Fibre-reinforced polymer (FRP) composites have been employed in the last few decades largely for the strengthening and seismic retrofitting of existing reinforced concrete (RC) structures. Several studies are available in the literature and different analytical models have been proposed for evaluating the FRP contribution in strengthened RC elements. This paper analyses the accuracy of analytical models widely used for evaluating the flexural and shear contributions provided by the FRP. Some of those models are included in design guidelines. In particular, the analytical models for evaluating the FRP strain at intermediate crack-induced debonding failure are analysed. The accuracy of each formulation is assessed comparing the analytical provisions with the experimental results collected from two databases, one for bending and one for shear. The results obtained show that most of the analytical flexural models achieve a good level of accuracy and only a few models provide inadequate results. A new formulation proposed for evaluating the FRP shear contribution is shown to be generally conservative, which comes at the expense of accuracy.

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.

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

Strut-and-tie modelling constitutes a powerful tool for the design of complex structural reinforced concrete elements. It has been proved numerically that strut-and-tie (ST) models obtained using structural optimization methods produce designs that are more efficient. However, to the best of the authors' knowledge, no experimental evidence of such results has been published. This paper presents experimental results for nine test specimens; five of them were designed using optimal models derived from a full homogenization structural optimization algorithm, and the remaining four using conventional ST models for comparison purposes. Although all specimens carry loads higher than the factored design load, specimens based on ST models derived using full homogenization with reinforcement parallel to the ties exhibit better structural performance regarding crack growth control, more ductile modes of failure and a greater increase in load capacity.

This paper concerns the shear capacity of keyed joints that are transversely reinforced with overlapping U-bar loops. It is known from experimental studies that the discontinuity of the transverse reinforcement affects the capacity and the failure mode. However, to the best knowledge of the authors, previous theoretical works and current design equations in standards do not account for this important effect. This paper introduces a detailed model based on finite element limit analysis to assess the effect of the discontinuous reinforcement. The model is based on the lower bound theorem and uses the modified Mohr-Coulomb yield criterion, which is formulated for second-order cone programming. The model provides a statically admissible stress field as well as the failure mode. Twenty-four different test specimens were modelled and the calculations compared with the experimental results. The results of the model show satisfactory agreement with the experimental observations. The model produces estimates of the shear capacity that are significantly better than those of the Eurocode 2 design equations.

Tall hollow concrete piers with high width-to-thickness ratios are commonly used in long-span box girder bridges. Such thin-walled structures present the possibility of failure due to local buckling. So, in common practice, diaphragms are usually included in hollow piers to improve the local stability; however, is that necessary? Although experimental research on the buckling behaviour of hollow piers has been conducted extensively, few analytical attempts have been performed to reveal the effects of the width-to-thickness ratio on local buckling behaviour. To this end, an analytical model has been proposed to investigate the local buckling behaviour of hollow piers. Following the Ritz-Timoshenko method, an analytical formula for critical local buckling stress has been developed and verified to have good accuracy compared with finite element analyses. Based on the buckling failure mode of a hollow pier with a slenderness ratio > 6, it can be reasonably postulated that the strength of the hollow pier will be unaffected by local compression flange buckling when the wall width-to-thickness ratio is < 24, and it is entirely unnecessary to include diaphragms in hollow piers for stability. Additionally, it is equally interesting that the critical width-to-thickness ratio of a hollow pier with a slenderness ratio > 4 derived using the proposed model is the same as the value given by the current AASHTO-LRFD Bridge Design Specifications.

When constructing reinforced concrete (RC) building structures, knowing the loads to which the shoring system will be subjected during the entire process is one of the key aspects for ensuring safety during the work. Although various simplified methods of estimating the load transmission between shores and slabs during construction have been proposed to date, none of these methods can estimate the loads on individual shores during the different construction phases. This paper proposes a calculation method that allows the loads on individual shores to be calculated for each construction phase without having to resort to the use of advanced software. The proposal was validated by comparison with the results obtained from two actual buildings under construction and represents a step forward in the construction of RC building structures, as it is the first method that offers the possibility of estimating the loads acting on each shore during all the construction phases.

This paper includes a presentation of a shear test database that contains 278 tests conducted on reinforced concrete beams with vertical stirrups and no horizontal skin reinforcement. These beams are commonly referred to as non-slender beams since they were tested using loading arrangements that created shear span-to-depth ratios a/d < 2.4. In an effort to arrive at a database that can be used for the purposes of evaluating the accuracy and conservativeness of design provisions, several control and filtering criteria were applied. After this process, 178 beams remained in the evaluation database. The analyses conducted using this database indicated that the application of the strut-and-tie models (STM) of Eurocode 2 (EC2) to non-slender beams with stirrups is unconservative, i.e. the database analyses yielded results that were above the desired 5 % fractile. Almost all unconservative strength estimations were obtained for test specimens containing large numbers of stirrups. Conversely, statistical evaluations showed that the FIP Recommendations model for beams with point loads near supports is conservative.

Progressive collapse is a phenomenon in which local failure of a structural component due to a gas explosion or blast may lead to failure of the entire structure or a significant part of it. RC structures can resist progressive collapse through various mechanisms such as frame action and catenary action.
In this paper, the effect of catenary action on the resistance of concrete frame structures to progressive collapse is modelled using limit analysis. Non-linear optimization is performed for this. It is observed that although frame action is known to be the main mechanism resisting progressive collapse, at the end of this action, after rupture of bottom bars, catenary effects may bring about a noticeable increase in the resistance of the structure. The results show good agreement with the experimental results of other researchers.

Software for calculating the internal forces, moments and deflections of sandwich elements with reinforced concrete facings has been developed as part of a research project at Technische Universität Kaiserslautern. Sandwich elements with stiff concrete facings are internally statically indeterminate. Cracking of the concrete facings leads to a redistribution of the internal forces and moments over the length and across the cross-section of the element. This redistribution must be considered in the structural design of such elements.
An existing program for calculating metal-faced sandwich elements was considerably extended by an iterative approach that allows the internal forces and moments to be calculated with the exact stiffness of the cracked facings. This iterative approach and the calculation algorithm behind the new software, called swe2+, are explained in this paper. A verification of the calculation results and a parametric study of a two-span sandwich element are also presented.

Chloride-induced corrosion of reinforced concrete (RC) bridge girders has led to a huge loss of national resources. One of the important concerns affecting RC bridge girders is corrosion of the stirrups, which can even cause the failure mechanism to change from a ductile flexural mode to a brittle shear mode. Hence, analysis of the reduction in shear capacity overtime is essential in the reliability assessment of bridge girders, which is the topic of the paper. This paper proposes a stochastic modelling approach for estimating the time-variant shear capacity and reliability within the framework of a Monte Carlo simulation, which assists in the sustainability-based service life design of bridge girders. Such modern design concepts require methodologies for estimating whole life cost at the design stage itself. The development of such methodologies would provide the designer with various options for arriving at an optimum design having the desired performance level during the service life. The proposed approach takes into account: 1) the randomness in basic variables, 2) the effect of micro-environments and the spatial variation of corrosion, 3) the number of stirrups resisting web shear failure, and 4) the ductile to brittle transition of stirrup steel as corrosion propagates. The incorporation of this transition is found to have a significant influence on the time-variant reliability of the girder. Although PFA concrete is known to have better durability characteristics than OPC concrete, this paper gives a framework for its quantification in terms of time-variant reliability.

Strut-and-tie models (STMs) have been wildly used for the design of disturbed regions in structural concrete members. The STM developed based on the load path method or with the aid of stress trajectories is not unique and varies with the designer's intuition and past experience. As a result, topology optimization methods have been adopted to generate STMs in reinforced concrete structures. However, such models are just a preliminary configuration and the detailed layout of ties in an STM cannot be determined by the optimal topology. This is because reinforced concrete is assumed to be a uniform elastic continuum. Therefore, the effect of the steel reinforcement on the load transmission cannot be considered in the optimization process. Recently, the criterion of minimum strain energy has been proposed to determine the optimal layout of STMs obtained by the modified optimization method. However, the strain energy criterion does not work when the minimum strain energy in ties is zero when evaluated by mathematical equations. To address this issue, the maximum stiffness criterion is proposed to discover the optimal layout of ties in STMs by evaluating the stiffnesses of strut ties.

In steel-concrete composite structures, innovative composite dowels can be used for the connection of ultra-high-performance concrete (UHPC) slabs and high-strength steel members. In addition to sufficient shear capacity, composite dowels have to ensure the transmission of tensile forces in the composite connection in order to prevent lifting of the concrete slab. This may lead to structural problems, particularly in the very slender concrete slabs of high-strength composite beams, where composite dowels have very small embedment depths. Although findings concerning the structural anchorage behaviour of composite dowels under static loads are already available, studies on the fatigue of composite dowels under cyclic pull-out loading are still lacking. As fatigue behaviour is crucial for applications in bridge construction, the present paper introduces cyclic pull-out tests on composite dowels in UHPC slabs in which the influence of different load-dependent parameters (upper load level and load range) as well as the use of transverse reinforcement has been investigated. Furthermore, an approach to assess the lifetime of composite dowels in UHPC under cyclic pull-out loading is proposed.

This paper is a comprehensive background document on the state of the art in European seismic design provisions which was assembled by fib committee 5.1 to support the development of design guidelines regarding the use of externally applied fibre reinforced polymer (FRP) materials in the seismic retrofitting of reinforced concrete structures. In the context of developing design guidelines, the underlying mechanistic models that support the derivation of provisions were assembled following critical evaluation of the existing proposals and with careful reference to the experimental evidence available, the comparative assessment of past models in the literature and requirements established from first principles.

The behaviour and modelling of concrete columns confined with FRP composites under monotonic compression has been extensively studied, but far fewer studies of the cyclic behaviour of FRP-confined circular and rectangular columns have been carried out. A reliable model indicating the cyclic stress-strain behaviour of FRP-confined columns is of great importance, especially for seismic retrofits and the design of these columns. In this paper, based on the results from a series of cyclic compressive loading tests on FRP-confined specimens, a unified cyclic stress-strain model is proposed for circular, square and rectangular columns confined with FRP composites. The model contains different parts of the cyclic stress-strain curve, including plastic strain, maximum strain in unloading path and corresponding stress, stress deterioration, effect of loading history, partial unloading and partial reloading. New expressions are also proposed for predicting unloading and reloading paths. The proposed model agrees well with the test results.

The behaviour of the bond between fibre-reinforced polymers (FRP) and concrete greatly influences the behaviour of concrete structures strengthened with FRP composites. Although numerous experimental studies have investigated this bond, experimental data concerning fatigue tests on carbon FRP plates attached to concrete blocks are still lacking. Therefore, a series of double-lap shear tests under monotonic and fatigue loadings were performed on concrete prismatic specimens reinforced with CFRP plates. First, a series of experimental investigations are summarized. Thereafter, the fatigue behaviour of CFRP plate debonding is characterized using S-N diagrams that represent the relationship of the upper-limit fatigue load with the monotonic load strength and the number of cycles to debonding on a semi-logarithmic scale.

Fibre orientation and volume distribution affect the post-cracking tensile strength, which is one of the main design parameters of fibre-reinforced concrete (FRC). This paper discusses the influence of unidirectional and grid reinforcement on fibre orientation and distribution in FRC slabs. Slabs without conventional reinforcing bars were used as a reference. The slab size was 1200 × 1200 × 150 mm. Numerical simulations were used to predict the fibre orientation and X-ray computed tomography (CT) to determine the actual fibre orientation and distribution. Beams were sawn from each slab, CT-scanned and tested in three-point bending tests in accordance with EN 14651. Both the numerical simulations and the CT results show that the rebars caused a more isotropic fibre orientation in the lower halves of the slabs. This was confirmed in the bending tests, where the lowest variation and highest residual tensile strengths were documented for beams sawn from slabs with grid reinforcement. Fibre migration from the upper layer to middle and lower layers of the slabs due to gravity was observed in all slabs, and in the reinforced slabs, migration also depended on the distance from the casting point. The reinforcement led to an accumulation of fibres above the rebars in the middle layer of each reinforced slab. A set of mechanisms is proposed to explain the experimental results.

Cross-section deformation is considered an important indicator for assessing the structural safety in the inspection and maintenance of tunnels. The way it increases over its lifetime is an indication of the gradual degradation in structural performance. In order to take timely and appropriate maintenance measures before the tunnel reaches the ultimate limit state, a predictive degradation model of cross-section deformation should be established. In this paper, a probabilistic degradation model is developed based on an average uniform rigidity ring model for circular tunnels assembled from segmental linings. By considering the uncertainties and relevant performance of parameters that vary over time, the model is able to supply probabilistic and time-dependent predictions. Critical parameters are identified and the model is simplified following sensitivity analysis. Based on the measuring data, a Bayesian updating method is proposed to improve the input assumptions and predictions of the model. This research provides a perspective on the degradation modelling of the cross-section deformation of circular tunnels assembled from segmental linings and methods for improving the proposed predictive model.

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.

The growing concern for the ready-mixed concrete industry is the disposal of returned unused concrete. In its plastic state, the concrete is a perishable product and the disposal of any unused concrete presents a set of challenges. An increase in environmental regulations requires the industry to implement the best practices that effectively reduce the quantity of by-product materials requiring disposal. This paper describes a preliminary experimental study on the effect of commercial stabilizer on the plastic and hardened properties of concretes made with three different types of cement commonly used in Australia, namely, general-purpose Portland cement (GP) (100 % ordinary Portland cement (OPC)), general-purpose blended (GB) cement (75 % OPC + 25 % class F fly ash (FA)) and low-heat (LH) cement (35 % OPC + 65 % blast-furnace slag). The effect of various stabilizer dosages on the efflux time (flow time) of GP, GB and LH cement grouts was studied in the initial phase. The results show that for a constant efflux time, the holding duration of the grouts increases with increasing stabilizer dosages (or amounts) and in the case of GB and LH cement grouts, the holding duration is longer than the GP cement grout for the same stabilizer dosage. In the next phase, the predicted stabilizer dosage was added to concretes made with the above three cements to evaluate the plastic and hardened properties of fresh concretes, stabilized concretes and blends of fresh concretes with 10, 25 and 50 % stabilized concretes. The results show that the initial slump values are within the tolerance, except they are higher when the stabilizer dosage is added after 1 h, but the final slump is within the tolerance of the control concrete. After stabilization of the concretes, the initial and final setting times of stabilized concretes increased to > 24 h. The initial and final setting times of the blended concrete containing fresh concrete and 10, 25 and 50 % stabilized concretes are similar to those of fresh concrete for all cement types. The stabilized concretes do not have any significant effect on the compressive strength and shrinkage compared with the control concrete.

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

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

Compressive arch action is one of the main resistance mechanisms against progressive collapse in reinforced concrete (RC) buildings. Hence, many studies have investigated the development of arching action in RC beams and frames but less attention has been paid to calculating the corresponding enhancement in structural capacity. In the present study, a theoretical method is introduced in order to calculate the arching capacity of RC beams and also to obtain a quantitative assessment regarding structural robustness against progressive collapse. The proposed method is validated using the experiments in the literature. The evaluation indicates that the procedure introduced here could establish a reliable foundation for estimating the arching capacity of beams and also structural robustness.

A detailed investigation was conducted to study the behaviour of reinforced concrete (RC) beams with large openings strengthened by externally bonded carbon fibre-reinforced polymer (CFRP) laminates. A total of six simply supported beams consisting of two solid beams and four beams with openings were cast and tested under four-point bending. Each beam had a cross-section of 120 × 300 mm and length of 2000 mm. Each beam had a large opening placed symmetrically at mid-span. Test parameters included the opening shape and size as well as the strengthening configuration for the CFRP laminates. The study was conducted by way of both experimental testing and finite element analysis. The experimental results show that including a large opening at mid-span reduces the beam capacity to about 50 %. In the experimental results, strength gain due to strengthening with CFRP laminates was in the range 80-90 %. The finite element and experimental results were compared.

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