Tension stiffening of steel-fiber-reinforced concrete

In this paper, the mechanical behavior of steel-fiber-reinforced concrete was investigated to analyze the influence of steel fibers on tension stiffening. Using tension tests, the tension stiffening coefficient was evaluated through the load versus strain responses obtained from strain gages fixed to reinforcement steels. Moreover, an empirical model is proposed to estimate the tension stiffening coefficient of steel-fiber-reinforced concrete from reinforcement strains. From the test results, it was verified that the addition of steel fibers to concrete reduced the reinforcement steel strains and the crack width and increased the stiffness of cracked concrete, mainly in concretes reinforced with high volumes of fibers.


Introduction
Tension stiffening reflects the ability of concrete to carry tension between cracks, which increases the rigidity of a reinforced concrete member before the reinforcement yields.This effect is primarily due to the mobilization of bonds at the steel-concrete interface.The tension stiffening is affected by the reinforcement ratio, the distribution and diameter of reinforcement bars, the concrete shrinkage, and the brittleness of the matrix.There are several empirical relationships to evaluate tension stiffening (Fields & Bischoff, 2004).For all relationships, the decrease of stiffness in a cracked member can be taken into account using a modified relationship for the loadstrain response of the reinforcement steel (Figure 1a), using an average stress-strain response for concrete in the post-cracking range (Figure 1b), or both (Belarbi & Hsu, 1994).There are also some analytical models based on the bond-slip between concrete and reinforcement steel (Floegl & Mang, 1982;Gupta & Maestrini, 1990;Wu, Yoshikawa, & Tanabe, 1991;Choi & Cheung, 1996).
Figure 1a shows a typical load-strain response of a tension specimen and of a bare steel bar.In this figure, the contribution of concrete to the tension response is given by the difference between the strains in the tension specimen and the bare steel bar.The tension specimen response is initially linearly elastic with uniform stresses in the concrete and steel along the length of the member until the tensile strength of the concrete is reached.In Figure 1b, after the first crack (C 1 ), the average tensile stress in the concrete decreases with increasing strain, which reduces the tension stiffening as the load increases (Fields & Bischoff, 2004).New cracks (C 2 , C 3 , and C 4 ) arise as the load increases, further reducing the distance between them until this distance is more than twice the anchorage length.At the end of the cracking stage, the cracking becomes stable and no new cracks will form.During the stabilized cracking stage, the crack widths increase while the tensile stress and the tension stiffening decrease.However, the tension stiffening decreases more slowly due to the loss of bonding, which is due to internal micro-cracking near the interface between the steel and concrete (Fields & Bischoff, 2004).When the reinforcement steel yields, the transfer of tensile stresses at the steel-concrete interface is damaged, which makes it difficult to transfer loads after the yielding load of the reinforcement steel is reached.Concrete shrinkage negatively influences the tension stiffening once it causes an initial shortening of the member, which induces compressive stress in the reinforcement steel.To maintain equilibrium, the reinforcement steel induces tensile stress in the concrete, which reduces the cracking load (Lorrain, Maurel, & Seffo, 1998;Bischoff, 2001).In addition, high-strength concretes present larger shrinkage, and larger reductions of tension stiffening are expected when shrinkage is ignored.
In fiber-reinforced concrete, fibers improve the mechanical properties of the matrix due to the bridge effect through the cracks after cracking of the matrix.Furthermore, fibers improve the tenacity and ductility of the matrix by controlling the cracking process and increasing the tensile and bond strengths between the steel and concrete.The improvement of the bond strength and the ability to transfer tensile stress through the cracks should increase the tension stiffening of fiber-reinforced concrete (Abrishami & Mitchell, 1997;Yang, Walraven, & Den Uijl, 2009;Deluce & Vecchio, 2013;Lee, Cho, & Vecchio, 2013).Fibers also control splitting cracks and cracking caused by shrinkage.Fibers with a high modulus of elasticity are more efficient in limiting the shrinkage of the matrix because of the greater difference between the modulus of elasticity of the fiber and that of the matrix (Zhang & Li, 2001).
This paper aims to show the influence of steel fibers on the tension stiffening effect and proposes an empiric model for predicting the tension stiffening coefficient from the fiber content.In addition, this paper shows that the partial substitution of cement for less reactive materials, such as fly ash, is a possible strategy to reduce the consumption of cement because no changes in the tension stiffening of concrete due to mineral additions were observed.

Material and methods
Twenty-six tension tests of plain and steel-fiberreinforced concrete (SFRC), with and without mineral additions (silica fume and fly ash), were performed.One tension specimen was produced for plain concretes with and without mineral additions, but two were produced for the fiber-reinforced concrete.The variables analyzed were the fiber aspect ratio and fiber content.The specimens were stored in a humid chamber in which the temperature was kept at approximately 23ºC and the humidity was approximately 95%.Thus, there was no need to determine concrete shrinkage because the specimens were removed from the humid chamber only 12 hours before the tests.

Materials
In the production of the concretes, the following materials were used: blast furnace slag length, test setup, and measuring and evaluation techniques were used in both cases.The strain of the bare bar was measured by three electrical strain gages fixed to the same position of the tension specimens.
Testing procedure The tension tests were carried out under displacement control in an electrical-mechanical universal testing machine with a capacity of 300 kN (see Figure 3).The rate of the displacements used during all tests was 0.3 mm min -1 .The reinforcement steel strains were measured by three strain gages spaced 102 mm apart.The first strain gage was placed at 92 mm from the superior end of a concrete prism of 800 mm.The steel strains were measured at each 5 kN load increment.

Concrete properties
The mechanical properties of concretes without mineral additions are given in Table 3 and concretes with mineral additions are given in Table 4.
These tables show that the mechanical properties of the SFRC were positively affected by the presence of fibers.The compressive strength (f cm ) had a maximum increase of 28%.The flexure (f ctm,f ) and splitting (f ctm ) tensile strengths were also affected by fibers, and these properties increased as the fiber content increased.The same is true for the toughness factor.By comparing the results in Tables 3 and 4, it can also be observed that the mechanical properties of the SFRC were reduced by the 30% replacement of the cement by fly ash.

Crack width
The crack patterns in tension specimens were observed during tension tests.The plain concrete specimens showed a small number of transverse cracks.With the addition of steel fibers, multiple cracks were observed, which demonstrated that the best control of the cracking process was provided by the fibers.
Figure 4 shows how the average main crack width (w m ) varied as the load increased.The values presented in these figures refer to the mean of measurements carried out at several points of the crack (mainly in corners), which means that the crack width was not uniform along its path.The same figure shows the maximum limit of cracking recommended by the American Concrete Institute (ACI, 2005) for concretes without fibers, which in this case was 0.329 mm.A significant reduction in the crack width due to the addition of fibers was observed, and this reduction increased as the amount of fiber increased.In some cases, this reduction reached 75% compared to the crack width in the tension specimen made of plain concrete.Comparing the crack width to the maximum limit prescribed by the ACI 224R, it was noted that in tension specimens made of SFRC this limit was reached reinforc    o estimate the te C on stiffening c del based on d using the nd the reinforc lying the fiber nt ( f V ).For an parameters an s and Bischoff nsion stiffenin ained from th y distinction r tions because tension stiffe ons were per obtained from the linear mo ntal behavior.hould be inclu unt for the infl ffening.the correlati egression mod ment index, w h represents sion stiffening the maximum mited to 1.00. )

Figure 1 .
Figure 1.a) Typical load-strain response from a tension test and; b) reduction of the average tensile stress in concrete by tension stiffening.
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Table 3 .
Mechanical properties of concretes without mineral additions.

Table 4 .
Mechanical properties of concretes with mineral additions.