Stress-Strain Behavior of Steel Fiber-Reinforced Concrete Cylinders Spirally Confined with Steel Bars

,e compressive strength of concrete according to certain codes can be based on the compressive strength of unconfined plain standard concrete cylinders tests at the age of 28 days. In this paper, the standard concrete cylinders were spirally confined with steel bars and with/without hooked-end steel fibers.,e influence of the use of hooked-end steel fiber in spirally confined concrete with various pitches was investigated. It can be seen that the use of hooked-end steel fiber contributes significantly in improving both compressive strength and ductility of concrete. ,e compressive strength and ductility of steel fibered concrete also increase with the reduction of the spiral’s pitch.


Introduction
It has been widely reported from the results of several researches that the effects of confinement in concrete can increase its axial compressive strength and ductility.is is due to the presence of the lateral compressive force provided by the confining steel in concrete.In addition, the lateral stress acting on the concrete also increases the ductility of concrete.e lateral expansion of concrete core is confined by the lateral pressure produced by the lateral confinement steel such that the slope of the descending postpeak branch of the stress-strain curve of confined concrete decreases with the increase of confinement degree.e use of confinement in concrete core is intended to increase ductility.e resistance generated by the transverse reinforcement is influenced by, among others, the percentage of transverse reinforcement, the strength of transverse reinforcement, the compressive strength of concrete, the spacing of transverse reinforcement, and the configuration of transverse reinforcement in concrete.
ese proposed stress-strain relationships can be used further by an engineer for designing the concrete members.Both the use of confinement and steel fiber might increase the ductility of concrete.To further improve the ductility of concrete, the simultaneous effect of combined lateral confining steel and steel fibers needs to be investigated to observe its actual compressive stress-strain behavior [11][12][13][14][15][16][17][18].
Confinement in concrete can be in the forms of rectilinear or square hoops/stirrups or spiral.By laterally confining the concrete core with rectilinear or square hoops/stirrups or spiral, the increases in terms of compressive strength and ductility of concrete can be expected.e confinement serves to reduce the lateral expansion of concrete core and delay the crushing of concrete, thus further affecting the compressive strength and ductility of concrete.Spiral provides better continuous confining pressure on concrete core, whereas the rectilinear or square hoops/stirrups provides effective confining effect at the corners since the four sides of the hoops/stirrups tend to bend outwards.Although, it is not as good as the spiral in providing effective confining effect on concrete core, the rectilinear or square hoops/stirrups can still improve the compressive strength and ductility of concrete core significantly.
us, this type of confinement is still adopted to be used for rectangular or square concrete cross sections to provide confinement to concrete core and thus improve its ductility.
Ou et al. [17] have observed the compressive behavior of SFRC with reinforcing index (RI) up to 1.7.When RI is greater than 1.7, the compressive strength of steel fiberreinforced concrete (SFRC) starts to degrade.Ou et al. [17] concluded that the addition of steel fiber in concrete improves the compressive strain and peak stress of SFRC significantly.However, the increase was only up to volume of fiber in concrete (V f ) of 2 percent.
Liu [18] showed that the use of hooked-end steel fiber with the dimensions of 35 × 0.55 mm in concrete can control better its compressive failure (better performance/ductility).However, Oliveira Júnior et al. [15] indicated that the compressive strength of unconfined concrete with hookedend steel fiber is comparable with that of the unconfined concrete without steel fiber.ey also found that the addition of steel fiber in concrete does not increase its compressive strength [15].e slightest descending slope and the longest ultimate strain of SFRC were found at V f equal to 2 percent.
Several proposed models [11,13,16,17] related to the use of steel fiber in concrete are given as follows: Ezeldin and Balaguru [11]: ( Nataraja et al. [13]: Ou et al. [17]: Soroushian and Lee [16]: where f cf ′ is the compressive peak strength of SFRC, f c ′ is the compressive peak strength of non-SFRC, RI is the reinforcement index by fiber weight, ε pf is the strain corresponding to the peak stress of SFRC, ε co is the strain corresponding to the peak stress of non-SFRC, W f is the fiber weight, L f is the fiber length, D f is the fiber diameter, I f is the fiber reinforcement index, and V f is the fiber volume.
All the above studies have not explored the use of combined spiral as confinement and steel fiber in concrete.
is study focuses on the compressive behavior of concrete considering the contribution of both spiral and steel fiber.Based on Oliveira Júnior et al. [15], Ou et al. [17], and Liu [18], the study investigated further on the effect of combined spiral confinement and steel fiber on the compressive behavior of concrete.ere are two main findings of the study.First, the compressive strength of concrete with and without steel fiber is similar, that is, 23.0981 and 23.2634 MPa, respectively.
is confirms the study by Oliveira Júnior et al. [15].Second, the combination of spiral and steel fiber improves both the compressive strength and the strain (strain at peak strength and ultimate strain) significantly.

Material and Mix Design.
e designed compressive strength of normal-weight concrete (f c ′ ) was 22.5 MPa.Both the coarse and fine aggregates used for concrete satisfied the standard mix design requirements.e concrete was made in the hot weather condition, and thus, it required the addition of retarder to delay the setting time during the casting and compaction.Steel fiber was also added in some of the concrete mixture to study its effect on concrete properties compared to those without steel fiber.Superplasticizer was also used to improve its workability.e physical and mechanical properties of steel fiber used in the study are shown in Figure 1. e concrete mixture proportion obtained from the mix design is listed in Table 1.According to Figure 1 and Table 1, the value of I f can be calculated as

Concrete Confinement.
Since the application and effectiveness of spiral as confinement in concrete have been widely studied and well established both analytically and experimentally, the study concentrates mainly on the use of combination of both spiral and steel fiber together to know their interaction impact on the compressive behavior of concrete.When used together, the compressive behavior of concrete is considerably influenced by the combination of confining steel bars (spiral) and steel fiber.ese two parameters were observed in the study.e size of the specimen, diameter of spiral, compressive strength of concrete, pitch of spiral, yield strength of spiral, and volumetric ratio of spiral are the parameters required to determine the value of Z m of modified Kent-Park [12] (given by ( 5)-( 8)).Several Z m values were set (discussed further in Section 2.2) to study the combined effect of spiral confinement and steel fiber in 2 Advances in Civil Engineering terms of compressive strength and ductility (represented by the ultimate compressive strain of concrete).e e ect of con nement in concrete is very important to be incorporated (con ning parameter Z m ) when analyzing its compressive behavior since it is completely di erent from that of the uncon ned concrete: where Z m is the con ning parameter of con ned concrete (modi ed Kent-Park [12]), ρ s is the volumetric ratio of spiral to the con ned concrete core measured outer to outer of spiral, h ″ is the width of con ned concrete core measured outer to outer of spiral, s h is the spacing of spiral measured center to center of spiral, K is the multiplying factor, f yh is the yield strength of spiral, A g is the gross area of concrete section, and A ch is the area of concrete core spirally con ned with steel bars [19,20] measured outer to outer of spiral.

Specimen Details.
e details and cross section of the specimens are illustrated in Figure 2. e specimens listed in Table 2 were designed based on ( 5)-(8).

Test Method
e compressive strength and shortening deformation of concrete cylinders are the main parameters observed in the study.e value of f c ′ was obtained from the compressive strength tests of the standard plain concrete cylinders (150 × 300 mm) (without steel ber) at the age of 28 days after the curing period.

Test Setup.
e test setup to perform the compressive test is shown in Figure 3. e test was carried out until the concrete specimens failed in the compressive crushing mode.e data collected during the tests were the compressive load and shortening until the failure of the specimens.
e compressive pressure was generated from the universal testing machine (UTM) with a maximum capacity of 100 tons, and the load was read by the load cell (maximum capacity of 100 tons).For measuring the shortening displacements, a pair of LVDTs was installed at the two opposite sides of the specimen to average the values.All the measurements were transferred to the data logger or universal recorder (UR), and the data were recorded and displayed in the computer.

Test Procedure.
e experimental tests were conducted in the laboratory.First, the course and ne aggregates were evaluated for their compliances with the ASTM standards for normal-strength concrete.e cement used was OPC.
en, the mix design can be calculated and mixed in the laboratory including the curing process until 28 days.e loading type applied to the concrete cylinder specimens was the static monotonic compressive loading.Tensile tests were also carried out for all the steel bars used for spirals as con nement in concrete.Based on the mix design and using the selected materials as mentioned previously, the spirals that have been prepared earlier were cast to produce the concrete cylinders specimen as shown in details in Figure 2.After curing for 28 days, the molds of the specimens were removed and left to dry in the air for a few hours before they were ready for loading tests.
e compressive test was conducted until the specimens failed in a crushing manner.From the tests, all the data were collected such as loads and displacements to calculate the compressive stresses and strains of the specimens.e loading was terminated when the spiral has ruptured.3 and 4 show the compressive strength test results of the specimens with and without steel ber, respectively.Concrete with and without steel ber con rms that there is an insigni cant di erence in terms of compressive strength.In fact, all of them tend to similarly approach the target compressive strength of Advances in Civil Engineering concrete (f c ′ ) of 22.5 MPa.us, it can be concluded that the addition of steel ber did not a ect the compressive strength of concrete signi cantly [15].e test results can be seen in Tables 3 and 4.

Maximum Compressive Stress.
e maximum compressive stresses of each concrete specimen from the experimental results can be obtained from their corresponding stress-strain curves.It can be seen that the maximum compressive strengths of all specimens vary with the variation of volumetric ratio of spiral and steel ber.Based on the calculated volumetric ratios of the spiral as con nement, the values of Z m can also be obtained, namely, Z m1 28.625, Z m2 16.926, and Z m3 11.118 for specimens C F1 , C F2 , and C F3 , respectively.e compressive strengths of spirally con ned concretes without steel ber can reach up to f C WF 24.0269 MPa, while for those with steel ber can reach up to f C F1 26.0262 MPa, f C F2 29.2993 MPa, and f C F3 33.4394 MPa (Figure 4).Table 2: Details of test specimens.e failure modes indicated the combined e ect of steel ber and spiral as con nement.All the test specimens failed in their midheights as shown in Figure 5. e plain concrete cylinder specimen performed a brittle sudden failure.For spirally con ned specimens, it indicated better performance (more ductile) as the failures of the specimens can be delayed slowly in the postpeak responses.
e failures of the specimens were obtained when the steel spirals were ruptured.e specimens with steel ber failed at the compressive strains in the range of 0.0823 < ε c < 0.1031, whereas the compressive stresses were in the range of 14.826 < f c < 23.549 MPa.When compared to the uncon ned concrete without steel ber (plain concrete), its failure occurred when the strain and stress were ε c 0.018 and f c 11.818 MPa, respectively.

Ductility.
From the experimental results, it can be seen that the spirally con ned specimens with steel ber indicated very ductile failure manners.At the loading of a half of P max , they showed low degradation of sti ness.In the postpeak responses, they performed better strain ductility compared to that without steel ber.e increase in strain ductility is due to the combined e ect of spiral and steel ber [12].However, from the experimental results, it indicates that the steel ber contributes signi cantly to the tensile strength of concrete, and consequently, the strain ductility of the concrete also increases considerably.e comparison of the experimental stress-strain curves of the specimens with various con nement ratios is shown in Figure 6.

E ect of Con ning Parameter
e con ning parameter Z m [12] was adopted to consider the e ect of con nement of the specimens.e value of Z m is very crucial in the determination of con nement of the specimens.If the value of Z m is known, then the value of s h (spiral's pitch) can be found, or vice versa; if the spiral's pitch is known, then the value of Z m can be obtained.Better concrete con nement can be achieved by lowering the value of Z m .To reduce the value of Z m , ρ s can be increased.
e greater the value of ρ s , the better con ning e ect to the concrete core such that the value of Z m is lower.us, the lower the value of Z m , the better the ductility of the concrete (longer ultimate compressive strain).e study con rmed the phenomenon.With the lowest value of Z m equal to 11.118, the concrete specimen is capable of attaining an ultimate compressive strain of 0.1031 with a slightly descending slope.4.6.Proposed Model.Assuming that the compressive strength of concrete without steel ber equals to that of concrete with steel ber, Equations ( 9)- (11) were proposed in the study.e comparison of the peak stresses and the corresponding strains at peak stresses between the proposed equations and the experimental results is given in Figure 7 and Tables 5 and 6. e comparison of the strains at failures between the proposed equations and the experimental results is given in Table 7. e increases of stresses and strains are also listed in Tables 8 and 9. e proposed equations developed based on the data obtained from the experimental tests in the study are given as follows: where f cfc ′ is the compressive strength of spirally confined SFRC, f cc ′ is the compressive strength of spirally confined non-SFRC, ε pfc is the strain corresponding to the peak stress of spirally confined SFRC, ε cc is the strain corresponding to the peak stress of spirally confined non-SFRC � 0.0035, ε ffc is the strain at failure of spirally confined SFRC, and ε pfc is the strain corresponding to the peak stress of spirally confined SFRC.e proposed equations ( 9)-( 11) can be used for predicting the compressive behavior of SFRC (2 percent) spirally confined with various volumetric ratio of steel bars.

Conclusions
Based on the discussion above, it can be concluded that due to the use of combination of steel ber and spiral as con nement in concrete, both the stress and the strain of concrete increases, and thus, it becomes more ductile.e peak stress of the concrete can increase up to 39.17 percent, while the strain value can increase up to 657.14 percent (when it is compared to the ultimate strain of plain or uncon ned concrete which is considered about 0.0035).e uncon ned concrete behavior performed signi cantly di erent behavior with the con ned concrete where the con ned concrete indicated much more ductile behavior than the uncon ned concrete.In the study, the peak stress and the corresponding strain at peak stress can be well predicted with the proposed equations particularly for the spirally con ned concrete with steel ber.e proposed equations include parameter Z m to consider the combined e ect of spiral and steel ber.

Figure 2 :
Figure 2: Details of spiral and specimens: (a) details of spiral, (b) dimensions of spirally con ned specimens, and (c) cross section of specimens.
Note.C WF is the spirally con ned concrete cylinder without steel ber, C Fn is the spirally con ned concrete cylinder with steel ber, D is the cylinder diameter, and L is the cylinder height.

Figure 3 :
Figure 3: Schematic of test setup.UR universal recorder; LVDT linear variable displacement transducer.

Figure 5 :
Figure 5: Failure modes of all specimens after completion of the tests: (a) specimen C WF , (b) specimen C F1 , (c) specimen C F2 , and (d) specimen C F3 .

Figure 6 :Figure 7 :
Figure 6: Comparison of experimental stress-strain curves of the specimen with various con nement ratios.

Table 1 :
Concrete mixture proportion from mix design.

Table 3 :
Uncon ned concrete specimens without steel ber.

Table 4 :
Uncon ned concrete specimens with steel ber.

Table 5 :
Comparison of peak stresses between the proposed and experimental results.

Table 6 :
Comparison of strains at peak stresses between the proposed and experimental results.

Table 7 :
Comparison of strains at failures between the proposed and experimental results.

Table 8 :
Increase of peak stresses.

Table 9 :
Increase of strains at peak stresses.