The paper reports on a benchmark of European deemed-to-satisfy rules for exposure class XC (carbonation exposed structural members). The benchmark of the descriptive rules was carried out following the probabilistic design approach for carbonation-induced corrosion developed in [1] and adopted in fib bulletin 34: Model Code for Service Life Design (2006) [2] and fib Model Code for Concrete Structures 2010 [3], respectively. To perform a representative study, three groups of European countries were selected, representing different parts of Europe, south (Spain, Portugal), middle (Netherlands, Great Britain and Germany) and northern Europe (Denmark, Norway). Reliability ranges for carbonation-induced depassivation of rebar were calculated for “favourable” and “unfavourable” design situations in exposure classes XC2, XC3 and XC4 [4]. In each design situation the deemed-to-satisfy rules of selected countries were followed. The probabilistic calculations were mainly based on short-term carbonation data. However, some calculations were also based on long-term observation. The latter was implemented for independent validation purposes. The calculated reliability ranges are very broad and in some “unfavourable” situations, the deemed-to satisfy requirements do not guarantee the required limit state (LS) arget reliabilities for the particular exposure. In “favourable” situations less stringent demands would have been sufficient.

The analysis of the mechanical behaviour of a reinforced concrete tie subjected to a monotonic loading in the stabilized cracking stage is performed here by way of a theoretical general model that considers the effect of the so-called Goto cracks (secondary cracks). It is shown, in particular, that the average bond stress along the transmission length depends not only on the concrete strength as assumed by the fib Model Code for Concrete Structures 2010, but also on reinforcement ratio and bar diameter. In this regard, tabulated theoretical values of the average bond stress are proposed as a function of the aforementioned parameters. Moreover, the secondary cracks reduce the effect of tension stiffening on the relative mean strain. On the basis of the main results obtained with the general model, some improvements are suggested for the calculation methods proposed by fib Model Code 2010 and Eurocode 2 concerning the average value of the bond stress and taking into account the influence of the secondary cracks on the mean deformation. An improved calculation method is therefore performed. Finally, the theoretical results of crack spacing and crack width obtained with the general and improved methods are compared with experimental data obtained from extensive research on RC ties.

Structures made of a material with a very high standard deviation, such as fibre-reinforced concrete, exhibit an exceptionally safe prediction of the maximum bearing capacity when this is derived from characteristic values identified by means of small specimens. This is emphasized when the structures are characterized by high redundancy. In this regard, two reference tests representing two extreme situations are considered: a) simply supported unnotched full-scale beams characterized by a statically determinate loading scheme and b) full-scale slabs on the ground characterized by a statically indeterminate loading scheme. The Italian standard and, more recently, the fib Model Code for Concrete Structures 2010 have introduced a coefficient (structural redistribution factor) that is able to take into account the reduced variability of mechanical bearing capacity when associated with a large volume involved in the failure process and/or when the structure is able to redistribute stresses significantly, thus favouring the average rather than the minimum strength. A numerical procedure taking into account the expected heterogeneity of the mechanical characteristics in the structure is introduced for the first time to evaluate the redistribution factor.

The fib Model Code for Concrete Structures 2010 introduces a new design concept for punching shear based on critical shear crack theory. This paper presents and provides the background to the design provisions for punching shear according to fib Model Code 2010, Eurocode 2 and the corresponding German National Annex to Eurocode 2. The different punching shear design provisions are critically reviewed by means of parameter studies and a comparison of the calculated resistances and test results. The safety levels of the code provisions are verified and the influence of the different punching parameters on the calculated resistances is examined in detail.

In comparison with a vibrated concrete (VC) of the same strength class, self-compacting concrete (SCC) typically has a lower coarse aggregate content and, possibly, a smaller maximum aggregate size. This may result in reduced aggregate interlock between the fracture surfaces of a SCC. Since aggregate interlock plays an important role in the shear strength of slender beams, SCC beams may have a shear strength lower than that of similar VC beams, but studies on that subject are still limited.
This article summarizes an experimental programme that includes beams of high-strength SCC and transverse reinforcement ratios around the minimum given by different codes - a case that had not been investigated so far. The shear strengths of those SCC beams are compared with those of VC beams with similar concrete compressive strength and small ratios of transverse reinforcement and also compared with beams calculated according to different code procedures.

All researchers who have tested the shear capacity of RC members without stirrups have observed a large scatter in the results.
The objective of this paper is to conduct an overview study of the causes of the great shear failure scatter of RC beams without stirrups. Thirteen groups of shear tests on comparable experiments, extracted from the ACI-DAfStb evaluation database, are considered. The amount of data available is increased numerically. To this end, based on Eurocode 2 equations for shear resistance and shrinkage strain, a full probabilistic model is defined according to the JCSS Probabilistic Model Code. A multivariate statistical evaluation of outcomes is then performed.
The investigation highlights the fact that both the tensile strength of concrete and high shrinkage values may be usefully considered for more in-depth studies of the phenomenon, whereas geometrical properties and concrete compressive strength seem to be less important or can even be neglected.

To increase the efficiency of new structures and perform safety evaluations of existing structures, it is necessary to model and analyse the non-linear behaviour of reinforced concrete. The applicability of the safety formats in present design codes is unclear for indeterminate structures subjected to loading in several directions. The safety formats in fib Model Code 2010 have been evaluated for a reinforced concrete frame subjected to vertical and horizontal loading and the influence of load history studied. Basic reliability methods were used together with response surfaces to assess the failure probabilities and one safety format did not meet the intended safety level. The results indicate the importance of load history and it is concluded that more research is required regarding how load history influences the safety level of complex structures.

Fibre-reinforced concrete (FRC) without any traditional reinforcement is used particularly extensively in structures such as pavements and tunnels. The fib Model Code for Concrete Structures 2010 introduced the possibility of using FRC for structural design and it is becoming a reference document for such structures. The application of fib Model Code 2010 suggestions for flexural and axial forces, once the constitutive relationships of the material are defined, allows for safe design. However, shear verification is often a cause of discussion in the design community. The aim of this paper is to clarify this aspect and provide a procedure that can be followed in the design process. A case study is also presented.

Strain penetration of the longitudinal reinforcement in reinforced concrete (RC) members at the joints and/or footings results in fixed-end rotations at the member ends. Several experimental studies have shown that fixed-end rotations caused by strain penetration contribute significantly (up to 50 %) to the total displacement capacity of RC members. Hence, accurate determination of these fixed-end rotations at yielding and ultimate limit states is of primary importance when defining the structural response of RC members. The purpose of this study is to present the theoretical background to and the assumptions made for the most common relationships found in the literature for determining strain penetration-induced fixed-end rotations at yielding and ultimate. Furthermore, new simple relationships are proposed on the basis of realistic and mechanically based assumptions. Comparisons between the existing and proposed relationships demonstrate the limitations of the former. Finally, the proposed relationships are calibrated against experimental measurements of RC column specimens subjected to cyclic loading with recorded fixed-end rotations due to strain penetration in the adjacent joints and/or footings.

A reliability-based investigation into the ductility measures for reinforced concrete (RC) beams designed according to the current fib Model Code for Concrete Structures 2010 is presented in this paper. Based on the ductility ratio (= ratio of strain in tensile rebar to yield stress of steel), a limit state to ensure adequate ductility in RC beams is proposed. Results show that the ductility ratio generally follows a right-skewed distribution, and due to variability in the material properties and model error, there is high variability in the strain ductility. This high variability in the ductility ratio leads to a high probability of non-ductile behaviour for RC beam designs based on the code. This is more pronounced for normal-strength concrete and grade S500 steel. Based on a target probability taken from the literature, a modification to the allowable neutral axis depth advised by the code is proposed. The results presented in this paper indicate that more reliability-based studies of the safety factors provided by fib Model Code 2010 are needed in order to ensure adequate ductility in RC beams.

The probabilistic assessment of structures damaged by corrosion calls for deterministic models of the degradation of the structural performance and probabilistic models accounting for the uncertainties in material properties, geometry and models used in the reliability analysis. This paper describes the development of a probabilistic model of the uncertainties that arise from the prediction of the loadbearing capacity of reinforced concrete structures damaged by corrosion of the reinforcement. The investigation focuses on the flexural failure of simply supported beams suffering from chloride-induced corrosion. The loss of steel cross-sectional area, the reduction in strength and ductility of the corroded bars, the loss of bond between reinforcement and concrete and the cracking of the concrete cover are taken into account in a non-linear finite element analysis. The comparison between experimental results and numerical predictions of the failure load allows the quantification of the model uncertainty according to the framework proposed by the Joint Committee on Structural Safety. A Bayesian updating methodology is proposed to account for prior knowledge and experimental results.

The fib Model Code for Concrete Structures 2010 introduced the concept of levels of approximation (LoA) as a strategy for simplifying the procedures involved in preliminary design stages or the design of non-critical structural elements while still providing the tools for engineers to use state-of-the-art techniques in the assessment of existing structures or in the advanced stages of design for critical structural elements. In this paper, this concept is applied to the determination of the punching shear resistance of reinforced concrete slabs. A procedure is validated for the highest LoA involving non-linear finite element analysis (NLFEA) with multi-layered shell elements and the critical shear crack theory (CSCT). The safety format proposed for use in the safety verification assisted by NLFEA is based on the definition of a global resistance safety factor. A semi-probabilistic approach is followed, based on the assumption of a lognormal distribution for the resistance and on an estimate of its coefficient of variation. This approach is validated by means of a comparison with the results from a probabilistic analysis.
The LoA approach is initially applied to the study of statically determinate slabs supported on one column to verify the effectiveness of the procedure presented here compared with other validated methods available in the literature. The paper concludes with a case study illustrating the application of the proposed procedure to a bridge deck slab and highlighting the benefits of using a higher LoA.

EN 1992 [1] is currently under revision. In that context it is justified to pass a critical eye over the standard, particularly if the models and resistance functions for the ultimate limit state comply with results from tests. The present contribution is limited to S&T models. The results of the analysis will primarily have relevance to corbels; however, some conclusions are general and should be considered when choosing the mathematical model for any S&T model. Ref. [1] is not sufficiently detailed to provide a basis for the complete design of, for example, corbels. The European Concrete Platform [2], which contains worked examples, has been prepared in accordance with and to support [1].
The two topics dealt with are 1) selection of the main model, and 2) details and use of the S&T model in [1] and [2], and particularly its ability to predict results from tests. The tests for the analysis are taken from a thorough study described in [3]. To evaluate results from using [1] and [2], a concept for the design of corbels suggested earlier has been used to calculate the same tests [4].
It will be claimed that the models in [1] and [2] and their ability to predict the outcome of tests have some flaws compared with calculations according to [4]. The detailed calculations are given in annexes, i.e. Part 1 for design according to [1] and [2] and Part 2 for design according to [4]. The annexes as well as [4] can be obtained from the publisher or the author.

A design procedure based on a simplified FE model for underground tunnels subjected to internal explosion and possibly preceded by fire accidents is proposed in this article. The procedure can provide a valuable tool for designers who have to check the structural safety of a tunnel for the case of an internal blast event. The tunnel geometry considered is the same adopted for the metro line in Brescia, Italy. It has an internal diameter of about 8.15 m, is about 13.7 km long and is located about 23.1 m below the surface. Six segments and a smaller key segment (6+1) make up the tunnel. The ring has an average width of about 1.5 m. The FE model is first tested under static serviceability loads. Dynamic analyses are carried out in order to reproduce the blast scenario. The aim of this work is to generate pressure-impulse (p-i) diagrams for underground tunnels for the case of internal explosion and pre-explosion fire actions. An ultimate limit state criterion based on the eccentric ultimate flexural capacity and capable of including fire-blast interaction is introduced. An innovative layered precast tunnel segment solution made of different fibre-reinforced cementitious composites is compared with a traditional solution with the lining section made of reinforced concrete. The potential applications of this new solution are also discussed in the paper.

This paper describes the changes to design provisions for embedded steel reinforcement in the fib Model Code for Concrete Structures 2010. The changes introduce new coefficients for steel grade and clear spacing between bars, and extend the range of concrete strengths covered. The way in which the contribution of hooks or anchorages is calculated has been revised and the contribution of end bearing to laps and anchorages of compression bars is recognized. The revised rules represent a move away from a distinction between laps and anchorages per se towards a distinction based on the presence or absence of transverse pressure perpendicular to the bar axis within the bond length. The benefits of staggering laps with only a proportion of bars lapped at a section are also reviewed. Finally, the potential impact of lap and anchorage performance on structural robustness is discussed, and it is concluded that this can only be achieved if bar yield precedes splitting mode bond failures.

The effect of concrete grade on the bond between 12 mm diameter deformed steel bars and recycled aggregate concrete (RAC) has been investigated with the help of 45 pullout tests with concentric rebar placement for coarse recycled concrete aggregate (RCA) replacement levels of 25, 50, 75 and 100%. For all the three concrete grades, the measured bond-slip relationships indicate similar mechanisms of bond resistance in the RAC and the natural aggregate (NA) concrete. The most accurate and least conservative predictions of the measured bond strengths were obtained from the local bond-slip model in the fib Model Code for Concrete Structures 2010. Bond strength normalized to fc(3/4) resulted in an improved match with test data and increased with an increase in the RCA replacement levels and decreased with an increase in compressive strength. An attempt to explain this behaviour has been sought in terms of brittleness index, an analogous parameter from rock mechanics. An empirical bond stress versus slip relationship has been proposed for the 12 mm diameter bar and it is conservatively suggested that similar anchorage lengths for this bar in all three concrete grades can be adopted for the RAC and the NA concretes.

This paper presents a five-spring model capable of predicting the complete pre- and post-peak shear behaviour of deep beams. The model stems from a two-parameter kinematic theory (2PKT) for the shear strength and displacement capacity of deep beams under single curvature. Four of the springs of the model represent the shear resistance mechanisms of the beam, while the fifth spring models the flexural behaviour. The model predicts not only the load-displacement response, but also the deformation patterns of the beam and how these patterns change with increasing load. Validation studies are performed by using 28 tests from the literature, showing excellent results. The model is used to interpret the tests and to draw conclusions about the behaviour of deep beams. It is shown that shear strength variations of up to 60 % between nominally identical specimens can be caused by variations in the path of the critical shear cracks. It is also demonstrated that loss of bond of large reinforcing bars increases the shear capacity of deep beams. Finally, the five-spring model is shown to predict the post-peak shear behaviour effectively, which is important for the analysis of structures under extreme loading.

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.

Mit Model Code 2010 wurde ein neues Bemessungskonzept für den Durchstanznachweis vorgestellt, welches auf der Theorie der kritischen Schubrissbreite (Critical Shear Crack Theory) basiert. Im Rahmen dieses Beitrags werden die Durchstanzwiderstände nach Model Code 2010, Eurocode 2 und den Regelungen des deutschen Anhangs zu Eurocode 2 vorgestellt und um Hintergrundinformationen ergänzt. Anhand von Parameterrechnungen und der Nachrechnungen von Durchstanzversuchen erfolgt ein Vergleich der unterschiedlichen Bemessungskonzepte. Dabei werden Sicherheitsdefizite identifiziert und die Auswirkungen unterschiedlicher Einflussparameter auf die Durchstanztragfähigkeit von Flachdecken-Stützenknoten herausgearbeitet.

Comparison of punching shear design according to Model Code 2010 and Eurocode 2
Model Code 2010 introduces a new design concept for punching shear, which bases on the so-called Critical Shear Crack Theory. In this paper, the design provisions for punching shear according to Model Code 2010, Eurocode 2 and the corresponding German National Annex to Eurocode 2 are presented and background information is given. By means of parameter studies and a comparison of the calculated resistances to test result, the different punching shear design provisions are critically reviewed. The safety levels of the code provisions are verified and the influence of the different punching parameters on the calculated resistances is examined in detail.

Nach den heutigen aktuell gültigen Normen und Vorschriften (z. B. CEB-FIP-Model Code 2010 [1]) werden für den Ermüdungsnachweis und auch für die Bestimmung des Schädigungsgrades von Betonbauteilen Lastzyklen gezählt und lineare Schadens-Akkumulations-Hypothesen angewandt. Die so gewonnenen Ergebnisse entsprechen nicht der Realität, da Beton ein sehr stark nicht lineares Verhalten aufweist. Ein Weg, diese Ergebnisse zu verbessern, ist die Anwendung von Monitoring, um die Veränderung in der inneren Struktur des Betons mittels eines lastunabhängigen Messverfahrens überwachen zu können. In diesem Artikel wird ein Monitoring-Konzept vorgestellt, mit welchem es möglich ist, diese Ziele zu verwirklichen. Die zugehörigen Laborversuche wurden bereits in [2] beschrieben. Nun folgt deren tiefergehende Auswertung. Am Ende dieses Artikels werden dynamische Tests an vorgespannten Monoblockschwellen gezeigt. Diese wurden mithilfe des im Rahmen dieser Veröffentlichung beschriebenen Monitoring-Konzepts überwacht. Die dadurch erhaltenen Sensormesswerte wurden mit einer numerisch nichtlinearen Simulation der Schwelle korreliert.

Monitoring of the real degree of Fatigue deterioration within concrete structures - Research Project MOSES
According to actual codes and regulations (e.g. CEB-FIP-Model Code 2010 [1]) the verification concept for fatigue and the determination of the real degree of deterioration of Concrete structures is based on counted load cycles and the linear Palmgren-Miner summation. The results gained in this manner will never depict the reality because of the not considered heavily non-linear behavior of concrete. A way to improve the results is the application of monitoring sensors, which are able to image the changes in the inner part of the concrete matrix independently from applied loads. In this article a monitoring concept will be proposed which can achieve these objectives. The laboratory tests are already described in [2] and now a deeper assessment of the measured results will be made. At the end of this article dynamic tests with prestressed railway sleepers and mounted monitoring system are presented. The measurement data of the sensors will be correlated with results of a numerical nonlinear simulation of the sleeper.

The present contribution focuses on a comparative study of shrinkage prediction models according to the European Standard Eurocode 2 (EC2), the recommendation by ACI committee 209 and fib Model Code for Concrete Structures 2010. The estimated ultimate drying shrinkage strains and the predicted evolution of drying shrinkage strains are compared with respective shrinkage strains measured on normal-strength concrete specimens of different sizes. For all prediction models, the estimated ultimate values are found to agree quite well with the ultimate drying shrinkage strains measured on thin concrete slices. Whereas the evolution of drying shrinkage strains measured on small concrete prisms agree quite well with the predicted values, substantial differences between code values and experimental data are encountered for larger specimen sizes.

Eurocode 2 and the corresponding National Annex were introduced in Germany in 2012. Most of the design provisions for these new standards were adopted from Model Code 1990 and provide a new design approach for ground slabs and footings. For the fib Model Code for Concrete Structures 2010, the punching shear design concept has been revised and introduced in Swiss standard SIA262:2013. This paper presents in detail the design equations for determining the punching capacity according to Eurocode 2, the German National Annex to Eurocode 2, fib Model Code 2010 and SIA 262:2013.
Parametric studies have been used to examine the influence of the main parameters (shear span-depth ratio, effective depth, longitudinal reinforcement ratio and concrete compressive strength) on the punching shear resistance of footings. To quantify the level of safety and the efficiency, the design provisions are compared with systematic test series.

When it comes to dynamically loaded concrete structures, determining the real degree of fatigue damage of a structure on site is a very demanding process that has not been explored in depth. Calculation concepts according to current codes and specifications (e.g. fib Model Code for Concrete Structures 2010 [1]) do not offer efficient results for this task. However, the permanent monitoring from the erection of a structure up to the end of its lifetime is seen as a very promising possibility for assessing the degree of damage constantly. This article takes a closer look at the concrete fatigue concept of fib Model Code 2010 [1], shows an FE simulation of a time-dependent fatigue process for an offshore wind turbine foundation and presents a fatigue monitoring concept including laboratory tests, which enables the detection of the real degree of deterioration in a concrete structure. During tests, the use of ultrasound was identified as the most appropriate method. Measuring wave velocity enables the determination of the dynamic E-modulus, which correlates to the degree of damage within the cross-section of the structure considered.

When reinforcing bars are post-installed in holes drilled in cured concrete, adhesive mortars are used to create a bond between concrete and bars. Appropriate adhesives can develop higher bond strengths than standard ribbed bars cast into concrete. A detailed design concept for the anchorage length of reinforcing bars has been developed by taking into account splitting/spalling of the concrete and pullout. Pullout and splitting tests on reinforcing bars set in concrete were carried out with different adhesive mortars and with varying concrete strengths and concrete covers. When higher bond strengths than those recommended for cast-in reinforcement are taken into account, it is important to check deformations and crack widths at the serviceability limit state (SLS) separately. For this reason, structural tests on slabs and corbels were carried out. Moreover, pullout tests on post-installed reinforcing bars were performed in order to measure displacements at service load level.

The aim of this research is to compare the predictions of the design load-carrying capacity of slabs obtained with simplified analytical and numerical procedures which can be readily used by analysts in the current design process. The research fits into a research programme initiated by the Dutch Ministry of Infrastructure and the Environment for the re-examination of the load-carrying capacity of existing bridges and viaducts, and the beams and slabs they include, through the use of non-linear finite-element analyses. The behaviour of reinforced concrete slabs subjected to concentrated loads close to their supports is investigated in this contribution. Three tests from a series of 18 slabs with a total of 108 tests, tested at Delft University of Technology, were selected as case studies and analysed with non-linear finite-element analyses and analytical models either proposed by design codes or available in the literature. The research agrees well with the philosophy of the fib Model Code for Concrete Structures 2010, which offers different analytical and numerical calculation methods for evaluating the design shear resistance of reinforced concrete members according to different levels of approximation. For the three slabs investigated in this study, it indeed pays to use higher levels of approximation. The highest level (level IV) based on non-linear finite element analysis gives the highest design load resistance, but still well below the resistance obtained experimentally.