitely more complex and for such a reason, improvements are needed for the Winkler's model to introduce other parameters typical of actual structures. Hence, a new formulation is introduced in this study for the bearing stiffness, that is calibrated based on mechanical considerations and measurements with optical fibers. The proposed formulation also accounts for the following parameters: angle between the crack and the bar, concrete-cover thickness, number of load cycles and the softening effect caused by the local secondary cracks radiating from bar ribs during the pull-out process. The predictions of the model-implemented with the proposed bearing stiffness-fit fairly well the test results under both monotonic and cyclic loads, in terms of shear force-transverse displacement response and peak stress in the reinforcing bars.
Many of the existing reinforced and prestressed concrete infrastructures, such as bridges, subways or overpasses have reached or will reach, in this decade, half a century of existence, making it timely to assess their structural safety accounting for their state. It is desirable that the assessment of existing structures is carried out following a design philosophy by Levels-of-Approximation (LoA) as described in Model Code 2010. This design philosophy consists in starting with a lower LoA corresponding to simple and fast calculations with some safety margin (corresponding to an approach typically used in the design of new structures), refining in the following stages (higher LoAs) only the calculations associated with the governing structural verifications. This work aims at addressing the fundamental aspects of this methodology, based on the experience in Switzerland in the last three decades, discussing briefly the calculation methods that can be applied in higher LoA and that allow considering some reserves of structural resistances typically neglected for design of new structures.
Due to the significant shear forces developing around columns and the potential brittle failure associated, the punching capacity of flat slabs is the main concern at ultimate limit state. An effective way to understand the behaviour of slab-column connections has typically been by testing isolated specimens in the laboratory. While there exist many slab-column connection types in actual slabs, most research efforts have focused on the punching resistance at internal columns. Specifically, edge connections appear largely underrepresented in the literature when the number of existing tests is compared to their importance in typical building floor configurations. Furthermore, the favourable effect of slab continuity is generally neglected in this type of tests. This paper presents the results of an experimental campaign on two edge slab-column connections: one had no shear reinforcement, while the other had a large amount of shear reinforcement to evaluate maximum punching. A novel test setup was conceived to apply representative boundary conditions of actual continuous slabs, introducing moment continuity perpendicularly to the slab free edge. Refined measurement techniques were extensively used, monitoring the visible slab faces using Digital Image Correlation, and instrumenting the flexural and shear reinforcement with distributed fibre-optic sensors. The failure of the slab-column connection without shear reinforcement was triggered in the region of shear stress concentrations and propagated around the column thereafter. Well-anchored vertical legs of flexural reinforcement at the free face induced a smeared-like shear crack pattern. In the shear-reinforced slab-column connection, an initial crushing of the concrete at the column front corners was followed by the formation of a local yield line along the slab axis. In addition to the enhancement of the resistance and rotation capacity, the shear studs also served for increasing the moment redistribution capacity of the system. The experimental results are compared to different codes of practice, showing that improvements are needed to better assess the resistance of edge columns.
The minimum amount of shear reinforcement to be provided in reinforced concrete members has been a topic of debate and research for decades without reaching a consensus. Defining such values is however instrumental to build in an economic manner and to safely ensure the applicability of the models used for design or assessment. This paper presents the results of an investigation addressed at the activation and contribution of shear reinforcement to the resistance, particularly when low amounts are arranged. The research comprises an experimental part, where 10 tests are performed on full-scale beams with varying amounts of shear reinforcement and different mechanical properties of the reinforcement. The tests were instrumented with refined measurement techniques such as digital image correlation and fiber-optic measurements, allowing for a detailed tracking of the strains in the concrete and the reinforcement. The results of the program clearly show that the transition from strain localization with a single shear crack to distributed cracking is influenced by both the ratio of shear reinforcement and its post-yield response. The results are confirmed by the analysis of a comprehensive database of 236 specimens collected from the literature, where the influence of the different parameters is analyzed. Finally, it is discussed how such findings can be implemented into codes of practice, explaining the recent changes introduced in prEN 1992-1-1:2021 (draft for the 2nd generation of Eurocode 2) and fib MC2020.
Within the frame of the revision of the Eurocode 2 for concrete structures, the section devoted to strut-and-tie design has been updated to enhance its applicability, its consistency with other sections and its ease-of-use. As a result, a number of changes have been introduced. Namely, the use of stress fields and their combination with classical strut-and-tie models has been incorporated. The changes in this section can be seen as an effort to provide a more comprehensive and general tool for designers, that can be transparently applied to any structural member with sufficient reinforcement for crack control. In this paper, the consistency between the strut-and-tie and the stress field methods is clarified as well as the fundamentals of the revision performed in Eurocode 2. The paper also elaborates how the code can be used for advanced analyses, considering in an explicit manner the compatibility of deformations to obtain refined estimates of the structural resistance.
Abstract The Critical Shear Crack Theory (CSCT) has been developed since 1985 to assess the shear resistance of members without shear reinforcement and the punching shear resistance of reinforced concrete slabs in a rational manner. The main idea of the CSCT is that the shear resistance is governed by the development of a critical shear crack, its geometry and its kinematics. Recent shear tests with detailed measurements have confirmed that the shear force can be carried through the critical shear crack by a combination of aggregate interlocking, residual tensile strength of concrete, dowel action of the longitudinal reinforcement, inclination of the compression zone and activation of the shear reinforcement crossed by the critical shear crack if present. On the basis of advanced constitute laws, all these contributions can be calculated as a function of the crack geometry and its kinematic. Simplifications of the resulting general formulations have been implemented in several standards including the fib Model Code 2010 and, in its recent closed-form format, in the second generation of the European Standard for Concrete Structures. The generality of the models allows accounting for several materials and cases, as for instance the presence of axial forces, fiber reinforced concrete, non-metallic reinforcements and designing strengthening using several techniques. This document presents the historical framework of the development of the theory, followed by a short presentation of its most up-to-date refined models. The derivation of closed-form solutions based on the CSCT and how it leads to expressions in a format similar to the current European Standard for Concrete Structures is also discussed. Eventually, for the case of punching, some recent developments are shown in what refers the capability of the refined mechanical model to capture the relationship between the acting punching load, the rotation and the shear deformation during loading and at failure.