ai`2bb@bi` BM 2H iBQMb?BT 7Q` ai22H 6B#2`@`2BM7Q`+2/ GB;?i ... · AM Q`/2` iQ /2i2`KBM2 i?2 BKT +i Q7 bi22H }#2` QM i?2 bi`2bb@bi` BM +m`p2 M/ i?2 #2? pBQ` Q7 Gq *- M 2t@ T2`BK2Mi

Journal of Stress AnalysisVol. 4, No. 1, Spring − Summer 2019

Stress-strain Relationship for Steel Fiber-reinforced Light-weight Aggregate Concrete under Uniaxial Compression

H. Dabbagh∗, K. AmoorezaeiDepartment of Civil Engineering, University of Kurdistan, Sanandaj, Iran.

Article info

Article history:Received 14 February 2019Received in revised form19 June 2019Accepted 11 September 2019

Keywords:Lightweight concreteSteel fiberCompressive behaviorStress-strain model

Abstract

The current study presents a series of tests on steel fiber-reinforced lightweightaggregate concrete (SFRLWAC) cylinders in order to develop a stress-strainmodel for SFRLWAC subjected to compressive monotonic loading. In thisexperiment, steel fiber ratios of 0, 0.5, 1, and 1.5 percent by volume ofthe sample were used in the mixtures. The findings show that addingsteel fiber to the lightweight concrete has a slight impact on the ascendingbranch of the stress-strain curve; however, it has a noticeable influenceon the descending branch. The peak stress, strain at peak stress, andmodulus of elasticity were investigated. To this end, some equationswere established. To predict the complete SFRLWAC stress-strain curve,a stress-strain model was introduced and the validity of the model wasexplored. There was a good agreement between the proposed model dataand experimental findings. Using ABAQUS software, numerical simulationof the SFRLWAC beams subjected to monotonic loading was conducted;the simulated results had an acceptable agreement with the experimental data.

1. Introduction

Compared with normal-weight concrete, lightweightconcrete has lower density. Different kinds oflightweight concrete based on the production type, in-cluding using porous lightweight aggregate, introduc-ing the large voids within the mortar or concrete, andexcluding the fine aggregate from the mixture, are de-fined. Moreover, given the application objective, it isdivided into structural lightweight concrete, masonry-unit concrete, and insulating concrete [1]. This studyalso delves into structural lightweight aggregate con-crete (LWAC). According to ACI 318, the compressivestrength of cylinders in a 28-day time interval must beover 17MPa, and the maximum point for density mustbe 1840kg/m3 for LWAC [2].

Adequate thermal insulation, appropriate durabil-ity, dead-load decline, and preferable fire resistance,

are instances of LWAC advantages [3, 4]. Hence,thanks to its suitable characteristics, LWAC was em-ployed for structural purposes [5-8]. However, factorsincluding brittleness and low strength, limit the ex-tensive structural application of LWAC [9-11]. On theother hand, adding steel fibers, as a ductile material,enhances many characteristics of concrete such as flex-ural and tensile strength and toughness [12-16].

The impact of steel fiber on the characteristics ofconcrete will be controlled by the fiber material, fiberaspect ratio (ld), and fiber content (Vf ) [17]. The im-pact of Vf and ld on the workability and mechanicalproperties of concrete has been reported in the litera-ture [18-21].

In addition, steel fiber is capable to alter the struc-tural performance of LWAC. In order to model andstimulate the reaction of a structure under various con-ditions, statistical data of the material behavior should

∗Corresponding author: H. Dabbagh (Assistant Professor)E-mail address: [email protected]://dx.doi.org/10.22084/jrstan.2019.18088.1077ISSN: 2588-2597

43

be available. Therefore, for an efficient prediction ofthe structural response, one must determine the im-pact of materials that are used on the behavior of con-crete members. Besides, the significance of studyingthe compressive stress-strain curve of concrete shouldnot be overlooked [22-24]. Some studies have beenconducted on the compressive behavior of steel fiber-reinforced concrete [25-28]. Despite some proposedmodels for steel fiber-reinforced concrete, none are ca-pable of precise prediction of compressive response ofsteel fiber-reinforced lightweight concrete. Therefore,proposing a new model for SFRLWAC is of major im-portance.

At the first stage of a step-by-step research, authorsinvestigated the impact of steel fiber content on thecompressive behavior of SFRLWAC [29]. In the cur-rent paper, as the second stage of the main research,the primary aim as well as the novelty of the researchis linked to proposing a stress-strain model for steelfiber-reinforced lightweight aggregate concrete.

2. Experimental Program

In order to determine the impact of steel fiber on thestress-strain curve and the behavior of LWAC, an ex-perimental plan was designed and the uniaxial com-pressive test was carried out. The exhaustive specifi-cations of the experimental plan are as follows.

2.1. Materials and Mix Proportions

In providing the specimens, the scoria aggregate (max-imum size, 12.5mm) was used as fine and coarselightweight aggregate. The fine and coarse aggregatesshowed water absorption of 16% and 12%, respectively.The used cement was ordinary Portland cement (Type

I). The aggregate grading was conducted according toASTM C330 [30].

As it is illustrated in Fig. 1, two types of steel fibersused in this study were straight hooked-end (SF1) andcrimped (SF2). Steel fibers with contributing contentof 30% crimped and 70% straight hooked-end fiber wereadded to the mix to make the optimum mix design [31].For the mixes that consisted of steel fiber, fiber con-tents of 0.5%, 1%, and 1.5% were used. Furthermore,to obtain a better practical level in terms of workabil-ity, a Polycarboxylic ether-based superplasticizer wasadded to the mixtures. Table 1 indicates further in-formation on the employed materials. To design theconcrete mix, the volumetric method, ACI 211.2 [32]was used. Table 2 presents the structure and charac-teristics of the mixtures.

Fig. 1. Steel fibers used in this study.

Table 1Material properties.

Materials Type Specific density (kg/m3)Cement Ordinary portland (Type I) 3150Fine lightweight aggregate Scoria Bulk density: 772

Apparent specific gravity: 1650Coarse lightweight aggregate Scoria Bulk density: 680

Apparent specific gravity: 1530Superplasticizer Polycarboxylic ether 1080Steel fiber (SF) Straight-hooked end steel fiber 7800

Table 2Mix proportions.

Samples C CA FA W/C SP SF(kg/m3) (kg/m3) (kg/m3) Ratio (kg/m3) (Vol %)

F00 (Ref) 460 528 584 0.31 2.4 -F05 (0.5% fiber) 460 528 584 0.31 2.5 0. 5F10 (1% fiber) 460 528 584 0.31 2.6 1.0F15 (1.5% fiber) 460 528 584 0.31 2.7 1. 5

C: Cement, CA: Coarse aggregate, FA: Fine aggregate, W: Water, SP: Super plasticizer, SF: Steel fiber

Stress-strain Relationship for Steel Fiber-reinforced Light-weight Aggregate Concrete under UniaxialCompression: 43–52 44

Fig. 2. Test setup for generating stress-strain curve.

2.2. Test Specimens, Mixing, Casting, andCuring

In the present study, four mixes were prepared thatcontained 0%, 0.5%, 1%, and 1.5% steel fiber ratios byvolume of the sample.

Initially, fine lightweight aggregate was blendedwith coarse lightweight aggregate. Then, some othermaterials, including water with superplasticizer, steelfibers, and cement were added to the mixtures. Sub-sequent to the mixing process, the mixed compositionswere cast into the molds and vibrated with shakingtable. To prevent the humidity loss, the polyethylenesheets were utilized to cover the cylinders’ surface. Af-ter 24 hours, the specimens were demolded and curedover 28 days in water at 23±2◦C. In order to achievea smooth surface for the uniformed transfer of theload, the cylindrical specimens were capped with sulfurcapping compound before testing. Three 150×300mmcylinders were tested for each mix to accomplish themonotonic stress–strain curve; the average of which isshown as the result of the test.

2.3. Test Procedure and Setup

The schematic design of the test set-up is illustrated inFig. 2. In order to discover the monotonic curves, a3000kN hydraulic compressive testing machine was em-ployed for testing the specimens. Hydraulic jacks with50mm maximum ram travel, a bottom platen, and aload spreader, formed the loading assembly. ASTMC469 [33] was used to investigate the modulus of elas-ticity whereas compressive strength was examined us-ing ASTM C39 [34]. In order to plot the stress-straincurves, the displacement was measured by two linearvariable differential transducers (LVDTs); they wereset parallel to the loading direction. Moreover, a cir-

cular steel frame was made to grip the LVDTs. Theaxial deformation of the cylinders was monitored bythe LVDTs and was captured using a data logger. Theoutput of the data logger was averaged for more accu-rate results.

In this investigation, the middle two-thirds of theheight of the cylindrical specimens were considered tocalculate the deformation of samples in order to avoidend effects. With the progress of the loading, the uni-axial load continued to be concentric to the specimens.

3. Experimental Results

Steel fiber-reinforced lightweight concrete was sub-jected to the compressive monotonic loading. Thestress-strain curve was achieved and the compressivebehavior of SFRLWAC was probed. Strain at peakstress (ε0), modulus of elasticity (E), and the compres-sive strength (fc), that are among the most importantparameters of the stress-strain curve, were all delin-eated. Applying regression analysis gave the equationsfor defining these parameters. In addition, the effectof fiber on the failure mode was also studied.

3.1. Monotonic Stress-strain Curve

According to Fig. 3, for the monotonic curve of allspecimens, the linear elastic part of the ascendingbranch extends up to approximately 80% of the peakstress. The findings indicate that steel fibers have aminor influence on the ascending part and the signifi-cant values on the monotonic curve, i.e., fc, E, and ε0have a slight increase (Table 3). However, the impacton the descending branch is considerable. MonotonicCurve of SFRLWAC was explored in details by authorsin another paper [29].

Journal of Stress Analysis/ Vol. 4, No. 1, Spring − Summer 2019 45

Fig. 3. Compressive stress-strain curve of SFRLWAC[29].

3.2. Compressive Strength

As it is illustrated in Fig. 4, the compressive strength ofSFRLWAC at various volume portions was determined.The compressive strength of SFRLWAC is associatedwith the fiber volume fraction. Applying regressionanalysis gives the following equation:

fc = 134Vf + f ′c, R2 = 0.99 (1)

where fc is compressive strength of SFRLWAC inMPa, f ′

c is compressive strength of plain lightweightconcrete in MPa, and Vf is steel fiber volume fraction.

Fig. 4. Relationship between fc and Vf .

3.3. Strain at Peak Stress

The strain at peak stress versus the respective fc, foreach specimen, is presented in Fig. 5. The resultsshow that by adding steel fiber, ε0 increases which ispresented in Table 3. By applying regression analysis,the following expression for ε0 is derived:

ε0 = 11.78× 10−5fc − 0.00058 (2)

R2 = 0.99

where ε0 is strain at peak stress in mm/mm.

Fig. 5. Relationship between ε0 and fc.

3.4. Modulus of Elasticity

For samples containing 0, 0.5, 1, and 1.5 percent steelfiber, modulus of elasticity is 12.18, 12.32, 12.48, and12.67GPa, respectively. Results show that adding steelfiber does not have a noticeable impact on the modu-lus of elasticity. In comparison with F00, E upgrades1.15%, 2.5%, and 4% for specimens containing 0.5%,1%, and 1.5% steel fiber, respectively. The trivial ef-fect of steel fiber on the enhancement of E has beenconsidered in the past research [35]. According to theexperimental findings, the following relationship for Eof SFRLWAC is established (Fig. 6).

E = 2.296√

fc, R2 = 0.97 (3)

where E is modulus of elasticity in GPa.

Fig. 6. Relationship between E and fc.

3.5. Failure Mode

The response of the cylindrical specimens at or nearthe peak load affects fc and ε0. At the peak loadlevel, cracks will be created in the cylindrical specimensin consequence of lateral expansion in LWAC. Fig. 7shows the failure mode of LWAC containing differentvolume fractions of steel fiber after testing.

Stress-strain Relationship for Steel Fiber-reinforced Light-weight Aggregate Concrete under UniaxialCompression: 43–52 46

Table 3Experimental results.

Samples No. fc (MPa) E (GPa) ε0 (mm/mm)Specimen Average Specimen Average Specimen Average

F001 28.55

28.212.28

12.180.00269

0.002742 27.88 12.11 0.002783 28.17 12.15 0.00275

F051 28.72

28.912.26 12.32 0.00286

0.002832 29.80 12.65 0.002803 28.12 12.05 0.00283

F101 29.10

29.612.35

12.480.00296

0.002902 30.55 12.83 0.002833 29.15 12.26 0.00291

F151 29.30

30.212.38 12.67 0.00302

0.002982 30.82 12.89 0.002953 30.45 12.74 0.00297

Fig. 7. Failure mode of SFRWAC.

The crack propagation in the plain lightweight con-crete is parallel to the loading direction (Fig. 7a); rais-ing the steel fiber content, the cracks bend slowly andchange perpendicularly to the loading direction (Figs.7b, c, and d). Convexity in the lateral direction withthe formation of the cracks along the outer surface andadjacent to the middle belt of cylindrical specimens isnoticeable in this type of failure. The regular failuresurface is established in plain concrete. However, thefailure surface of SFRLWAC is unstable. Steel fiberscontribute to keeping the concrete matrix together bybridging across the cracks and limiting the crack prop-agation.

4. Proposed Equation (Stress-strainModel)

To propose an expression for stress-strain curve of con-crete, the conditions, including the concordance be-tween the proposed model and experimental findings,defining both ascending and descending branches of

the monotonic curve, the simplicity of the equation,and the establishment of the model based on the phys-ically important parameters, fc, ε0, and E, should beconsidered. These parameters can be delimited by theexperimental findings [36].

A number of studies have been conducted to pro-pose a stress-strain model for concrete. Some of themost important empirical stress-strain models accessi-ble in the literature were investigated and the empiricalequation established by Popovics [22] was employed asa basis to study an equation suitable for the SFRLWACdue to its plainness and exactness. Popovics’s modelwas established for normal-weight concrete; in addi-tion, it could not indicate the influence of steel fiberon the stress-strain curve. The following can be in-troduced for the stress-strain model of the compressivestress-strain curve of SFRLWAC:

σ

fc=

β

(ε

ε0

)β − 1 +

(ε

ε0

)α

(4)

Journal of Stress Analysis/ Vol. 4, No. 1, Spring − Summer 2019 47

α = β = 6− 32(Vf )0.66, ε ≤ ε0 (5)

α = 1.6− 70Vf , ε > ε0 (6)

β = 0.6− 25Vf , ε > ε0 (7)

where σ and ε are the stress and strain values on thecurve, respectively and α and β are the material pa-rameters dependent on the stress-strain curve shape.

Based on the experimental findings, the best fit-ting statistical analysis was conducted to establish arelationship between the material parameters α and βregarding Vf .

5. Fit of the Experimental Findings andEmpirical Equation

Figs. 8 (a-d) show the stress-strain curve of SFRLWACobtained by the proposed model and the experimentaltests. Fit of the predicted curve and the experimentaltest result curve demonstrates a good agreement at dif-ferent steel fiber volume fractions. The experimentalfinding and the suggested equation for the ascendingbranch of the stress-strain curve indicate a remark-able congruity. The suggested equation displays the

insignificant influence of steel fiber on the developingE and fc of LWAC. The model explains that by addingmore steel fibers, the ascending branch of the mono-tonic curve has a slight transformation, which accordswith the experimental findings. The formed curve forthe descending part by the model shows that employ-ing steel fiber ends in drop-decrease of strength afterthe peak stress, which contributes to an adequate fitwith the test results. Thus, the established model canbe useful to predict the behavior of SFRLWAC by pro-ducing the stress-strain curve.

The uniaxial monotonic tests of Libre et al. [37]and Campione et al. [38] were considered and theexperimental findings were compared with the resultsobtained by the proposed model. Libre et al. usedpumice stone as coarse aggregate and the river sand asfine aggregate. The samples of their study contained0%, 0.5%, and 1% hooked-end steel fiber. Campioneet al. utilized pumice and river sand as coarse and fineaggregate, respectively. Furthermore, in their study,0%, 0.5%, 1%, and 2% hooked-end steel fibers wereused. Fig. 9 shows the experimental test results com-pared with the proposed model. The findings indicatea notable correspondence between laboratory test re-sults and the suggested model for the descending andascending branches of the stress-strain curve.

Fig. 8. Experimental versus proposed model result.

Stress-strain Relationship for Steel Fiber-reinforced Light-weight Aggregate Concrete under UniaxialCompression: 43–52 48

Fig. 9. Comparison between experimental results of other studies and the proposed model [37, 38].

Fig. 10. Details of beam and material properties [39].

6. Analysis of Beam

To get an initial proof of the fittingness of the pro-posed approach to the monotonic response modeling ofsteel fiber-reinforced lightweight aggregate concrete, ananalysis of beams was undertaken. The experimentaldata for lightweight concrete and steel fiber-reinforcedlightweight concrete beam subjected to the monotonicloading when the point load acts uniformly at the mid-span came from literature [39].

In this experimental program, reinforced LWACbeams of 200×150mm rectangular cross section and1200 mm overall length were fabricated. No. 8 de-formed bar and No. 6 bar were used for longitudinaland transverse reinforcements, respectively. The min-imum amount of steel bar reinforcement was consid-ered for all beam specimens (ACI 318, 2011) to ac-curately assess the effects of steel fibers used in theLWAC mixes. The value of longitudinal reinforcementratio was 0.72% for specimens.

Journal of Stress Analysis/ Vol. 4, No. 1, Spring − Summer 2019 49

Fig. 11. Finite element mesh used to model beam.

Fig. 12. Response of Beam: Experimentally measured response versus predicted response.

Two types of beams were prepared: lightweight ag-gregate concrete beam (BLC, as reference), and steelfiber-reinforced lightweight aggregate concrete beam(BLC-F, containing 1% steel fiber). Reinforcement de-tails and material properties are given in Fig. 10.

Beam BLC and BLC-F were modeled in ABAQUSusing the finite element mesh shown in Fig. 11. 8-nodecubic mesh and 2-node mesh was applied to model thebeam and bars, respectively; Wire model was used forbars. It should be noted that mesh size of all elementswas 25mm. Concrete damaged plasticity model wasemployed for the analysis of concrete materials. Be-sides, the established stress-strain model, Eqs. (4-7),was applied in ABAQUS software in order to simulatebeams.

The load-displacement data from experimental testand finite element method analysis of reference andsteel fiber-reinforced lightweight beam is illustrated inFig. 12. The comparison between the experimentalfindings and finite element analysis data in linear andnonlinear region indicates an acceptable agreement.

7. Conclusions

Based on the present experimental research, the fol-lowing conclusions can be derived:

1. Steel fiber addition has an insignificant impacton the ascending branch of the monotonic curvein LWAC; which results in a slight increase inthe compressive strength, the strain relevant to

the maximum stress, and the modulus of elastic-ity. Steel fibers have a significant impact on thedescending part of the stress-strain curve. More-over, the reduction rate in strength beyond themaximum stress drops, which is caused by theductility and energy absorption of fiber.

2. Employing data fitting process resulted in es-tablishing a relationship between the steel fibervolume fraction and the compressive strength.Moreover, after the regression analysis, what wasderived was the expressions for the strain at peakstress and modulus of elasticity regarding thecompressive strength.

3. Adding steel fibers results in changes in the direc-tion of crack propagation. For plain lightweightconcrete, the cracks propagate parallel to theloading direction. Yet, in steel fiber-reinforcedlightweight concrete, the cracks slowly incline,becoming perpendicular to the loading direction.

4. In order to predict the ascending and descend-ing branches of the stress-strain curve of steelfiber-reinforced lightweight aggregate concrete, astress-strain model was suggested. The compar-ative study shows a proper agreement betweenthe experimental test results and the proposedstress-strain curve.

5. Steel fiber-reinforced lightweight concrete beamssubjected to monotonic loading were modeled in

Stress-strain Relationship for Steel Fiber-reinforced Light-weight Aggregate Concrete under UniaxialCompression: 43–52 50

ABAQUS software. The results showed an ac-ceptable agreement between the simulated andexperimental results.

Acknowledgements

We express our gratitude to the Concrete ResearchLaboratory, University of Kurdistan, Iran, for their co-operation.

References

[1] A.M. Neville, J.J. Brooks, Concrete technology,Harlow, Essex UKf: Longman Scientific & Tech-nical, New York, John Wiley, (1987).

[2] ACI Committee, Building code requirements forstructural concrete (ACI 318-05) and commen-tary (ACI 318R-05). American Concrete Institute,(2005).

[3] C.L. Hwang, M.F. Hung, Durability design andperformance of self-consolidating lightweight con-crete, Const. Build. Mater., 19(8) (2005) 619-626.

[4] A. Bilodeau, V.K.R. Kodur, G.C. Hoff, Optimiza-tion of the type and amount of polypropylene fibresfor preventing the spalling of lightweight concretesubjected to hydrocarbon fire, Cem. Concr. Com-pos., 26(2) (2004) 163-174.

[5] K. Melby, E.A. Jordet, C. Hansvold, Long-spanbridges in Norway constructed in high-strengthLWA concrete, Eng. Struct., 18(11) (1996) 845-849.

[6] A.K. Haug, S. Fjeld, A floating concrete platformhull made of lightweight aggregate concrete, Eng.Struct., 18(11) (1996) 831-836.

[7] J.A. Rossignolo, M.V. Agnesini, J.A. Morais, Prop-erties of high-performance LWAC for precast struc-tures with Brazilian lightweight aggregates, Cem.Concr. Compos., 25(1) (2003) 77-82.

[8] E. Yasar, C.D. Atis, A. Kilic, H. Gulsen, Strengthproperties of lightweight concrete made withbasaltic pumice and fly ash, Mater. Lett., 57(15)(2003) 2267-2270.

[9] M.N. Haque, H. Al-Khaiat, O. Kayali, Strengthand durability of lightweight concrete, Cem. Concr.Compos., 26(4) (2004) 307-314.

[10] M.H. Zhang, O.E. Gjvorv, Mechanical propertiesof high-strength lightweight concrete, ACI Mater.J., 88(3) (1991) 240-247.

[11] T.P. Chang, M.M. Shieh, Fracture propertiesof lightweight concrete, Cem. Concr. Res., 26(2)(1996) 181-188.

[12] G. Campione, N. Miraglia, M. Papia, Mechani-cal properties of steel fibre reinforced lightweightconcrete with pumice stone or expanded clay ag-gregates, Mater. Struct., 34(4) (2001) 201-210.

[13] T. Uygunoğlu, Investigation of microstructure andflexural behavior of steel-fiber reinforced concrete,Mater. Struct., 41(8) (2008) 1441-1449.

[14] M. Hassanpour, P. Shafigh, H.B. Mah-mud, Lightweight aggregate concrete fiberreinforcement–a review, Const. Build. Mater.,37 (2012) 452-461.

[15] Y. Hao, H. Hao, G. Chen, Experimental inves-tigation of the behaviour of spiral steel fibre rein-forced concrete beams subjected to drop-weight im-pact loads, Mater. Struct., 49(1-2) (2016) 353-370.

[16] K.H. Mo, S.H. Goh, U.J. Alengaram, P. Visintin,M.Z. Jumaat, Mechanical, toughness, bond anddurability-related properties of lightweight concretereinforced with steel fibres, Mater. Struct., 50(1)(2017) 46.

[17] P. Suraneni, P.C.B. Anleu, R.J. Flatt, Factors af-fecting the strength of structural lightweight aggre-gate concrete with and without fibers in the 1,200-1,600kg/m3 density range, Mater. Struct., 49(1-2)(2016) 677-688.

[18] A. Bentur, S. Mindess, Fibre reinforced cementi-tious composites, CRC Press, (2014).

[19] P. Pierre, R. Pleau, M. Pigeon, Mechanical prop-erties of steel microfiber reinforced cement pastesand mortars, J. Mater. Civ. Eng., 11(4) (1999) 317-324.

[20] W. Abbass, M.I. Khan, S. Mourad, Evaluation ofmechanical properties of steel fiber reinforced con-crete with different strengths of concrete, Const.Build. Mater., 168 (2018) 556-569.

[21] J. Thomas, A. Ramaswamy, Mechanical proper-ties of steel fiber-reinforced concrete, J. Mater. Civ.Eng., 19(5) (2007) 385-392.

[22] S. Popovics, A numerical approach to the com-plete stress-strain curve of concrete, Cem. Concr.Res., 3(5) (1973) 583-599.

[23] P. Kumar, A compact analytical material modelfor unconfined concrete under uni-axial compres-sion, Mater. Struct., 37(9) (2004) 585-590.

[24] A.A. Tasnimi, Mathematical model for completestress-strain curve prediction of normal, light-weight and high-strength concretes, Mag. Concr.Res., 56(1) (2004) 23-34.

Journal of Stress Analysis/ Vol. 4, No. 1, Spring − Summer 2019 51

[25] M.C. Nataraja, N. Dhang, A.P. Gupta, Stress–strain curves for steel-fiber reinforced concrete un-der compression, Cem. Concr. Compos., 21(5-6)(1999) 383-390.

[26] J.A.O. Barros, J.A. Figueiras, Flexural behav-ior of SFRC: testing and modeling, J. Mater. Civ.Eng., 11(4) (1999) 331-339.

[27] A.S. Ezeldin, P.N. Balaguru, Normal-and high-strength fiber-reinforced concrete under compres-sion, J. Mater. Civ. Eng., 4(4) (1992) 415-429.

[28] P. Soroushian, C.D. Lee, Constitutive modeling ofsteel fiber reinforced concrete under direct tensionand compression, In: R.N. Swamy, B. Barr, editors,Fiber reinforced cement and concrete recent devel-opments, Cardiff, UK: University of Wales; Publi-cation of: Elsevier Applied Science Publishers Lim-ited, 18(20) (1989) 363-377.

[29] H. Dabbagh, K. Amoorezaei, S. Akbarpour, K.Babamuradi, Compressive toughness of lightweightaggregate concrete containing different types ofsteel fiber under monotonic loading, AUT. J. Civ.Eng., 1(1) (2017) 15-22.

[30] ASTM C330/C330M, Standard specification forlightweight aggregates for structural concrete,American Society for Testing and Materials, (2014).

[31] K. Amoorezaei, Behavior of steel fiber reinforcedlightweight concrete under compressive cyclic load-ing, MSc Thesis, Iran: University of Kurdistan,(2016).

[32] ACI 211.2, Standard practice for selecting propor-tions for structural lightweight concrete, AmericanConcrete Institute, 1998 (Reapproved 2004).

[33] ASTM C469/C469M, Standard test method forstatic modulus of elasticity and Poisson’s ratio ofconcrete in compression, American Society for Test-ing and Materials, (2014).

[34] ASTM C39/C39M, Standard test method forcompressive strength of cylindrical concrete speci-mens, American Society for Testing and Materials,(2015).

[35] P. Mehta, P.J.M. Monteiro, Concrete: microstruc-ture, properties, and materials, McGraw-Hill Pub-lishing, (2006).

[36] D.J. Carreira, K.H. Chu, Stress-strain relationshipfor plain concrete in compression, ACI J. Proc.,82(6) (1985) 797-804.

[37] N.A. Libre, M. Shekarchi, M. Mahoutian, P.Soroushian, Mechanical properties of hybrid fiberreinforced lightweight aggregate concrete madewith natural pumice, Const. Build. Mater., 25(5)(2011) 2458-2464.

[38] G. Campione, L. La Mendola, Behavior in com-pression of lightweight fiber reinforced concreteconfined with transverse steel reinforcement, Cem.Concr. Compos., 26(6) (2004) 645-656.

[39] S. Akbarpour, The effects of nano-silica and steelfibers on flexural behavior of reinforced lightweightaggregate concrete beams, PhD Thesis, Iran: Uni-versity of Kurdistan, (2018).

Stress-strain Relationship for Steel Fiber-reinforced Light-weight Aggregate Concrete under UniaxialCompression: 43–52 52