Residual fatigue strength assessment of concrete considering tension softening behavior

In this study, the residual strength of plain concrete beams under fatigue loading is assessed. The quasi-brittle nature of the material is considered by including the effect of tension-softening taking place in the fracture process zone. A two step approach is followed. In the first step, the effective critical crack length for unstable fracture to occur is determined by using two different methods, namely a modified LEFM based fatigue crack propagation law and the crack resistance method. In the second step, the moment carrying capacity as a function of increasing effective crack length is obtained in order to assess the residual strength of the member. A parametric study is performed by considering three different softening laws: linear, bilinear and power laws. It is seen that the bilinear softening law matches close to the experimental predictions of other investigators.     

Shear strength of reinforced concrete beams with stirrups

This study presents alternative shear strength prediction equations for reinforced concrete (RC) beams with stirrups. The shear strength is composed of the contribution of the nominal shear strength provided by stirrups and the nominal shear strength provided by concrete. For the concrete contribution, cracking shear strength values estimated by Arslan’s equations are almost same those obtained with ACI 318 simplified equation in terms of coefficient of variation (COV). However, mean values estimated by ACI 318 tend to be more conservative comparing to the mean values obtained with Arslan’s equations. Thus, for the consideration of concrete contribution to shear strength, Arslan’s equations are used. To obtain the shear strength of RC beams, shear strength provided by stirrups is added to the concrete shear strength estimated by Arslan’s equations. Results of existing 339 beam shear tests are used to investigate how accurate proposed equation estimates the shear strength of RC beams. Furthermore, ACI 318 and TS500 provisions are also compared to the aforementioned test results. It is found that proposed equations for beams with shear span to depth ratios (a/d) between 1.5 and 2.5 are also conservative with a lower COV than ACI 318 and TS500. However, when a/d ratios exceed 2.5 (both normal and high strength concrete beams), ACI 318, TS500 and proposed equations give similar COV value.     

Residual strength of blast damaged reinforced concrete columns

Columns are the key load-bearing elements in frame structures and exterior columns are probably the most vulnerable structural components to terrorist attacks. Column failure is normally the primary cause of progressive failure in frame structures. A high-fidelity physics-based computer program, LS-DYNA was utilized in this study to provide numerical simulations of the dynamic responses and residual axial strength of reinforced concrete columns subjected to short standoff blast conditions. The finite element (FE) model is discussed in detail and verified through correlated experimental studies. An extensive parametric study was carried out on a series of 12 columns to investigate the effects of transverse reinforcement ratio, axial load ratio, longitudinal reinforcement ratio, and column aspect ratio. These various parameters were incorporated into a proposed formula, capable of estimating the residual axial capacity ratio based on the mid-height displacement to height ratios.     

Mechanical damage of ordinary or prestressed reinforced concrete beams under cyclic bending

The behaviour of metallic materials under repeated loading has been examined since the 19th century, but extended studies are more and more needed especially for reinforced concrete structures such as bridges, where high-cycle fatigue phenomena can be significant. In the present paper, a theoretical model based on fracture mechanics concepts is proposed in order to analyse the mechanical damage of ordinary or prestressed reinforced concrete beams with a rectangular or a T cross-section subjected to cyclic bending. Local phenomena, such as fracturing or crushing of concrete and yielding or slippage of the longitudinal steel reinforcement, are examined. Further, fatigue life is predicted by applying a crack growth law, and the energy dissipated during the plastic shake-down phenomenon is evaluated.     

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.     

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.     

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.     

Size effect on failure of overreinforced concrete beams

The results of full-scale failure of singly reinforced four-point-bend beams of different sizes containing deformed longitudinal reinforcing bars are reported. The tests consisted of four groups with one, two and three different size combinations. The specimens were made of concrete with a maximum aggregate size of 10 mm. The beams were geometrically similar in one, two and three-dimensions, and even the bar diameter and cover thicknesses were scaled in proportion. The reinforcement ratio was 3%. The results revealed the existence of a significant size effect, which can approximately be described by the size effect law previously proposed by Bazant. The size effect is found to be stronger in two-dimensional similarities than for one and three-dimensional similarities.     

Strengthening of reinforced concrete beams in flexure by partial jacketing

This work investigates the structural behaviour of reinforced concrete beams strengthened in bending by the addition of concrete and steel on their tension sides using expansion bolts as shear connectors, technique here denominated partial jacketing. The experimental program comprised tests on eight full-scale reinforced concrete beams, simply supported, with rectangular cross section (150 mm × 400 mm) and 4,500 mm length. Five of these beams were strengthened in bending by partial jacketing, while the other three did not receive any strengthening and served as reference beams. The flexural reinforcement ratio in the beams varied between 0.49% and 2.33% and the beams target concrete strength was 35 MPa. On the basis of the obtained test results, the studied strengthening technique proven to be efficient in terms of increasing the resistance and stiffness of the beams. The used expansion bolts as shear connectors proven to be practical and added ease to the application of this technique.     

Nonlinear finite element analysis of reinforced concrete beams strengthened by fiber-reinforced plastics

Numerical analyses are performed using the ABAQUS finite element program to predict the ultimate loading capacity of rectangular reinforced concrete beams strengthened by fiber-reinforced plastics applied at the bottom or on both sides of these beams. Nonlinear material behavior, as it relates to steel reinforcing bars, plain concrete, and fiber-reinforced plastics is simulated using appropriate constitutive models. The influences of fiber orientation, beam length and reinforcement ratios on the ultimate strength of the beams are investigated. It has been shown that the use of fiber-reinforced plastics can significantly increase the stiffnesses as well as the ultimate strengths of reinforced concrete beams. In addition, with the same fiber-reinforced plastics layer numbers, the ultimate strengths of beams strengthened by fiber-reinforced plastics at the bottom of the beams are much higher than those strengthened by fiber-reinforced plastics on both sides of the beams.     

Experimental study and code predictions of fibre reinforced polymer reinforced concrete (FRP RC) tensile members

Due to their different mechanical properties, cracking and deformability behaviour of FRP reinforced concrete (FRP RC) members is quite different from traditional steel reinforced concrete (SRC) having great incidence on their serviceability design. This paper presents and discusses the results of an experimental programme concerning concrete tension members reinforced with glass fibre reinforced polymer (GFRP) bars. The main aim of the study is to evaluate the response of GFRP reinforced concrete (GFRP RC) tension members in terms of cracking and deformations. The results show the dependence of load-deformation response and crack spacing on the reinforcement ratio. The experimental results are compared to prediction models from codes and guidelines (ACI and Eurocode 2) and the suitability of the different approaches for predicting the behaviour of tensile members is analysed and discussed.     

Experimental investigation into flexural retrofitting of reinforced concrete bridge beams using FRP composites

End cover separation and shear crack debond are the two most critical debonding modes in beams retrofitted with fibre reinforced polymer composites due the brittle nature of the failures. However, these failures are still not fully understood. A testing program including 18 rectangular reinforced concrete beams is carried out to investigate the failure mechanisms and the influence of several parameters on these debond modes. Testing shows that end cover separation starts from FRP ends and fails in the form of shear failure at steel reinforcement level at the root of the concrete teeth between shear cracks. Shear crack debond failure is due to the opening of one of those inclined cracks. Several debond prediction models are then verified with the experiment proving to work relatively well.     

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.     

Two-layer pre-stressed beams consisting of normal and steel fibered high strength concrete

The paper is focused on analysis of two-layer bending pre-stressed beams consisting of steel fibered (SF) high strength concrete (HSC) in compressed zone and normal strength concrete (NSC) in tensile zone. Investigation of such beams is important for RC structural design, because calculation of fibers volume ratio is significant, like that of reinforcing steel bars for usual RC elements. In other words, such elements are made of high performance concrete (HPC). There is a growing tendency that more effective HPC structures replace NSC ones, first of all in pre-stressed elements. Definition of the HSC class lower limit, to be used in the compressed zone of a two-layer pre-stressed beam, is given. It was demonstrated that SF have little effect on the beam elastic deflections. However, the ultimate deflections of the section increase because additional potential for plastic energy dissipation (PED) in the bending element. NSC, used in the section tensile zone, contributes additionally about 20% to the section’s PED potential compared to one-layer HSC beams. In order to guarantee sufficient section’s ductility of the pre-stressed beams, required to withstand dynamic loadings, a minimum SF ratio is proposed to be considered. The fibers take the tensile stresses, yielding cracks in the concrete matrix. A design method for calculation of the SF volume ratio, as a function of required ductility, is proposed. A numerical example, illustrating the efficiency of this method is presented.     

Normal perforation of reinforced concrete target by rigid projectile

An analytical model on the normal perforation of reinforced concrete slabs is constructed in the present paper. The effect of reinforcing bars is further hybridized in a general three-stage model consisting of initial crater, tunnelling and shear plugging. Besides three dimensionless numbers, i.e., the impact function I, the geometry function of projectile N and the dimensionless thickness of concrete target χ, which are employed to predict the ballistic performance of perforation of concrete slabs, the reinforcement ratio ρ_s of concrete (or area density) and the tensile strength f_s of reinforcing bars are considered as the other main factors influencing the perforation process. Simpler solutions of ballistic performances of normal perforation of reinforced concrete slabs are formulated in the present paper. Theoretical predictions agree well with individual published experimental data and have a higher degree of accuracy than the model suggested by Dancygier [Effect of reinforcement ratio on the resistance of reinforced concrete to hard projectile impact. Nucl Eng Des 1997;172:233–45].     

Residual strength of reinforced concrete columns exposed to fire

Abstract

Several methods were employed to evaluate the residual strength of reinforced concrete columns exposed to different durations of fire. These methods included the analytical method, ultrasonic tests, hammer tests and load tests. Fifty columns were involved in the tests. Calculated temperatures and residual strengths of the test columns were compared with those measured. Comparisons were also made between results from load tests and those from nondestructive tests. The results showed that using analytical procedures is acceptable while the nondestructive test methods are accurate only for shorter durations of fire.     

Fatigue life prediction of fiber reinforced concrete under flexural load

This paper presents a semi-analytical method to predict fatigue behavior in flexure of fiber reinforced concrete (FRC) based on the equilibrium of force in the critical cracked section. The model relies on the cyclic bridging law, the so-called stress–crack width relationship under cyclic tensile load as the fundamental constitutive relationship in tension. The numerical results in terms of fatigue crack length and crack mouth opening displacement as a function of load cycles are obtained for given maximum and minimum flexure load levels. Good correlation between experiments and the model predictions is found. Furthermore, the minimum load effect on the fatigue life of beams under bending load, which has been studied experimentally in the past, is simulated and a mechanism-based explanation is provided in theory. This basic analysis leads to the conclusion that the fatigue performance in flexure of FRC materials is strongly influenced by the cyclic stress–crack width relationship within the fracture zone. The optimum fatigue behavior of FRC structures in bending can be achieved by optimising the bond properties of aggregate–matrix and fiber–matrix interfaces.     

Residual strength of metal particulate reinforced ceramics with parallel cracks

This work investigates the residual strength of metal particulate reinforced ceramic matrix composites with periodically spaced, parallel cracks. A Fourier transform/integral equation method is used to obtain the stress intensity factor at the tips of the cracks bridged by the plastically stretched metal particulates. The crack bridging of metal particulates is described by a linear softening bridging law that relates the bridging stress and crack opening. The residual strength of the cracked composites is calculated using a stress intensity factor criterion with consideration of crack bridging. Numerical results are presented for three composite systems, i.e., WC/Co, Al₂O₃/Ni, and glass/Al composites to illustrate the effects of interactions between multiple cracks/bridging zones on the residual strength behavior of the reinforced ceramics with parallel cracks. It is found that for given volume fraction of metal particulate and debonding length of the particulate–matrix interface the residual strength increases with decreasing crack spacing. For a given crack spacing, the residual strength initially decreases dramatically with an increase in initial crack length and levels off for long initial cracks.     

Flexural analysis of reinforced concrete beams strengthened with a cement based high strength composite material

The structural behaviour of reinforced concrete beams strengthened with a system made by fibre nets embedded into an inorganic stabilized cementitious matrix named Fibre Reinforced Cementitious Mortars (FRCM), was investigated in this paper. The main issues focussed in the paper are: (i) the strengthening effect of the FRCM system on the flexural behaviour of reinforced concrete beams in terms of both ultimate capacity, deflections and ductility and (ii) the influence of the fibre reinforcement ratio on the occurrence of premature failure modes.The analysis refers to a FRCM system made by ultra-high strength fibre meshes such as the Polypara-phenylene-benzo-bisthiazole (PBO) fibres; PBO fibres have, in fact, great impact tolerance, energy absorption capacity superior than the other kind of fibres and chemical compatibility with the cementitious mortar.A total of 12 reinforced concrete beams strengthened in flexure with the PBO-FRCM system have been tested. The influence of some mechanical and geometrical parameters on the structural behaviour of strengthened beams, is analysed both at serviceability and the ultimate conditions. Results of a comparison between experimental results and theoretical predictions, obtained by models usually adopted for the analysis of FRP strengthened concrete structures, are, also, presented and discussed.     

Behaviour of concrete beams under torsion: NSC plain and hollow beams

A simple computation procedure is developed to predict the general behaviour of reinforced concrete beams under torsion. Both plain and hollow normal strength concrete beams are considered. Different theoretical models are used to reflect the actual behaviour of the beams in the various phases of loading. To pass from a phase to the following one, transition criteria need to be taken into consideration. Such criteria are explained. The theoretical predictions are compared with result from reported tests. Conclusions are presented. The main conclusion is that the calculation procedure described in this paper gives good predictions when compared with the actual behaviour of the plain and hollow beams.