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Reinforced concrete structures are often subjected to corrosion, inducing a decreasing reliability over time. This corrosion often exhibits spatial variation, which can be modelled by random fields...

Realistic structural models incorporating the time-dependent effects of concrete are essential in order to make accurate predictions of the time-dependent deflections at any time of the service life. Experimental databases are used to calibrate and validate existing models for creep and shrinkage available in international standards. However, extensive research campaigns on large-scale prestressed beams are scarce. In 1967-1985, a research program comprising a unique set of long-term experimental data on concrete beams was conducted in joint collaboration with four Belgian research institutes to determine the influence of creep and shrinkage on the long-term behavior of reinforced and prestressed concrete members. The main aim of the final part of the research campaign was the determination of the long-term behavior of prestressed and partially prestressed beams subjected to permanent loads, considering the influence of the magnitude of the loads, the degree of prestressing, the shape of the cross-section, the type of prestressing and the stress conditions. This paper reports on the obtained unique set of long-term tests. Additionally, also information related to the creep and shrinkage data of prisms and the results of the static tests in a four-point bending configuration until failure at the age of 28 days and 5 years are presented in this paper. The measurements of the prestressed members are compared with a simplified calculation method based on the direct stiffness method, which accounts for aging, creep, and shrinkage. The proposed simplified calculation model allows fast and accurate predictions of strains, stresses, and deflections as a function of time. The results show that the direct stiffness method in combination with the current models of EN1992-1-1 and fib Model Code 2010 can predict the long-term behavior of concrete beams in good agreement with the available experimental data. The research allows to develop more accurate calculation guidelines with respect to the evolution of deflections, concrete deformations and stresses of prestressed beams as function of the prestress-degree, shape of the cross-section, and the type of prestressing.

Despite the recent amount of theoretical and technological developements, structural robustness is still an issue of controversy being underlined by serveral progressive collapses in te past. Current design codes point out different strategies, among which strategies to limit progressive structual damage by applying prescriptive design and detailing rules. For example, for consequence class 2 structures, EN1991-1-7 defines a risk class CC2b for which also vertical ties are required. However, te background of the design values of vertical ties in current code is not clear and their adequacy should be validated. Moreover, effects such as membrane action and Vierendeel action are important to consider when assessing structural robustness and are difficult to incorporate when applying only traditional design methodologies. To this extent, a set of numerical simulations have been executed in this contribution in order to verify and investigate the progressive collapse behavior of RC frames including the redistribution of internal forces and the response of the vertical ties in columns.

Reinforced concrete structures degrade over time, among others due to corrosion. This degradation process is not uniform along the structure. Monitoring and inspections can be used to detect damage and update a deterioration model of the structure. In this work, a model-based method is used to identify damage through the calibration of a FEM model based on modal characteristics. The model calibration is performed by means of a Bayesian method, using MCMC to sample the posterior distributions of model parameters for the time-dependent degradation of material properties. The calibrated model can then be used for a more accurate prediction of the remaining service life. Furthermore, it enables to be implemented in a pre-posterior analysis framework to determine theVoI of the monitoring and inspection program for comparison of different monitoring and inspection strategies.

The UCO textile factory was built in Ghent (Belgium) in the period 1947-1948. The roof structure covered an area of about 35,000 m(2) and consisted of 100 primary beams and 600 secondary beams. These post-tensioned beams were designed by prof. Gustave Magnel, who was a world-leading expert in the field of prestressed concrete. This project was one of the first important large-scale applications of prestressed concrete in industrial buildings in the world and also the first large scale application of on site prefabrication. Recently, part of the factory building was demolished and a primary beam and secondary beam of the roof structure were transferred to the Magnel-Vandepitte Laboratory for Building Materials and Structures for testing at an age of approximately 70 years. The primary beams have a span of 20.5 m and a maximum depth of 1.7 m. The secondary beams have a span of 13.7 m and a depth of 1 m. Only prestressing tendons (Blaton-Magnel system with o 5 mm wires) were present in the beams but no passive reinforcement nor stirrups are present except for the reinforcement in the corbels and the end blocks. This article describes the results of the loading tests up to failure on the beams. The experimental results are compared with results from analytical calculations. Furthermore, a nonlinear finite element model was developed and validated. Subsequently, this numerical model was used for a Bayesian-based assessment of the prestressing losses in these beams. As such, the article presents novel information related to time-dependent prestress losses after 70 years in service as well as the structural performance of such existing post-tensioned concrete structures dating from that pioneering period.

Existing concrete bridges can show signs of deterioration, e.g. due to corrosion, in which case the question arises whether these bridges still have an acceptable safety level. To obtain additional information about the state of the structure, different types of information can be gathered. However, the measurements performed are often not used directly to update the estimate of the corrosion degree of the bridge and the resulting information from different measurement types is not combined. In this contribution, it is investigated how parameters of the service life models for concrete girders subjected to chloride-induced corrosion can be updated based on heterogeneous measurement data, with the focus on modal measurements and strain measurements. The posterior distributions of these parameters are generated based on Bayesian updating. These updated distributions can be used to get a more accurate estimate of the real deterioration state of the bridge. Based on this, the failure probability of the bridge and its remaining service life can be estimated more accurately.

Many existing bridges are reaching the end of their technical service life. To estimate the remaining lifetime of reinforced concrete structures, it is important to assess the parameters of the corrosion process (i.e. parameters governing the corrosion propagation, but also parameters of the chloride or carbonation ingress). The level of corrosion and its spatial distribution can be inferred from strain data under static loading or modal data. In addition, information from visual inspections is often available as well, although not often used to quantify the level of corrosion. In this work, it is investigated how visual inspections can supplement the strain and/or modal data and provide information on corrosion parameters. The developed framework is applied to a simply supported beam subjected to corrosion.

The alternative load path (ALP) method is widely used to investigate the performance of reinforced concrete (RC) buildings in case of progressive collapse (or disproportional collapse) scenarios. This kind of analysis can be carried out either in a static way or in a dynamic way. In this contribution, these methods are compared by means of nonlinear static and nonlinear dynamic analysis methods. A 5-storey RC frame subjected to two different sudden column removal scenarios is adopted as a case study. The probabilistic analysis considers 12 random variables. On the basis of the stochastic results, a dynamic amplification factor (DAF) is calculated. The mean values of the DAF are 1.114 and 1.102 for the external column removal scenario (Case A) and the internal column removal scenario (Case B), respectively. Compared to the failure probabilities obtained through a static analysis, the failure probabilities for the incremental dynamic analysis results are 184.0% and 180.7% higher for Case A and Case B, respectively.

Membrane structures are widely used because of their lightweight properties and expressive architectural shapes. However, there does not yet exist a unified design approach for membrane structures as is available for conventional buildings. Because of their flexibility, membrane structures exhibit a different structural behaviour than conventional buildings. Membrane structures are doubly curved, prestressed and the prestress contributes to the stiffness. The structural response of these structures is non-linear, and the hanging and arching directions interact. A probabilistic framework for tensioned membrane structures is developed herein. Using this tool, partial factors are calibrated for a representative tensioned hypar membrane structure made of PVC-coated polyester fabric. Reliability analyses are performed using a First Order Reliability Method in combination with Latin Hypercube Sampling. The approach is illustrated for two load cases, i.e. considering snow load and wind uplift load, respectively. Three hypars are investigated, each with a different rise to span ratio. The partial factors are determined through a minimisation process. As a result of the performed process, the recommended partial factor for prestress is 1.0, for snow load is 2.0 and for wind uplift load is 2.0 for the investigated membrane structure. In this study, the hanging direction under snow load proves to be decisive for the calibration of the partial factors. The obtained partial factors are not in line with the partial factors found in the Eurocode (1.5 for variable loads). Alternatively, when considering a partial factor for snow load and wind uplift load of 1.5, partial factor for prestress should be increased to 1.2 for the structural type which have been investigated. The application of Latin Hypercube Sampling in combination with the structural analysis of membrane structures enables to perform the reliability analysis calculations in a more computationally efficient way. Moreover, the used optimisation procedure for the calibration of the partial factors makes it possible to interpret the obtained results with respect to the complex non-linear behaviour of the investigated tensile membrane structures.

The design of tensioned membrane structures is not yet addressed by standards like the Eurocodes. Currently, in cooperation with the TensiNet Association, Working Group 5 of CEN TC250, is working on a general standardised design approach for membrane structures, consistent with the partial factor framework used in the Eurocodes (as specified in EN1990). To achieve such a design approach, research focusing on developing a methodology to verify the reliability of a membrane structure is needed. The structural behaviour of a tensioned membrane can be represented by a tensioned cable-net. This article starts from the investigation of a cable-net structure, as such structures are addressed in EN1993-1-11, followed by applying the established method to a membrane structure. This article evaluates the influence of the partial factor for pretension. If the cable-net and membrane structure are dimensioned according to a partial factor 1.0, the obtained reliability index is lower than the considered target reliability index. If the structures are dimensioned according to a partial factor 1.35 the obtained reliability index is higher than the considered target reliability index and therefore meet the safety requirements. The study shows that the influence of the structurally non-dominant direction plays an important role in the reliability analysis.

Although traditionally the fire resistance rating of concrete elements is determined through standardized tests or tabulated data, there is a growing trend towards the use of performance-based approaches to evaluate structural behaviour during or after a fire. The safety format to be applied with these advanced numerical evaluations is however unclear. In this paper, the applicability of the concept of a global resistance factor (GRF) safety format is explored for simply supported concrete slabs exposed to the Eurocode parametric fire curve for a wide range of parameters. The safety of the slab is evaluated in relation to its ability to withstand a complete burnout scenario, i.e. its ability to resist the applied loads throughout the entire duration of a fire including the cooling phase. Using a full-probabilistic model, the required GRF is numerically derived for a specified target safety level in case of fire. Additionally, a calculation method is provided which allows to determine the GRF of fire exposed slabs for any given compartment through the use of a reference compartment and equivalency equations.

Glass is increasingly used to produce structural elements for buildings. For the case of glass beams, a lot of hybrid glass concepts, in which glass is combined with another material (e.g. steel, reinforced concrete, fibre reinforced polymers) were developed and successfully tested to overcome the material’s brittle nature and hence provide post-fracture capacity. Being one of the most widely tested concepts, the reinforced laminated glass beam demonstrates satisfactory load-carrying behaviour, both for statically determinate and indeterminate support conditions, for a variety of environmental conditions (temperature, humidity, etc.) and for several reinforcement percentages and beam sizes. Contemporary building codes do not only require sufficient structural safety and robustness for individual components, but also for parts -or the entire structural system- of a building. For the reinforced glass beam concept, component safety is demonstrated by post-fracture strength and ductile ultimate collapse behaviour. System action can be achieved through plastic hinge formation and stress redistribution. Additional system safety and robustness can be provided through the activation of membrane action in case of horizontal restraints at the beam ends. When a support is (accidentally) removed, membrane action can provide an additional safety mechanism which prevents collapse of the beam system. This paper presents an experimental program to assess the potential of activating membrane action for reinforced laminated glass beams. Statically indeterminate five-point bending tests with horizontal restraints, with or without intermediate support, are performed on 4.3 m long beam specimens. In addition, the effect of reinforcement percentage is investigated.

Transparency has become a trend in architecture. In the near future, the scale of application of structural glass will grow from elements (beams, columns, etc.) to entire systems (floors, roofs, facades, frames, etc.). Especially beams, being one of the most important and common building components, will be combined into load-carrying systems (e.g. a supporting grid for floors and roofs). However, this scale-up cannot be realized without incorporating structural safety and robustness on an element and system level, as required by modern building codes. For glass beams, research resulted in the concept of hybrid glass beams, in which a glass web is combined with flanges or reinforced with another material that provides post-fracture strength and ductility, hence providing structural element safety and robustness. Especially the stainless steel reinforced glass beam, based on the principle of reinforced concrete proved satisfactory. To investigate the feasibility of applying this concept in innovative beam systems, experimental five-point bending tests on 3.0 m beams and membrane action tests on 4.3 m beams were performed, resulting in satisfactory load-carrying behaviour with significant stress redistribution due to plastic hinge formation and membrane action, both compressive and tensile. Both features/mechanisms resulted in significant increases in the post-fracture capacity of the beam systems. For the latter's design, focusing only on glass fracture is insufficient, as the element and system safety requirements should also be satisfied. Therefore, post-fracture capacity and ductility should be incorparated in design. the latter requires an amount of reinforcing material, wihich decreases the beam's overall transparency. Therefore it is important that design aims at achieving maximum capacity and ductility with as little reinforcing material as possible. this paper investigates the effect of stress redistribution and membrane action on the achievable capacity of a reinforced glass beam system. It is concluded that both features/mechanisms, and especially membrane action can make a significant contribution to the ultimate capacity and ductility of the beam system. This paper also considers the incorporation of these mechanisms in design, resulting in optimal (i.e. minimal) usage of materials. Compared to statically determinate beams, a decrease in reinforcing material is possible, resulting in ever more transparent structures.

In contemporary architecture, glass is more and more applied not only to make up the cladding of the building, but also for structural members such as beams and facade fins. The trend to increase the scale of these structural entities makes it increasingly structurally efficient to apply statically indeterminate beam systems. For these systems to be approved, contemporary building codes require them to provide structural safety on an element and system level. Therefore, a lot of hybrid glass beam concepts, in which glass is combined with another material that provides post-fracture capacity, were developed and investigated. Among others, reinforced glass beams have experimentally proven their feasibility for statically determinate (element safety) and indeterminate (system safety) support conditions by providing significant post-fracture capacity, ductility, plastic hinge formation and load redistribution capacity. However, system safety can also benefit from the effects of membrane action, which can result in yet higher post-fracture performance. Moreover, the latter can make a significant contribution to the robustness of a beam system when an accidental event occurs such as collapse of one of the supports. This paper presents experimental test results of statically indeterminate five-point bending tests with clamping end-supports on twelve 4.3 m long stainless steel reinforced beam specimens in which the horizontal membrane forces are assessed. Two series of tests were performed, with and without intermediate support, for two types of beams with varying reinforcement percentage (i.e. solid and hollow profile reinforcement). During the tests, significant compressive as well as tensile membrane action was observed. The effects of the latter on the load-carrying behaviour is discussed by comparing the load-deflection diagrams with those of similar reinforced glass beam systems without clamped external supports. From this comparison, it is concluded that membrane action provides significant contribution to the load-carrying behaviour of such beam systems. Significantly higher post-fracture capacities can be achieved for both reinforcement sections and both types of tests. It is concluded that membrane action can be incorporated in design, which will lead to more economical, slender and more transparent reinforced glass beam systems.

Recent research has shown that the compressive membrane action (CMA) significantly enhances the load bearing capacity of FRP strengthened concrete beams. It is of great interest to investigate the effect of CMA on the structural reliability of such beams and how to incorporate the benefits of CMA into partial factor based design. Following a CMA model and the probabilistic models of its corresponding design variables, the effect of CMA on the reliability indices of FRP strengthened concrete beams was investigated. A parameter study as well as a sensitivity analysis were also conducted with parameters including properties of FRP and steel reinforcement, concrete properties and geometrical properties. The reliability indices with respect to load ratios i.e. ratios of the variable load to the total loads is selected to quantify the effect of CMA. The results show that the CMA effect significantly improves the structural reliability of FRP strengthened concrete beams. The parameter study indicates that an increase of the concrete strength and yield strain has positive effect on the structural reliability while an increase of FRP ratio, FRP modulus, steel ratio as well as the concrete ultimate strain has an adverse effect. Furthermore, it is found that the variations of the concrete strength, the FRP Young’s modulus as well as the concrete cover have a significant influence on the reliability index; the variations of the ultimate strain of FRP, the yield strain of steel reinforcement and the ultimate strain of concrete have a moderate influence on the reliability index. Finally, an adjusted partial factor for the FRP strength is derived for cases where CMA would already be considered in the design stage.

Traditional design of reinforced concrete structures is usually based on small deformation theories whereas in order to assess the ultimate load bearing capacity of RC structures against progressive collapse significant deformations should be taken into account. The alternate load paths facilitated by membrane action which develop under large deformation can activate a significant strength reserve, redistribute the loads and hence limit the damage progression in the structure. Up to date, no uniform approach is available on how to incorporate these membrane effects in the structural design or verification procedures against progressive collapse. In this article, sensitivity analyses were performed to investigate the effect of the stochastic nature of membrane action on the load bearing capacity for three distinct RC elements, i.e. a beam, one-way slab and two-way slab. It was found that variables which are usually not explicitly taken into account by traditional design methods, such as the axial restraint stiffness and ultimate reinforcement strain have a significant influence on the resistance of the considered elements. Subsequently, the design resistance of the elements was assessed using a probabilistic method and the ECOV method. It was found that the ECOV method and the probabilistic method considering a lognormal distribution provide similar results in case one observes a single failure mode for which the variability of the resistance is limited. In case of multiple failure modes and a large variability of the resistance, a mixed lognormal distribution proved to enable a more accurate design resistance estimation.

Concrete structures are able to resist high temperatures due to fire relatively well and they can be repaired afterwards. In order to select appropriate repair strategies, assessment of the condition of a concrete structure after fire is of crucial importance. Previous research has mostly been focusing on the strength of concrete during fire and considering slow cooling of elements to room temperature. Guidelines and models related to these conditions have been incorporated into structural design codes. However, in reality, fast cooling of concrete by means of water occurs frequently and the effect of this cooling method has been much less the subject of research investigations. Nevertheless, the effect of water cooling can be significant. In this article the effect of water cooling on the residual compressive strength, stress-strain diagram and bond strength between concrete and reinforcement is investigated. Two cooling methods are considered, i.e. quenching and spraying of specimens. It is found that the investigated properties are extremely sensitive to heating with subsequent water cooling.

In 1967–1985, a research campaign comprising a unique set of long-term experimental data on concrete beams was conducted in joint collaboration with four Belgian research institutes to determine the influence of creep and shrinkage on the long-term behavior of reinforced concrete members. The main aim of the research campaign was the determination of the long-term behavior of cracking and deformations subjected to permanent loads considering the influence of the magnitude of the loads and various reinforcement ratios. The objective of this article is twofold: to provide an overview of the measured data of the reinforced beams of the research campaign, which has never been published before, and to propose a simplified calculation method based on available models in literature that can predict the available measurement data. A simplified calculation model is proposed, which accounts for nonlinear creep strains due to high stresses, shrinkage, aging, and cracking in reinforced concrete beams. This numerical method is based on a cross-sectional analysis formulated using the layered Euler-Bernoulli beam theory, allowing fast and accurate predictions of strains, stresses, and deflections as a function of time based on fib Model Code 2010 and EN1992-1-1. The measurements of the beams subjected to high permanent loads during a time period of 4 years are compared to the results evaluated with the proposed simplified calculation model. The results show that the proposed simplified calculation method based on the current models of EN1992-1-1 and fib Model Code 2010 can predict the long-term behavior of reinforced concrete beams subjected to high loads in good agreement with the measurements.

This paper proposes part of a framework for the development of a risk assessment methodology to quantify the life safety risk of building occupants in the context of fire safety design. An important aspect of quantitative risk analysis (QRA) concerns taking into account the variability of the design parameters. In QRA for life safety in case of fire, one of the key research challenges to take probability into account is the complexity of the different submodels. Another key aspect is the high computational time for performing a set of simulations. In order to tackle these problems, a response surface model (RSM) for sub-models, which support the global QRA method, is useful. In this paper, this is illustrated in particular for the modelling of smoke spread. More specifically, the focus is on the development of a method and a model for estimating the RSM using a Least Squares (LS) technique or the Polynomial Chaos Expansion (PCE) approach. Both methods were found to be suitable for the intended purpose, but PCE provides the best fitting response surface model based on the obtained data for the case at hand. The model is tested in a practical case study with Computational Fluid Dynamics (CFD) incorporating the Fire Dynamics Simulator (FDS) model.

The rise of Performance Based Design methodologies for fire safety engineering has increased the interest of the fire safety community in the concepts of risk and reliability. Practical applications have however been severely hampered by the lack of an efficient unbiased calculation methodology. This is because on the one hand, the distribution types of model output variables in fire safety engineering are not known and traditional distribution types as for example the normal and lognormal distribution may result in unsafe approximations. Therefore unbiased methods must be applied which make no (implicit) assumptions on the PDF type. Traditionally these unbiased methods are based on Monte Carlo simulations. On the other hand, Monte Carlo simulations require a large number of model evaluations and are therefore too computationally expensive when large and nonlinear calculation models are applied, as is common in fire safety engineering. The methodology presented in this paper avoids this deadlock by making an unbiased estimate of the PDF based on only a very limited number of model evaluations. The methodology is known as the Maximum Entropy Multiplicative Dimensional Reduction Method (ME-MDRM) and results in a mathematical formula for the probability density function (PDF) describing the uncertain output variable. The method can be applied with existing models and calculation tools and allows for a parallelization of model evaluations. The example applications given in the paper stem from the field of structural fire safety and illustrate the excellent performance of the method for probabilistic structural fire safety engineering. The ME-MDRM can however be considered applicable to other types of engineering models as well.

Recently, several structural failures demonstrated the disastrous consequences of progressive collapse and raised the awareness of the engineering community. However the low probability of progressive collapse makes it uneconomical to design every building against progressive collapse using conventional design methods. Furthermore in most cases the initiating events of progressive collapses are unknown during the design. As such, consideration of secondary load-carrying mechanisms can be an effective alternative. These mechanisms include compressive arch action (CAA) and tensile catenary action (TCA) in reinforced concrete (RC) beams. Several researchers have investigated the effects of CAA and TCA experimentally and numerically in individual RC beams. However to date limited studies have been carried out to study these mechanisms in RC beam-grids. Hence in this contribution a validated numerical model is developed to study and quantify the individual contributions and development of the different mechanisms in RC beam-grids. Parametric studies are performed in relation to the influence of the aspect ratio of the grid, reinforcement ratio and ultimate reinforcement strain.

The Alternative Load Path (ALP) method is widely used to assess progressive collapse resistance of reinforced concrete (RC) structures by notional removal of one or more load-bearing elements. In general, a nonlinear time history analysis (NTHA) is needed to perform such an analysis if dynamic effects are explicitly taken into account. To avoid cumbersome nonlinear dynamic analyses, the energy-based method (EBM) is a promising technique to predict the maximum dynamic responses of a structural system. In this article, the accuracy and precision of the EBM is evaluated based on a validated finite element model of a tested RC slab subjected to a sudden column removal scenario, in particular in relation to the investigation of tensile membrane action (TMA). Influences of dynamic effects are evaluated, i.e. in relation to strain rate effects, damping, and the time duration of support removals. Strain rate effects are observed to have only slight influences on the dynamic responses. The strain rate dependency of reinforcement is found to have a more significant influence on the responses in TMA stage, although also to a limited extent. The magnitude of the load has a significant influence on the dynamic response, as do increasing damping ratios due to the corresponding significant energy dissipation. Finally, the dynamic response reduces with increasing time duration of the column removal. Based on the results of the stochastic analyses, the EBM is observed to perform well based on a comparison with the results of NTHA in both flexural and TMA stages. Furthermore, in relation to the analyzed case studies on reinforced concrete slabs, the model uncertainty of the responses obtained through the EBM compared with the NTHA is found to be represented well by a lognormal distribution with mean of 0.95 and a standard deviation of 0.20, for evaluating the loads of first rupture of reinforcement. Furthermore, a lognormal distribution with mean 0.96 and standard deviation 0.13 is found appropriate to represent the model uncertainty on ultimate load-bearing capacity predictions. Model uncertainties are also obtained with respect to the model predictions for displacements at the moment of the first rupture of reinforcement, displacements at the ultimate load-bearing capacities, and both loads and displacements at second load peaks.

This study focuses primarily on examining the compressive membrane action (CMA) in FRP (fibre reinforced polymer) strengthened reinforced concrete (RC) beams or one-way slabs. Considering a rigid-plastic mechanism, in combination with strain compatibility and force equilibrium, a model is proposed to predict the load bearing capacity of FRP strengthened RC members when considering CMA. Comparison with experimental tests proves the proposed model to be realistic and effective. A parametric study has been undertaken and an enhancement factor was used to qualify the CMA effect in FRP strengthened RC members. The parameters include the properties of FRP, steel reinforcement and concrete, and the span to depth ratio. The results indicate that CMA can effectively enhance the load bearing capacity of FRP strengthened RC members. Results also indicate that the effect of CMA increases with the increase of FRP area, steel reinforcement ratio, strength and ultimate strain of concrete but decreases with increasing span to depth ratio.

Deterioration due to corrosion has been a growing concern in the last decades since it compromises the serviceability of structures and results in a decrease of the structural safety. Apart from deterioration, also the awareness of the importance of structural robustness has increased due to several failures with progressive collapse. The activation of membrane action in reinforced concrete slabs can significantly increase the structural robustness by providing an alternate load path. A validated numerical model for the tensile membrane behavior of reinforced concrete slabs is used to investigate the influence of (simulated) corrosion effects on this membrane behavior. A two-step analysis is adopted: first a cross-section analysis is performed, followed by an analysis of the structural member. It was observed that even for small corrosion levels, there was a significant influence on the ultimate bearing capacity of the slab. Finally, also the influence of different corrosion locations was investigated.

A lot of ‘hybrid’ structural glass beam concepts were developed in the past years to overcome the brittle failure behaviour of glass. These beams possess a safe failure behaviour through post-fracture strength and ductility. Promising is the concept of reinforced laminated glass beams in which stainless steel reinforcement sections are included in the glass laminate and provide a post-fracture load-carrying mechanism. This type of beams was extensively tested in three- and four-point bending for a variety of environmental conditions (e.g. temperature and humidity), geometrical scale, reinforcement percentage and element robustness. The concept proved to be satisfying. In addition to element safety, today’s buildings also require significant system safety. This paper presents an experimental test programme in which the load-carrying behaviour of statically indeterminate reinforced laminated glass beams is investigated. The beam specimens were tested in five-point bending (three supports and two load points) at 23 °C and 60 °C, at a humidity level of 55%. In addition, two different reinforcement percentages were investigated. The beams illustrated satisfying failure behaviour in all cases, proving the effectiveness of applying reinforced laminated glass beams in statically indeterminate systems. The effect of temperature is primarily observed in the fractured and plastic phases. There, the specimens at 60 °C illustrated lower bending stiffness and slip of reinforcement, which resulted in a lower post-fracture strength. The temperature effect was larger for the beams with high reinforcement percentage. The load-carrying behaviour and load redistribution were highly dependent on the reinforcement percentage. A higher reinforcement percentage resulted in higher bending stiffness in all phases of the model. In addition, a higher initial failure load, yield point and post-fracture strength was achieved. Finally, also a different collapse mechanism was observed for both tested reinforcement percentages.

There is a trend for increasing the scale of structural glass components, which is possible e.g. due to industrial investments in ever larger autoclaves. As a result, load-bearing glass beams will increasingly be incorporated in more complex structural systems. Most important, these beams are required to provide structural safety both on an element level (the beam itself) and system level (a part of, or the whole structure). Past research has resulted in a multitude of possible hybrid glass beams which provide element safety when applied with statically determinate support conditions. In particular, the stainless steel reinforced glass beam has proved to be a promising concept. Moreover, the authors performed a test programme which proved the feasibility of applying the latter beams in statically indeterminate systems. However, due to production, transportation and on-site manoeuvrability limits, safe butt connections will be inevitable for the creation of large-scale beam systems. Currently, no transparent and safe connection detailing is available. As a result, a research project was initiated to develop a connection prototype making use of the beam’s reinforcement sections. This paper presents experimental test results of statically indeterminate five-point bending tests on reinforced laminated glass beams in which the glass section is interrupted at the central support. It was concluded that these hypothetical ‘connected’ beams provide safe load-carrying behaviour in all cases.

A significant number of investigations has been performed to improve the unsafe (brittle) failure behaviour of glass beams. Similar to reinforced concrete, reinforced glass beams have been developed in which stainless steel is embedded in the glass laminate to obtain safe failure behaviour. The concept has been proven to be feasible when assuming statically determinate systems. However, the additional system safety of statically indeterminate systems has not been investigated yet. This paper presents numerical research outcomes on reinforced glass beams with statically determinate as well as statically indeterminate support conditions. In a first step, a model of a two-sided reinforced beam subjected to three-point bending was created for validation purposes. The thickness and height of the constituents making up the model were based on experimental measurements of test specimens. Subsequently, the same numerical model was made using nominal dimensions for the glass and reinforcement. In this way, the effect of dimensional tolerances on the load-carrying behaviour was investigated. Furthermore, a single-sided reinforced glass beam was modelled under the same loading conditions to assess the effect of adding compressive reinforcement. In a second step, statically indeterminate two-sided reinforced beam models were constructed based on the statically determinate model. From these preliminary models, the load-carrying behaviour and effect of reinforcement percentage were evaluated. Finally, also the stress redistribution capacity of both beam models was assessed. It is concluded that dimensional tolerances have a significant effect on the load-carrying behaviour and should therefore be accounted for in the design of reinforced glass beams. The additional compressive reinforcement provides slightly higher bending stiffness, initial failure load and yield load to the glass beams, although it does not contribute in the yield phase. However, a different ultimate collapse mechanism is expected as the compressive reinforcement can take the stress when the glass compressive zone has failed. The statically indeterminate simulations proved the feasibility of applying reinforced glass beams in statically indeterminate systems as a safe failure behaviour was observed with significant stress redistribution capacity. Changing the reinforcement percentage has a significant effect on the load-carrying behaviour of these systems. However, the overall behaviour remains safe.

In order to achieve durable concrete structures, concrete code provisions typically require a minimum cement content, a maximum water cement ratio, and a minimum strength class. These ‘deemed-to-satisfy’ rules are mainly based on long-term practical experience. However, as there is a clear trend to use new binder types, considering alternative cement replacing and environment-friendly powders, this prescriptive approach can be criticized. Classical definitions such as cement content and water cement ratio are open to heavy debate in case of the alternative binder systems. Furthermore, the relation between durability performance of concrete based on new binder systems and the prescriptive parameters (cement content, water cement ratio, strength) is not without criticism either. The equivalent concrete performance concept (ECPC) offers a first step to a more soundly based evaluation of durability requirements for new binder types. Nevertheless, ECPC also has its limitations, as it is based on comparative te...

In architecture, there is a growing trend to include more transparency in structures. To increase the transparency, structural elements such as columns, beams, floors and roofs can be built in glass. However, glass is a brittle material and weak in tension, making it less evident to function as a key structural element. To provide robust and safe elements, researchers have tried to develop hybrid glass elements in which glass is combined with other materials. For the case of structural beams, composite glass beams were developed. These beams have typically T- or I-sections, in which the web is a glass laminate and the flanges are composed of another material. Both entities are then put together by using an adhesive or a bolted connection system. Also other concepts exist which have a layered section or in which the materials are combined to make trusses. In this paper, all developments and experimental investigations of this kind of glass beams are summarised using a classification based on the combined material. The concepts are evaluated considering load–displacement diagrams from bending tests. Most of the concepts described illustrate beneficial failure behaviour when subjected to bending, meaning significant post-breakage strength and ductility. Several concepts even possess a post-breakage strength that is larger than the initial glass failure load, while demonstrating extensive deformation capacity. With respect to practical applications, the latter concepts can be considered as very suitable as they generally provide significant robustness.

Knowledge of the temperature dependent material properties of concrete and steel bars is important for understanding the fire-response of a reinforced concrete (RC) structure. At high temperatures, the total strain of concrete is for a large extent influenced by load dependent strains, including transient strain and creep strain, which is also called transient creep strain in literature. The transient creep strain is much larger than the instantaneous stress-related strain under elevated temperature, and can lead to large influences on the deformation of the RC structure. Computer simulations that study the behaviour of heated concrete structures should consider this transient creep strain parameter, otherwise the deformations will be slightly overestimated. This remark is especially necessary for columns, because of their large compression area. However most of the fire resistance simulations use the implicit material models of concrete, as presented by EN 1992-1-2, which is a viable tool in current design practice, but cannot be used whenever transient creep may have an effect on the behaviour of the structural members. So it is necessary to compare the difference of the fire performance of RC beams with implicit and explicit models and study the factors influencing the difference between the two models. To solve this problem, a simplified numerical model proposed by the authors is adopted in this paper, the difference between fire performance of simple supported members with implicit and explicit models are compared and validated by experimental results from previously executed fire tests. Three influencing factors are discussed by comparing the fire behaviour simulation results of RC rectangular beams. The parameters that may have an impact on the difference of fire behaviour of members with the two models studied in this paper are heating curves, reinforcement and the size effect of the cross-section. The conclusions of the parametric study may lead to a better use of material models and more precise simulations on fire behaviour of RC elements, which are required by performance-based fire-resistance design.

The present paper describes the development of a risk assessment methodology to quantify the life safety risk for people present in a rail tunnel in the context of the creation of a fire safety design. A bow-tie structure represents the risk assessment model, starting from major contributing factors leading to disastrous events. Using past accidents for the construction of the event tree part of the bow-tie, the most important factors are determined to be: human behaviour; fire growth; ventilation conditions; safety system (e.g. Smoke & Heat Exhaust, detection, voice communication, etc.); population density. These factors are incorporated into the event tree using pathway factors. Frequencies are calculated for each branch outcome based on data from research projects, fault tree analysis and engineering judgement. For the determination of the consequences, the method makes use of three integrated models: the smoke spread, the evacuation and the consequence model. The models can take into account all types of geometry and materials, human behaviour and different susceptibilities of people for smoke. Together, they determine the possible number of fatalities, by means of an FID (Fractional Incapacitation Dose) value, in case of a fire in a rail tunnel. The final risk is presented by the expected number of fatalities, the individual risk and the societal risk. The societal risk is demonstrated by means of an FN-curve (Frequency/Number of Casualty-curve).

Reinforced concrete slabs are traditionally designed to carry a specified design load for adequate capacity at ultimate limit state (ULS). In case of an accidental event, however, tensile membrane ...

Concrete columns exhibit a loss of both strength and stiffness during fire. The current contribution focusses on the fire performance of concrete columns subjected to biaxial bending in combination with axial loads, as such information is rarely available in literature. First, the second-order effects are quantified using a numerical tool. In Eurocode 2, the most important parameters which influence second-order effects of columns during fire are the slenderness ratio, fire duration as well as the magnitude of the axial loading. The influences of these parameters are investigated using a parametric study. Additionally, from the viewpoint of fire safety and structural reliability, uncertainties should be incorporated in the second-order analysis in order to achieve reliability-based design guidelines. Hence, the numerical tool is further developed in order to take into account uncertainties. Furthermore, the tool is validated using the Eurocode provisions and existing experimental data, while considering an ISO 834 standard fire. Finally, examples are given for the fire resistance design of concrete columns.

The stresses and deformations in concrete change over time as a result of the creep- and shrinkage deformations of concrete. Different material models are available in literature in order to predict this time-dependent behaviour. These material models mostly have been calibrated on large datasets of creep specimens. In order to verify the accuracy of the contemporary material models with respect to the prediction of the creep behaviour of reinforced concrete beams, a cross-sectional calculation tool which employs the age-adjusted effective modulus has been developed and used to analyse an original set of 4 year-long creep data on reinforced beams from the 1960’s. Six commonly used material models for the prediction of creep and shrinkage are considered in the current investigation: CEB-FIP Model Code 1990–1999, fib Model Code 2010, the model of EN1992-1-1, model B3, the Gardner Lockmann 2000 model, and ACI 209. The data on reinforced beams relates to an experimental investigation in collaboration with six major research institutes in Belgium. From 1967 until 1972 thirty-two reinforced beams with different reinforcement ratios were subjected, up until 4.5 years, to different stress levels in a four point bending configuration with a span of 2.8 m. In this paper a comparison between the measurements and the calculated deflections and strains is reported. Further, the deflections were also predicted using the contemporary creep models in combination with the nonlinear creep correction factor provided in EN1992-1-1, since the maximum concrete stresses in the beams were outside the service stress range of each of the models. Correcting for the nonlinearity of the creep coefficient significantly improves the calculated deflections. The most accurate predictions of the deflections at early age were obtained by the model of fib Model Code 2010. The Gardner Lockmann 2000 model exhibits the highest accuracy with respect to deflections at the end of loading and with respect to the creep rate.

In order to overcome the problems of the current deemed-to-satisfy approach with respect to a durable concrete design, an adaption is required. Limiting values derived from measured material properties can be used as reference values. In case of chloride induced corrosion, the chloride migration coefficient is the most appropriate variable. Based on a full probabilistic design the maximum allowed chloride migration coefficient for a particular concrete type is determined in order to withstand the conditions of the exposure class. The results are given as tabulated values in function of the exposure class, the concrete cover and the initial chloride content. By utilizing the PSF-approach design charts have been derived. Values for the maximum chloride content at the depth of the reinforcing steel in function of material properties and exposure class can be determined for critical environmental conditions and a design service life of 50 years.

In normal design situations, RC slabs are in general designed using small deformation theories while taking into account linear elastic behaviour. However as indicated by previous large structural failures the importance of considering the behaviour of RC slabs at large deformations is as important. Based on multiple experimental studies it is clear that RC slabs can develop alternate load paths and consequently generate a significant strength reserve by membrane action once large deformations occur due to the removal of a load-bearing element. This strength reserve is of major importance as this could result in an important increase of the structural robustness for RC buildings. In this contribution a parametric study with a numerical model is performed to investigate the design possibilities on membrane action in RC slabs. Next the reliability of the developed membrane action and alternate load path is calculated for a reference case which is subjected to the removal of a central support considering the static and pseudo-static behaviour.

Fire has a significant influence on concrete structures and members. A concrete column, compared to other structural members, has most often to cope with vertical forces and bending moments from slabs and beams. Therefore, it is important to investigate the fire resistance of concrete columns. In fact, simplified methods are often adopted to evaluate the capacity of concrete columns. In the fib Model Code 2010, a curvature approximation is introduced. However, this method has not been validated to be used in case of fire. Hence, a parametric study is performed in this paper to investigate the application of this method. As a first step of this paper, a curvature approximation formula used at ambient temperature is introduced. As this formula is based on the curvature and in order to verify the application, a numerical tool that can obtain the bending moment and curvature relationships is presented and validated. Further, an ISO 834 standard fire is adopted. Finally, parameters like dimensions, the reinforcement ratio and the slenderness ratio are investigated. Comparing the effect of dimensions, the reinforcement ratio as well as the slenderness ratio, it is concluded that only the slenderness ratio has a significant influence on the column capacity with the proposed formula. The difference between the deflections obtained with the simplified method and the numerical values increase in function of the slenderness ratio (in case of the same axial load). However, this method is proven to be easy-to-use and safe for the prediction of the fire resistance of concrete columns. Published version

The deformations of concrete elements can increase significantly over time as a result of creep and shrinkage. Different material models, which have been calibrated on large datasets, are available in literature in order to predict this time-dependent behaviour. A cross-sectional calculation tool which employs the age-adjusted effective modulus has been developed to verify the accuracy of six models with respect to creep data available for 24 prestressed beams. These prestressed beams with a span of 8 m were loaded up until 4.5 years in a four point bending configuration. This paper reports on the comparison between the measured and calculated compression strains and deflections. It was observed that the mid-span deflection of the prestressed beams at the end of loading is best prescribed by the model B3 and the Gardner Lockmann 2000 model.

The structural safety of a simply supported one-way concrete slab exposed to the ISO 834 standard fire curve is investigated. The proposed methodology allows for an objective comparison of the structural performance of different concrete slab design alternatives and to derive indirectly a lower bound of the fire ignition frequencies that can be associated to the Eurocode guidelines. A comparison is made with empirical fire ignition frequencies found in literature and a detailed study is presented of the significance of the concrete cover and its uncertainty on the safety level and fire resistance time. Results indicate that the safety level during fire and the fire resistance time are both highly sensitive to the ratio of the variable to the permanent load and that the accepted design solutions given in EN 1992-1-2 are rather conservative.

After a concrete structure has been exposed to fire, a combination of destructive and non-destructive testing, expert judgment and calculations is used to decide whether the structure should be demolished, can be repaired, or may be used without repair or rehabilitation. However, many uncertainties are associated with both the fire duration and the effect of elevated temperatures on the residual mechanical properties of the materials. Consequently, the maximum service load after fire exposure should be assessed based on reliability considerations in order to provide an adequate level of safety. As this type of calculations is too complex and time-consuming for normal use by practitioners, a reliability-based assessment tool has been developed for concrete structures and applied to slabs, which determines the maximum service load after fire. When using the proposed method, a safety level is targeted which is comparable to the safety level associated with the Eurocode format for the design of new structures. It is concluded that the proposed assessment method is both user-friendly and directly applicable for practitioners.

In case of existing concrete structures, the estimation of the characteristic strength values from limited data is a difficult, but important task. There are currently different commonly used estimation methods available, among which the classical coverage method, a Bayesian procedure with vague prior distributions (as mentioned in EN 1990) and the method described in EN 13791. There exists however currently no comprehensive framework in order to quantify the influence of these concrete strength estimation methods on the safety assessment of existing structures. In order to analyse this effect, a previously developed semi-probabilistic partial factor approach for the evaluation of existing structures is considered herein, namely the Adjusted Partial Factor Method. The influence of the different concrete strength estimation methods on the safety level of existing concrete columns is investigated, considering both the application of unchanged partial factors compared to new structures and partial factors adjusted according to the Adjusted Partial Factor Method. The performance of the different estimation methods are evaluated and compared using Monte Carlo simulations and FORM analyses. The relative performance of the estimation methods seem to be rather independent of the partial factor approach applied, however the Adjusted Partial Factor Approach allows to achieve a coherent performance with respect to a target reliability index and alternative reference period. The performance of the classical coverage method and a Bayesian method with vague prior information are comparable and yield a higher safety level when more than 5 test samples are considered. In case only very few concrete samples are used for the assessment (i.e. 3–5), the EN 13791 yields a comparable safety level, mainly due to the reduced variability with respect to the estimation error. Finally, the analysis also showed that for the investigated situation, taking more than about 8 test samples into account does not lead to an increase in assessed safety level.

A Bayesian response surface updating procedure is applied in order to update the parameters of the covariance function of a random field for concrete properties based on a limited number of available measurements. Formulas as well as a numerical algorithm are presented in order to update the parameters of response surfaces using Markov Chain Monte Carlo simulations. The parameters of the covariance function are often based on some kind of expert judgment due the lack of sufficient measurement data. However, a Bayesian updating technique enables to estimate the parameters of the covariance function more rigorously and with less ambiguity. Prior information can be incorporated in the form of vague or informative priors. The proposed estimation procedure is evaluated through numerical simulations and compared to the commonly used least square method.

In this paper, the existing formulas for the shape factors for uniaxial compressive strength of vibrated concrete, in which the influence of the shape, size and damage due to drilling has been included, are adapted for powder-type self-compacting concrete. An extensive test program was executed and Bayesian updating techniques were applied in order to calculate posterior distributions of the parameters involved in the conversion formulas for shape factors. Using this method, differences between the shape factor formulas of vibrated and self-compacting concrete could be analysed despite the large variability in the experimentally obtained test results. The methodology developed in this paper for the Bayesian updating of shape factor formulas can also be applied to other material properties of self-compacting concrete and even other materials, especially in cases where a limited number of samples are available or in cases where a considerable variability in the test data is observed.

The present paper is concerned with the development and influence of catenary action in one-way slabs. The testing of two longitudinally restrained large-scale slab specimens subjected to an accidental event (removal of the central support) and subsequent monotonic vertical loading until collapse is described. The observed increase in the load-carrying capacity as well as the change in the structural behaviour in slabs that are restrained against inward movement is investigated. Whereas the first specimen is designed with continuous flexural reinforcement over the entire length, the second slab test is subjected to the same loading scheme and has the same geometrical dimensions, but differs in the reinforcement arrangement, considering a more conventional reinforcement curtailment. Comparisons are made with respect to the development of displacements, strains and cracks in the critical sections. The failure of the top reinforcement bars over the supports occurs at approximately the same load level. In addition, the failure mode (failure of the bottom reinforcement bars over the supports) is the same for both slabs. However, the final collapse load in case of the slab with curtailed reinforcement is strongly reduced due to the reduction of reinforcement in the bottom layer over the supports. The results of this contribution are of particular importance with respect to the validation of numerical and deterministic models related to the development of tensile membrane action in concrete slabs in the framework of robustness assessment.

Contemporary societal concerns emphasize the importance of cost optimization and sustainable constructions. However, with respect to structural fire safety, the application of prescriptive design rules remains common practice and optimization procedures are generally limited to a few examples of performance based design. Both methods consider an explicit or implicit prescribed safety level which is based on societal and empirical considerations. A more rational approach is to take into account the characteristics of the structure and to determine the economic optimum fire safety design. This economic optimum is obtained by minimizing the total costs, explicitly taking into account e.g. the fire ignition frequency, the probability of successful fire suppression and the damage costs due to a fire-induced failure. Applying this methodology to the design of simply supported concrete slabs indicates that in specific situations additional investments beyond the legally required minima constitute a more cost-effective design. It is concluded that the cost optimization of structural fire safety is a powerful tool to assess the utility of additional safety investments beyond the legal requirements.

The Eurocodes currently do not provide a coherent, straightforward framework for the semi-probabilistic design of temporary structures. Besides the need for suitable target reliability levels, a coherent definition of partial factors is needed in order to adjust them according to the chosen target reliability level and the intended reference period of the temporary structure. Further, attention should be given to the coherency with current Eurocodes in order to avoid conceptual discrepancies between the design of long-term and temporary structures. A framework is presented here in order to derive appropriate partial factors for temporary structures, considering a simplified level II approach. The target reliability level and the reference period are considered as parameters and can be adjusted, so the framework remains valid under alternative economic considerations or requirements for human safety. Further, a set of easy-to-use graphs are provided for implementing the proposed procedure in practical standards. Finally, a framework is presented to adjust the target reliability index, considering human safety and economic criteria in case of temporary structures. © 2013 Copyright Taylor and Francis Group, LLC.

The edge strength of glass is affected by the load history. To quantify this effect, 12 series of glass specimens were subjected to either linearly increased (reference value), constant or cyclic loading. For constant loading the experimental values could be accurately predicted by linear elastic fracture mechanics (LEFM). However, for cyclic loading the LEFM prediction was 48% more conservative than the test results. Furthermore, a comparison of the experimental results with the prediction method provided in the standards shows that for cyclic loading the number of cycles should be taken into account in the rules of the standards.

When a support of a statically indeterminate concrete slab is lost due to an accidental event, tensile membrane or catenary forces can be activated at large deflections. This effect can considerably increase the load-carrying capacity compared to predictions obtained from small deformation theories neglecting membrane and catenary forces. Thus, these actions can prevent a progressive collapse and hence increase the robustness of concrete structures. A novel experimental large-scale test set-up is described which allows the testing of continuous, longitudinally restrained, reinforced concrete slab strips exposed to a simulated accidental failure of the central support and subsequent vertical loading until collapse. The details of this test set-up as well as the measurements related to the load–displacement behaviour are explained. Within this investigation the development of catenary action associated with the formation of large displacements was found to increase the ultimate bearing capacity significantly.

Quality inspection plays an important role in the production process of concrete, as it inherently stimulates producers for obtaining a higher performance with respect to the investigated properties. In case of the conformity assessment of concrete compressive strength, the concrete strength distribution is filtered due to the rejection or acceptance of certain batches and this filter effect can be quantified using Bayesian updating techniques. As a consequence of the filter effect, conformity control has a positive influence on the structural reliability of concrete structures. This filter effect can be quantified by using an approximation method as developed herein or also by using classical FORM/SORM techniques. In order to illustrate the influence of conformity control on structural reliability, concrete elements (columns and beams) which are designed according to the Eurocodes, are analysed considering basic limit state equations, i.e. for compression and bending. Moreover, the influence of the reinforcement ratio and the load ratio on the filter effect is investigated. Numerical analyses reveal that the filter effect may positively influence especially reliability of lightly reinforced concrete members exposed to compression. It appears that it has a minor effect where reinforcement properties govern failure.

If deterministic creep prediction models are compared with actual measurement data, often significant differences can be observed. These inconsistencies are associated to various uncertainties. First, the physical mechanism causing creep of concrete is not yet fully understood. Hence, uncertainty of prediction models can be attributed to an insufficient description of the physical mechanism causing creep. It is very likely that certain influences of creep of concrete are not fully considered in current prediction models, resulting in systematic model errors. Because this error is due to a lack of understanding of the underlying physical mechanisms it can only be quantified by comparing prediction results with experimental data. Secondly, the stochastic character of the input parameters form an additional source of uncertainty which can be quantified by the variance of the model response. The coefficient of variation in function of time-duration is a useful measure to quantify the level of uncertainty due to the stochastic nature of the input parameters. In literature statistical analysis by means of numerical simulations are often used for this matter. However, even for specialized sampling techniques, a large amount of samples is necessary to cover the relevant ranges of various input parameters. The aim of the present study is to provide an approximate uncertainty quantification based on a Taylor series approach. Such method has the advantage that is does not require sampling nor the knowledge of the probability density function of the input parameters. This approximate method to quantify the uncertainty due to the input parameters is evaluated and compared with the statistical analysis for several creep prediction models available in literature and design codes.