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.

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.

Punching tests on 13 specimens under uniform soil pressure were conducted to evaluate the punching shear behaviour of footings with practical dimensions. The test series included square footings with and without punching shear reinforcement. The dimensions of the footings varied between 1.20 × 1.20 m and 2.70 × 2.70 m and the slab thickness varied between 0.45 and 0.65 m, resulting in shear span-depth ratios a&lgr;/d between approx. 1.25 and 2.00.
In addition to the measured steel strains in the flexural reinforcement and the stirrups, the increase in the slab thickness as well as the saw-cuts were examined to investigate the internal cracking and failure characteristic. In combination with previous tests conducted at RWTH Aachen University, this test series permits a description of the effect of the main parameters on the punching shear strength of footings. These parameters are the size effect of the effective depth, the concrete compressive strength, the flexural reinforcement ratio and the punching shear reinforcement.

This paper aims to put into perspective the influence of long-term effects, such as concrete creep and shrinkage, on concrete cracking. Long-term experimental results obtained at the Centre for Infrastructure Engineering & Safety (CIES) are reported and compared to design estimates made using the fib Model Code for Concrete Structures 2010. The influence of factors such as stirrup spacing and concrete cover are discussed. Results show that time-dependent shrinkage-induced cracking can considerably modify the cracking patterns obtained in short-term tests. For crack control in real structures and for the development of models for inclusion in codes of practice, it is strongly recommended that account be taken of time-dependent effects. Limiting observations to those made in short-term tests may lead to erroneous conclusions that are simply not applicable for structures that are more than a few weeks old.

The experimental results for quasi-brittle materials such as concrete and fibre-reinforced concrete exhibit high variability due to the heterogeneity of their aggregates, additives and general composition. An accurate assessment of the fracture-mechanical parameters of such materials (e.g. compressive strength fc and specific fracture energy Gf) turns out to be much more difficult and problematic than for other engineering materials. The practical design of quasi-brittle material-based structures requires virtual statistical approaches, simulations and probabilistic assessment procedures in order to be able to characterize the variability of these materials. A key parameter of non-linear fracture mechanics modelling is the specific fracture energy Gf and its variability, which has been a research subject for numerous authors although we will mention only [1, 2] at this point. The aim of this contribution is the characterization of stochastic fracture-mechanical properties of four specific, frequently used classes of concrete on the basis of a comprehensive experimental testing programme.

This paper presents an experimental campaign aiming to assess the cracking behaviour of flexural members made with self-compacting concrete (SCC) and reinforced with both rebars and steel fibres recycled from end-of-life tyres (ELT). The characteristics, constructability and performance of this new type of fibre are first discussed. The results of the tests carried out are then presented and discussed. The parameters that have been investigated are: &phgr;/&rgr;s,ef, concrete cover and fibre content. The results obtained show improvement in cracking behaviour, especially for low reinforcement ratios and large covers. Results are compared with the predictions of the recently published fib Model Code for Concrete Structures 2010. The main objective of this investigation is to evaluate the efficiency of a new type of fibre technology for crack width control of RC elements, with advantages in sustainability from the point of view of recycling and durability.

Fibre-reinforced polymers (FRP) in the form of externally bonded reinforcement have been used successfully in the rehabilitation of concrete structures. Although considerable data has been produced on the performance of strengthened RC structures, the reliability of strengthened structures can be significantly reduced due to the variability in the FRP properties, especially when the wet layup technique is used. In addition to this, structural engineers are concerned about the durability of FRP-strengthened structures under extreme loading conditions. Nonetheless, knowledge of the behaviour of strengthened elements under fatigue loading may be important to raise confidence in the strengthening systems. This paper presents the results of an experimental programme developed to investigate the behaviour up to failure of RC beams strengthened with high-performance carbon and aramid fibre sheets and subjected to static and cyclic loadings in terms of ultimate loads, deflections, cracking behaviour, failure modes and fatigue life by means of loading, crack width and deflection monitoring. Experimental data on fatigue life were used to validate analytical models developed for strengthened and unstrengthened beams.

Part I of this paper introduces an experimental programme carried out on RC members with thick-walled hollow circular cross-sections to study their behaviour under combined bending and shear. The study looked at ultimate resistance and propagation of characteristic crack pattern as well as the shape and behaviour of the failure sections as a function of wall thickness, amount of longitudinal and transverse reinforcement, shear span and axial force. Test results were used to verify a newly developed calculation model describing the behaviour of the members investigated at failure under combined bending and shear. This model will be presented in Part II.

Staggering lapped joints increases the complexity of detailing and steel fixing, and may require additional resources and slow construction on site. Major design codes encourage staggering lapped joints in tension by imposing a penalty on lap length depending on the proportion of bars lapped at the same section. There are, however, inconsistencies in the value of the coefficients to be applied, and little evidence is available for validation. A programme of 17 physical tests found no evidence of an increase in strength when laps were staggered, and when allowance is made for increases in transverse spacing, staggering was found to reduce lap strength. Differences in the distribution of bond stress through a lap joint and in the share of the tension force taken by continuous and lapped bars are demonstrated to be responsible for the reduction.

Considering the depletion of resources and energy and the risks of climate change on a global scale, a thoughtless increase in the use of resources and energy in the construction sector is obviously unacceptable. The sector has until now constructed a system of technology focused on safety and comfort, with priority given to economic and social benefits. Such demands remain extremely important; however, in the future we ought to give additional consideration to the depletion of resources, energy consumption and other, ensuing environmental issues. This means that the sector needs to incorporate sustainability - including the environmental, economic and social aspects - into its systems of design and technology. The fib decided to incorporate a “concrete sustainability” concept in its new fib Model Code for Concrete Structures 2010. This paper explains sustainability as expressed in this code together with the background to it. In addition, the essence of sustainability with respect to future Model Codes is discussed.