Tension Stiffening Effect Research Articles

Experimental and Numerical Investigation on Tensile Concrete Elements Bonded with External CFRP Sheets

An experimental study is carried out on tensile concrete elements with external carbon fiber reinforced polymer sheets as reinforcement without any internal bars. The load-strain, tension stiffening relationships and mean distances between cracks are presented for the twin specimens. Additionally, a numerical analysis based on the stress transfer approach is implemented to investigate available bond-slip models and compare the deformation behavior with the experimental findings. Certain models were found to be better at predicting the tension-stiffening effect, whereas others were found to be more accurate at estimating number of cracks and crack spacing values, as the available bond models differ in their formulations and variables.

Experimental study on confining-strengthening, confining-stiffening, and fractal cracking of circular concrete filled steel tubes under axial tension

This paper studies the mechanical behavior of the circular concrete filled steel tubes (CCFTs) under axial tension. A group of three CCFTs with different steel ratios and in-filled concrete diameters are tested and compared with hollow steel tubes (HTs). Based on the experimental results in the present and previous studies, three key issues of CCFTs under tension, i.e. the confining-strengthening effect, the confining-stiffening effect, and the tension-stiffening effect, are studied at both the stress-resultant level (i.e., force-displacement relationship) and stress levels (i.e., stress-strain relationship). Due to the tendency of the shrinking and slipping of the steel tube in relation to the infilled concrete, the confining contact stress and bonding shear stress, in the vertical and tangential direction respectively, are distributed in the interface between the steel and concrete, which results in the confining and bonding effect of the CCFTs. At the stress-resultant level, the test results demonstrate that the strength and stiffness of CCFTs are average 10% and 29% larger than those of HTs, respectively. The strength increase is contributed by the confining-strengthening effect, and the stiffness enhancement is a combined result of the confining-stiffening and tension-stiffening effects. At the stress-strain level, the measured strains show that the steel tube of the CCFT is in the state of the bi-axial tensile stress state because of the difference of the Poisson's ratio between steel tube and infilled concrete, which contributes to the confining-strengthening and confining-stiffening effects of the CCFTs. In addition, a fractal cracking phenomenon of the core concrete of tensile CCFTs is observed and discussed.

Theoretical and experimental in-service long-term deflection response of symmetrically and non-symmetrically reinforced concrete piles

Reinforced concrete piles employed in earth retaining systems are typically designed with symmetric reinforcement. The non-symmetric RC wall piles have recently been introduced by the authors, obtaining savings of up to 50% in weight in longitudinal reinforcing steel compared with the traditional solutions, leading to significant financial savings while also reducing associated environmental impacts.The structural behavior of this new RC member under long-term loading is studied, comparing it with its symmetrical counterpart. An experimental campaign has been carried out. Full scale specimens with circular cross sections symmetrically and asymmetrically reinforced were tested. Results have shown that asymmetrically RC pile developed a slightly higher deflection than its symmetrical counterpart. A new expression for the effective area of concrete in tension applicable to non-symmetrical piles is introduced. Moreover, a new stress–strain law for cracked concrete that accounts the tension stiffening effect for long-term loading is proposed. Finally, for non-symmetrical RC wall piles, the evolution of the parameter that takes into account the duration of loading in deformations is presented. Although more evidence is needed, it is shown that tension stiffening effect contribution could be overestimated by Eurocode 2 in the case of non-symmetrically or underestimated in case of symmetrically RC piles.

Rapid prediction of inelastic bending moments in RC beamsconsidering cracking

A methodology using neural networks has been proposed for rapid prediction of inelastic bending moments in reinforced concrete continuous beams subjected to service load. The closed form expressions obtained from the trained neural networks take into account cracking in concrete at in-span and at near the internal supports and tension stiffening effect. The expressions predict the inelastic moments (considering the concrete cracking) from the elastic moments (neglecting the concrete cracking) at supports. Three separate neural networks are trained since these have been postulated to represent all the beams having any number of spans. The training, validating, and testing data sets for the neural networks are generated using an analytical-numerical procedure of analysis. The proposed expressions are verified for example beams of different number of spans and cross-section properties and the errors are found to be small. The proposed expressions, at minimal input data and computation effort, yield results that are close to FEM results. The expressions can be used in preliminary every day design as they enable a rapid prediction of inelastic moments and require a computational effort that is a fraction of that required for the available methods in literature.

A formulation to reduce mesh dependency in FE analyses of RC structures under imposed deformations

It is well known that in analyses of plain concrete members using smeared crack models, the constitutive behaviour of cracked concrete has to be defined as a function of the crack bandwidth so that the results are not significantly affected by the adopted mesh discretization. Crack localization can also occur in reinforced concrete (RC) elements subjected to imposed (or restrained) deformations. In that case, a different approach has to be followed to reduce the influence of the adopted mesh discretization because the mechanical response in the vicinity of each crack is governed by tension stiffening effects. This paper presents an original formulation to define a tension stiffening diagram that reduces the dependency of the results with respect to the adopted mesh refinement in structures in which crack propagation is governed by mode I (crack opening). This formulation can be applied in FE analyses based on a large-scale, smeared crack approach. Simple closed-form equations are obtained to define this type of diagram. It is demonstrated that objective results are obtained in terms of both the stiffness decrease due to cracking and the crack opening values. Concrete creep and shrinkage effects are taken into account.

Simultaneous optimal design of topology and size for a flexure-hinge-based guiding mechanism to minimize mass under stiffness and frequency constraints

ABSTRACTThe guiding mechanism based on flexure hinges (FHs) is widely used in micro/nano-manufacturing technology. Both the stiffness and the frequency of FHs play significant roles in their dynamic performance, so the design task of such a structure is to find the optimal topology and corresponding size of FHs under stiffness and frequency constraints. However, the existing optimization methods pay more attention to the stiffness than to the frequency constraint owing to difficulties in dynamic topology optimization. In this article, with the symmetrical layout assumption of FHs and the analytical equivalent stiffness and mass expression of a single FH, the simultaneous topology and size optimization problem is converted to an analytical optimization formula with both discrete and continuous variables. Finally, the tension stiffening effect is used to compensate for manufacturing errors. A design case is used to illustrate the efficiency of the proposed method.

An improvement to Eurocode 2 and fib Model Code 2010 methods for calculating crack width in RC structures

AbstractThe analysis of the mechanical behaviour of a reinforced concrete tie subjected to a monotonic loading in the stabilized cracking stage is performed here by way of a theoretical general model that considers the effect of the so‐called Goto cracks (secondary cracks). It is shown, in particular, that the average bond stress along the transmission length depends not only on the concrete strength as assumed by the fib Model Code for Concrete Structures 2010, but also on reinforcement ratio and bar diameter. In this regard, tabulated theoretical values of the average bond stress are proposed as a function of the aforementioned parameters. Moreover, the secondary cracks reduce the effect of tension stiffening on the relative mean strain. On the basis of the main results obtained with the general model, some improvements are suggested for the calculation methods proposed by fib Model Code 2010 and Eurocode 2 concerning the average value of the bond stress and taking into account the influence of the secondary cracks on the mean deformation. An improved calculation method is therefore performed. Finally, the theoretical results of crack spacing and crack width obtained with the general and improved methods are compared with experimental data obtained from extensive research on RC ties.

Post-cracking behavior of UHPC on the concrete members reinforced by steel rebar

Since the concrete strength around the reinforcement rebar affects the tension stiffening, the tension stiffening effect of ultra high performance concrete on the concrete members reinforced by steel rebar is examined by testing the specimens with circular cross section with the length 850 mm reinforced by a steel rebar at the center of a specimen's cross section in this research. Conducting a tensile test on the specimens, the cracking behavior is evaluated and a curve with an exponential descending branch is obtained to explain the post-cracking zone. In addition, this paper proposes an equation for this branch and parameters of equation is obtained based on the ratio of cover thickness to rebar diameter (c/d) and reinforcement percentage (<TEX>${\rho}$</TEX>).

Evaluation of tension stiffening and momentcurvature of high performance reinforced concrete beams under sustained load.

In this paper, the effects of creep and shrinkage on the deflection and cracking of&#x0D; reinforced high performance concrete beams subjected to sustained load type in bending&#x0D; are investigated. Mid-span deflections, cracking and surface strain profiles were&#x0D; monitored over a 90 day period so that to verify the structural response of HPRC (high&#x0D; performance reinforced concrete) beams. Using the results obtained from the&#x0D; experiments, the effect on tension stiffening was examined. Four concrete strengths 52,&#x0D; 95, 96 and 100 MPa were included as a major experimental parameter. The results&#x0D; showed that as higher strength concrete was employed, not only cracks along the&#x0D; reinforcement more extensive, but also the transverse crack spacing became smaller.&#x0D; Thereby, the effective tensile stiffness of the high-performance concrete specimens at&#x0D; the stabilized cracking stage was much smaller than those of normal-strength concrete&#x0D; specimens. This observation is contrary to the current design provisions, and the&#x0D; reduction in the tension stiffening effect by employment of high-performance concrete&#x0D; is much greater than that would be expected. Measured surface strains in both the&#x0D; tension and compression zones of beams of HPC subjected to sustained load were&#x0D; considerably higher than the normal strength concrete beam. This was thought to be&#x0D; primarily due to the effects of creep in the compression zone and a higher degree of&#x0D; cracking within the tension zone. The progressive long-term increase in deflection is&#x0D; shown to be a result of strain development primarily in the compression zone. The&#x0D; sustained load is shown to affect the section stiffness most significantly within the early&#x0D; stages of loading. Using experimental results, the validity of Eurocode 2 (EC2) is&#x0D; examined.

Numerical simulation of reinforced concrete nuclear containment under extreme loads

A finite element model for the non-linear dynamic analysis of a reinforced concrete (RC) containment shell of a nuclear power plant subjected to extreme loads such as impact and earthquake is presented in this work. The impact is modeled by using an uncoupled approach in which a load function is applied at the impact zone. The earthquake load is modeled by prescribing ground accelerations at the base of the structure. The nuclear containment is discretized spatially by using 20-node brick finite elements. The concrete in compression is modeled by using a modified Drucker-Prager elasto-plastic constitutive law where strain rate effects are considered. Cracking of concrete is modeled by using a smeared cracking approach where the tension-stiffening effect is included via a strain-softening rule. A model based on fracture mechanics, using the concept of constant fracture energy release, is used to relate the strain softening effect to the element size in order to guaranty mesh independency in the numerical prediction. The reinforcing bars are represented by incorporated membrane elements with a von Mises elasto-plastic law. Two benchmarks are used to verify the numerical implementation of the present model. Results are presented graphically in terms of displacement histories and cracking patterns. Finally, the influence of the shear transfer model used for cracked concrete as well as the effect due to a base slab incorporation in the numerical modeling are analyzed.

An effective stiffness model for GFRP RC cracked flexural members

Abstract There is no complete consensus of researchers on the problem of evaluating tension stiffening phenomena in cracked flexural glass fibre-reinforced polymer reinforced concrete members and, therefore, various empirical correction factors are used in the existing weighted averaging techniques for obtaining consistent estimates of experimental deflection of traditional steel bars reinforced concrete cross-sections. This paper presents an alternative method for deformational analysis of cracked GFRP RC flexural members based on constitutive modeling, taking into account the direct or inverse approach to evaluating the post-cracking stress-strain response of concrete in tension. The effect of tension stiffening is defined analytically by the derived formula for the effective moment of inertia, omitting the empirical correction of the moments of inertia of the uncracked or fully cracked RC cross-sections. Analytical formulae are also proposed to derive the parameters of tension stiffening based on the test data of GFRP RC beams subjected to bending. The relative systematic and random errors of the method are considered in the statistical analysis, involving the experimental sample of deflections for 42 beams. The case studies of manual calculation of the mid-span deflection of the beams by using the proposed technique and the inverse analysis for deriving tension stiffening parameters based on of the experimental data are also provided.

EXPERIMENTAL INVESTIGATION FOR MECHANICAL PROPERTIES OF FOAM BALLS LIGHTWEIGHT CONCRETE

Researchers and industrialists' interest in foam balls lightweight concrete (FBLWC) to be used in structural applications is steadily increasing, since the increase in demand for structures are light in weight. FBLWC is currently believed to have a promising future. It was restricted to use as partition wall, thermal insulation and rehabilitation work in the past. In the last few decades with the understanding of the phenomenon underlying (FBLWC), efforts have been made to use it in structural application. A new kind of LWC was developed for foam balls lightweight concrete, in which conventionally aggregates is partially replaced by polystyrene foam particles, which combined the advantages of normal density concrete, cellular concrete and high workability [3]. The main objective of the research was to investigate and evaluate the mechanical properties of (FBLWC). The investigation focused on studying the compressive strength, tensile splitting strength, modulus of elasticity, stress-strain relationship in (compression and tension) and tension stiffening effect. The research work included includeeeeeekKOPOFPF;LL;D, an experimental and a numerical phase. The experimental program included the testing of (FBLWC) specimens under concentric axial load in both tension and compression to obtain the actual stress strain properties of the produced FBLWC. This study showed that the use of foam balls in lightweight concrete clearly reduced the density of the concrete from 24.00 kN/m3 to 18.45 kN/m3 which represented a reduction of 23%. The average compressive strength for cube specimens was 27 MPa. And the average compressive strength for the cylinder specimens was 22.4 MPa.

Modelling the tension stiffening effect in SFR-RC

The understanding of the performance and cracking behaviour of steel fibre reinforced concrete (SFRC) has developed greatly in recent times. Many of these studies, however, are limited to SFRC without conventional reinforcement. This paper reports on the tensile behaviour of SFRC members co-reinforced with conventional reinforcing bars (SFR-RC). A physical description of the behaviour of the specimens is presented and an analytical model is derived. The model adopts the load-sharing concept between the tensile stresses resisted by the steel fibres and the steel reinforcing bar as well as the bond between the concrete and reinforcing bar to the tension stiffening effect of these members. The model is founded upon a previously reported tension chord model and allows for explicit identification of the three components to the tension stiffening effect. An experimental programme is reported here and the model is shown to correlate well with the experimental data and test data reported elsewhere.

Experimental study on the tensile behavior of square concrete-filled steel tubes

This paper presents an experimental study on the mechanical behavior, particularly the tensile stiffness, of square concrete-filled steel tubes (SCFTs) under axial tension, from both the force/displacement-level and strain-level perspectives. A group of SCFT and hollow tube specimens are tested with extensive data of the steel tube strains measured. From the force/displacement-level perspective, it is found that the tensile stiffness of SCFTs is 31.8% higher than that of hollow tubes on average. It is proposed that tensile stiffness enhancement is a combined result of the confine-stiffening effect and tension-stiffening effect. The confine-stiffening effect is because of the biaxial tensile stress state of the steel tube due to the concrete-to-steel tube confinement of SCFTs. From the strain-level perspective, the existence of the concrete-to-steel tube confinement is proved by comparing the measured transverse-to-longitudinal strain ratio of the steel tube between SCFT and hollow tube specimens. Besides, the evidence for the tension-stiffening effect in SCFTs is also provided by the non-uniformly distributed longitudinal steel strain of the steel tube. In addition, the fractal cracking phenomenon is experimentally observed and quantitatively measured, indicating the interaction of the concrete-to-steel tube confinement and tension-stiffening effect. It is concluded that the tensile stiffness of SCFTs will be underestimated if the SCFTs under tension are simply treated as equal to the hollow tubes by neglecting the concrete-to-steel tube confinement and tension-stiffening effect; this underestimation may cause non-conservative inaccuracies in calculating the component internal forces, structural natural frequencies, and seismic effects in the design and analysis of structures.

Nonlinear analysis of containment structure based on modified tendon model

This paper proposes a modified stress–strain relation for bonded internal tendon in containment structures on the basis of the tension stiffening effect and the bond characteristics between a tendon and its surrounding concrete. Differently from general approaches for the consideration of bond-slip, which take the double nodes in defining the displacement field, the proposed model indirectly considers the bond-slip effect through the modification for the stress–strain relation of tendon. Since the proposed tendon model takes into account the bond-slip effect without taking double nodes in the numerical modeling of containment structures, it can effectively be implemented into commercialized programs which have a lot of limitation in considering the bond-slip effect at large complex containment structures. The solution algorithm for an un-bonded internal tendon whose structural response is not section-dependent but member-dependent is also introduced. The different structural responses from those in bonded tendon are evaluated by successive iterations and finally considered by the additional modification for the stress–strain relation of tendon. The validity of the proposed tendon model is verified through correlation studies between analytical and experimental results for PSC beams and 1/4 PCCV containment structures.

Theoretical and experimental short-term behavior of non-symmetrical wall pile retaining systems

Optimized non-symmetrically reinforced piles for retaining walls constitute a new structural element recently used in constructions such as the underground floors of San Antoni Market in Barcelona or in the Riyadh metro. Piles usually have circular cross sections with longitudinal reinforcement composed of bars of the same diameter and with constant clear distances between them. The use of non-symmetrical piles in retaining walls means savings of up to 50% in the weight of the longitudinal reinforcement, compared with traditional symmetrical piles.Intuition suggests that a non-symmetrical pile, compared with its symmetrical counterpart -both having the same ultimate flexural moment-, deforms less and has smaller crack widths. This point is analyzed in this paper both theoretically and experimentally.The majority of the studies conducted on RC members were developed only for rectangular cross sections. In this paper, results from an experimental campaign of circular RC cross-sections are presented. The main objective of this campaign is the formulation of the effective area of concrete in the tension stiffening effect of RC circular cross-sections.

Moment-curvature Model for Steel Plate-concrete Composite Beams

The rapid development of composite structures has led to a new design concept of the steel plate-concrete composite beam in which a thin steel plate is attached to the reinforced concrete beam. The shear connection is established by the use of headed studs and the joined parts can act as a unit due to the adequate bond between the steel and concrete. The behavior of this type of structures can be classified as intermediate between composite and reinforced concrete structures.The experimental studies have shown that the methods described in standard codes allow to determine the ultimate load of the structure, while the structure's deflection is underdetermined. More sophisticated analyses of beams are more accurate but they are used in practical design rather reluctantly. The purpose of this paper is to present a moment-curvature model which can be used in simplified calculation of deflection of steel plate-concrete composite beams. Instead of adopting the complex theoretical analysis, a trilinear model is represented by pre-cracking, post-crack and post-yielding stages. The additional deflection due to shear slip at the interface plane is taken into account. The slip effect always exists both in fully and partially composite beams and experimental studies have shown that it has a significant impact on the response of the structure. Tension stiffening effects are also considered since beam rigidity is reduced when cracking is developing due to an increase of the applied load. For validation purposes a theoretical analysis based on the presented model was performed and compared with the experimental results. The predicted results of the analytical studies were compared with the measurements of the tested beam to confirm the validity of the proposed method. It was confirmed that including the shear slip effect has significantly improved the accuracy of prediction.

Ajuste de modelos de cortante en hormigón estructural mediante algoritmos evolutivos

The behavior of reinforced and prestressed concrete members subjected to shear has been traditionally studied by the so-called Compression-Field Theories. In the last years several authors have modified the mechanical model of such theories in order to include the tension-stiffening effect of the concrete in the steel constitutive model; the resulting system of equations is highly non-linear and involves a great number of unknowns. From an experimental database of RC beams, this work performs an adjustment of the shear model proposed by one of these theories using evolutionary algorithms. Evolutionary algorithm is a branch of Natural Computing. Its computations start from an initial population of individuals (randomly generated) and proceed according to rules of selection and other operators, such as recombination and mutation. The main objective of such algorithms is to find good solutions in a reasonable time-frame. Numerical results show a relative error between numerical results and experimental data less than 10%, what validates genetic algorithms as a good alternative for solving these computationally-intensive adjustment problems.

Intermediate crack-induced debonding analysis for RC beams strengthened with FRP plates

This paper presents the analysis of intermediate crack-induced (IC) debonding failure loads for reinforced concrete (RC) beams strengthened with adhesively-bonded fiber-reinforced polymer (FRP) plates or sheets. The analysis consists of the energy release and simple ACI methods. In the energy release method, a fracture criterion is employed to predict the debonding loads. The interfacial fracture energy that indicates the resistance to debonding is related to the bond-slip relationships obtained from the shear test of FRP-toconcrete bonded joints. The section analysis that considers the effect of concrete‟s tension stiffening is employed to develop the moment-curvature relationships of the FRP-strengthened sections. In the ACI method, the onset of debonding is assumed when the FRP strain reaches the debonding strain limit. The tension stiffening effect is neglected in developing a moment-curvature relationship. For a comparison purpose, both methods are used to numerically investigate the effects of relevant parameters on the IC debonding failure loads. The results show that the debonding failure load generally increases as the concrete compressive strength, FRP reinforcement ratio, FRP elastic modulus and steel reinforcement ratio increase.

STRENGTHENING OF SLENDER RC SHEAR WALL WITH FRP SHEETS

Concrete shear walls are the most prevalent structural systems resisting lateral loads due to earthquakes in high-rise buildings. Very large in-plane stiffness of shear walls provides an excellent drift control in the structure. However, structural damages and early code shortcomings threaten the efficiency of existing structural walls against earthquake. Recently, fiber reinforced polymer (FRP) materials have been used considerably in strengthening and retrofitting of structural elements. High tensile strength and excellent tensile modulus along with other unique features of FRP materials make them the first alternative in the strengthening projects. However, the literature shows that few analytical and/or experimental studies have been conducted on the strengthening of slender reinforced concrete (RC) shear walls with FRP materials so far. In this paper, the effect of strengthening of boundary elements in slender RC shear walls with FRP on the overall behavior of shear walls is investigated. Nonlinear finite element is used to analyse the RC walls, using damage plasticity model and tension stiffening effects. Results of the current study show that applying FRP sheets vertically on the lateral faces of the boundary elements causes the load-displacement curves of the strengthened walls to have a larger load carrying capacity up to 20% compared to that of wall specimens without FRP strengthening. Furthermore, applying the FRP sheets on the boundary elements only in the plastic hinge region of wall can improve the wall load carrying significantly.