{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T13:19:23Z","timestamp":1780406363477,"version":"3.54.1"},"reference-count":92,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2020,6,29]],"date-time":"2020-06-29T00:00:00Z","timestamp":1593388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The use of fibers as mass reinforcement to delay cracking and to improve the strength and the post-cracking performance of reinforced concrete (RC) beams has been well documented. However, issues of common engineering practice about the beneficial effect of steel fibers to the seismic resistance of RC structural members in active earthquake zones have not yet been fully clarified. This study presents an experimental and a numerical approach to the aforementioned question. The hysteretic response of slender and deep steel fiber-reinforced concrete (SFRC) beams reinforced with steel reinforcement is investigated through tests of eleven beams subjected to reversal cyclic loading and numerical analysis using 3D finite element (FE) modeling. The experimental program includes flexural and shear-critical SFRC beams with different ratios of steel reinforcing bars (0.55% and 1.0%), closed stirrups (from 0 to 0.5%), and fibers with content from 0.5 to 3% per volume. The developed nonlinear FE numerical simulation considers well-established relationships for the compression and tensional behavior of SFRC that are based on test results. Specifically, a smeared crack model is proposed for the post-cracking behavior of SFRC under tension, which employs the fracture characteristics of the composite material using stress versus crack width curves with tension softening. Axial tension tests of prismatic SFRC specimens are also included in this study to support the experimental project and to verify the proposed model. Comparing the numerical results with the experimental ones it is revealed that the proposed model is efficient and accurately captures the crucial aspects of the response, such as the SFRC tension softening effect, the load versus deformation cyclic envelope and the influence of the fibers on the overall hysteretic performance. The findings of this study also reveal that SFRC beams showed enhanced cyclic behavior in terms of residual stiffness, load-bearing capacity, deformation, energy dissipation ability and cracking performance, maintaining their integrity through the imposed reversal cyclic tests.<\/jats:p>","DOI":"10.3390\/ma13132923","type":"journal-article","created":{"date-parts":[[2020,6,29]],"date-time":"2020-06-29T11:17:17Z","timestamp":1593429437000},"page":"2923","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":74,"title":["Effect of Steel Fibers on the Hysteretic Performance of Concrete Beams with Steel Reinforcement\u2014Tests and Analysis"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1430-0149","authenticated-orcid":false,"given":"Violetta","family":"K. Kytinou","sequence":"first","affiliation":[{"name":"Laboratory of Reinforced Concrete and Seismic Design of Structures, Civil Engineering Department, Faculty of Engineering, Democritus University of Thrace (D.U.Th.), 67100 Xanthi, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8283-1382","authenticated-orcid":false,"given":"Constantin","family":"E. Chalioris","sequence":"additional","affiliation":[{"name":"Laboratory of Reinforced Concrete and Seismic Design of Structures, Civil Engineering Department, Faculty of Engineering, Democritus University of Thrace (D.U.Th.), 67100 Xanthi, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chris","family":"G. Karayannis","sequence":"additional","affiliation":[{"name":"Laboratory of Reinforced Concrete and Seismic Design of Structures, Civil Engineering Department, Faculty of Engineering, Democritus University of Thrace (D.U.Th.), 67100 Xanthi, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anaxagoras","family":"Elenas","sequence":"additional","affiliation":[{"name":"Laboratory of Reinforced Concrete and Seismic Design of Structures, Civil Engineering Department, Faculty of Engineering, Democritus University of Thrace (D.U.Th.), 67100 Xanthi, Greece"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1002\/suco.201800079","article-title":"Influence of steel, glass and polymer fibers on the cracking behavior of reinforced concrete beams under flexure","volume":"20","author":"Conforti","year":"2019","journal-title":"Struct. Concr."},{"key":"ref_2","first-page":"032059","article-title":"Effect of curing period on properties of steel and polypropylene fibre reinforced ultra-high performance concrete","volume":"245","author":"Smarzewski","year":"2017","journal-title":"Mater. Sci. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bencardino, F., Nistic\u00f2, M., and Verre, S. (2020). Experimental investigation and numerical analysis of bond behavior in SRG-strengthened masonry prisms using UHTSS and stainless-steel fibers. Fibers, 8.","DOI":"10.3390\/fib8020008"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2777","DOI":"10.1007\/s12205-017-0939-5","article-title":"Self-healing capacity of fiber reinforced cementitious composites. State of the art and perspectives","volume":"21","author":"Cuenca","year":"2017","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Guerini, V., Conforti, A., Plizzari, G., and Kawashima, S. (2018). Influence of steel and macro-synthetic fibers on concrete properties. Fibers, 6.","DOI":"10.3390\/fib6030047"},{"key":"ref_6","first-page":"64.1","article-title":"Post-cracking response of hybrid recycled\/industrial steel fiber-reinforced concrete","volume":"326","author":"Martinelli","year":"2018","journal-title":"ACI Spec. Publ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1061\/(ASCE)0899-1561(2008)20:9(599)","article-title":"Design aspects on steel fiber-reinforced concrete pavements","volume":"20","author":"Belletti","year":"2008","journal-title":"J. Mater. Civ. Eng."},{"key":"ref_8","first-page":"179712","article-title":"Mechanical parameters and post-cracking behaviour of HPFRC according to three-point and four-point bending test","volume":"2013","author":"Bencardino","year":"2013","journal-title":"Adv. Civ. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1016\/j.conbuildmat.2016.08.068","article-title":"Experimental characterization of the post-cracking response in hybrid steel\/polypropylene fiber-reinforced concrete","volume":"125","author":"Caggiano","year":"2016","journal-title":"Constr. Build. Mater."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"153","DOI":"10.2495\/ERES090141","article-title":"Steel fiber high-strength reinforced concrete: A new solution for earthquake strengthening of old R\/C structures","volume":"104","author":"Tsonos","year":"2009","journal-title":"WIT Trans. Built Env."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Vougioukas, E., and Papadatou, M. (2017). A model for the prediction of the tensile strength of fiber-reinforced concrete members, before and after cracking. Fibers, 5.","DOI":"10.3390\/fib5030027"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Abambres, M., and Lantsoght, E.O.L. (2019). ANN-Based Shear Capacity of Steel Fiber-Reinforced Concrete Beams without Stirrups. Fibers, 7.","DOI":"10.31224\/osf.io\/aydv8"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.engstruct.2012.03.055","article-title":"Behaviour of concrete deep beams with openings and low shear span-to-depth ratio","volume":"41","author":"Campione","year":"2012","journal-title":"Eng. Struct."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ma, K., Qi, T., Liu, H., and Wang, H. (2018). Shear behavior of hybrid fiber reinforced concrete deep beams. Materials, 11.","DOI":"10.3390\/ma11102023"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Smarzewski, P. (2019). Analysis of failure mechanics in hybrid fibre-reinforced high-performance concrete deep beams with and without openings. Materials, 12.","DOI":"10.3390\/ma12010101"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.compositesb.2015.01.037","article-title":"Influence of concrete matrix and type of fiber on the shear strength behavior of self-compacting fiber reinforced concrete","volume":"75","author":"Cuenca","year":"2015","journal-title":"Compos. Part B Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"273","DOI":"10.2495\/MC090261","article-title":"Ultra-high-performance fiber reinforced concrete: An innovative solution for strengthening old R\/C structures and for improving the FRP strengthening method","volume":"64","author":"Tsonos","year":"2009","journal-title":"WIT Trans. Eng. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.conbuildmat.2017.11.101","article-title":"Fiber-reinforced concrete with low content of recycled steel fiber: Shear behavior","volume":"161","author":"Leone","year":"2018","journal-title":"Constr. Build. Mater."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1016\/j.cemconcomp.2003.07.001","article-title":"Effectiveness of stirrups and steel fibres as shear reinforcement","volume":"26","author":"Cucchiara","year":"2004","journal-title":"Cem. Concr. Compos."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Zhao, J., Liang, J., Chu, L., and Shen, F. (2018). Experimental study on shear behavior of steel fiber reinforced concrete beams with high-strength reinforcement. Materials, 11.","DOI":"10.3390\/ma11091682"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Torres, J.A., and Lantsoght, E.O.L. (2019). Influence of fiber content on shear capacity of steel fiber-reinforced concrete beams. Fibers, 7.","DOI":"10.20944\/preprints201908.0301.v1"},{"key":"ref_22","first-page":"56","article-title":"Seismic retrofit of beam-to-column joints with high-strength fiber jackets","volume":"16","author":"Tsonos","year":"2002","journal-title":"Europ. Earthq. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1080\/19648189.2011.9714854","article-title":"Flexural behaviour of external R\/C steel fibre reinforced beam-column joints","volume":"15","author":"Amato","year":"2011","journal-title":"Europ. J. Env. Civ. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Kabir, M.R., Alam, M.S., Said, A.M., and Ayad, A. (2016). Performance of hybrid reinforced concrete beam column joint: A critical review. Fibers, 4.","DOI":"10.3390\/fib4020013"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/j.engstruct.2013.10.046","article-title":"Seismic response of steel fiber reinforced concrete beam-column joints","volume":"59","author":"Abbas","year":"2014","journal-title":"Eng. Struct."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/j.conbuildmat.2013.11.048","article-title":"Concrete columns confined with fibre reinforced cementitious mortars: Experimentation and modelling","volume":"52","author":"Colajanni","year":"2014","journal-title":"Constr. Build. Mater."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/j.conbuildmat.2017.09.004","article-title":"Compressive strength of confined column with fiber reinforced mortar (FRM): New design-oriented-models","volume":"156","author":"Cascardi","year":"2017","journal-title":"Constr. Build. Mater."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2064","DOI":"10.1016\/j.proeng.2011.07.259","article-title":"Shear performance of steel fibrous concrete beams","volume":"14","author":"Chalioris","year":"2011","journal-title":"Procedia Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.cemconcomp.2009.02.007","article-title":"Effectiveness of the use of steel fibers on the torsional behavior of flanged concrete beams","volume":"31","author":"Chalioris","year":"2009","journal-title":"Cem. Concr. Compos."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1061\/(ASCE)ST.1943-541X.0000127","article-title":"Simple plastic model for shear critical SFRC beams","volume":"136","author":"Spinella","year":"2010","journal-title":"J. Struct. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"227","DOI":"10.12989\/cac.2012.9.3.227","article-title":"Generalization of shear truss model to the case of SFRC beams with stirrups","volume":"9","author":"Colajanni","year":"2012","journal-title":"Comput. Concr."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"365","DOI":"10.12989\/cac.2013.11.5.365","article-title":"Shear strength of full-scale steel fibre-reinforced concrete beams without stirrups","volume":"11","author":"Spinella","year":"2013","journal-title":"Comput. Concr."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Lantsoght, E.O.L. (2019). Database of shear experiments on steel fiber reinforced concrete beams without stirrups. Materials, 12.","DOI":"10.20944\/preprints201902.0264.v1"},{"key":"ref_34","first-page":"1","article-title":"Mechanical model for the shear strength of steel fiber reinforced concrete (SFRC) beams without stirrups","volume":"53","author":"Bernat","year":"2020","journal-title":"Mater. Struct."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1061\/(ASCE)0899-1561(2003)15:2(174)","article-title":"Tension stiffening and cracking of steel fiber-reinforced concrete","volume":"15","author":"Bischoff","year":"2003","journal-title":"ASCE J. Mat. Civ. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1007\/s11029-013-9385-8","article-title":"Determination of the stress-crack opening relationship of SFRC by an inverse analysis","volume":"49","author":"Meskenas","year":"2014","journal-title":"Mech. Compos. Mater."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Morelli, F., Amico, C., Salvatore, W., Squeglia, N., and Stacul, S. (2017). Influence of tension stiffening on the flexural stiffness of reinforced concrete circular sections. Materials, 10.","DOI":"10.3390\/ma10060669"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1155\/2016\/4913536","article-title":"Steel fibers: Effective way to prevent failure of the concrete bonded with FRP sheets","volume":"2016","author":"Gribniak","year":"2016","journal-title":"Adv. Mater. Sci. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Gribniak, V., Tamulenas, V., Ng, P.-L., Arnautov, A.K., Gudonis, E., and Misiunaite, I. (2017). Mechanical behavior of steel fiber-reinforced concrete beams bonded with external carbon fiber sheets. Materials, 10.","DOI":"10.3390\/ma10060666"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Gribniak, V., Ng, P.-L., Tamulenas, V., Misiunaite, I., Norkus, A., and \u0160apalas, A. (2019). Strengthening of fibre reinforced concrete elements: Synergy of the fibres and external sheet. Sustainability, 11.","DOI":"10.3390\/su11164456"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2930","DOI":"10.1016\/j.compositesb.2012.06.003","article-title":"Flexural behaviour of RC beams in fibre reinforced concrete","volume":"43","author":"Meda","year":"2012","journal-title":"Compos. Part B Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"5024353","DOI":"10.1155\/2018\/5024353","article-title":"Flexural toughness of high-performance concrete with basalt and polypropylene short fibres","volume":"2018","author":"Smarzewski","year":"2018","journal-title":"Adv. Civ. Eng."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/j.engstruct.2012.04.032","article-title":"Deriving stress-strain relationships for steel fiber concrete in tension from tests of beams with ordinary reinforcement","volume":"42","author":"Gribniak","year":"2012","journal-title":"Eng. Struct."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.compositesb.2013.02.003","article-title":"Comparative analysis of deformations and tension-stiffening in concrete beams reinforced with GFRP or steel bars and fibers","volume":"50","author":"Gribniak","year":"2013","journal-title":"Compos. Part B Eng."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/s11029-014-9428-9","article-title":"Experimental investigation of the deformation behavior of SFRC beams with an ordinary reinforcement","volume":"50","author":"Kaklauskas","year":"2014","journal-title":"Mech. Compos. Mater."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"82","DOI":"10.3846\/bjrbe.2017.10","article-title":"Experimental investigation of cracking behaviour of concrete beams reinforced with steel fibres produced in Lithuania","volume":"12","author":"Meskenas","year":"2017","journal-title":"Baltic J. Road Bridge. Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s11029-016-9592-1","article-title":"Experimental investigation of the capacity of steel fibers to ensure the structural integrity of reinforced concrete specimens coated with CFRP sheets","volume":"52","author":"Gribniak","year":"2016","journal-title":"Mech. Compos. Mater."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"2056","DOI":"10.1002\/suco.201800286","article-title":"Tension stiffening approach for deformation assessment of flexural reinforced concrete members under compressive axial load","volume":"20","author":"Ng","year":"2019","journal-title":"Struct. Concr."},{"key":"ref_49","first-page":"182","article-title":"Postpeak behavior of fiber-reinforced concrete under cyclic tensile loads","volume":"97","author":"Plizzari","year":"2000","journal-title":"ACI Mater. J."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1016\/j.engstruct.2012.06.030","article-title":"Fatigue resistance and cracking mechanism of concrete pavements reinforced with recycled steel fibres recovered from post-consumer tyres","volume":"45","author":"Graeff","year":"2012","journal-title":"Eng. Struct."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.conbuildmat.2017.02.094","article-title":"Experimental investigation on the stress-strain behavior of steel fiber reinforced concrete subjected to uniaxial cyclic compression","volume":"140","author":"Li","year":"2017","journal-title":"Constr. Build. Mater."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1236","DOI":"10.1016\/j.conbuildmat.2018.09.140","article-title":"Cyclic tensile behavior of SFRC: Experimental research and analytical model","volume":"190","author":"Li","year":"2018","journal-title":"Constr. Build. Mater."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"04014241","DOI":"10.1061\/(ASCE)MT.1943-5533.0001200","article-title":"Effect of cyclic loading on the residual tensile strength of steel fiber-reinforced high-strength concrete","volume":"27","author":"Gonzalez","year":"2015","journal-title":"ASCE J. Mater. Civ. Eng."},{"key":"ref_54","first-page":"248","article-title":"Behavior of high-strength fiber-reinforced concrete beams under cyclic loading","volume":"99","author":"Daniel","year":"2002","journal-title":"ACI Struct. J."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1617\/s11527-006-9129-5","article-title":"The effect of steel fibers on the earthquake-resistant design of reinforced concrete structures","volume":"40","author":"Kotsovos","year":"2007","journal-title":"Mater. Struct."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"864","DOI":"10.1061\/(ASCE)0899-1561(2007)19:10(864)","article-title":"Effect of steel fibers on bond performance of steel bars in NSC and HSC under load reversals","volume":"19","author":"Harajli","year":"2007","journal-title":"ASCE J. Mater. Civ. Eng."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"2970","DOI":"10.1016\/j.engstruct.2008.04.019","article-title":"Fibrous reinforced concrete beams in flexure: Experimental investigation, analytical modelling and design considerations","volume":"30","author":"Campione","year":"2008","journal-title":"Eng. Struct."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.14359\/51686967","article-title":"Concrete beams reinforced with high-strength steel subjected to displacement reversals","volume":"111","author":"Tavallali","year":"2014","journal-title":"ACI Struct. J."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.conbuildmat.2016.06.045","article-title":"Monotonic and cyclic behaviour of lightweight concrete beams with and without steel fiber reinforcement","volume":"122","author":"Caratelli","year":"2016","journal-title":"Constr. Build. Mater."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1061\/(ASCE)0733-9445(2007)133:3(421)","article-title":"Deformation capacity and shear strength of fiber-reinforced cement composite flexural members subjected to displacement reversals","volume":"133","author":"Chompreda","year":"2007","journal-title":"ASCE J. Struct. Eng."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"75","DOI":"10.14359\/51687940","article-title":"Behavior of steel fiber-reinforced concrete under reversed cyclic shear","volume":"113","author":"Luo","year":"2016","journal-title":"ACI Struct. J."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.engstruct.2012.10.010","article-title":"Steel fibrous RC beams subjected to cyclic deformations under predominant shear","volume":"49","author":"Chalioris","year":"2013","journal-title":"Eng. Struct."},{"key":"ref_63","unstructured":"Smith, S.T. (2007, January 12\u201314). FRP strengthening of RC columns: Parametric finite element analyses of bar quality effect. Proceedings of the 1st Asia-Pacific Conference on FRP in Structures (APFIS 2007), Hong-Kong, China."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"G\u00f3mez, J., Torres, L., and Barris, C. (2020). Characterization and simulation of the bond response of NSM FRP reinforcement in concrete. Materials, 13.","DOI":"10.3390\/ma13071770"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Zhelyazov, T. (2020). Structural Materials: Identification of the constitutive models and assessment of the material response in structural elements strengthened with externally-bonded composite material. Materials, 13.","DOI":"10.3390\/ma13061272"},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Chalioris, C.E., Kosmidou, P.-M.K., and Karayannis, C.G. (2019). Cyclic response of steel fiber reinforced concrete slender beams: An experimental study. Materials, 12.","DOI":"10.3390\/ma12091398"},{"key":"ref_67","unstructured":"(2017). Dassault Syst\u00e8mes Simulia System Information. Abaqus 2017 User\u2019s Manual, SIMULIA. Version 6.12.1."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/0020-7683(89)90050-4","article-title":"A plastic-damage model for concrete","volume":"25","author":"Lubliner","year":"1989","journal-title":"Int. J. Solids Struct."},{"key":"ref_69","first-page":"83","article-title":"A numerical approach to steel-fibre reinforced concrete under torsion","volume":"7","author":"Karayannis","year":"1995","journal-title":"Struct. Eng. Rev."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"107079","DOI":"10.1016\/j.compositesb.2019.107079","article-title":"How do steel fibers improve the shear capacity of reinforced concrete beams without stirrups?","volume":"175","author":"Lantsoght","year":"2019","journal-title":"Compos. Part B Eng."},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Yun, H.-D., Lim, S.H., and Choi, W.-C. (2019). Effects of reinforcing fiber strength on mechanical properties of high-strength concrete. Fibers, 7.","DOI":"10.3390\/fib7100093"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1680\/stco.2005.6.1.1","article-title":"Compressive behaviour of steel fibre reinforced concrete","volume":"6","author":"Neves","year":"2005","journal-title":"Struct. Concr."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1061\/(ASCE)0899-1561(2008)20:3(255)","article-title":"Stress-strain behavior of steel fiber-reinforced concrete in compression","volume":"20","author":"Bencardino","year":"2008","journal-title":"ASCE J. Mater. Civ. Eng."},{"key":"ref_74","unstructured":"Chang, S.-Y., Al Bahar, S.K., Husain, A.-A.M., and Zhao, J. (2015). Tests and simplified behavioral model for steel fibrous concrete under compression. Advances in Civil Engineering and Building Materials IV., CRC Press\/Balkema."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"1442","DOI":"10.3390\/ma8041442","article-title":"Compressive behavior of fiber-reinforced concrete with end-hooked steel fibers","volume":"8","author":"Lee","year":"2015","journal-title":"Materials"},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Zhao, M., Zhang, B., Shang, P., Fu, Y., Zhang, X., and Zhao, S. (2019). Complete stress\u2013strain curves of self-compacting steel fiber reinforced expanded-shale lightweight concrete under uniaxial compression. Materials, 12.","DOI":"10.3390\/ma12182979"},{"key":"ref_77","first-page":"11","article-title":"Flexural analysis of steel fibre-reinforced concrete members","volume":"22","author":"Chalioris","year":"2018","journal-title":"Comput. Concr."},{"key":"ref_78","doi-asserted-by":"crossref","unstructured":"Choi, W.-C., Jung, K.-Y., Jang, S.-J., and Yun, H.-D. (2019). The influence of steel fiber tensile strengths and aspect ratios on the fracture properties of high-strength concrete. Materials, 12.","DOI":"10.3390\/ma12132105"},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/j.conbuildmat.2009.09.009","article-title":"Experimental and numerical analysis on effect of fiber aspect ratio on mechanical properties of SFRC","volume":"24","author":"Wang","year":"2010","journal-title":"Constr. Build. Mater."},{"key":"ref_80","doi-asserted-by":"crossref","unstructured":"Choi, S.W., Choi, J., and Lee, S.C. (2019). Probabilistic analysis for strain-hardening behavior of high-performance fiber-reinforced concrete. Materials, 12.","DOI":"10.3390\/ma12152399"},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Bezerra, A., Maciel, P.S., Corr\u00eaa, E., Soares Junior, P.R.R., Aguilar, M.T.P., and Cetlin, P.R. (2019). Effect of high temperature on the mechanical properties of steel fiber-reinforced concrete. Fibers, 7.","DOI":"10.3390\/fib7120100"},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1061\/(ASCE)0733-9445(2000)126:6(638)","article-title":"Smeared crack analysis for plain concrete in torsion","volume":"126","author":"Karayannis","year":"2000","journal-title":"ASCE J. Struct. Eng."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1061\/(ASCE)0733-9445(2000)126:6(646)","article-title":"Experimental validation of smeared analysis for plain concrete in torsion","volume":"126","author":"Karayannis","year":"2000","journal-title":"ASCE J. Struct. Eng."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"107088","DOI":"10.1016\/j.engfracmech.2020.107088","article-title":"Uncertainty of the smeared crack model applied to RC beams","volume":"233","author":"Rimkus","year":"2020","journal-title":"Eng. Fract. Mech."},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Kytinou, K.V., and Chalioris, C.E. (2020). Analysis of residual flexural stiffness of steel fiber-reinforced concrete beams with steel reinforcement. Materials, 13.","DOI":"10.3390\/ma13122698"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"323","DOI":"10.12989\/sem.2000.9.4.323","article-title":"Nonlinear analysis and tests of steel-fiber concrete beams in torsion","volume":"9","author":"Karayannis","year":"2000","journal-title":"Struct. Eng. Mech."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"1411","DOI":"10.1002\/suco.201800224","article-title":"Post-cracking behavior of polypropylene fiber reinforced concrete under bending and uniaxial tensile tests","volume":"20","author":"Mudadu","year":"2019","journal-title":"Struct. Concr."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/j.cemconcomp.2018.07.012","article-title":"The effect of fiber orientation on the post-cracking behavior of steel fiber reinforced concrete under bending and uniaxial tensile tests","volume":"93","author":"Mudadu","year":"2018","journal-title":"Cem. Concr. Compos."},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.compositesb.2009.09.002","article-title":"Experimental evaluation of fiber reinforced concrete fracture properties","volume":"41","author":"Bencardino","year":"2010","journal-title":"Compos. Part B Eng."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/BF02486267","article-title":"Crack band theory for fracture of concrete","volume":"16","author":"Bazant","year":"1983","journal-title":"Mater. Constr."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.engstruct.2015.04.016","article-title":"Finite element analysis of punching shear of concrete slabs using damaged plasticity model in ABAQUS","volume":"98","author":"Genikomsou","year":"2015","journal-title":"Eng. Struct."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.conbuildmat.2013.02.039","article-title":"Analytical approach for the evaluation of minimum fiber factor required for steel fibrous concrete beams under combined shear and flexure","volume":"43","author":"Chalioris","year":"2013","journal-title":"Constr. Build. 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