Post-cracking Stiffness Research Articles

Shear Behavior of Steel-Fiber-Reinforced Recycled Aggregate Concrete Deep Beams

Results of an experimental investigation aimed at studying the effect of steel fibers on the shear behavior of concrete deep beams made with a 100% recycled concrete aggregate (RCA) are presented in this paper. The study comprised testing of seven concrete deep beam specimens with a shear span-to-depth ratio (a/h) of 1.6. Two beams were made of natural aggregates (NAs) without steel fibers, two beams were made of a 100% RCA without steel fibers, and three beams were made of RCA-based concrete with steel fibers at volume fractions (vf) of 1, 2, and 3%. Two of the beams without steel fibers included a minimum shear reinforcement. Test results showed that the beam with a 100% RCA without steel fibers exhibited a lower post-cracking stiffness, reduced shear cracking load, and lower shear capacity than those of the NA-based control beam. The detrimental effect of the RCA on the shear response was less pronounced in the presence of the minimum shear reinforcement. The addition of steel fibers significantly improved the shear response of the RCA-based beams. The post-cracking stiffness of the RCA-based concrete beams with steel fibers coincided with that of a similar beam without fibers containing the minimum shear reinforcement. The use of steel fibers in RCA beams at vf of 1 and 2% restored 80 and 90% of the shear capacity, respectively, of a similar beam with the minimum shear reinforcement. The response of the RCA specimen with vf of 3% outperformed that of the NA-based control beam with the minimum shear reinforcement, indicating that steel fibers can be used in RCA deep beams as a substitution to the minimum shear reinforcement. The shear capacities obtained from the tests were compared with predictions of published analytical models.

Formulation and calibration of two-dimensional constitutive models for composite structures based on panel tests

Steel Plate Concrete (SC) composite members have been widely adopted because of its cost-efficiency and enhanced structural behavior. While researchers have attempted to study its in-plane shear behavior in the past twenty years, very limited number of large-scale pure shear tests were performed due to the challenge of experimental set-up and the availability of facilities. In this paper, a series of uniaxial loading tests and two full-scale pure shear panel tests of SC members were reported, on which the “mechanics-based Membrane Model of SC elements (MM-SC)” is developed. The MM-SC model is based on the fixed-angle crack formulation and the smeared-crack formulation, in which the experimental-based uniaxial constitutive models are implemented, considering the local buckling of faceplate, the tension stiffening of steel plate, the strength degradation of cracked concrete and the confinement effect of concrete. The proposed MM-SC model is subsequently incorporated into the object-oriented software OpenSEES. The simulation results of proposed model well predict the SC test observations in terms of critical branch points and structural behaviors, including initial stiffness, cracking strength, post-crack stiffness, yield strength, maximum strength, and failure modes.

Mechanical behavior of cement composites reinforced by aligned Enset fibers

Driven by the search towards new materials with reduced ecological impact, several investigations on plant-based natural fibers for composite reinforcement have been undertaken by researchers in the past decades. However, Ensete Ventricosum (Ev) fiber as reinforcement in a cementitious matrix has not yet been studied. This research aims to assess the mechanical performance of aligned Ev fiber reinforced cementitious composites and particularly the influence of the fiber volume fraction on the flexural performance of the composite. Four different fiber content ratios (from 3 % up to 6 %) were compared to plain mortar specimens. Not only the flexural load–displacement but also the cracking behavior was studied in depth utilizing the optical Digital Image Correlation (DIC) technique. The developed material presented multiple cracking behavior under bending. The post-cracking stiffness, toughness and flexural strength of Ev fiber reinforced specimens were increased with higher fiber content: 3 %, 4 % and 5 % fiber content resulted in a strength increase of 260 %, 274 % and 396 %, respectively, compared to that of the reference mortar specimen. These results are promising for the development of a Ev fiber-based green composite.

A novel casting procedure for SFRC piles without shear reinforcement using the centrifugal forming technique to manipulate the fiber orientation and distribution

The structural performance of steel fiber-reinforced concrete (SFRC) members primarily depends on the distribution and orientation of the fibers. Previous experimental studies revealed that the distribution and orientation of fibers are random and hardly controlled during the fabrication process. The centrifugal forming technique may improve the orientation and distribution of steel fibers in hollow circular SFRC piles and increase the shear strength of the piles. Accomplishing this task can lead to the possible replacement of shear reinforcements with steel fibers in piles, thereby improving the demanding productivity that is desired in the pile construction industry by saving considerable time and labor. This paper presents a novel experimental program to (a) develop the casting procedure for SFRC piles and (b) investigate the shear strength of SFRC piles without shear reinforcement compared to that of conventional reinforced concrete (RC) piles with shear reinforcement. With the aid of X-ray technology, different mix proportions and casting methods were investigated to determine the optimum procedure, which produced fiber distributions and orientations in SFRC piles superior to those of RC piles. The centrifugal forming method influenced the orientation of the fibers so that they were oriented in the shear stress direction (i.e., circumferential direction). The loading test demonstrated that the steel fibers effectively worked as shear reinforcement and that the shear capacity increased with the steel fiber content. Moreover, the SFRC piles exhibited stable crack propagation and improved post-cracking stiffness without severe concrete damage compared to that of the RC piles.

Repair of pre-damaged RC beams using hybrid fiber reinforced strain hardening cementitious composites

This article investigates the feasibility of using hybrid fiber reinforced Strain Hardening Cementitious Composites (SHCC) to the repair of pre-damaged RC beams. For this study, PVA, polyethylene and steel fibers were used, and hybrid combinations were developed by replacing PVA and polyethylene fibers by steel fibers. The mechanical behavior of the composites was studied under uniaxial tension tests and the crack pattern was studied using a high-resolution image capturing procedure. The results have shown that the hybridization increases the strength and post-crack stiffness of the composites but reduces the strain capacity. Then, the developed composites were used as a repair layer of RC beams subjected to previous damage. The results have shown that the repair technique considerably increases the load-bearing capacity of the beams and delays the growth of pre-existing cracks. The hybrid composites had similar performance to the non-hybrid in controlling the existing cracks. It was also found that the hybrid composites are promising materials for improving the performance of structural members in serviceability limit states and at low strain values.

Numerical simulation of GFRP-reinforced glass structural elements under monotonic loading

Several reinforcing strategies have recently been developed to overcome glass brittleness and numerical simulations are essential to investigate the structural behaviour of such hybrid systems. Based on previous experimental results from monotonic quasi-static tests, this paper presents a numerical study about the flexural behaviour of glass beams reinforced with glass fibre reinforced polymer (GFRP) laminates bonded with two different adhesives: polyurethane and epoxy. The main objective of this study is to evaluate the efficiency of different constitutive models to simulate the non-linear behaviour of glass, considering the following factors: initial stiffness, cracking load, post-cracking stiffness, crack pattern and progressive failure. The glass is simulated using smeared crack (SCM) and damaged plasticity (DPM) models with static and dynamic numerical approaches. Particular attention is paid to the influence of the several parameters that influence the structural behaviour of glass (e.g. threshold angle), as well as to the interfaces between all the materials involved (e.g. thickness of the adhesive layer). In relation to static numerical approaches, dynamic numerical approaches require more computational effort and their dynamic effects may influence the structural responses obtained; however, they also show to be able to capture all the stages of cracking in greater detail, because stability during cracking formation is guaranteed even at smaller loading stages. Since DPM models do not allow considering a maximum absolute damage factor of 1.0, the smeared crack models simulate better the non-linear behaviour of glass.

On the mechanical behavior of hybrid fiber reinforced strain hardening cementitious composites subjected to monotonic and cyclic loading

This article presents the results of an experimental investigation on the mechanical behavior of hybrid fiber reinforced Strain Hardening Cementitious Composites (SHCC) subjected to monotonic and cyclic loadings. For the study, PVA, ultra-high molecular weight polyethylene (UHMWPE) and steel fibers were used in a constant volume fraction of 2.0%. To study the synergetic effects between the fibers, hybrid compositions were also produced by replacing PVA and polyethylene by steel fibers in 0.5% and 1.0% volume fractions. The mechanical response was measured under direct tension tests, four-point bending tests on plates and three-point bending tests on notched specimens while the crack pattern was investigated using optical microscopy. To study the mechanical performance of the materials when subjected to loading/unloading cycles, cyclic three-point bending tests were also carried on. The partial replacement of PVA and polyethylene fibers by steel fibers increased the strength and post-cracking stiffness but reduced the ductility of the composites. The hybrid SHCCs presented a good mechanical performance when subjected to cyclic loadings, since the load bearing capacity and the multiple cracking behavior were maintained even for high crack opening values. The stiffness degradation and the dissipated energy over the loading/unloading cycles varied when different fibers combinations were used.

Steel fibers for replacing minimum reinforcement in beams under torsion

This paper concerns an investigation on six large-scale Steel Fiber Reinforced Concrete (SFRC) beams tested in pure torsion. All beams had longitudinal rebars to facilitate the well-known space truss resisting mechanism. However, in order to promote economic use of the material, the transverse reinforcement (i.e. stirrups/links) was varied in the six large scale beams. The latter contained either no stirrups, or the minimum amount of transverse reinforcement (according to Eurocode 2), or hooked-end steel fibers (25 or 50 kg/m3). Material characterization were also carried out to determine the performance parameters of SFRC. The results of this study show that SFRC with a post-cracking performance class greater than 2c (according to Model Code 2010) is able to completely substitute the minimum reinforcement required for resisting torsion. In fact, the addition of steel fibers contributes to significantly increase the maximum resisting torque and maximum twist when compared to the same specimen without fibers. Moreover, SFRC provides a rather high post-cracking stiffness and a steadier development of the cracking process as compared to classical RC elements. This phenomenon improves beam behavior at serviceability limit state. The experimental results are critically discussed and compared to available analytical models as well as with other tests available into the literature.

Static and fatigue flexural performance of ultra-high performance fiber reinforced concrete slabs

This paper investigates the static and fatigue flexural performance of ultra-high performance fiber reinforced concrete (UHPFRC) decks on the basis of a 500 m cable-stayed bridge, namely, the Malukou Bridge. A series of numerical studies was conducted on the bridge to reveal the stress level in the deck under service loads, and then two kinds of steel bar reinforced UHPFRC decks with different steel fibers (i.e., hooked-end and straight steel fibers) were fabricated and tested to verify the design safety. Compared with traditional 280 mm-thick ordinary concrete decks, due to the high tensile strength (over 10 MPa) of the UHPFRC in this study, the deck thickness could be reduced to 170 mm with a maximum calculated tensile stress in the deck of 8.82 MPa induced by local wheel loads. Subsequently, the weight of the deck could be reduced by 35% due to the significant reduction in the deck thickness, leading to a smaller compressive stress (13.3 MPa) in the deck under service loads. In addition, in contrast to straight steel fibers, the use of hooked-end steel fibers could had a better advantage to increase in the crack resistance and post-cracking stiffness of the deck specimens. Due to the use of steel fibers and steel bars, cracks in the UHPFRC deck specimens propagated rather slowly under both static and fatigue loads. The deck specimens with hooked-end and straight steel fibers showed superior allowable tensile stresses of 23.2 MPa and 16.1 MPa, respectively, both satisfying the design requirement (8.82 MPa) of the bridge under service loads. The fatigue life of the former deck specimen was revealed as 9 million cycles under the stress range of 1.3–7.0 MPa only with a small reduction in the load carrying capacity, which greatly met the fatigue criteria of Chinese bridge design standards in terms of the crack width in UHPFRC. Based on the numerical and experimental investigations, the design safety of applying the UHPFRC deck was verified for the Malukou Bridge.

Comparative study on seismic vulnerability of RC bridge piers reinforced with normal and high-strength steel bars

Use of high-strength steel bars (HSSB) in RC bridge piers reduces the amount of reinforcement or enhances bearing capacity of RC piers. However, the use of HSSB could come with reduction in the energy dissipation of RC member, which used to be considered detrimental to the seismic performance of RC bridge piers. This paper revaluates the effects of HSSB on seismic performance of RC piers by comparing that with normal steel bars (NSB) through fragility analysis. Maximum drift ratio (MDR) and maximum section curvature (φm) are considered as engineering demand parameters (EDPs) to represent the deformation demands and section damage of RC piers, respectively. A fiber-based finite element model (FEM), calibrated by a set of shaking table tests of RC portal frames reinforced with NSB and HSSB, is adopted to simulate the nonlinear dynamic response of RC piers. Fragility curves using probabilistic seismic demand model (PSDM) are developed to compare the relative vulnerability of RC bridge piers reinforced with steel of different yield strengths. The analysis results indicate that, when using HSSB to replace NSB by equal volume replacement, the RC piers have similar deformation demands (MDR) but significantly less section damage. On the other hand, when using HSSB to replace NSB by equal strength replacement, the deformation demands (MDR) of RC piers slightly increase (about 5%) due to the decrease of post-cracking stiffness under small reinforcement ratio. In spite of slight increase of deformation demands, the use of HSSB by equal strength replacement still reduces RC piers’ section damage since the use of HSSB enhances the elastic deformation and then reduces the plastic deformation of RC piers. Moreover, as elastic deformation accounts for a higher proportion of total deformation for taller piers, the reduction amplitudes of section damage are more evident when using HSSB in taller piers. On the whole, the application of HSSB to replace NSB is more likely to be beneficial to the seismic performance of RC piers.

Influence of fibre volume on the structural behaviour of ultra-high-performance fibrous concrete

Compression, flexural and tensile behaviour of ultra high performance fibre reinforced concrete (UHPFRC) has been experimentally studied in the present research to investigate the influence of fibre volume on its structural behaviour. UHPFRC mix corresponding to M0-M6 with fibre volume fraction from 0-10% were cast and tested under different loading conditions. It has been demonstrated that due to an increase in fibre volume content, the mechanical properties like compressive, tensile, flexural strengths, load-carrying capacity, and post-cracking stiffness were increased significantly, whereas first crack load was decreased marginally. Ductility-associated parameters like ductility, ductility index, toughness, and toughness index were also enhanced tremendously after the addition of micro steel hybrid fibres corresponding to 8% by volume. Therefore, it has been concluded that an optimum fibre content corresponding to 8% by volume is found at which corresponding strength characteristics and ductility associated properties are maximum.

Effect of reinforcement ratio, fiber orientation, and fiber chemical treatment on the direct tension behavior of rebar-reinforced UHPC

The direct tension performance of rebar-reinforced ultra-high performance concrete (UHPC) was investigated in this paper. Nine series of dog-bone specimens were tested under the direct tension load at both material and component levels. The experimental variables include the reinforcement ratio, fiber orientation, and fiber chemical treatment. The experiments showed that the rebar-reinforced UHPC members exhibited the tensile failure with the rupture of steel rebars. Meanwhile, a single and localized main crack was observed, accompanied by closely spaced short and small micro-cracks. It is concluded that the addition of longitudinal reinforcement can effectively improve the post-cracking stiffness, the ability to restrain the crack width and the peak load of UHPC members under direct tension load, whereas indicated little influence on the elastic linear behavior and their first cracking load. Moreover, increasing the reinforcement ratio not only has these effects but also can significantly enhance the yield load and ultimate load. Nevertheless, increasing the reinforcement ratio has little effect on the pre-cracking stiffness and the first cracking load. In addition, the employment of parallel fiber orientation can significantly increase the post-cracking stiffness, first cracking load, yield load and peak load, and can significantly restrain the propagation of the crack width, as well as improve the tension stiffening response of UHPC. However, this method has little effect on the pre-cracking stiffness and the ultimate load. Besides, the fiber chemical treatment with ZnPh had no noticeable effect on the direct tension behavior of rebar-reinforced UHPC specimens. Finally, a formula was set up to calculate the tensile loading capacity of UHPC members and the prediction agreed well with the test results in the present and previous studies.

Shear Behavior of Corroded Post-Tensioned Prestressed Concrete Beams with Full/Insufficient Grouting

This paper experimentally studied the shear behavior of corroded post-tensioned prestressed concrete beams with full grouting. The effects of insufficient grouting in shear span on the shear behavior were also investigated. Eight beams were fabricated and divided into two groups: four beams with full grouting and four beams with insufficient grouting. Three beams in each group were subjected to accelerated corrosion. All beams were tested to failure in four-point loading. Experimental data on shear cracking, load-deflection response, shear strength and failure modes were presented. Results showed that strand corrosion accelerated the formation and propagation of diagonal crack. Insufficient grouting decreased the number of diagonal cracks. Strand corrosion degraded the post-cracking stiffness and shear strength. Insufficient grouting aggravated the propagation of diagonal crack and the degradation of post-cracking stiffness. The shear strength of corroded beam with 31.7% corrosion loss decreased by 15.44% as compared to that of the uncorroded beam. Strand corrosion loss less than 31.7% did not change the shear compression failure mode in fully grouted beams. The failure modes of locally ungrouted beams changed from shear compression failure to rupture of wires as the corrosion loss exceeded 39.6%.

Failure-mode analysis of macro-synthetic and hybrid fibre-reinforced concrete beams with GFRP bars using acoustic emission technique

Replacement of steel rebars with fibre-reinforced polymer (FRP) bars in concrete members has become prominent in recent years to avoid the corrosion issues. To improve the shear behaviour of glass FRP (GFRP) bars reinforced concrete (RC), macro-synthetic polyolefin (PO) fibres and a hybrid combination of PO with steel fibres are added. The influence of these fibres on the failure mode of GFRP beams are studied by applying acoustic emission (AE) technique. Seven full-scale GFRP-RC beams are cast by varying fibre dosages of 0.35%, 0.70% and 1.0% by the volume of concrete and tested under three-point bending with the shear span to effective depth ratio (a/d) of 2.2. Experimental results reveal that the addition of fibres increases the post-cracking stiffness, peak load and ductility, compared to the control beam. The increase in AE events, average RA values and shear-to-tensile crack-ratios indicate the effects of fibres on improving the shear capacity and ductility of the beams. The failure zones localised by AE events correlate well with crack patterns observed in the experiments. In particular, cracks (AE sources) distribute close to the loading point in the control specimen. The crack angle increases with the increase in fibre dosage, indicating the change in failure modes. With the addition of moderate and high fibre dosages, the failure mode is converted from shear to flexure-shear and flexure respectively, thereby producing more tensile fracture modes.

Flexure Performance of Externally Bonded CFRP Plates-Strengthened Reinforced Concrete Members

This paper investigates the flexural behavior of CFRP plate-strengthened concrete structures. Specimens of the CFRP plate-reinforced beam were designed and tested by the four-point flexural test. The load-deflection relationship, failure modes, and crack propagation were analyzed. The results showed that the postcracking stiffness and bearing capacity of the test beams can be improved by the additional anchoring measures for CFRP strengthening. The relationship between flexural moment and curvature was analyzed by introducing a MATLAB program. The calculation model between curvature, flexural moment, and stiffness was derived for the CFRP plate-strengthened structure. The recommended calculation model was applied in the analysis of deflection, and the theoretical values were compared with the test results.

Flexural strengthening of reinforced concrete beams using hybrid near-surface embedded/externally bonded fabric-reinforced cementitious matrix

The efficacy of hybrid near-surface embedded/externally bonded (NSE/EB) fabric-reinforced cementitious matrix (FRCM) for flexural strengthening of reinforced concrete (RC) beams was assessed experimentally. Bending tests were conducted on eight RC beams: 6 strengthened and two reference beams. The test parameters were (a) the internal tensile reinforcement ratio and (b) the FRCM fabric type (glass, polyparaphenylene benzobisoxazole (PBO), and carbon). The experimental results revealed that the hybrid NSE/EB-FRCM could effectively be used for the flexural strengthening of RC beams based on the test parameters. The strengthened beams exhibited an enhanced flexural behavior as evidenced by their increased load-carrying capacity (Pu) that ranged between 24.7% and 109%. The maximum enhancement in the load-carrying capacity was measured in carbon FRCM strengthened beams owing to the higher axial stiffness of carbon FRCM relative to PBO and glass FRCM. The strengthening efficacy of the FRCM was increased with an increase in the FRCM axial stiffness. An increase in the internal tensile reinforcement ratio showed an adverse effect on the gain in Pu. The stiffness factor (βf) was used to study the combined effect of the test parameters. An almost linear relationship was observed between the increase in Pu and βf with a good coefficient of correlation of 97%. Moreover, the strengthening system has increased the post-crack stiffness of the beam with an average increase of 52%. Finally, the prediction of the ACI 549 provisions was examined and compared with the experimental results.

Flexural behavior of an innovative dovetail ultra-high performance concrete joint using steel wire mesh interface treatment in composite bridges

An experimental program investigating the flexural behavior of an innovative dovetail ultra-high performance concrete joint for connecting precast ultra-high performance concrete slabs in composite bridges is reported in this study. Test parameters included interface treatment method, joint material, reinforcing bar overlapping form, and prestressing level. Specifically, a new steel wire mesh interface treatment was proposed, which could generate an additional fiber-bridging mechanism in the joint surface. An enhancement of 17.4%, 20.1%, and 50% on flexural cracking strength, ultimate strength, and ductility were obtained by using the steel wire mesh. Joint material showed no significant influence, while prestressing had obvious influence on the flexural behavior of ultra-high performance concrete joints. The post-cracking behavior, ductility performance, and stiffness degradation of the tested specimens were analyzed. Good deformability was obtained for the jointed ultra-high performance concrete slabs as the ratio of deflection to span was about 1/50 at failure. The post-cracking stiffness was retained at about 90% of the initial stiffness, while the ultimate stiffness was retained at about 10% of the initial stiffness. The research findings are useful in popularizing and applying the proposed innovative dovetail ultra-high performance concrete joints in composite bridges.

Behavior of lightly reinforced fiber reinforced concrete panels under pure shear loading

The load-deformation response of Fiber Reinforced Concrete (FRC) elements subjected to pure shear is still matter of strong debate within the scientific community. In this paper, the tests on six fiber reinforced concrete panels under pure shear are presented and discussed. The tests were conducted under displacement control and a peculiar loading frame was designed to ensure that a pure shear state of stress was established. Steel fibers were added in relatively low amounts (20 and 50 kg/m3), and two steel reinforcements (0.21% and 0.74%) were selected, aiming at simulating lightly reinforced elements. A critical discussion on the influence of fibers on both global and local behavior (tension stiffening, cracking formation and propagation, post-cracking stiffness and residual strength) is presented. Finally, a novel crack spacing formulation, extended to FRC, is proposed and compared against available experimental data.

Behavior of fiber reinforced concrete members under sustained axial/flexural load

AbstractThe inclusion of steel or polypropylene fibers in the concrete mix can substantially improve the serviceability characteristics of reinforced concrete members. For fiber reinforced concrete (FRC) members, the fibers enhance the postcracking stiffness, thereby reducing the short‐term and long‐term deflections, and very significantly reducing the width of cracks and the spacing between them. Relatively little experimental and analytical research has been undertaken on the effects of creep and shrinkage on the long‐term performance of FRC structural members after cracking. Failure to account for creep and shrinkage of the concrete and creep of the fibers can lead to a serious under‐estimation of the extent and severity of cracking, as well as long‐term curvatures and deformations. This paper describes a method of analysis and the material modeling required to determine the time‐dependent behavior of cracked, steel or macro‐synthetic FRC members containing conventional bar reinforcement and subjected to a sustained bending moment and/or axial force. The model is versatile in that it can handle a range of inputs (fiber type, specimen geometry, loading conditions, etc.) and is simple enough for routine use. The model is validated against available test data and is shown to produce satisfactory correlations.

Experimental Tests on Fiber-Reinforced Alkali-Activated Concrete Beams Under Flexure: Some Considerations on the Behavior at Ultimate and Serviceability Conditions.

Alkali-activated concrete (AAC) is an alternative concrete typology whose innovative feature, compared to ordinary concrete, is represented by the use of fly ash as a total replacement of Portland cement. Fly ash combined with an alkaline solution and cured at high temperature reacts to form a geopolymeric binder. The growing interest in using AACs for structural applications comes from the need of reducing the global demand of Portland cement, whose production is responsible for about 9% of global anthropogenic CO2 emissions. Some research studies carried out in the last few years have proved the ability of AAC to replace ordinary Portland cement concrete in different structural applications including the construction of beams and panels. On the contrary, few experimental results concerning the structural effectiveness of fiber-reinforced AAC are currently available. The present paper presents the results of an experimental program carried out to investigate the flexural behavior of full-scale AAC beams reinforced with conventional steel rebars, in combination with fibers uniformly spread within the concrete matrix. The experimental study included two beams containing 25 kg/m3 (0.3% in volume) of high-strength steel fibers and two beams reinforced with 3 kg/m3 (0.3% in volume) of synthetic fibers. A reference beam not containing fibers was also tested. The discussion of the experimental results focuses on some aspects significant for the structural behavior at ultimate limit states (ULS) and serviceability limit states (SLS). The discussion includes considerations on the flexural capacity and ductility of the test specimens. About the behavior at the SLS, the influence of fiber addition on the tension stiffening mechanism is discussed, together with the evolution of post-cracking stiffness and of the mean crack spacing. The latter is compared with the analytical predictions provided by different formulations developed over the past 40 years and adopted by European standards.