Reliability of reinforced concrete structures under fatigue

This paper focuses on time-variant reliability assessment of deteriorating reinforced concrete structures under fatigue conditions. A strategy combining two time scales, namely the micro-scale of instantaneous structural dynamics (or statics) and the macro-scale of structural lifetime, is proposed. Non-linear response of reinforced concrete structures is simulated by means of the finite element method with adequate material model. A phenomenological fatigue damage model of reinforced concrete is developed and calibrated against experimental results available in the literature. Reliability estimates are obtained within the response surface method using the importance/adaptive sampling techniques and the time-integrated approach. The proposed assessment strategy is illustrated by an example of a concrete arch under fatigue loading. The obtained results show a general inapplicability of local and linear fatigue models to system level of structures.     

Constitutive modeling of reinforced concrete and prestressed concrete structures strengthened by fiber-reinforced plastics

A batch of constitutive models for steel reinforcing bar, prestressing tendon, concrete and fiber-reinforced plastic are proposed for the nonlinear finite element analysis of reinforced concrete structures, prestressed concrete structures, reinforced concrete structures strengthened by fiber-reinforced plastics and prestressed concrete structures strengthened by fiber-reinforced plastics. These material models have been tested against series of experimental data and good agreements have been obtained, which justifies the validity and the usefulness of the proposed nonlinear constitutive models.     

Shear behaviour of steel fibre reinforced self-consolidating concrete beams based on the modified compression field theory

A series of steel fibre reinforced self-consolidating concrete (SFRSCC) beams have been tested to investigate the influence of steel fibres and the combined effect of fibres and stirrups on the deflection and cracking, ultimate loads and failure pattern. The experiment indicates that the shear strength increases clearly with the increasing of fibre content. The combination of steel fibres and stirrups demonstrates a positive composite effect on the ultimate load, ductility and failure pattern of concrete beam. This study also examines the feasibility of applying the modified compression field theory (MCFT) for the suitable assessment of shear resistance in fibre and steel rebar reinforced self-consolidating concrete beams. For fibre reinforced concrete member, a theoretical method is proposed based on the MCFT. The proposed ultimate shear capacity model was verified by the comparison with different test results.     

Shear strength of concrete beams reinforced with steel bars milled from scrap metals

The paper reports a study on the shear resistance of concrete beams reinforced with mild steel bars that are milled from scrap metal such as old vehicle parts and obsolete machinery. It has been previously reported that because the chemical compositions of carbon, sulphur and phosphorus in these reinforcing steel bars exceed the maximum allowable limits, the characteristic tensile strengths are too high and ductility too low for standard mild steel. Concrete beams reinforced with such bars to resist flexural tensile and shear stresses were tested under a two-point loading system to provide a central constant moment region and outer shear spans. Tested beams exhibited little deflection and very low ductility prior to collapse. Experimental failure loads for the beams averaged 123% of the theoretical failure load, which was generally governed by either shear or yielding of the tension steel. Shear failure was mostly initiated by diagonal tension cracks, followed by either crushing of the concrete, or splitting of the concrete over the longitudinal tensile bars near the supports. Failure of the beams was brittle and the post-cracking strain energy absorption averaged 357.9 Nm. At failure the maximum crack width in the beams ranged from 1.12 to 5.0 mm, the largest sizes forming in the diagonal shear cracks.     

Thermo-mechanical loading of GFRP reinforced thin concrete panels

The experimental investigation is focused on the thermo-mechanical behaviour of thin concrete panels reinforced with GFRP rebars. The considered thin panels (thickness of 4 cm) were exposed to increasing temperature and bending loading. These concrete elements are typical for low bearing function concrete layers in façade claddings. The influence of two aspects was studied: the concrete cover and the external surface of rebars. The heating condition was such that the temperature of the internal GFRP rebars reached about the transition temperature of the resins. This allowed to verify the variation of the deformability and the load carrying capacity of the panels with post-heating bending tests. As main outcome, the imposed temperature did not generate evident degradation of the GFRP reinforcement and of its adhesion to the concrete, while a reduction of the initial global stiffness was measured.     

Development of self-compacting high and ultra high performance concretes with and without steel fibres

This paper describes the steps taken to develop self-compacting high and ultra high-performance concretes with and without steel fibres. For the self-compacting concrete mixes without steel fibres the fulfilment of flow and cohesiveness criteria are sufficient for the mix design. However, for the design of self-compacting concrete mixes with steel fibres it is found, as expected, that they must additionally meet the passing ability criterion. The plastic viscosity of the mixes with and without steel fibres has been estimated from the known plastic viscosity of the cement paste using simple micromechanical relations.     

Prediction of ductility factor of corroded reinforced concrete beams exposed to long term aging in chloride environment

An experimental study using a three-point bending test on RC beams with dimensions of 150 × 280 × 3000 mm, naturally corroded over many years was conducted to evaluate the influence of steel corrosion on structural performance and, in particular, to better understand the change in ultimate deflection in bending and then in ductility. Some previous works by different authors are also discussed. The results show that the conventional ductility factor hardly applies to the assessment of ductile behaviour of corroded beams. A new ductility factor, based on the ratio between ultimate deflection of corroded and non-corroded beams, is proposed. In addition, the relation between ductility factor of corroded beams and cross-section loss in the corroded reinforcing steels was studied on the RC beams tested. The service life of corroded structures appears to be limited by the reduction of ductility in bending behaviour, which is more pronounced on the reduction of load-bearing capacity. This was linked to the change in mechanical properties of corroded steel bars in comparison with non-corroded steel bars.     

A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures

A three-dimensional meshfree method for modeling arbitrary crack initiation and crack growth in reinforced concrete structure is presented. This meshfree method is based on a partition of unity concept and formulated for geometrically non-linear problems. The crack kinematics are obtained by enriching the solution space in order to capture the correct crack kinematics. A cohesive zone model is used after crack initiation. The reinforcement modeled by truss or beam elements is connected by a bond model to the concrete. We applied the method to model the fracture of several reinforced concrete structures and compared the results to experimental data.     

Short and long-term cracking behaviour of GFRP reinforced concrete beams

A total of ten simply supported beams reinforced with different amounts of GFRP and steel bars were subjected to two consecutive test phases in order to evaluate their short and long-term cracking behaviour. The beams were initially tested up to service load and subjected to two additional load cycles. Subsequently, the specimens were subjected to two different levels of sustained load for 250 days. The effect of cyclic load during short-term tests resulted in an increase in crack width up to 25% more than the initial value. The sustained load led to an increase in crack width up to 2.9 times larger than that measured under the corresponding short-term load. A similar cracking behaviour was observed when reinforcing solutions with similar stiffness (GFRP or steel bars) were used.Existing models to estimate crack spacing and crack width for FRP and steel reinforced concrete elements, including ACI 440.1R-06, Eurocode 2 and Model Code 2010 are discussed and their performance is assessed against the experimental results. Model Code 2010 was found to yield more accurate predictions of the cracking behaviour of the test specimens under both short-term and long-term loading.     

Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling

Design of reinforced concrete structures is governed by the nonlinear behavior of concrete and by its different strengths in tension and compression. The purpose of this article is to present a computational procedure for optimal conceptual design of reinforced concrete structures on the basis of topology optimization with elastoplastic material modeling. Concrete and steel are both considered as elastoplastic materials, including the appropriate yield criteria and post‐yielding response. The same approach can be applied also for topology optimization of other material compositions where nonlinear response must be considered. Optimized distribution of materials is achieved by introducing interpolation rules for both elastic and plastic material properties. Several numerical examples illustrate the capability and potential of the proposed procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

Behaviour of fiber reinforced concrete columns in fire

This paper presents the results of a research program on the behaviour of fiber reinforced concrete columns in fire. Several fire resistance tests on fiber concrete columns with restrained thermal elongation were carried out. The percentage of steel reinforcing bars on the testing columns varied in function of the percentage of steel fibers being always the total amount of steel (steel fibers + steel reinforcement) similar. The aim of this research was to study the possibility of replacing the longitudinal reinforcement bars on the concrete columns by steel fibers. Furthermore, polypropylene fibers were also used on the concrete in order to enhance the fire behaviour of the columns and avoid the concrete spalling. Polypropylene fibers under fire action will create a network of micro-channels for the escape of the water vapour.     

Terahertz spectroscopy to study the orientation of glass fibres in reinforced plastics

We employ terahertz time-domain spectroscopy (THz TDS), a novel, non-destructive testing method, to study the fibre orientation and fibre content in reinforced plastics. The birefringent properties of plastics filled with differing amounts of short glass fibres are measured at frequencies from 100 GHz up to 1 THz. To predict the permittivity of the experimentally examined composite materials, we use an effective medium theory first introduced by Polder and van Santen. On the basis of the measured data and this model, we deduce the additive content ξ, the preferential orientation of the fibres φ and the fraction of orientated fibres a. Our findings agree well with corresponding mold flow simulations performed with commercially available software.     

Development of solid state embeddable reference electrode for corrosion monitoring of steel in reinforced concrete structures

Corrosion of steel reinforcement concrete structures is monitored through the surface mounting techniques using liquid based reference electrodes. Due to the limited usage of liquid based reference electrodes solid state reference electrode are introduced recently. In the present study, we fabricated and characterized Mn₃O₄ based pellet electrode for corrosion assessment of steel rebar in high alkaline medium through electrochemical methods and the results are compared with conventional saturated calomel reference electrode (SCE). The results indicate that the fabricated pellet electrode exhibits better characteristics suitable for high alkaline concrete environment and differentiate the passive and active status of steel rebar.     

Optimum detailed design of reinforced concrete frames using genetic algorithms

This article presents the application of the genetic algorithm to the optimum detailed design of reinforced concrete frames based on Indian Standard specifications. The objective function is the total cost of the frame which includes the cost of concrete, formwork and reinforcing steel for individual members of the frame. In order for the optimum design to be directly constructible without any further modifications, aspects such as available standard reinforcement bar diameters, spacing requirements of reinforcing bars, modular sizes of members, architectural requirements on member sizes and other practical requirements in addition to relevant codal provisions are incorporated into the optimum design model. The produced optimum design satisfies the strength, serviceability, ductility, durability and other constraints related to good design and detailing practice. The detailing of reinforcements in the beam members is carried out as a sub-level optimization problem. This strategy helps to reduce the size of the optimization problem and saves computational time. The proposed method is demonstrated through several example problems and the optimum results obtained are compared with those in the available literature. It is concluded that the proposed optimum design model can be adopted in design offices as it yields rational, reliable, economical, time-saving and practical designs.     

Reliability assessment and design load factors for reinforced concrete containment structures

The current ASME code for reinforced concrete containment structures is not based on probability concepts. This paper develops reliability assessment and probability-based design load factors for reinforced concrete containment structures. The purpose of constructing reinforced concrete containment structures is to protect against radioactive release, and so the use of a serviceability limit state related to cracking that can cause the emission of radioactive materials is suggested as a critical limit state for reinforced concrete containment structures. Load factors for the design of reinforced concrete containment structures are proposed. The proposed load factors are also examined in terms of a set of code performance objectives and consistency in limit state probability.     

Drift-controlled design of reinforced concrete frame structures under distant blast conditions—Part II: Implementation and evaluation

The model for the calculation of an equivalent static force (ESF) and the design procedure with ESF for single-degree-of-freedom (SDOF) systems presented in the first part of the two-part paper are extended into the design for a reinforced concrete (RC) frame structure under distant blast conditions. An empirical formula for the ESF factor involved in the ESF model is presented based on sample points obtained by comparing the nonlinear dynamic responses of frame structures under the blast loading with the corresponding nonlinear pushover analysis of the structure due to an ESF. The use of the method is demonstrated with two six-storey RC frame structures. Numerical verification of the method indicates that the maximum inter-storey drift ratios (MIDR) of the two designed frame structures in comparison to their respective targets are conservative to some extent. The reasons that may lead to the conservative designs are discussed.     

Comparison between solid and hollow reinforced concrete beams

Comparison between test results of seven hollow and seven solid reinforced concrete beams is presented. All of the fourteen beams were designed as hollow sections to resist combined load of bending, torsion and shear. Every pair (one hollow and one solid) was designed for the same load combinations and received similar reinforcement. The beams were 300 × 300 mm cross-section and 3,800 mm length. The internal hollow core for the hollow beams was 200 × 200 mm creating a peripheral wall thickness of 50 mm. The main variables studied were the ratio of bending to torsion which was varied between 0.19 and 2.62 and the ratio in the web of shear stress due to torsion to shear stress due to shear force which was varied between 0.59 and 6.84. It was found that the concrete core participates in the beams’ behaviour and strength and cannot be ignored when combined load of bending, shear and torsion are present. Its participation depends partly on the ratio of the torsion to bending moment and the ratio of shear stress due to torsion to the shear stress due to shear force. All solid beams cracked and failed at higher loads than their counterpart hollow beams. The smaller the ratio of torsion to bending the larger the differences in failure loads between the hollow and solid beams. The longitudinal steel yielded while the transverse steel experienced lower strain values.     

Structural response of hyperstatic concrete beams reinforced with GFRP bars: Effect of increasing concrete confinement

The design of concrete structures reinforced with glass fibre reinforced polymer (GFRP) bars is influenced by their reduced stiffness and brittleness. In hyperstatic structures, the methodology used in force analysis depends on the ductility of the structural systems, which in this case, being essentially provided by the concrete, can be potentially increased by confining concrete in critical zones. This paper presents experimental and numerical investigations about the flexural behaviour of continuous beams reinforced with GFRP bars, namely of their service and failure responses, and the effect of increasing concrete confinement in critical cross-sections. A calculation procedure to quantify the confinement effect in beams due to the reduction of the spacing between shear stirrups is first presented. The experimental investigations comprised a comparative study in which two-span concrete beams reinforced with either GFRP or steel bars were tested in bending. In the former, the effect of reducing the shear stirrups spacing was analyzed together with the under- and over-reinforcement at the central support and midspan cross-sections, respectively. The development of a crack hinge in the continuity support zone highlighted the better performance of beams under-reinforced on the top layer with GFRP bars compared to “equivalent” beams reinforced with steel, namely at the resistance level. In addition, the confinement at critical zones increased significantly the strength and ductility. The numerical investigations included the development of non-linear finite element models for all beams tested - numerical results are in good agreement with test data and seem to confirm the confinement effect observed in the experiments.