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In an effort to calibrate design methods and code provisions, an ACI‐DAfStb database was assembled for deep beams and non‐slender beams with vertical stirrups and horizontal web/skin reinforcement subjected to point loads. This collection database includes 218 tests, and with the exception of a few, all tests have a shear span to effective beam depth ratios less than 2.4, that is, κ = a/d < 2.4. For the purposes of evaluating the accuracy and conservativeness of design provisions, several control and filtering criteria were applied, and after this process, 89 beams remained in the evaluation database. In light of this database, the performance of shear design provisions of ACI 318‐14 and Eurocode 2, as well as strut‐and‐tie models (STMs) of the FIP Recommendations were examined. The analyses conducted using this database indicated that the application of STMs of ACI 318‐14 is conservative, that is, the database analyses yielded less unsafe tests than the desired 5% fractile. Furthermore, statistical evaluations showed that shear design expressions of Eurocode 2 and FIP Recommendations for non‐slender beams and deep beams are conservative too. [ABSTRACT FROM AUTHOR]

There are different approaches to predict the shear strength of reinforced concrete (RC) beams, but their predictive performance is still relatively low due to several and complex resisting mechanisms involved in shear. In addition, most of design approaches ignore the influence of the flange of T cross section beams on the ultimate shear capacity. This paper aims to present a design‐oriented approach to predict the load carrying capacity of RC beams failing in shear. This approach is based on the simplified modified compression field theory (SMCFT). A sensitivity analysis is carried out to assess the importance of the input parameters that mostly affect the shear strength of RC members. Taking into account the results of the sensitivity analysis, two simple equations are proposed for obtaining the: (a) tensile stress factor in the cracked concrete (β) and (b) inclination of the diagonal compressive stress in the web of the section (θ). The obtained equations eliminate the iterative process required by the SMCFT and provide a straightforward design methodology to find β and θ with suitable accuracy for design purposes. In addition, a coefficient is presented to take into account the effect of the flange on the shear capacity of T shaped cross section beams. To appraise the predictive performance of the new approach, a database is set. By evaluating the ratio between the experimental results and the analytical predictions, an average value of 1.24 with a coefficient of variation of 20.9% is obtained. [ABSTRACT FROM AUTHOR]

In this paper, a finite element model (FEM) based on a concrete damage‐plasticity approach was developed to investigate the size effect of ultra‐high performance fiber reinforced concrete (UHPFRC) and normal‐strength concrete or high‐strength concrete (NSC/HSC) composite beams. The material behavior of UHPFRC was modeled by introducing a suitable tension stiffening model to simulate the behavior of UHPFRC beams in tension. Specimens containing UHPFRC with different fiber volume content that have an overall height between 300 and 1,200 mm, a constant shear span‐effective depth ratio of 3 and no stirrups were investigated. The validity of the proposed model was established through comparisons between the experimental test results and those obtained in other studies. The results revealed that the size effect of UHPFRC members was diminished for fiber volume content higher than 1.5% due to the high ductility of UHPFRC material. [ABSTRACT FROM AUTHOR]

This computational investigation focused on numerical modeling of the shear behavior of ultra‐high‐performance concrete (UHPC) beams reinforced longitudinally with high‐strength rebars and ordinary‐strength steel (stirrups). Nonlinear three‐dimensional finite element model, using the concrete damaged plasticity model and material properties obtained from uniaxial compressive and tensile laboratory tests, was conducted to simulate UHPC concrete beams within a commercial finite element software package ABAQUS 6.13. This investigation included the effects of various parameters; shear span‐to‐effective depth ratio (a/d), volume fraction of steel fibers, Vf, longitudinal reinforcement ratio, ρ, and stirrups spacing, s, on shear behavior of UHPC beams. Numerical results compared with previously obtained experimental results in terms of shear force–midspan deflection and cracking‐propagation behaviors. The results showed that finite element analysis predicted the shear behavior of UHPC beams in good agreement with the experimental data and predicted the response of the beam with variation in various parameters with a good accuracy. [ABSTRACT FROM AUTHOR]

In this work, the second part of an experimental campaign investigating the efficiency of an alternative retrofitting method for increasing the flexural and/or shear capacity in reinforced concrete beams, based on the use of prestressed stainless steel ribbons and steel angles, is presented and analytically reproduced. This group of tests focuses on the ability of the adopted retrofitting method to improve the shear strength and ultimate deformation of reinforced concrete structural elements. As described in a companion paper, the adopted retrofitting method is alternative to traditional techniques of reinforced concrete retrofitting, being easy to install and usually reversible, and characterized by high fire resistance and avoiding corrosion. The experimental results obtained from shear tests carried out on nine reinforced concrete beams are presented. The efficiency of stainless steel ribbons as shear reinforcement that wrap a portion of cross-sectional depth are analyzed, and the interaction between existing stirrups and stainless steel ribbons examined. The tests results are critically analyzed, highlighting the ability of the retrofitting method in increasing the shear strength and ductility of reinforced concrete beams. The experimental shear strength was also analytically evaluated by extending the theoretical approach of the fib Model Code 2010 formulation, originally suggested for reinforced concrete beams with or without stirrups. [ABSTRACT FROM AUTHOR]

Rotation capacity of reinforced concrete ( RC) beams is a vital property for its relationships with moment redistribution, energy absorbability, and so on. Evaluation of the rotation capacity has been one of the classic and intractable problems in structural engineering over the past decades. The precise prediction about rotational behavior of a RC beam is the primary basis of quantifying its rotation capacity. In this paper a displacement-based finite layer element method considering the factors of flexural cracks, concrete crushing, and pre-and postyield behavior of bond is presented to predict the rotational behavior. In conclusion, it shows good agreement between simulation results, implemented by the proposed method, and the test results in the literature. [ABSTRACT FROM AUTHOR]

In the authors' previous study, the dual potential capacity model (DPCM) was proposed to evaluate the shear strengths of reinforced concrete (RC) members, in which the shear contributions of both the cracked tension zone and the compression zone are considered. In this paper, the main concept and formulations of the proposed DPCM were briefly introduced, and the simplified DPCM was developed for the practical application of the proposed model. A total of 1019 data sets of shear test results on RC members were collected for detailed verifications of the detailed and simplified DPCM. The verification results demonstrated that the proposed models can appropriately assess the effects of key influential factors including compressive strength of concrete, shear span-to-depth ratio, size of coarse aggregate, sizes of members, and shear reinforcement on the shear strengths of RC members. [ABSTRACT FROM AUTHOR]

The first step in the design of a structure is the definition of the geometry. This process includes the definition of the depth of slabs and beams. The depth of a flexural member is often determined by control of deflections, which can only be checked in detail at an advanced stage of the project. In order to optimize the design process, it is therefore very important to choose well the span-to-depth ratio at the beginning. In order to achieve this task in an easy manner, a lower limit to the slenderness of the beams in terms of span divided by the effective depth is proposed in most major codes. However, current proposals are rather coarse and are not necessarily on the safe side. In this paper, a new formulation for the slenderness limits, based on the physics of the problem, is presented. This formulation includes the effect of the composition of the load (live load to total load ratio) as well as the possibility of using different limits to maximum deflection and considering different, more general, support conditions. It is therefore more complete and has a larger application field than current proposals. [ABSTRACT FROM AUTHOR]

This paper describes the development and validation of a comprehensive numerical model enabling the simulation of reinforced concrete beams under serviceability conditions using a discrete crack approach. The highly nonlinear behavior introduced by the different material models and the many localized cracks propagating within the member pose a challenge to classic iterative solvers, which often fail to converge. This limitation is solved using a noniterative solution-finding algorithm to overcome critical bifurcation points. The finite element model was validated using experimental data on lightweight aggregate concrete beams under flexural loading. It was shown that the model properly simulates both the overall and localized features of the structural response, including curvature, crack openings, and crack patterns. The model was used to carry out a numerical study of the role of longitudinal reinforcement ratios and crack widths in reinforced concrete beams. It was observed that the total crack openings along a member seem to remain nearly independent of the tensile reinforcement for ratios >2.5% and the same level of strength. [ABSTRACT FROM AUTHOR]

Models and full-scale statically determinate two-layer beams (TLBs) made of steel-fiber high-strength concrete (SFHSC) in the compression zone and normal-strength concrete (NSC) in the tensile zone have been tested by the authors. The present study is a further stage of these investigations, focused on testing a continuous, two-span TLB with optimal steel/fiber ratio as in the previous stages. This is the first experimental investigation of continuous TLBs (CTLBs). The study is aimed at testing the CTLB behavior under positive and negative bending moments in the span and above the middle support. An additional issue that is studied in the course of this work is the influence of bending moment redistribution on the behavior of a CTLB. As in the previous research stages, interaction of the concrete layers in a CTLB was studied to demonstrate the efficiency of such beams for real structures. No cracks between the SFHSC and NSC layers were observed up to the ultimate limit state of the tested beam, which demonstrates proper interaction between the layers. The results obtained in the present study enable the recommendation of CTLBs for practical application as effective and economical continuous bending elements. [ABSTRACT FROM AUTHOR]

A simplified mechanical model is presented for the shear strength prediction of reinforced and prestressed concrete members with and without transverse reinforcement, with I, T or rectangular cross-section. The model, derived with further simplifications from a previous one developed by the authors, incorporates the contributions of the concrete compression chord, the cracked web, the dowel action and the shear reinforcement in a compact formulation. The mechanical character of the model provides valuable information about the physics of the problem and incorporates the most relevant parameters governing the shear strength of structural concrete members. The predictions of the model fit very well the experimental results collected in the ACI-DAfStb databases of shear tests on slender reinforced and prestressed concrete beams with and without stirrups. Due to this fact and the simplicity of the derived equations it may become a very useful tool for structural design and assessment in engineering practice. [ABSTRACT FROM AUTHOR]

This study examines the flexural behaviour of high-strength concrete (HSC) beams confined using an innovative steel strapping tensioning technique (SSTT) able to provide active confinement. Twelve over-reinforced HSC beams (fc = 50 or 80 MPa) were designed to fail prematurely by concrete crushing at mid-span. The mid-span region of eight such beams was confined externally using the SSTT with different steel strap confinement ratios, the aim of which was to delay concrete crushing. The test results are discussed in terms of the failure modes, load-deflection response and the concrete and tensile reinforcement strains observed. Although the unconfined beams failed in a brittle manner with no post-peak deflection, the steel straps were very effective at enhancing the post-peak deformation of the SSTT-confined beams by up to 126 %. Moreover, for the beams tested in this study, the use of the SSTT led to failures after yielding of the tensile reinforcement. The proposed SSTT can be used to confine HSC elements where ductility is required. [ABSTRACT FROM AUTHOR]

FRP rebars with low compressive strength concrete is desirable in order to avoid the accelerated corrosion processes that could occur with steel rebars. For this purpose, an experimental programme was designed to identify the failure modes and bending behaviour. The experimental results are compared with equations from ACI 440.1R-06, CSA S806-12 and other design codes as well as with other results from a review of the literature. The comparisons indicate that the resistance moment is well predicted by codes for flexural failure. At ultimate loads, the deflection of the beams is further underestimated compared with the deflection of Reinforced Concrete beams with a higher compressive strength. An analytical simulation of 690 beams indicates that deflection is the major limiting criterion at the serviceability limit state. Finally, the formulation problem of the optimal FRP design for reinforced concrete beams can be turned into a programming problem. The space of the feasible design solutions and the optimal solutions can be obtained using only a reduced number of design variables and an existing design method. [ABSTRACT FROM AUTHOR]

Self-compacting concrete (SCC) is defined as highly flowable and non-segregating concrete that does not require mechanical -vibration during application. Load testing of bridge girders was investigated on full scale T-beams of pre-tensioned high strength self-compacting concrete (PHSSCC). The girders were monitored by fixing different types of sensors at different locations. The results of ultimate moment are compared to evaluate if such girders can be designed using AASHTO Load and Resistance Factor Design (LRFD) Specifications; AASHTO Standard Specifications for Highway Bridges (STD) and the PCI Bridge Design Manual are intended for structures constructed using conventional (non-vibrated) concrete. It is concluded that good agreement in results exists for the two methods. Investigations (theoretical and experimental) are needed on the issue of ductility in structural prestressed elements constructed in seismic zones or even, the issue of high strength in SCC. These have also been studied here, with the conclusion that -suitable ductility for this type of structure, as would be needed in seismic regions, can be achieved. [ABSTRACT FROM AUTHOR]

This paper presents a critical comparison of the existing code provisions for the shear strength of concrete beams. The comparison is based on the computerized filtering-out of the inevitable statistical bias from the available multivariate database on shear strength, on an examination of the predicted size effects on shear strength and their underlying hypotheses and on the results of recent high-fidelity numerical simulations of shear failure. In addition to examining the existing models, the present comparison also provides several key considerations for testing the scientific soundness of any model of shear failure in concrete beams, which is necessary for future revisions to the design code provisions. [ABSTRACT FROM AUTHOR]

This paper presents a new theory for the shear capacity of reinforced concrete members without shear reinforcement. While recognizing that there are multiple failure mechanisms, the theory attributes the opening of a critical flexural shear crack as the lower bound of the shear capacity. It proposes that the shear displacement of an existing flexural crack can be used as the criterion for the unstable opening of the critical flexural shear crack. Based on the theory, the paper presents a simplified shear evaluation model. Compared with the current shear provisions in the design codes, the model is characterized by good accuracy and a solid physical background. It demonstrates a great flexibility for dealing with complex design conditions. As an example, the paper discusses the possibility of extending the theory to the shear resistance of higher-strength concrete. The suggested method provides a more logical and fluent transition from normal- to high-strength concrete and shows good agreement with experimental observations. [ABSTRACT FROM AUTHOR]

The dynamic response of a cracked beam subjected to moving loads has been studied extensively in the past decades. However, very little is known about the dynamic impact factors and crack propagation when vehicles move along the cracked beam. It can be reasonably postulated that a crack extension may occur when the vehicle loads cross the cracked bridge at a high speed. As a result, the dynamic response will be enlarged significantly due to the flexural rigidity reduction induced by cracks, which may result in a dangerous effect on structures. To address this problem, a three-dimensional vehicle-bridge model was developed to investigate the dynamic response of cracked bridges with crack breathing. Crack breathing is simulated at the crack surface using contact elements. The modified crack closure method is adopted to calculate the stress intensity factors. The results showed that the impact factors for the damaged bridge under a moving load could be notably larger than those for the intact bridge, and could exceed the value specified in the AASHTO bridge design code. Meanwhile, crack propagation may occur when the vehicles move along the cracked bridge at a high speed. So, it is very necessary to limit the velocity and transverse position of the vehicles to avoid further damage to the cracked bridge. [ABSTRACT FROM AUTHOR]

This article presents an experimental programme on reinforced concrete beams retrofitted with steel angles and pre-stressed stainless steel ribbons to increase their flexural strength and ductility. Two different configurations of the steel ribbon were designed, and two companion specimens for each type considered were subjected to a four-point bending test to facilitate a direct comparison in the analysis of the effectiveness of the retrofitting technique. The influence of longitudinal steel angles and transverse stainless steel ribbons is analysed, and the concrete confinement due to stainless steel ribbons examined. The strengthened beams show remarkable increments in flexural strength and ductility with respect to the as-built beam. Moreover, a simple cross-sectional model was adopted to calculate the flexural strength; then sophisticated numerical tools were used to reproduce both the experimental load-displacement curve and crack pattern for each specimen. [ABSTRACT FROM AUTHOR]

Most classic investigations on bonding properties in reinforced concrete have been performed on the basis of pull-out tests, where a reinforcement bar is pulled out from an uncracked concrete cylinder, prism or cube. In these tests, the bond is governed by the concrete strength and bar surface properties of the reinforcement (bond index, rib geometry) or by the splitting strength of the concrete (concrete cover). In the latter case, bond failure occurs due to uncontrolled cracking of the concrete specimen. In contrast to these fundamental tests, bond in many structural members is activated within already cracked concrete. This is particularly relevant for the reinforcement in beams and slabs (both for flexural and transverse reinforcement), as the reinforcing bars might be located at planes where flexural cracks develop. The opening of these cracks along the reinforcement is nevertheless not uncontrolled (as opposed to splitting failures), but it is governed by the bending deformations. The bond properties and strength of the reinforcement in actual members are therefore influenced by the opening of these cracks and are potentially different from those observed in classic pull-out tests. The present paper aims to address this topic by presenting the results of an experimental investigation with 89 monotonic pull-out tests performed on cracked ties. The opening of the cracks was controlled while transverse bars - located in the plane of these cracks - were pulled out from the specimens. The tests were performed for crack openings ranging from 0.2 mm to 2.0 mm in order to cover conditions both at the serviceability and ultimate limit states. The results show a very significant influence of in-plane cracking on both strength and bond-slip stiffness, with decreasing mechanical performance for increasing crack openings. The performance of different actual anchorage types (straight, hooked, U-shaped and headed bars) - generally characterized through force-slip relationships - is finally analytically investigated and compared to the test results. [ABSTRACT FROM AUTHOR]

When it comes to the efficient design of reinforced concrete beams and frames, moment redistribution is used to: reduce the absolute maximum magnitude of the moment in the critical region, equalize the critical moments on either side of interior columns and fully utilize the capacity of the non-critical regions of a member. Although important, historically, moment redistribution has proved to be difficult to quantify due to the complexity of quantifying hinge rotations. Although numerous empirical expressions exist for plastic hinge lengths, i.e. the length over which the ultimate curvature can be integrated in order to give hinge rotations, a comparison with a global dataset yields poor results. Using a recently developed mechanics-based moment-rotation approach, it is possible to quantify the moment-rotation characteristics of reinforced concrete hinges. In the tension region, the approach applies partial interaction theory directly to simulate the mechanisms associated with slip of the reinforcement relative to the surrounding concrete as cracks widen, whereas in the compression region, partial interaction shear-friction theory is used to describe the formation and failure of concrete softening wedges. It is shown how the moment-rotation approach explicitly allows for the size dependency. Furthermore, mechanics-based solutions for moment redistribution are then derived and it is shown how these can be simplified at the ultimate limit state for use in the design office. [ABSTRACT FROM AUTHOR]

The shear resistance mechanisms of a reinforced concrete (RC) member with shear reinforcement can be divided into the contributions of the concrete and the shear reinforcement. The shear resistance mechanisms of concrete can be further divided into the shear resistance of the intact concrete in the compression zone, the aggregate interlock in the cracked tension zone and the dowel action of the longitudinal tension reinforcement. The shear demand curves and potential shear capacity curves for both tension and compression zones have been derived in this study, with the assumption that the shear failures of RC members are dominated by the flexural-shear strength. The shear capacity model was also proposed on this basis. In the proposed model, the crack width and the local stress increase in reinforcement were calculated based on the bond behaviour between the reinforcement and its surrounding concrete. Further, the crack concentration factor was introduced to consider the formation and propagation of the critical shear crack that developed from the flexural cracks. The results of a total of 1,018 shear tests were collected and compared with the analysis results provided by the proposed model. It was demonstrated that the proposed model provides a good estimate of the shear strengths of RC beams. [ABSTRACT FROM AUTHOR]

Durability at the corners of the cross-section is relatively weak in the concrete beams of bridges; the reinforcement at the corners therefore corrodes first. In order to delay durability failure at the corners, measures should be taken such as the application of corner concrete coatings or adjustments to the reinforcement at the corners. In this way, the durability resistance would be adjusted to be equal in the section, which is called the equal durability design method. In this paper, the life cycle analyses of a component designed with equal durability and one designed in the traditional way - both in a carbonation environment - are conducted and compared. A probabilistic model of service life is established based on empirical degradation models. Service life distribution is calculated with the Monte Carlo simulation method. Costs associated with durability failure are estimated based on the service life distribution. Related influencing factors are analysed as well. Finally, life cycle cost analyses of the component designed with equal durability and the one designed in the traditional way are conducted and compared. The results show that the component designed with equal durability is more economic over the life cycle if construction cost is kept within about 1.1 times that of the component designed traditionally. [ABSTRACT FROM AUTHOR]

A method of analysis for predicting the shear strength and behaviour of shear-dominated reinforced concrete beams is presented in this paper. The proposed model is based on the softened membrane model that accounts for the Poisson's effect on the behaviour of reinforced concrete beams subjected to the combined effect of shear and flexure. The softened membrane model is appealing for modelling the shear behaviour of concrete elements as it is based on solid mechanics of materials fundamentals. The accuracy of the proposed mathematical model was validated against the experimental results of 66 reinforced concrete elements tested under pure shear as well as 167 shear-dominated RC beams available in the literature. Analysis results showed that the proposed model could satisfactorily predict the shear strength as well as the entire shear stress-shear strain behaviour of shear-dominated beams. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

According to current design codes, many existing road bridges exhibit shear capacity deficits. This is partly due to increased traffic loads and partly due to changes in the code provisions. In order to extend the service lives of these bridges, either refined design approaches may be used or strengthening measures performed. This paper describes the results of experimental investigations into how additional external prestressing influences the shear capacity of continuous prestressed concrete beams. Within the research project, six shear tests were performed on three test beams with parabolic internal post-tensioning and additional, variable external prestressing. The aim of the project was to determine the effect of external prestressing on the shear capacity of existing bridges, and whether current design approaches lead to conservative results when used for recalculating existing bridge structures. [ABSTRACT FROM AUTHOR]

Authors' closure on the discussion of the article: "Assessing the influence of fibers on the flexural behavior of reinforced concrete beams with different longitudinal reinforcement ratios" (discussion by Marki'c et al.) The authors would like to thank the discussers for their interest and for opening a discussion on the ductility of RC elements with fibers, which is a very important topic. This possible negative influence is related to both longitudinal reinforcement (type and ratio) and the weighted ratio between the post-cracking performances of fiber reinforced concrete (FRC) and reinforcement strength properties. [Extracted from the article]

This paper presents a proposal for estimating the shear capacity of reinforced concrete deep beams. The proposed model is based on the fixed-angle softened truss model and utilizes a newly proposed formula for the effective transverse compressive stress acting on the beam web. The proposed formula is developed using a stepwise multiple linear regression analysis of the reported shear capacity values of 445 experimental deep beams. The validity of the mathematical model is examined by comparing its response with the experimental results as well as the predictions of other formulas available in the literature, and it results in the one best fitting the measured shear strengths. The mathematical model leads to an explicit single closed-form expression for computing the shear strength of deep beams. The proposed expression is dimensionless and contains four variables that express the horizontal and vertical reinforcement ratios, the concrete strength and the shear span-to-depth ratio. On the basis of the results of this paper, a design formula is proposed with predictions that are more consistent and also more reliable than those of the ACI Code and the Eurocode. [ABSTRACT FROM AUTHOR]

Some experimental research studies have reported that longitudinal reinforcement in beams and columns exhibits larger strains inside the joint than at the joint periphery (defined as the intersection of the outer surfaces of beam and column). This may explain why several technical specifications and state-of-the-art programs recommend basing the design of beams and columns on internal force values larger than those at the joint periphery. These results and procedures are questionable and are investigated in this paper. The non-linear finite element analysis presented here for reinforced concrete frames under gravity and quasi-static monotonic lateral loads examines (i) the stress fields in reinforcement inside interior, exterior and roof exterior joints, and (ii) the load-carrying capacity of representative sub-frame models incorporating such joints. The results prove that it is actually safe, with respect to the joint load capacity, to base the design of longitudinal reinforcement in beams and columns on the internal force values at the joint periphery. This result also contributes to the recommendation to use real-size beam-column joint models in the analysis procedure. [ABSTRACT FROM AUTHOR]

Fatigue loading and its sometimes inevitable fatigue failure are common in many civil engineering construction projects. The behaviour of vibrated concrete (VC) under this type of loading is well understood. However, the fracture and fatigue resistance of self-compacting concrete (SCC) is poorly documented in literature. Considering the substantially different composition of the two concrete types (VC and SCC), it is uncertain whether their mechanical properties are similar or not. This paper describes the results of a series of destructive static and cyclic four-point bending tests on inverted T-shaped reinforced concrete beams, made from VC and SCC in equal quantities and of equal compressive strength. A comparison of the two concrete types is made, based on deflection, strain, crack width evolution and failure mechanism. The experiments prove that these mechanical properties of VC and SCC, subjected to a fatigue load, in some cases relate differently from a static loading process. Furthermore, the results reveal a faster concrete strain and crack width development for SCC during the fatigue tests. Regarding the number of cycles to failure, the applied load level is crucial. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The prescriptions provided by codes of practice for assessing the minimum reinforcement amount for strength purposes in reinforced concrete beams usually disregard the non-linear contribution of concrete in tension and size-scale effects. In the present paper, these phenomena are taken into account correctly in the description of the flexural failure in lightly reinforced concrete beams by means of a numerical algorithm based on non-linear fracture mechanics. In this context, the application of dimensional analysis permits a reduction in the number of governing parameters. In particular, it is demonstrated analytically that only two dimensionless parameters, referred to as reinforcement brittleness number and stress brittleness number, are responsible for the brittle-to-ductile transition in the mechanical response. According to this approach, new formulae suitable for evaluating the minimum reinforcement in practical applications is proposed for both rectangular and T-sections. A comparison with experimental results demonstrates the effectiveness of the proposed model for different reinforcement percentages and beam depths. [ABSTRACT FROM AUTHOR]

High-performance concretes such as high-strength concrete (HSC) or lightweight aggregate concrete (LWAC) are generally used to reduce member sizes and self-weight, and to optimize the construction of reinforced concrete structures. The bond between the aggregate particles and the cement paste can be strong enough in HSC and LWAC to cause the aggregate to fracture at cracks, which in turn reduces the shear stress that can be transferred across cracks by means of aggregate interlock. Relatively smooth cracks can also develop in self-compacting concrete due to the low coarse aggregate content. The contribution of aggregate interlock to the shear strength of RC beams is uncertain and depends on parameters such as the amount of shear reinforcement or the contribution of arching action for loads applied close to the support. Existing tests on slender RC beams without shear reinforcement have shown that shear strength is reduced by aggregate fracture. However, there is a lack of similar test data for members with stirrups and for members with varying shear span/effective depth ratios. This paper reviews the findings and contributions in this area from the experimental and analytical research of the author's PhD thesis, which was awarded the fib Achievement Award for Young Engineers in 2011. [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]

Two-layer high-performance RC beams can be used in the traffic (longitudinal) direction of long-span bridges. The beam section consists of two parts: a bottom part made of normal-strength concrete (NSC), which has a U-type section, and an upper one made of steel fibre-reinforced high-strength concrete (HSC), which has a rectangular section. Using two-layer beams is logical because as the beam span becomes longer and the service load increases, so a higher concrete strength is required in the beam's compression zone to withstand rather large bending moments. As concrete in the tension zone of the section contributes little to the beam's loadbearing capacity, this zone is made of NSC. This is an important economical advantage of two-layer beams. Steel fibres are only used in the compression zone made of HSC. The addition of steel fibres results in a higher ductility for the HSC layer, allowing proper design of two-layer bridge beams for dynamic loads. The design parameters for such beams include the HSC class, where the HSC layer depth is known and is equal to the depth of the rectangular section (above the U-section). The bottom NSC part (U-section) of a long-span beam is usually prestressed. Taking into account this circumstance, the total beam section depth should be checked for the serviceability limit state. [ABSTRACT FROM AUTHOR]

The design shear resistance of an existing structure can be evaluated with analytical design procedures and numerical procedures provided by non-linear finite element analyses. The new fib Model Code 2010 proposes different calculation methods that fall into four different levels of approximation. As the level of approximation rises, so the complexity and the accuracy of the calculated shear resistance increases. Non-linear finite element analyses belong to the highest level of approximation, but although they are more and more becoming a customary tool in the daily design process, building codes do not provide guidance on how to perform these analyses. This paper describes non-linear finite element analyses performed on prestressed beams, which underwent shear failure during experimental loading, in order to assess and criticize the finite element approaches. The aim of this work is to propose guidelines for numerical simulations in order to reduce model and user factors. The results obtained from the non-linear finite element analyses have been compared with the analytical results using different levels of approximation. The design shear resistance obtained with the highest level of approximation, level IV, derived from non-linear finite element analyses, turned out to be higher than the design shear resistance obtained with analytical procedures (levels I/II/III). [ABSTRACT FROM AUTHOR]

This article describes an experimental programme aimed at studying the effect of cover, ratio between diameter and effective reinforcement ratio (ϕ/ρs, ef) and the influence of stirrup spacing on the cracking behaviour of reinforced concrete elements. The experimental programme was conceived in order to contribute to the debate - fuelled by the publication in recent years of Eurocode 2 EN1992-1-1 and the revision of the Model Code under way when the tests were carried out (and now published as a finalized document) - regarding the influence of these parameters on cracking. Important theoretical aspects are discussed, including where the crack width is estimated by current code formulations and what relevance this may have on the correlation between crack opening and durability of RC structures, especially with regard to structures with large covers. The effect of stirrup spacing, a variable absent from current codes, is also discussed. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to improve the performance of a twodimensional finite element approach, called the Rotating Compression Field Model (RCFM). The RCFM capability for reproducing the non-linear behaviour of reinforced concrete (RC) beams, tested in shear with monotonic load increase, has been tested and amended. Concrete is treated as a quasi-orthotropic material with smeared cracks and smeared reinforcement. A modified version of the Sargin relationship for concrete in compression is adopted, introducing a new model for the softening branch of the stress-strain compression curve in the RCFM to take into account compression softening and the effect of confinement due to inplane reinforcement. In addition, this paper considers out-ofplane confinement effects using the model suggested by Eurocode 2. A key issue in the RCFM approach consists of relating the decay of effective concrete strength to the deviation angle between the inclination of the compression stress field at first cracking and its inclination at the load level considered. The validity of this relation has been extended from the original 15° up to more than 30°. A new stress-strain curve is implemented in the code to model the tensile behaviour of concrete without reinforcement (tension softening) in addition to the tension stiffening effect already present for concrete with reinforcement. This model leads to a successful comparison with experimental results on RC beams for a significant range of design parameters and mechanical material properties. [ABSTRACT FROM AUTHOR]

Strengthening reinforced concrete (RC) beams in shear using carbon fibre-reinforced polymer (CFRP) has been found to enhance, significantly, the shear capacity of existing RC beams. In previous studies the use of steel plates bonded externally to the RC beams was found to improve the shear performance of these beams. Most of the previous work was conducted on RC beams having rectangular sections. The main objective of this paper is to gain a better understanding and enhance the experimental database of shear behaviour of RC T-beams strengthened with externally bonded reinforcement (EBR) systems. The present study encompasses some of the important parameters such as direction of EBR fibre alignment and the strengthening materials made of carbon-fibre sheets, steel plates or steel bars for shear strengthening. The contribution of EBR to the shear capacity of the T-beams was computed using three design codes and compared with the experimental output. A series of RC T-beams was tested experimentally with the CFRP and steel strips carefully aligned and spaced. A reference T-beam and a rectangular beam were tested as well to explore the effect of the internal shear reinforcement and the existence of the flange on the shear capacity of the beam. [ABSTRACT FROM AUTHOR]

The flexural response of reinforced concrete (RC) beams exposed to fire is investigated in this paper. A macroscopic finite element model, capable of tracing the behaviour of RC beams from pre-fire stage to collapse in fire is used in the analysis. The model includes the three stages associated with fire resistance analysis, namely establishing the fire temperature-time development, calculating the heat transfer through the structure from fire and the structural analysis. The model is applied to investigate the effect of six parameters, namely the fire scenario, load level, concrete cover thickness, aggregate type, failures criteria and span length on the fire response of RC beams. Through the results of the parametric study, it is shown that the type of failure criterion, load level, fire scenario, concrete cover thickness and aggregate type have significant influence on fire resistance of RC beams. It is also shown that, while the span length has significant influence on the overall fire behaviour, it has a minor effect on the fire resistance of RC beams. [ABSTRACT FROM AUTHOR]

Member analysis is the main verification method adopted for reinforced concrete (RC) beams by most codes. The verification by means of member analysis consists of comparing the design forces (bending moment, axial force and shear force) with the resisting forces, where the former are computed at ambient temperature and the latter are evaluated using simplified methods considering the prescribed fire duration. The main objection that might be raised against member analysis is that, by computing the design forces at ambient temperature, indirect actions arising in the structure owing to thermal expansion are not taken into consideration; the time-dependent response of the structure is also neglected. In this paper, the behaviour of a set of fixed-end rectangular beams with varying axial restraints is discussed. The results are used to illustrate a simplified plastic verification procedure that allows determination not only of the load-carrying capacity of the beams, but also evaluation of the deflections for any given fire duration. [ABSTRACT FROM AUTHOR]

The new Svinesund Bridge is an arch motorway bridge on the border separating Norway and Sweden. The arch is a single, centrally located concrete structure with a span of 247.3 m, which is believed to be the longest span for a single free-standing concrete arch in the world. The bridge decks consist of two steel orthotropic boxes, one on each side of the arch and connected by cross beams. The total length of the bridge is 704 m between abutments. The design is the winning concept of an international competition. The bridge was opened to traffic in 2005, and received the fib Award for Outstanding Structures, Special Mention, in 2006. [ABSTRACT FROM AUTHOR]

The article proposes a model of corroded reinforced concrete behavior of the structural elements. The CEB-FIB model code allows the quantification of the coupled effect of the steel cross-section reduction and the loss of the steel-concrete bond on deflection of reinforced concrete beams under service loads. Meanwhile, an environmental-damage variable is introduced into the steel-concrete bond relationship to take into account the slip between the steel and the concrete.

The shear strength of reinforced concrete beams with stirrups has been a highly controversial matter since Ritter and Mörsh proposed the first truss models. Since then, different analytical models have been discussed, such as truss models with concrete contribution, shear/compression theories, truss models with variable angle of inclination, and compression field theories. However, some of these models were too complex to be implemented in a code of practice and they had to be simplified. As Regan has pointed out, for simpler models the problem is mostly that of the need to neglect some factors, considered secondaries. However, what is secondary in one case may be primary in another.With the release of the new Eurocode 2 (prEN 1992-1-1:2003) the controversy has been raised again. The EC-2 proposes a very simple formulation based on a truss model. However, the authors think that it is a gross oversimplification of a complex problem as it neglects important key variables. In this paper the new EC-2 shear procedure predictions are compared to empirical tests and to other simplified formulations. It is concluded that the EC-2 procedure is very easy to use by practising engineers but it presents a great scatter of results. On the one hand, it may be too conservative for slightly shear-reinforced beams or for prestressed beams. On the other, it may be slightly unconservative for heavily reinforced members. [ABSTRACT FROM AUTHOR]

A total of twelve partially prestressed concrete T-beams were cast without and with fibres in partial and full depth. These beams were tested to assess the effect of fibre addition in different zones in the cross-section, namely, flange, web or the entire cross-section, on the load-deflection performance of the flexure critical beam specimens. An attempt has been made to predict the load-deflection characteristics of the beam specimens utilising the tension softening effects in the stress-strain behaviour of fibre-reinforced concrete. The proposed model accounts for the interaction of the matrix with the fibre pull-out mechanism. The details of the constitutive material properties used and the proposed layer-based analysis are presented in this paper. Comparisons with test data show good agreement. [ABSTRACT FROM AUTHOR]

Moment redistribution has traditionally been considered as an ultimate limit state (ULS) phenomenon closely linked to considerations of reinforcement ductility. This paper demonstrates that a significant proportion of this redistribution will frequently occur at the serviceability limit state (SLS) because of the mismatch between the flexural stiffness assumed when calculating moments for the ULS and those actually occurring at the SLS owing to variations in the reinforcement layout along the member and the influence of cracking. This was demonstrated by tests on 37 two-span beams, the parameters investigated being values of redistribution, beam depth, reinforcement arrangements, concrete strength and the effect of brittle reinforcement. The results showed that there is scope for increasing the permissible limits for redistribution from supports into adjacent spans beyond those currently prescribed in design codes. This was supported by numerical modelling. However, considerations of crack width and reinforcement yield at the SLS may be limiting factors. Caution is advised if redistribution from the spans back to the supports is intended since it may prove difficult in practice to achieve the levels of redistribution anticipated in the design. [ABSTRACT FROM AUTHOR]

The strength and ductility of high-strength concrete (HSC) beams are enhanced through the application of helical reinforcement located in the compression region of the beams. The pitch of the helix is an important parameter controlling the level of strength and ductility enhancement of over-reinforced HSC beams. This paper presents an experimental investigation of the effect of helix pitch on the beam behaviour by testing five helically confined, full-scale beams. The helix pitches were 25, 50, 75, 100 and 160 mm. The cross-section of the beams was 200 × 300 mm, and with a length of 4 m and a clear span of 3·6 m subjected to four-point loading, with emphasis placed on the midspan deflection. The main results indicate that the helix had negligible effect when the helical pitch was 160 mm (helix diameter), the concrete cover spalling-off load increased linearly as the helical pitch increased, and the ultimate load decreased as the helical pitch increased. [ABSTRACT FROM AUTHOR]