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In this paper, the effects of bond deterioration due to fatigue loading on the structural response of reinforced concrete tension members are studied. A comprehensive experimental campaign on reinforced concrete ties and pull-out specimens was carried out under monotonic and repeated loading. The use of distributed fibre optical sensing to assess the local strains allowed the bond deterioration mechanism under repeated loading to be observed. Previously applied load cycles caused a reduction in tension stiffening for load levels below the maximum cyclic load but did not significantly influence the deformation behaviour of the member near the ultimate load. The bond stresses at the maximum cyclic load decreased fairly linearly with the logarithm of load cycles, with the most pronounced reduction in bond stresses near the cracks. At the minimum cyclic load, the bond stress distribution along the tie changed and bond stresses reversal occurred close to the cracks. This caused negative tension stiffening in some cases, i.e., the mean strains exceeded those occurring in a bare reinforcing bar at the same load. The mean steel stresses and the steel stress amplitudes between the cracks increased with the number of load cycles due to the gradual reduction of the concrete contribution and bond degradation. Bond degradation occurred linearly on a semi-logarithmic scale, as expected for the generated bond stresses, which were below the fatigue bond strength. The test results highlight that accounting for shrinkage-induced strains is essential for a realistic evaluation of tension stiffening and residual deformations in particular. Based on the experimental observations and previously developed models for monotonic and cyclic loading, two approaches were used to predict the response of reinforced concrete tension members under repeated loading: the Local Fatigue Damage Model (LFDM), based on the local bond stress-slip relationship, and the adapted Tension Chord Model (TCM) which assumes constant bond stresses and mean strains. The results of both approaches agree well with the test results at the maximum load but yielded less satisfactory predictions at the minimum loading level where only the LFDM was able to be applied successfully. Further research is required to validate the negative bond stresses occurring upon slip reversal in the LFDM and the reduction factor proposed in the adapted TCM., Engineering Structures, 289, ISSN:0141-0296

One of the most hazardous scenarios for reinforced concrete (RC) members is due to the actuation of impact loads. Such impacts may be either accidental or induced events. Experimental research has demonstrated that the failure mode of RC beams is strongly governed by shear, due either to the formation of a shear plug close to the impact point or to the full development of inclined shear-bending cracks along the shear span. In order to analyze the shear strength under impact conditions, it is essential to understand how the development of inertia forces leads to a time-dependent distribution of shear forces and bending moments which differs significantly to those produced by quasi-static loads. In the paper, an experimentally-based determination of shear forces and follow-up of crack pattern is presented for RC beams tested under impact loads. A Digital Image Correlation technique supported by a high-speed camera is used to understand the evolution of shear forces at critical sections and to discuss the ultimate shear strength provided by M-V interaction diagrams.

The use of high- and ultra-high-performance fiber-reinforced concretes (HPFRC and UHPFRC, respectively) has increased significantly in the last few years as a result of large research efforts and collaboration between research and industry [...]

Reinforced concrete (RC) structures typically present brittle failures by shear or punching under impact loading. High-performance fiber-reinforced concrete (HPFRC) has great potential due to its superior strength and energy absorption. The higher price and environmental cost of HPFRC compared to conventional RC can be effectively overcome by partially strengthening impact-sensitive RC members with HPFRC. To study the feasibility of this technique, HPFRC was applied as a tensile layer at the bottom of RC beams. Drop weight impact tests were carried out on beams with two values (35 and 55 mm) of HPFRC thickness, in addition to companion RC beams. Results show that the impact response can be divided into two stages: a first stage governed by local effects and shear plug formation at midspan, and a second stage governed by global beam behavior with formation of shear web cracks. A new resisting mechanism was observed for beams strengthened with HPFRC, as the strengthening layer worked similarly to a stress ribbon retaining the damaged RC and reducing fragmentation-induced debris. Such mechanism was fully achieved by the specimens with 35 mm HPFRC layer but was limited for the specimens with 55 mm HPFRC layer due to impact-induced interface debonding.

The flexural behavior of circular concrete-filled steel tubes (CFST) is addressed in the present paper, with the aim of understanding the contribution of the concrete infill and the steel tube to the flexural stiffness under in-service loads. The provisions given by current codes of practice are oversimplified and they result in a very different contribution of the concrete infill from one code to another. In the present paper, a mechanical approach is proposed by taking into account the stress transfer mechanism from the steel to the concrete through bond stresses. The paper firstly addresses the response of the cracked section in pure bending. Secondly, a tension chord model for CFST is proposed, so that the contribution of concrete in tension between cracks (tension stiffening) can be evaluated. The model capabilities are compared with experimental results from the scientific literature and with own experimental results of the author, showing that the proposed approach can predict the flexural stiffness of CFST very satisfactorily. For the first time, a model with sound mechanical background is introduced to calculate the bending stiffness of CFST.

The impact strength of reinforced concrete beams without shear reinforcement is studied in this paper, with emphasis on the improvement of the impact performance achieved by using steel fiber-reinforced concrete (SFRC). Drop-weight and companion quasi-static tests have been completed on 2000 × 125 × 250 mm beams containing ordinary longitudinal steel bars. Seven SFRC mixes have been studied, including three fiber types (smooth, hooked and prismatic) and three volumetric fractions (0% i.e. plain concrete, 0.5% and 1.0%). The study has confirmed the brittle impact behavior of beams without fibers, which failed by shear. With the addition of 0.5% steel fibers, shear failures were obtained with hooked and prismatic fibers but not with smooth fibers. Finally, all beams with 1.0% steel fibers developed a flexural failure mode. The improvement of the impact behavior of beams with SFRC is also confirmed by the fact that most of the specimens which developed a flexural failure had thin diagonal cracks in the webs of the shear spans, but such cracks did not progress due to the fiber-bridging capacity. In the paper, the study is completed with an analysis of the rate sensitivity of the shear strength and the capacity for energy absorption of tested beams.

Prestressed concrete sleepers have been widely used in railway tracks for some decades with excellent performance. The traditional design rule for prestressed concrete sleepers has been based on limiting the long-term tensile stress at the most loaded point of the cross section to avoid cracking. In broad gage tracks, the centre section is subjected to higher bending moment than the rail seat section. Controlled cracking has been allowed at the centre section by recent design guidelines (prEN 13230-6) but fatigue and durability issues may arise under such situation. In addition, it is realistic that single events like overloads or dynamic effects may lead to cracking. Therefore, the performance of the centre section under controlled cracking situation should be studied, with emphasis on fatigue and residual cracks. The present paper presents an experimental campaign and a theoretical analysis on prestressed concrete sleepers subjected to severe fatigue loading at the centre section. According to the results, it can be concluded that the fatigue performance of studied sleepers is rather satisfactory. Moreover, the study has also focused on the evolution of the residual crack width and it is shown that residual cracks remain smaller than 0.05 mm for bending moments significantly larger than the characteristic bending moment.

Resumen El hormigon reforzado con fibras metalicas (SFRC por sus siglas en ingles) ha mostrado su eficacia mejorando las propiedades del hormigon. Una aplicacion interesante de dicho material es en las estructuras sometidas a impactos. Con el objetivo de caracterizar las propiedades dinamicas del SFRC se ha llevado a cabo una campana experimental con una maquina de impactos instalada recientemente en el Laboratorio de Estructuras de la Universidad Politecnica de Madrid. Las probetas ensayadas, reforzadas con distintos tipos de fibras metalicas en diferentes dosificaciones, muestran que las mezclas de SFRC presentan mejores propiedades dinamicas y una sensibilidad a la velocidad de carga diferente que el hormigon convencional.

The research presented in this paper deals with the impact behavior of steel fiber-reinforced concrete (SFRC). An experimental campaign on unnotched prismatic specimens has been carried out, covering three types of steel fibers (smooth, hooked and prismatic), two volumetric contents (0.5 and 1%), and companion unreinforced plain concrete specimens. Impact tests have been performed with an instrumented drop weight testing machine recently installed at the Technical University of Madrid (UPM), Spain. According to experimental results, the peak strength and fracture energy of tested SFRC mixes are strain-rate dependent, showing dynamic increase factors (DIF) well larger than 1. On the one hand, the analysis has shown that the DIF of the peak bending strength of SFRC reinforced with smooth and prismatic fibers is higher than the DIF of the tensile strength of plain concrete and increases with the fiber content. SFRC reinforced with hooked fibers presented higher DIF with 0.5% fiber content than with 1.0%. The influence of rate-dependent size effect in the former results is discussed in the paper. On the other hand, the DIF of the fracture energy showed the highest rate sensitivity for plain concrete specimens and decreases with the addition of fibers due to the rate dependence of the mechanisms involved in the fiber-matrix interaction.

A study of the rate sensitivity of prismatic specimens of steel fiber-reinforced concrete (FRC) is carried out in this contribution. Experimental results are analyzed from impact tests carried out with an instrumented drop weight testing machine. FRC mixes with two types of fibers have been studied, namely short straight fibers and long hook-ended fibers. The experiments have included two amounts of fibers (volumetric fractions of 0.5% and 1.0%), and also companion unreinforced plain concrete specimens are studied. The analysis has focused on the bending properties of the studied mixes, i.e. bending strength and absorbed energy. The study shows that each particular mix of FRC has different rate sensitivity because the dynamic behavior is a consequence of the rate dependence of the mechanisms governing the interaction between fibers and matrix. For the impact strain-rate domain achieved in the tests (1-10 s -1 ), it is shown that the study has to be done in terms of the energy absorption capacity of FRC. According to the results, the rate sensitivity decreases as the amount of fibers increases and, furthermore, the rate sensitivity of FRC mixes with hook-ended fibers is smaller than that of FRC mixes with straight fibers.

Accidental hazards are associated with large uncertainties regarding their occurrence probability, their effects on a structure and the possible consequences these effects might entail in case of failure. Consequently, decision-making related to safety accounting for such hazards is difficult and prone to be based on irrational grounds. Gas explosions in buildings are a good example therefore. Although dealt with in many codes, they are seldom accounted for in design of building structures. As a consequence, the associated risks are often ignored or sometimes consciously accepted. If this is a justified practice cannot be easily judged however, since under the implicit approach adopted in practice for assuring structural safety the risks are not quantified nor are the acceptable risk levels established. On this background, the paper explores methods and tools for the practical application of explicit risk analysis in connection with the effects of gas explosions on RC structures. A procedure is established to determine structure-related risks to persons and applied to a representative set of structures designed according to current best practice. Target reliabilities for the design of key elements are deduced from the findings. Such target values facilitate rational decisions on both, the need and the appropriate choice of risk-reduction measures to counteract the effects of gas explosions in buildings.

The assessment of an existing structure to determine its suitability for present and future use entails different sorts of problems than encountered when designing new structures. The differences revolve essentially around the nature of the information available. In existing structures, deteriorated or otherwise, the accuracy of the models used for such assessments can usually be improved by acquiring more data. The most accurate way to find actual load and resistance would be to conduct a probabilistic analysis using site data. This is a time-consuming process, however, calling for a working knowledge of probabilistic methods that may not be suited to everyday use by practising engineers. For this reason, in the past few years various studies have been conducted to develop assessment approaches, compatible with Eurocodes, which include the same verification format as normally applied for designing new structures. In this paper, the application of several of these approaches is illustrated by means of the reliability verification of one of the main beams of the reinforced concrete structure of an industrial building from the 1940s, recently transformed into a cultural centre. The obtained results are discussed and compared to the findings of a full probabilistic analysis.

Serviceability requirements of concrete structures establish the limitation of deflections. Even though the exact prediction of deflections is a difficult task that is neither necessary nor possible, the assumptions of codes of practice to consider time- and cycle-dependent effects of reinforced concrete are conceptually questionable. A common rule is that both sustained and repeated loading result in a reduction of the tension stiffening contribution. Nevertheless, the cyclic behaviour of reinforced concrete is nonlinear and non-symmetrical during unloading and reloading, leading to deformations larger than those corresponding to the fully cracked member during unloading stages. In this paper, an approach is presented to distinguish between time- and cycle-dependent effects. A curvature component is added to the estimation of curvatures so that the cyclic effect can be understood as a different contribution to deflections with respect to creep and shrinkage. The comparison with experimental results indicates that the cyclic component of deformations cannot be neglected.

Concrete structures subjected to impact have shown a higher sensitivity to develop a brittle shear failure than under quasi-static loading. The differences between the dynamic and static behavior are due to the strain-rate dependence of material properties and the presence of inertial forces. Both effects should be accounted for when performing analyses of structures under impact. In the present paper, a simplified three-degree-of-freedom model is used to understand the improved impact response of reinforced concrete when steel fibers are added to the concrete matrix. The analysis shows that the higher capacity for energy absorption of fiber-reinforced concrete (FRC) may avoid local shear failure when the FRC is able to develop strain hardening prior to the peak strength. Various analyses are presented in order to understand the influence of different types and contents of fibers.

A significant increase of the use of high-performance fiber-reinforced concrete (HPFRC) to strengthen reinforced concrete structures (RC) has been noted for the past few years, thereby achieving composite RC-HPFRC elements. Such a technique tries to take advantage of the superior material properties of HPFRC in the ultimate and service load regimes. Many of the existing works on RC-HPFRC elements have focused on the strength increase at the ultimate load state and much less effort has been devoted to the serviceability response. The in-service performance of RC structures is governed by the behavior of the tension chord, which determines the crack pattern (crack widths are critical for durability) and deformations. The presence of HPFRC is supposed to improve serviceability due to its strain-hardening and tension-softening capacities. In this paper, the experimental analysis of composite RC-HPFRC tension members is dealt with. Specimens consisting of a RC tie strengthened with two 35 mm thick HPFRC layers have been subjected to loads in the service range so that the deformational and cracking response can be analyzed. The HPFRC has been a cement-based mortar with 3% volumetric amount of short straight steel fibers with a compressive and tensile strength of 144 MPa and 8.5 MPa, respectively. The experiments have shown that RC-HPFRC has higher stiffness, first cracking strength and reduced crack widths and deformations compared to companion unstrengthened RC. To understand the observed behavioral stages, the experimental results are compared with an analytical tension chord model, which is a simplified version of a previous general model by the authors consisting of 4 key points. In addition, the influence of time-dependent shrinkage has been included in the presented approach.

The application of a thin ultra-high performance fiber-reinforced concrete (UHPFRC) layer at the tensile side of reinforced concrete (RC) elements has lead to an efficient structural concept with promising capacities. Composite UHPFRC-RC elements have an increased bending capacity with respect to the RC member. In addition, the serviceability and durability are also improved as the composite element has higher stiffness and smaller crack widths. In order to widen the application of composite UHPFRC-RC elements, practitioners and designers need analytical and numerical tools with a sound mechanical background, if possible conceptually analogous to well-established models for conventional concrete structures. The paper starts with a discussion of the main drawbacks of existing models for UHPFRC-RC elements in bending. Secondly, new experimental basis is provided with own tests where the digital image correlation (DIC) technique is exploited to understand the crack pattern development and interfacial behaviour of UHPFRC-RC. Finally, the main goal of the paper is the proposal of a new model for UHPFRC-RC elements in bending which includes tension stiffening and the interaction at the steel-concrete and concrete-UHPFRC interfaces by means of a new composite tension chord model. The tension chord model is based on the stress transfer mechanisms between adjacent cracks, which include the explicit consideration of bond stresses between the constituent materials (i.e. steel and concrete, and UHPFRC and concrete). The compatibility condition between the UHPFRC and the RC layers is established in terms of the extension of each layer between adjacent cracks, as the classic compatibility of strains based on perfect bond assumption cannot be used upon macrocrack formation. Rather, the extension of the UHPFRC layer includes the contribution of cross-sections within the elastic, hardening or softening stages of the UHPFRC. The proposed model allows estimating the whole bending response, including calculation of crack widths and average curvatures between cracks.

Straight lap splices are employed in reinforced concrete to transfer loads from one steel reinforcing bar to another by bond between the embedding concrete and the two bars along a lapped length. In the last years, some concerns have arisen on the possibility of fatigue of bond-related structural problems, in part due to the very few models available to evaluate the bond fatigue strength. Regarding design standards, some codes for off-shore structures have addressed such a specific topic, by means of a simple S-N formulation. Besides that, recent experimental research has shown that fatigue failures of lap splices can occur because of the poor confinement conditions which result in a small static bond strength leading to high relative stress levels sensitive to fatigue. In the present paper, a mechanical model is proposed to understand the fatigue behaviour of lap splices. The model solves the lap splice problem by taking into account the particular equilibrium, compatibility, constitutive and boundary equations, which produce a different solution than other bond-related problems (anchorages, tension stiffening) in terms of stress distribution along the lapped length. For the local bond-slip behaviour, a cycle-dependent formulation is used for the increase of slip with load cycles and the fatigue failure criterion. The model is able to reproduce the real bond stress distribution, which is nonuniform along the lapped length, and the process of redistribution that takes place with load cycles. It is shown that the redistribution process is responsible for higher fatigue strength than that calculated under the assumption of uniform stress distribution.

Long term effects due to shrinkage may lead to deformations in steel-concrete composite members that are to be taken into account in the verification of the in-service condition. Simultaneously, tangential and normal stresses develop at the connection between concrete and steel and they can result in uplift effects, especially in end regions. In this paper, an analytical model is presented and closed-form solutions are derived in order to quantify deflections of composite members with partial interaction, as well as stresses and relative displacements at the connection. It is shown that deflections and tangential stresses/slips can be properly obtained if equal curvatures between the components of the composite member are assumed. Nevertheless, such a hypothesis must be abandoned in order to reproduce uplift effects at the interface and a new model is presented to derive the distribution of normal stresses.

Shear fatigue of reinforced concrete members without transverse reinforcement has been observed to be potentially governing for the strength of some structural members subjected to large live loads of repetitive nature (as traffic, wind or wave actions). Although extensive experimental programmes have been performed in the past and a rational approach to the problem can be performed on the basis of Fracture Mechanics, most design codes still ground shear fatigue design on empirical equations fitted on the basis of existing data. These empirical formulas show inconsistency amongst them and some neglect potentially relevant parameters as the ratio of maximum and minimum fatigue load levels. In this paper, a consistent design approach is presented, by using the principles of Fracture Mechanics applied to quasi-brittle materials in combination with the Critical Shear Crack Theory. This approach leads to a simple, yet sound and rational, design equation incorporating the different influences of fatigue actions (minimum and maximum load levels) and shear strength (size and strain effects, material and geometrical properties). The accuracy of the design expression is checked against available test data in terms of Wöhler (S-N) and Goodman diagrams, showing consistent agreement to experimental evidence. In addition, the estimate of the number of cycles until failure is shown to be significantly more accurate and with lower scatter than current empirical shear fatigue formulations of Eurocode 2 or fib-Model Code 2010.

It has been typically observed that concrete structures have a brittle failure mode by shear or punching under high-loading rates. The small capacity for energy absorption of plain concrete is responsible of such brittle failure development upon diagonal crack formation. High-performance fiber-reinforced cement composites (HPFRCCs) have superior performance than plain concrete in tension, not only by the higher tensile strength but especially regarding the energy absorption capacity associated to multiple cracking and crack-bridging ability. In order to understand the possible benefits of using HPFRCC under impact loading in structural applications, research must be done at both material and structural level. The present contribution deals with an experimental study on HPFRCC specimens subjected to impact. Reference quasi-static tests have been also carried out. The HPFRCC mix was reinforced with 1.6% volumetric amount of short straight high-strength steel fibers. The study at material level has focused on prismatic specimens subjected to pure bending, which allows to analyze the flexural strength and specific energy absorption capacity. Structural tests have consisted of beams reinforced with conventional longitudinal steel bars without stirrups, thereby assigning the resistance of the webs against shear to the contribution of the fibers. The results are presented in comparison with companion specimens of conventional plain concrete, which has allowed showing the higher strength, ductility and energy absorption capacity achieved with the utilization of the properties of the HPFRCC under both quasi-static and impact loading conditions.

The shear fatigue behaviour of reinforced concrete elements without stirrups is dealt with in this paper. Existing experimental results have shown significant differences between the static and fatigue failure mode of reinforced concrete. It has been reported that beams without shear reinforcement designed to have a ductile failure in flexure are able to develop a brittle shear failure when they are subjected to repeated loads. Shear fatigue of reinforced concrete beams without stirrups is a complex process from the mechanical viewpoint that has not been fully understood yet. Typical shear fatigue failure takes place by inclination of a flexural crack in the shear span and its progressive propagation into the compression zone until its destruction when its depth is too small to resist the applied compression force. This process is analyzed in this paper by means of a mechanical model that helps in understanding the formation of a diagonal crack and its propagation with load cycles. The failure mode and residual strength after diagonal cracking are studied as a function of the stress state at the tip of the effective diagonal crack.

The behaviour and failure mode of reinforced concrete elements strengthened with a thin tensile layer of ultra-high performance fiber-reinforced concrete (UHPFRC) is governed by the interface interaction between the UHPFRC and conventional concrete. In order to analyze the relative displacements at the interface and its influence on the crack pattern evolution and monolithic response, digital image correlation (DIC) has been used in this contribution. With the help of DIC, the distinct stages of the behaviour of UHPFRC-strengthened beams have been correlated with the crack formation and development. Special attention has been paid to the progressive debonding due to the strain incompatibility between UHPFRC and conventional concrete when cracks develop. It is shown that the utilization of the capacity of the UHPFRC can be achieved from a certain thickness of the strengthening layer for shear-critical elements, thereby providing a gain of shear strength and ductility. In contrast, a thinner UHPFRC layer has been more beneficial for flexure-critical elements.

Interest in precast construction system has been growing due to the emphasis on improving work zone safety, reducing construction time and environmental impact, while maintaining quality. This experimental study aimed to develop a method to connect precast elements avoiding the use of complex reinforcing details and inefficient construction processes. For that purpose, the outstanding properties of ultra high performance fibre reinforced concretes (UHPFRC) were used to develop continuity connections between precast elements. A two-stage experimental program was defined to study the behaviour of precast elements connected using short reinforcement splice lengths. In the first experimental stage, flexural beam tests were carried out to assess the use of short reinforcement splice lengths in continuity connections. In the second experimental stage, an alternative beam–column connection for precast construction using UHPFRC was proposed and tested. The configuration proposed avoids the interference between longitudinal and transversal reinforcement, reduces the in situ work and makes it possible to define an efficient and safe construction process.

It is well known that many factors affect the bond behaviour between concrete and steel reinforcement. Most of them characterize the degree of confinement, which is necessary for an appropriate determination of the bond strength and bond-slip relationship according to most extended models. Nevertheless, there are situations where the confinement is not known in advance or it can hardly be defined. That is, for example, the case of reinforced concrete under transverse pressure or tension. Under such conditions the confinement varies both longitudinally and circumferentially. This paper presents a 3D finite element approach to study the bond capacity of cases where the bond strength of the specimen is the result of the different contribution provided along the steel-concrete interface and cannot be described uniquely. A surface-to-surface contact model with frictional behaviour and debonding is used to study the influence of the local stress state at the interface. The model is able to reproduce the different failure modes (splitting or pull-out) obtained in experiments and provide a rational explanation of the influence of transverse tension.

The present contribution addresses the reliability level implicitly required by the current design codes for the principle load-bearing elements (beams and columns) in ordinary RC structures exposed to accidental situations associated with gas explosions. A representative set of members is defined varying the parameters with the greatest effect on design within reasonable ranges. Following the establishment of the significant hazard scenarios, limit state functions for the relevant member failure modes are defined taking account of dynamic effects induced by high loading rates. Subsequent to a strict member design (Ed = Rd) according to a consistent set of codes, structural failure probabilities are derived and analyzed in the light of target ceilings demanded by current codes. The findings may be used to deduce structure-related risks and acceptance criteria for their assessment. Such criteria would facilitate rational decisions on both, the need and the appropriate choice of risk-reduction measures to counteract the effects of gas explosions in buildings.

The bending strength of pin-box threaded connections for mortar-filled steel tubes used as micropiles is investigated in this paper. An experimental campaign has been carried out, including forty tests subjected to four-point bending until failure. The specimens consisted of mortar-filled steel tubes with a connection at the midsection. The results indicate that the failure mode of pin-box threaded joints is brittle and originates at the root of the last engaged thread of the pin end. Moreover, the bending strength of the connection is significantly smaller than the strength of jointless tubes. The analysis of the results suggests a considerable influence of the size effect, with the bending strength decreasing as the outer diameter of the tube increases. In addition, it is shown that, within the dimensions tested, the bending strength does not increase when the relative threaded length is increased.

The transverse fatigue behaviour of the top slab of box-girder bridges is dealt with in this paper. The cantilevers and central span of the top slab usually require a small reinforcement ratio and significant slenderness to fulfil the static design requirements. Nevertheless, the application of a high number of load cycles due to traffic or train passages may lead to fatigue damage accumulation. An experimental program on half-scale specimens reproducing the bridge slab was carried out. The fatigue failure was due to brittle fracture of the reinforcement, which could be predicted safely by available S–N curves. Furthermore, the experimental results showed the cycle-dependent reduction of tension stiffening, which was very significant due to the large tension stiffening capacity of lightly reinforced members. Special attention was paid to the development of negative tension stiffening contribution at unloading stages. This effect indicates that permanent and residual cracks and deflections are larger than those calculated with the fully cracked member. The experimental results showed that negative tension stiffening in members manufactured with self-compacting concrete can be larger than those with normally vibrated concrete.

It is widely accepted that tension stiffening of reinforced concrete reduces in the long term. In the codes of practice, this is accounted for by means of a modification in the empirical parameters to interpolate the average response of the reinforced member between the states I (uncracked) and II (bare steel). This average response is actually the result of the interaction of the different time-dependent mechanisms which develop in the element. In a tension member, the behaviour is mainly influenced by concrete creep and shrinkage and time-dependent bond deterioration. The role played by these processes is still unknown. An analytical approach is developed in this paper in order to understand the influence of such processes in the long-term decay of tension stiffening in tension members. The model is able to explain the experimental response of specimens tested in the literature and the results show the major influence of the time-dependent bond deterioration (bond creep and bond stiffness modification), rather than concrete creep and shrinkage.

One of the aspects that still require a deeper study regarding the tension stiffening effect of reinforced concrete is the behaviour under repeated loading. Due to the non-symmetric reloading–unloading bond–slip behaviour, negative bond stresses develop at the steel–concrete interface in the unloading stage, leading to compressive concrete stresses between cracks. This has been called the negative tension stiffening effect. Due to the negative tension stiffening effect, strains and crack widths are larger than those given by the naked reinforcement. In this paper existing experimental results are analyzed to study the main parameters governing the unloading behaviour of a tension member. Besides the negative frictional strength of the bond–slip mechanism, the parameters of a local crack closure formulation proposed in the paper are investigated. The crack closure effect leads to concrete compressive stresses at the crack when the crack tries to close. Finally, the influence of shrinkage prior to loading is analyzed. It is shown that the initial shortening of the member due to shrinkage has to be subtracted from the member behaviour in order to compare its response with the one experimented by a member without shrinkage and avoid erroneous considerations about negative tension stiffening under maximum load.

Fatigue of concrete is a microcracking process leading to the change of the macroscopic material properties. In particular, progressive stiffness decrease and increase of total and residual strains are developed as a function of the number of cycles and the stress level. The influence of the fatigue process on the behaviour of structural members is complex, because a cyclic redistribution of stresses develops within the structure. Owing to this fact, the employ of S-N curves to estimate the fatigue life usually leads to extremely conservative results. In this paper, a fatigue model for concrete is presented accounting for the evolution of the material properties. The model is able to obtain the fatigue life and the evolution of stresses and strains. The results are compared with other available design rules and a modification is proposed to estimate the number of cycles to failure in a simple way for the engineering practice.

The behaviour of a reinforced concrete tension member is governed by the contribution of concrete between cracks, tension stiffening effect. Under highly repeated loading, this contribution is progressively reduced and the member response approximates that given by the fully cracked member. When focusing on the unloaded state, experiments show deformations larger than those of the naked reinforcement. This has been referred to as negative tension stiffening and is due to the fact that concrete carries compressive stresses along the crack spacing, even thought the tie is subjected to an external tensile force. In this paper a cycle-dependent approach is presented to reproduce the behaviour of the axially loaded tension member, paying attention to the negative tension stiffening contribution. The interaction of cyclic bond degradation and time-dependent effects of concrete is investigated. Finally, some practical diagrams are given to account for the negative tension stiffening effect in reinforced concrete elements.

It is well known that repeated loads lead to increasing crack widths and deformations of reinforced concrete members. This is due to the progressive reduction of the parameters influencing the bond mechanism at the steel-concrete interface. However, current engineering methods employ severe simplifications to account for this influence, in particular to estimate values under permanent load. In this paper a model is presented to reproduce the distribution of longitudinal stresses and strains, bond stresses and relative slips along the crack spacing of a reinforced concrete tie with number of cycles. The model allows for a better understanding of the mechanical degradation sources affecting the evolution of tension-stiffening contribution. On the one hand, a cyclic degradation law is introduced to affect the local bond-slip behaviour. On the other hand, the mechanical damage of concrete is also introduced in the analysis. A parametric study is reported to show the role played by the different sources of degradation. Finally, the model capabilities are employed to analyse own experimental results.

This paper proposes a new model for reproducing the behaviour of concrete under fatigue capable to be used to analyze the response of reinforced concrete columns and beams. Such a model is firstly defined for concrete prisms under centric and eccentric compression, and then is applied to the structure of concrete–steel at the section level. The main parameters of the model have been fitted by means of comparison with experimental data. The paper illustrates how degradation of concrete by fatigue causes a process of redistribution of stresses along the section depth, and it may induce fatigue of the tensile reinforcement. The increase of permanent and total deformations observed in experiments is also studied and predicted at the section level, obtaining as well conclusions about the structure deflections.

In this paper, results of fatigue tests on reinforced concrete haunched beams without stirrups are presented for the first time. Two types of failure modes have been obtained, either due to fatigue of the reinforcement or due to shear fatigue. In addition, progressive increase of deflections with load cycles was measured. An analysis of tests is carried out in terms of the consequences of fatigue loading on ultimate strength and serviceability of reinforced concrete. Regarding fatigue strength, the limitations of existing models are shown and discussed. Regarding serviceability, it is shown that deflections are even higher than those theoretically obtained by the fully cracked member. This is due to development of shear deformations, cyclic creep, and negative tension stiffening during unloading stages.

Carlos Zanuy and Luis Albajar Assistant Professor, Dept. of Continuum Mechanics and Structures, Escuela Tecnica Superior de Ingenieros de Caminos, Canales y Puertos, Univ. Politecnica de Madrid, Calle del Profesor Aranguren S/N, 28040 Madrid, Spain (corresponding author). E-mail: czs@caminos.upm.es Associate Professor, Dept. of Continuum Mechanics and Structures, Escuela Tecnica Superior de Ingenieros de Caminos, Canales y Puertos, Univ. Politecnica de Madrid, Calle del Profesor Aranguren S/N, 28040 Madrid, Spain.

The present contribution deals with the behaviour of reinforced concrete beams under impact load. Moreover, the paper is intended as a discussion of advantages and limitations of different numerical models according to the degree of complexity. Two types of models are used. On the one hand, a simplified approach is presented, consisting of a three-degree-of-freedom model that reproduces the response of simply supported reinforced concrete beams subjected to an impact load at the midspan. The three degrees of freedom represent: 1) the contact between the beam and the projectile, 2) the flexural behaviour of the beam, and 3) the development of a critical shear crack. Nonlinear behaviour and damping are introduced into the three degrees of freedom. On the other hand, a comprehensive finite element model (Ansys LS-Dyna) has been used, which includes a concrete damage model with strain rate effect. It is discussed how the failure mode and the main physical behaviour are reproduced, comparing advantages and disadvantages regarding the reproduction of nonlinearities or strain rate effects, as well computational time required to perform parametric analyses.

The shear fatigue behaviour of reinforced concrete elements without stirrups is a complex process that involves a large number of variables. Because of its brittle nature, a better understanding of shear fatigue is convenient, so that practical recommendations with mechanical basis can be proposed. Experimental evidence indicates that shear fatigue failure starts with the formation of a diagonal crack from the inclination of a flexural crack in one of the shear spans. This diagonal crack then propagates with load cycles, both upwards to the load application point and downwards to the support. Final shear fatigue failure takes place by the destruction of the compression zone when its depth is too small to resist the compression force acting on it. In addition, it is also possible an unstable propagation of the diagonal crack as soon as it forms. A critical point of the process is therefore the formation of the diagonal crack. In this paper, the capabilities of a predictive model to estimate the number of cycles to diagonal cracking are explored. A comparison is carried out with first experimental results on haunched reinforced concrete beams without stirrups, which are typical of cantilever slabs of bridge decks.

This paper describes the dynamic analysis and vibration serviceability assessment of an in-service steel-plated stress-ribbon footbridge sited in Valladolid (Spain). Because of ist slenderness and singularity, this footbridge is a typical lightweight structure sensitive to dynamic excitation produced by pedestrians. A continuous vibration monitoring system which measures the acceleration and the environmental factors has been installed. The data collected have been used to identify the dynamics of the structure and assess ist vibration serviceability under in-service pedestrian traffic. Firstly, peak-acceleration-based test for single-frequency excitations are undertaken. Secondly, standards ISO 2631 and ISO 10137, suitable for general human exposure evaluation to whole-body vibrations, are used to evaluate the long-term vibration serviceability since they take into account the duration of the vibration exposure as well as the frequency content of the excitation.

Serviceability requirements of concrete structures often deal with control of crack widths and deflections. It is well known that such variables increase with number of cycles, but the currently available models assume some simplifications to include this cyclic increase. The estimation is usually made by affecting the monotonic response of the element by long term factors. Although this methodology usually yields conservative results, it does not actually account for the realistic cyclic behaviour of reinforced concrete in tension and may be unsafe under the permanent load level. In the paper, the progressive degradation of the bond properties in the tension chord with number of cycles is included in a cycle-dependent model. In addition, the fatigue damage of concrete in the compression zone is accounted for. The paper presents how both degradation mechanisms of the tension and compression zones are coupled. The proposed model allows the estimation of crack widths and deflections of flexurally loaded elements under cyclic loads. The model results are compared in the paper with experiments on cyclically loaded reinforced concrete beams. The study allows understanding the different interaction played by the degradation mechanisms in lightly and heavily reinforced concrete beams.

Fatigue is a continuous and progressive microcracking mechanism leading to increasing permanent strains and decreasing stiffness in concrete. This paper proposes a time-dependent (i.e, cycle-dependent) model for concrete that accounts for the changes of the mechanical properties during the fatigue life. The proposed method can be useful in estimating the fatigue-carrying capacity of existing structures that will be subjected to higher loads in the future. The model is implemented into a sectional algorithm to reproduce the evolution of the stress-strain state of reinforced concrete members. Redistribution capacity is found to be the main governing factor of the final failure mode. A comparison of theoretical results with existing experimental data of reinforced concrete beams indicates that the model is accurate in the prediction of strain evolution, fatigue life and the mode of fatigue failure.

The influence of fatigue may be an important but not usually contemplated aspect on the behaviour of some components of concrete structures. Here a study on the bridge approach slabs is presented. It is shown how the cyclic load causes a progressive deterioration of the compression zone of concrete and its contribution in the tensile chord between cracks. The increase of deflections and crack widths along the fatigue life is observed experimentally, under maximum and minimum loads. The growth of the remnant values of these variables evidences the important irreversibility of the fatigue degradation.