Tension Stiffening Behavior Research Articles

Behavior of textile‐reinforced concrete columns

AbstractThis work aims to investigate the behavior of textile‐reinforced concrete (TRC) members subject to compressive loads. An experimental program including concentric compression tests on I‐section columns with different lengths and simply‐supported ends was carried out. From compression tests, load versus lateral deflection curves obtained experimentally are reported along with maximum loads and apparent imperfections determined using the Southwell technique. Failure modes were characterized by excessive lateral deflections for longer columns, whereas concrete crushing failure due to combined bending and axial load occurred for shorter columns. Surrounding concrete was effective in restraining the textile reinforcement against buckling, allowing it to sustain the compressive loads. A single degree‐of‐freedom model accounting for normal‐moment‐curvature relation and tension stiffening behavior is validated against experiments and used to carry out a parametric study. Results show that the nonsway moment magnification method recommended by the ACI Code 440.11‐22 can be applied to TRC columns, although leading to overestimated second‐order effects.

Tension Stiffening and Cracking Behavior of Axially Loaded Alkali-Activated Concrete.

Alkali-activated concrete is an eco-friendly construction material that is used to preserve natural resources and promote sustainability in the construction industry. This emerging concrete consists of fine and coarse aggregates and fly ash that constitute the binder when mixed with alkaline activators, such as sodium hydroxide (NaOH) and sodium silicate (Na2SiO3). However, understanding its tension stiffening and crack spacing and width is of critical importance in fulfilling serviceability requirements. Therefore, this research aims to evaluate the tension stiffening and cracking performance of alkali-activated (AA) concrete. The variables considered in this study were compressive strength (fc) and concrete cover-to-bar diameter (Cc/db) ratios. After casting the specimen, they were cured before testing at ambient curing conditions for 180 days to reduce the effects of concrete shrinkage and obtain more realistic cracking results. The results showed that both AA and OPC concrete prisms develop slightly similar axial cracking force and corresponding cracking strain, but OPC concrete prisms exhibited a brittle behavior, resulting in a sudden drop in the load-strain curves at the crack location. In contrast, AA concrete prisms developed more than one crack simultaneously, suggesting a more uniform tensile strength compared to OPC specimens. The tension-stiffening factor (β) of AA concrete exhibited better ductile behavior than OPC concrete due to the strain compatibility between concrete and steel even after crack ignition. It was also observed that increasing the confinement (Cc/db ratio) around the steel bar delays internal crack formation and enhances tension stiffening in AAC. Comparing the experimental crack spacing and width with the values predicted using OPC codes of practice, such as EC2 and ACI 224R, revealed that EC2 tends to underestimate the maximum crack width, while ACI 224R provided better predictions. Thus, models to predict crack spacing and width have been proposed accordingly.

Experimental and analytical investigations on tension stiffening of reinforced engineered cementitious composites members

Experimental and analytical investigations on the performance of reinforced ECC members in tension were studied in this paper through direct tension load. The applied load and elongation of members were measured during testing. The number and width of major cracks in specimens were determined at failure. The influences of the cross-sectional dimension and steel reinforcement diameter on the tension stiffening of members were investigated. Comparisons were made among reinforced ECC members with different cross-sectional dimensions or reinforcement diameters in terms of the cracking load, ultimate load and ultimate strain. Experimental results showed that the load-deformation relationship of reinforced ECC members could be divided into three stages, namely, initial elastic stage, multiple cracking stage and major cracking stage. In addition to experimental tests, an analytical model for the tension stiffening behaviour of reinforced ECC members was proposed. The interaction between ECC and steel reinforcement was considered at different stages in this model. Comparisons with experimental data suggest that the analytical model could accurately predict the relationship between load and deformation of reinforced ECC members. The cracking load obtained by this model is conservative as compared with test data. Based on the validated analytical model, a parametric study was carried out on the effects of reinforcement ratio and bond stress on tension stiffening of reinforced ECC. The direct tension tests and analytical results in this study can be used to predict the load and deformation behaviour of reinforced ECC members in tension.

Analytical Modeling of Crack Widths and Cracking Loads in Structural RC Members

Crack width is a major performance criterion in reinforced-concrete structures, in general, and is of utmost importance in ensuring bridge performance, in particular. A reliable theory-based method is required to assess crack widths and gain insight into their dependence on material, geometry, and loading parameters. A new, exact analytical method is proposed for a one-dimensional reinforced concrete element based on equilibrium, constitutive, and kinematic relationships, accounting for the geometrical and material behavior of the concrete and reinforcement. A linear interfacial bond stress slip is assumed to represents the small slips associated with the limited allowed crack width. Closed-form expressions have been developed and a wealth of information can be calculated immediately, such as the cracking load levels, the crack width dependence on the load level, the expected number of cracks, and the cracks spacing. The entire nonlinear force-displacement relationship of a cracked reinforced-concrete element may be depicted, demonstrating the tension-stiffening behavior that depends on the variations in the crack width throughout the loading history. Comparisons of the model with experimental data demonstrate very good agreement.

Influence of Bond Characterization on Load-Mean Strain and Tension Stiffening Behavior of Concrete Elements Reinforced with Embedded FRP Reinforcement.

Based on the characterization of the bond between Fiber-Reinforced Polymer (FRP) bars and concrete, the structural behavior of cracked Glass-FRP (GFRP)-Reinforced Concrete (RC) tensile elements is studied in this paper. Simulations in which different bond-slip laws between both materials (FRP reinforcement and concrete) were used to analyze the effect of GFRP bar bond performance on the load transfer process and how it affects the load-mean strain curve, the distribution of reinforcement strain, the distribution of slip between reinforcement and concrete, and the tension stiffening effect. Additionally, a parametric study on the effect of materials (concrete grade, modulus of elasticity of the reinforcing bar, surface configuration, and reinforcement ratio) on the load-mean strain curve and the tension stiffening effect was also performed. Results from a previous experimental program, in combination with additional results obtained from Finite Element Analysis (FEA), were used to demonstrate the accuracy of the model to correctly predict the global (load-mean strain curve) and local (distribution of strains between cracks) structural behavior of the GFRP RC tensile elements.

Effects of Freeze-Thaw and Wet-Dry Cycles on Tension Stiffening Behavior of Reinforced RAC Elements

In the last several decades, the growth of Construction and Demolition Waste (CDW) production and the increased consumption of natural resources have led to promoting the use of secondary raw materials for a more sustainable construction. Specifically, the use of Recycled Concrete Aggregate (RCA), derived from waste concrete, for the production of Recycled Aggregate Concrete (RAC) has attracted a significant interest both in industry and in academia. However, the use of RAC in field applications still finds some barriers. In this context, the present study investigates experimentally the effects of freeze-thaw and wet-dry cycles on the stress transfer mechanisms of reinforced RAC elements through tension stiffening tests. First of all, the paper presents a detailed analysis of the degradation due to the aging process of RAC with RCAs obtained from different sources. Particularly, the results of tension stiffening tests are analyzed in terms of crack formation and propagation, matrix tensile strength contribution and steel-to-concrete bond. The results highlight that the pre-cracking elastic modulus, the first crack strength as well as the maximum concrete strength are strongly influenced by the presence of the Attached Mortar (AM) in RCA, as the former affects the concrete’s open porosity. Therefore, the amount of AM is identified as the key parameter for the evaluation of durability of reinforced RAC members: a degradation-law is also proposed which correlates the initial concrete open porosity with the damage observed in reinforced RAC elements.

Cyclic Behavior of Reinforced High Strain-Hardening UHPC under Axial Tension.

The cyclic tensile behavior of steel-reinforced high strain-hardening ultrahigh-performance concrete (HSHUHPC) was investigated in this paper. In the experimental program, 12 HSHUHPC specimens concentrically placed in a single steel reinforcement under cyclic uniaxial tension were tested, accompanied by acoustic emission (AE) source locating technology, and 4 identical specimens under monotonic uniaxial tension were tested as references. The experimental variables mainly include the loading pattern, the diameter of the embedded steel rebar, and the level of target strain at each cycle. The tensile responses of the steel-reinforced HSHUHPC specimens were evaluated using multiple performance measures, including the failure pattern, load–strain response, residual strain, stiffness degradation, and the tension-stiffening behavior. The test results showed that the enhanced bond strength due to the inclusion of steel fibers transformed the failure pattern of the steel-reinforced HSHUHPC into a single, localized macro-crack in conjunction with a sprinkling of narrow and closely spaced micro-cracks, which intensified the strain concentration in the embedded steel rebar. Besides, it was observed that the larger the diameter of the embedded steel rebar, the smaller the maximum accumulative tensile strain under cyclic tension, which indicated that the larger the diameter of the embedded steel rebar, the greater the contribution to the tensile stiffness of steel-reinforced HSHUHPC specimens in the elastic–plastic stage. In addition, it was found that a larger embedded steel rebar appeared to reduce the tension-stiffening effect (peak tensile strength) of the HSHUHPC. Moreover, the residual strain and the stiffness of the steel-reinforced HSHUHPC were reduced by increasing the number of cycles and finally tended toward stability. Nevertheless, different target strain rates in each cycle resulted in different eventual cumulative tensile strain rates; hence the rules about failure pattern, residual strain, and loading stiffness were divergent. Finally, the relationship between the accumulative tensile strain and the loading stiffness degradation ratio under cyclic tension was proposed and the tension-stiffening effect was analyzed.

Tension Stiffening Behavior of Polypropylene Fiber- Reinforced Concrete Tension Members

This paper focuses on comparing the behavior of RC tension members with and without the addition of polypropylene fibers at various corrosion levels. Eight cylindrical tensile specimens were tested to evaluate their tension-stiffening and cracking behavior. The content of polypropylene fiber added into the concrete mix was the main variable (0.25%, 0.50%, 0.75%, and 1.0% of total volume). The corrosion level was varied from slight (5%), medium (10%) to severe (30%) and, like the other variables, applied only to 1.0% polypropylene fiber-reinforced concrete (PFRC) specimens. The test results showed that the fiber addition significantly increased the tension-stiffening effect but was largely unable to reduce the effect of bond degradation caused by corrosion. Moreover, the addition of polypropylene fibers was able to improve the cracking behavior in terms of crack propagation, as shown by smaller crack spacing compared to the specimen without fiber addition at the same corrosion level.

Modeling of the tension stiffening behavior and the water permeability change of steel bar reinforcing concrete using mesoscopic and macroscopic hydro-mechanical lattice model

Mesoscopic and macroscopic hydromechanical lattice simulations are performed for studying the tension stiffening behavior, the change in permeability, and their linking of a tensioned reinforced normal strength concrete (NSC) member. In the lattice framework, the hydromechanical coupling is carried out by dual Delaunay triangles and Voronoi polygons, where transport elements are placed along the edges of the Voronoi polygons while mechanical elements are edges of Delaunay triangles. At the mesoscale, concrete is considered as a constitution of three phases: aggregate, cement paste and interfacial transition zones (ITZ). Two mesoscopic components cement paste and ITZ, as well as the concrete at the macroscale, are modeled by a damage model including softening strain feature. The crack opening is linked to the damage variable. Fluid flow obeys Darcy’s law in the intact conduit element and Poiseuille’s law in the crack. Validation against experimental results available in the open literature for NSC tie specimens shows that both current macroscopic and mesoscopic lattice hydromechanical models are appropriated to describe the tensile stiffening and damage induced permeability of NSC reinforced by a steel bar. Mesoscopic modeling helps to get insights of the aggregate volume fraction effect.

Hydromechanical couplings of reinforced tensioned members of steel fiber reinforced concrete by dual lattice model

AbstractThe durability of concrete structures strongly depends on the water and chloride penetration in cracked concrete during its service life. This work aims at modeling the damage effect of tension stiffening behavior on the permeability for concrete tie specimen under tensile load by a dual lattice model, which considers hydromechanical couplings. Three concrete materials, including normal strength concrete (NSC), steel fiber reinforced concretes (SFRC), and ultra high‐performance fiber reinforced concrete (UHPFRC), are considered. The hydromechanical lattice model is based on a dual element network modeling: the water transport and the mechanical response. The fiber bridging effect is considered by means of the cohesive law of Mazars. The water flow in the damaged conduit elements is proportional to the cube of the crack width, which results from the damage variable. Experimental results available in open literature for both NSC and SFRC tie specimens are used to analyze and validate the proposed model. Considering a UHPFRC tie specimen, the model well predicted the load drops due to macrocrack occurrence, load hardening, and permeability evolution. Based on the present results, the current lattice hydromechanical model is a useful tool for predicting the service life of steel bar reinforcing concrete structure with and without steel fiber reinforcement.

Experimental and analytical research on the flexural behaviour of steel–ECC composite beams under negative bending moments

Due to the strain-hardening and multi-cracking properties, engineered cementitious composite (ECC) is a new solution to the cracking issue in the negative bending moment region of steel–concrete composite beams. This paper presents an experimental and analytical study on the flexural performance of composite steel–ECC beams subjected to negative bending moments as well as the tension stiffening behaviour of reinforced ECC (R/ECC) flange slabs. Three beams with different slab materials and reinforcement ratios were tested under a hogging moment. Experimental results demonstrated significant enhancement in stiffness and crack resistance for the steel–ECC composite beams. A practical four-parameter fibre-bridging model was established to describe the strain-hardening behaviour of different ECC materials. Then, a modified analytical tension-stiffening model for R/ECC was formulated considering the strain-hardening behaviour of ECC and rebar–ECC bond–slip interaction based on the conventional tension-stiffening model for reinforced concrete. This modified model was verified by several direct tensile tests of R/ECC members. In addition, by applying the model to the traditional fibre beam–column element model, the mechanical performance and crack opening of general R/ECC structures were derived. The simulation results of the steel–ECC composite beams demonstrated satisfactory accuracy compared with the test results. Finally, a parametric study based on the new model was conducted to identify the influence of several important material and structural parameters on the flexural performance of steel–ECC composite beams under negative moments.

Direct tensile behaviors of steel-bar reinforced ultra-high performance fiber reinforced concrete: Effects of steel fibers and steel rebars

Based on strengthening the structural performance of ultra-high performance fiber reinforced concrete (UHPFRC), a steel-bar reinforced ultra-high performance fiber-reinforced concrete (R-UHPFRC) is presented in this study. To provide more information about the direct tensile behaviors of R-UHPFRC member, several dogbone-shaped R-UHPFRC specimens are tested, with the experimental variables including the volume content of steel fiber and the reinforcement ratio of steel rebar. The effects of the fiber volume fraction and reinforcement ratio of steel bars on the direct tensile properties of R-UHPFRC are evaluated using multiple performance parameters, including load-deformation relationship, tension-stiffening behavior, tensile stiffness and damage pattern. Test results indicate that there is minimal difference in overall load-elongation responses of R-UHPFRC specimens with an increasing fiber volume fraction. The variation in the reinforcement ratio of the steel bar, by contrast, has significant influence on the tensile responses of R-UHPFRC specimen, especially the peak strength and hardening modulus increases considerably with a growing reinforcement ratio as compared to non-reinforced UHPFRC specimens. Importantly, the tensile strain values of R-UHPFRC with rebars are significantly higher than the counterparts of UHPFRC without rebars, and this rising trend is even more pronounced when the reinforcement ratio increases. Further, the use of R-UHPFRC with combined reinforcements is beneficial to extend the strain hardening capacity of UHPFRC itself. Even, a desired post-peak ductility can be achieved by a rationally designed reinforcement ratio of steel bars. The increased reinforcement ratio of steel rebars transfers the tensile failure pattern of the R-UHPFRC members from a single, localized crack into multiple localized cracks.

The Effect of Shrinkage-Compensation on the Performance of Strain-Hardening Cement Composite (SHCC)

This study investigated the effects of shrinkage compensation on the tensile and cracking responses of strain-hardening cement composite (SHCC) by adding calcium sulfoaluminate (CSA)-based expansive additive (EXA) to the mixture. Such responses are closely related to the durability of concrete structures, of dumbbell-shaped SHCC specimens, and reinforced SHCC ties. For this study, two SHCC mixtures and a conventional concrete mixture with a specific compressive strength value of 30 MPa were prepared and measured in terms of shrinkage history, compressive strength, flexural strength, and direct tensile strength. The test results show that the mechanical properties of shrinkage-compensated SHCC with 10% CSA-based EXA are superior to those of conventional SHCC and concrete mixtures. Also, reinforced tension ties with shrinkage-compensated SHCC exhibited the best multiple cracking and tension-stiffening behavior among the three types of tension ties tested. The results show that shrinkage compensation using CSA-based EXA in SHCC with rich mixture is effective for resisting crack damage. Shrinkage-compensated SHCC may be used for civil infrastructure facilities that require high levels of durability and are exposed to extreme environments.

Insight into the tension stiffening behavior of reinforced concrete tension members revealed by finite element modeling

The disasters happened in recent past pointed out the need of design criteria, ensuring adequate safety levels against progressive collapse. The attention was focused on the behavior of composite beam-to-column joint components in the field of large displacements. This article presents the experimental and numerical study enabling the simulation of the RC elements under tension. This has helped in understanding the non-negligible contribution of concrete in tension stiffening response up to failure especially in the case of discontinuous geometry marked in composite structures. The finite element model proposed may be considered a mid-way between smeared and discrete crack modeling approaches.

Tension-stiffening effect in steel-reinforced UHPC composites: Constitutive model and effects of steel fibers, loading patterns, and rebar sizes

The tensile performance of steel-reinforced concrete members is closely associated with the bond interaction between concrete and the embedded rebar. Ultra-high performance concrete (UHPC) is a rapidly emerging concrete material that has an ultra-high compressive strength and bond strength. When it is reinforced with short, discontinuous fibers, it features a tensile strain-hardening behavior and a damage pattern of closely spaced narrow cracks. The present study investigated the tensile behavior of steel-reinforced UHPC members. Sixteen samples were tested, with the experimental variables including embedded rebar sizes, loading patterns, and steel fibers. The tensile responses of the steel-reinforced UHPC samples were evaluated using multiple performance measures, including the damage pattern, stiffness, load-deformation relationship, rebar strain, and the tension-stiffening behavior of UHPC. The test results showed that the enhanced bond strength due to the inclusion of steel fibers transformed the failure pattern of the steel-reinforced UHPC from multiple localized cracks into a single localized crack, which intensified the strain concentration in the embedded rebar. Although the addition of fibers substantially strengthened the tension-stiffening response of the UHPC, it also raised critical concerns about premature failure, especially when UHPC members were reinforced with small steel bars and subjected to monotonic loading. In addition to the experimental study, a tetra-linear constitutive model that was able to reasonably represent the tension-stiffening behavior of fiber-reinforced UHPC up to failure was suggested in this study.

Time-Dependent Tension-Stiffening Mechanics of Fiber-Reinforced and Ultra-High-Performance Fiber-Reinforced Concrete

AbstractThe tension-stiffening behavior of fiber-reinforced concrete is of fundamental importance for the characterization of crack widths and spacings as well as determination of the tensile respo...

Long-term performance of GFRP bars in concrete elements under sustained load and environmental actions

This paper presents an experimental study aimed at investigating the long-term tension stiffening and flexural behaviour of concrete elements reinforced with glass fibre reinforced polymer (GFRP) bars subjected to accelerated aging conditions. Six tension stiffening specimens and eight small-scale GFRP RC beams were exposed to different environments and sustained stress levels for 120 and 270 days, respectively. Subsequently, the specimens were tested to failure and their behaviour was compared to that of reference specimens. The test results revealed that stressed specimens conditioned in a wet environment experienced a reduction in tension stiffening response as a result of bond degradation and a reduced stress transfer from the bar to the surrounding concrete. The results also indicate that the accelerated aging conditions affected the overall flexural behaviour and led to higher deflections and larger crack widths. The long-term deformation of elements subjected to a stress level representing typical in-service conditions, however, always complied with the design limits suggested by current guidelines. Higher imposed loads (inducing maximum strain level in the reinforcement of about 5000 με) led to both deflections and crack widths in excess of the values recommended at serviceability limit state. Finally, the response of the tested specimens is compared to that predicted according to fib Model Code 2010 and Eurocode 2 and it is shown that both models fail to capture adequately the long-term structural behaviour of stressed GFRP RC specimens conditioned in wet environment.

Micromechanical modeling of tension stiffening in FRP-strengthened concrete elements

This article presents a micromodeling computational framework for simulating the tensile response and tension-stiffening behavior of fiber reinforced polymer–strengthened reinforced concrete elements. The total response of strengthened elements is computed based on the local stress transfer mechanisms at the crack plane including concrete bridging stress, reinforcing bars stress, FRP stress, and the bond stresses at the bars-to-concrete and fiber reinforced polymer-to-concrete interfaces. The developed model provides the possibility of calculating the average response of fiber reinforced polymer, reinforcing bars, and concrete as well as the crack spacing and crack widths. The model, after validation with experimental results, is used for a systematic parameter study and development of micromechanics-based relations for calculating the crack spacing, fiber reinforced polymer critical ratio, debonding strength, and effective bond length. Constitutive models are also proposed for concrete tension stiffening and average response of steel reinforcing bars in fiber reinforced polymer–strengthened members as the main inputs of smeared crack modeling approaches.

Time‐dependent serviceability behavior of reinforced concrete beams: Partial interaction tension stiffening mechanics

The partial interaction (PI) mechanics of tension stiffening governs crack widening and the consequential deflection of reinforced concrete (RC) beams and, therefore, is essential in the serviceability design of RC structures. Both behaviors are dependent on the PI global load slip behavior of the tensile reinforcement relative to the surrounding concrete at a crack face, which in turn is dependent on the local PI material bond‐stress/slip relationship between the reinforcement and adjacent concrete. Due to the complexity of PI theory, it has been difficult to directly incorporate PI mechanics into design procedures. Consequently, empirical approaches to quantify effective flexural rigidities and crack widths are commonplace. While empirical approaches can be derived relatively simply for short‐term loading, the influence of concrete shrinkage and creep is difficult to incorporate. In this paper, pure mechanics‐based PI solutions to describe the crack spacing and tension stiffening behavior of RC beams subjected to long‐term loads are derived. They only require material properties and clearly show the interaction among shrinkage, creep and bond properties. They are simple enough to use directly in design and will help in the experimental derivation of the material properties. The results of these PI analyses are used in a companion paper to develop design rules for the time‐dependent serviceability deflection of RC beams and compared with test results.

Tension stiffening approach for interface characterization in recycled aggregate concrete

This study proposes a comprehensive analysis on the structural performance of reinforced Recycled Aggregate Concrete members. Particularly, it summarizes the results of an experimental investigation aimed at analyzing the tension stiffening behavior of normal and high strength class concretes produced with Recycled Concrete Aggregates (RCAs). The mixtures were proportioned in order to achieve 25 and 65 MPa of compressive strength and, moreover, several recycled-to-natural coarse aggregates replacement ratios were considered: 0%, 25% and 50%. The results derived from this type of test furnish a comprehensive analysis on both the steel-to-matrix interaction and the crack formation and propagation on concrete elements as well as distributed cracking mechanisms. Using a finite difference numerical model, the experimental results are used to back-calculate and identify the steel-to-concrete bond slip law. Also, it is an alternative mean of developing the stress-crack-width law for concrete in tension. The results showed that the use of recycled concrete aggregate does not affect the resulting concrete performance and, therefore, the RCAs can be successfully employed, up to the levels analyzed herein, for the production of structural elements made with normal and high strength class concrete mix.