{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:40:40Z","timestamp":1760236840708,"version":"build-2065373602"},"reference-count":61,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,27]],"date-time":"2021-12-27T00:00:00Z","timestamp":1640563200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The ductility and strength of reinforced concrete (RC) columns could be noticeably improved by replacing steel bars with polymeric bars. Despite the previous research on RC columns, most of those studies focused only on the lateral load capacity of this structural member and were mainly costly experimental studies. However, this paper is concentrated on the previously occurred damages to the reinforced columns in the previous earthquakes. Subsequently, finite element analysis has been performed to examine 24 models including the various shapes of RC columns. In employing the plastic behavior of steel, carbon fiber-reinforced polymer (CFRP), and glass fiber reinforced polymer (GFRP) bars, the bilinear hardening has been considered. To capture both compressive and tensile behavior of the concrete, the concrete damage plasticity model has been implemented. Furthermore, the optimization technique is used for CFRP models to compare with other models. In this paper, the parameters of energy, seismic factor, stiffness, and ductility have been computed using the method proposed by the authors. This suggested method is considered to compare the results from each parameter. Finite element results of steel bars are compared with carbon and glass models. The results show the stiffness of models is improved by CFRP bars, while the energy absorption and ductility factor are enhanced with steel bars. Moreover, GFRP bars can enhance the seismic factor. The reduction of column stiffness to almost half would occur in some rectangular cross-section columns.<\/jats:p>","DOI":"10.3390\/a15010012","type":"journal-article","created":{"date-parts":[[2021,12,28]],"date-time":"2021-12-28T01:18:15Z","timestamp":1640654295000},"page":"12","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Optimization of Fiber-Reinforced Polymer Bars for Reinforced Concrete Column Using Nonlinear Finite Element Algorithms"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7765-1464","authenticated-orcid":false,"given":"Sajjad Sayyar","family":"Roudsari","sequence":"first","affiliation":[{"name":"Department of Computational Science and Engineering, North Carolina A&T State University, Greensboro, NC 27411, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9958-4998","authenticated-orcid":false,"given":"Liviu Marian","family":"Ungureanu","sequence":"additional","affiliation":[{"name":"TMR Department, Bucharest Polytechnic University, RO-060042 Bucharest, Romania"}]},{"given":"Soheil","family":"Soroushnia","sequence":"additional","affiliation":[{"name":"Faculty of Engineering and Design, Carleton University, Ottawa, ON K1S 5B6, Canada"}]},{"given":"Taher","family":"Abu-Lebdeh","sequence":"additional","affiliation":[{"name":"Department of Computational Science and Engineering, North Carolina A&T State University, Greensboro, NC 27411, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1627-5159","authenticated-orcid":false,"given":"Florian Ion Tiberiu","family":"Petrescu","sequence":"additional","affiliation":[{"name":"TMR Department, Bucharest Polytechnic University, RO-060042 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,27]]},"reference":[{"key":"ref_1","unstructured":"Xavier, H.F.B. (2021, December 20). Analysis of Reinforced Concrete Frames Exposed to Fire: Based on Advanced Calculation Methods. Available online: https:\/\/repositorio-aberto.up.pt\/bitstream\/10216\/58515\/1\/000136907.pdf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1061\/(ASCE)0887-3828(2007)21:4(257)","article-title":"Assessment of fire damage to a reinforced concrete structure during construction","volume":"21","author":"Dilek","year":"2007","journal-title":"J. Perform. Constr. Facil."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.firesaf.2014.11.009","article-title":"Experimental investigation of reinforced concrete and hybrid fibre reinforced concrete shield tunnel segments subjected to elevated temperature","volume":"71","author":"Yan","year":"2015","journal-title":"Fire Saf. J."},{"key":"ref_4","first-page":"3076","article-title":"Seismic performance of RC elevated water tanks with frame staging and exhibition damage pattern","volume":"14","author":"Soroushnia","year":"2011","journal-title":"ProcediaEng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/S0141-0296(02)00121-9","article-title":"Performance of reinforced concrete buildings during the August 17, 1999 Kocaeli, Turkey earthquake, and seismic design and construction practise in Turkey","volume":"25","author":"Sezen","year":"2003","journal-title":"Eng. Struct."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"04014125","DOI":"10.1061\/(ASCE)CF.1943-5509.0000532","article-title":"Field reconnaissance of the October 23, 2011, Van, Turkey, earthquake: Lessons from structural damages","volume":"29","author":"Murat","year":"2013","journal-title":"J. Perform. Constr. Facil."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.proeng.2013.03.010","article-title":"A Case Study on Corrosion in Concrete Floating Docks in Qeshm Port","volume":"54","author":"Ramesht","year":"2013","journal-title":"Procedia Eng."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Nakhostin, E., Kenny, S., and Sivathayalan, S. (2019, January 6\u20139). Buried Corrugated Steel Culvert Failure Mechanisms Due to Environmental Deteriorations. Proceedings of the International Conference on Sustainable Infrastructure 2019, Los Angeles, CA, USA.","DOI":"10.1061\/9780784482650.004"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1139\/cjce-2019-0316","article-title":"Numerical performance assessment of buried corrugated metal culvert subject to service load conditions","volume":"48","author":"Nakhostin","year":"2021","journal-title":"Can. J. Civ. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1016\/j.cemconcomp.2007.03.005","article-title":"A quantitative study on the plastic shrinkage cracking in high strength hybrid fibre reinforced concrete","volume":"29","author":"Sivakumar","year":"2007","journal-title":"Cem. Concr. Compos."},{"key":"ref_11","unstructured":"Sarray, A.A. (2021, December 15). The Deterioration of Concrete in Wastewater Treatment Plants. Available online: http:\/\/i-rep.emu.edu.tr:8080\/jspui\/bitstream\/11129\/1340\/1\/SarrayAnmar.pdf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1016\/j.conbuildmat.2012.06.006","article-title":"Full-scale fire tests of RC metro shield TBM tunnel linings","volume":"36","author":"Yan","year":"2012","journal-title":"Constr. Build. Mater."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1631\/jzus.A1300067","article-title":"Sulphate attack resistance of high-performance concrete under compressive loading","volume":"14","author":"Xu","year":"2013","journal-title":"J. Zhejiang Univ. Sci. A"},{"key":"ref_14","first-page":"15","article-title":"Sulphate attack in high-performance concrete-a review","volume":"1","author":"Alam","year":"2012","journal-title":"J. Adv. Struct. Geotech. Eng."},{"key":"ref_15","unstructured":"Freitag, S.A., Bruce, S.M., and Shayan, A. (2011). Concrete Pile Durability in South Island Bridges, NZ Transport Agency. Research Report 454."},{"key":"ref_16","unstructured":"Folliard, K.J., Thomas, M.D.A., Fournier, B., Kurtis, K.E., and Ideker, J.H. (2006). Interim Recommendations for the Use of Lithium to Mitigate or Prevent Alkali-Silica Reaction (ASR), US Department of Transportation."},{"key":"ref_17","unstructured":"Farny, J.A., and Kosmatka, S.H. (2021, December 15). Diagnosis and Control of Alkali-Aggregate Reactions in Concrete. Available online: https:\/\/www.cement.org\/docs\/default-source\/fc_concrete_technology\/is413-diagnosis-and-control-of-alkali-aggregate-reactions-in-concrete.pdf."},{"key":"ref_18","unstructured":"Jana, D. (2007, January 20\u201324). Concrete scaling\u2013a critical review. Proceedings of the 29th Conference on Cement Microscopy, Quebec, QC, Canada."},{"key":"ref_19","unstructured":"Portland Cement Association (2001). Concrete Slab Surface Defects: Causes, Prevention, Repair, Portland Cement Association."},{"key":"ref_20","unstructured":"Song, G., and Shayan, A. (1998). Corrosion of Steel in Concrete: Causes, Detection and Prediction: A State-of-the-Art Review, The Australian Road Research Board (ARRB)."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1016\/j.conbuildmat.2017.09.142","article-title":"Degradation of steel-to-concrete bond due to corrosion","volume":"158","author":"Jiang","year":"2018","journal-title":"Constr. Build. Mater."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Fran\u00e7ois, R., Laurens, S., and Deby, F. (2018). 1\u2014Steel Corrosion in Reinforced Concrete. Corrosion and Its Consequences for Reinforced Concrete Structures, Elsevier.","DOI":"10.1016\/B978-1-78548-234-2.50001-9"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1016\/j.scitotenv.2018.08.362","article-title":"Corrosion of reinforcing steel in concrete sewers","volume":"649","author":"Song","year":"2019","journal-title":"Sci. Total Environ."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Poursaee, A. (2016). 2\u2014Corrosion of steel in concrete structures. Corrosion of Steel in Concrete Structures, Woodhead Publishing.","DOI":"10.1016\/B978-1-78242-381-2.00002-X"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1016\/j.compositesb.2006.07.011","article-title":"Application of FRP composites for underwater piles repair","volume":"38","author":"Sen","year":"2007","journal-title":"Compos. Part B Eng."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1357","DOI":"10.1061\/(ASCE)0733-9445(1997)123:10(1357)","article-title":"Seismic retrofit of RC circular columns using prefabricated composite jacketing","volume":"123","author":"Xiao","year":"1997","journal-title":"J. Struct. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1061\/(ASCE)1090-0268(1997)1:2(52)","article-title":"Seismic retrofit of RC columns with continuous carbon fiber jackets","volume":"1","author":"Seible","year":"1997","journal-title":"J. Compos. Constr."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.compstruct.2007.04.002","article-title":"Design of FRP-wrapped reinforced concrete columns for enhancing axial load carrying capacity","volume":"82","author":"Wang","year":"2008","journal-title":"Compos. Struct."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.compstruct.2007.01.028","article-title":"Seismic retrofit of reinforced concrete short columns by CFRP materials","volume":"82","author":"Colomb","year":"2008","journal-title":"Compos. Struct."},{"key":"ref_30","first-page":"206","article-title":"Repair of earthquake-damaged RC columns with FRP wraps","volume":"94","author":"Saadatmanesh","year":"1997","journal-title":"ACI Struct. J."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1016\/j.conbuildmat.2016.12.100","article-title":"Repair and rehabilitation of concrete structures using confinement: A review","volume":"133","author":"Ma","year":"2017","journal-title":"Constr. Build. Mater."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1061\/(ASCE)1090-0268(2005)9:2(136)","article-title":"Underwater FRP repair of prestressed piles in the Allen Creek Bridge in the city of clearwater","volume":"9","author":"Mullins","year":"2005","journal-title":"ASCE. J. Composites Constr."},{"key":"ref_33","first-page":"1139","article-title":"FRP application in underwater repair of corroded piles","volume":"230","author":"Sen","year":"2005","journal-title":"Spec. Publ."},{"key":"ref_34","first-page":"70","article-title":"A demonstration of underwater FRP repair","volume":"28","author":"Mullins","year":"2006","journal-title":"Concr. Int."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/j.conbuildmat.2006.08.017","article-title":"Seismic retrofitting of R\/C columns having plain rebars using CFRP sheets for improved strength and ductility","volume":"22","author":"Yalcin","year":"2008","journal-title":"Constr. Build. Mater."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1554","DOI":"10.1177\/1369433218817988","article-title":"Experimental study on the axial compression performance of GFRP-reinforced concrete square columns","volume":"22","author":"Tu","year":"2019","journal-title":"Adv. Struct. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.istruc.2018.09.008","article-title":"Properties and applications of FRP in strengthening RC structures: A review","volume":"16","author":"MugahedAmran","year":"2018","journal-title":"Structures"},{"key":"ref_38","first-page":"589","article-title":"Behavior of Full-Scale Glass Fiber-Reinforced Polymer Reinforced Concrete Columns under Axial Load","volume":"107","author":"Antonio","year":"2010","journal-title":"Struct. J."},{"key":"ref_39","first-page":"551","article-title":"Concrete Columns Reinforced Longitudinally and Transversally with Glass Fiber-Reinforced Polymer Bars","volume":"109","author":"HanyTobbi","year":"2012","journal-title":"Struct. J."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1061\/(ASCE)CC.1943-5614.0000357","article-title":"Axial Load Behavior of Concrete Columns Confined with GFRP Spirals","volume":"17","author":"Pantelides","year":"2013","journal-title":"J. Compos. Constr."},{"key":"ref_41","first-page":"375","article-title":"Behavior of Concentrically Loaded Fiber-Reinforced Polymer Reinforced Concrete Columns with Varying Reinforcement Types and Ratios","volume":"111","author":"HanyTobbi","year":"2014","journal-title":"Struct. J."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"04013035","DOI":"10.1061\/(ASCE)CC.1943-5614.0000430","article-title":"Strength and Axial Behavior of Circular Concrete Columns Reinforced with CFRP Bars and Spirals","volume":"18","author":"Afifi","year":"2014","journal-title":"J. Compos. Constr."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/j.compositesb.2013.12.006","article-title":"Drop-weight impact behaviour of woven hybrid basalt\u2013carbon\/epoxy composites","volume":"59","author":"Sarasini","year":"2014","journal-title":"Compos. Part B Eng."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1061\/(ASCE)1090-0268(2006)10:4(279)","article-title":"Durability prediction for GFRP reinforcing bars using short-term data of accelerated aging tests","volume":"10","author":"Chen","year":"2006","journal-title":"J. Compos. Constr."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1061\/(ASCE)1090-0268(2002)6:2(73)","article-title":"Fiber-reinforced polymer composites for construction\u2014State-of-the-art review","volume":"6","author":"Bakis","year":"2002","journal-title":"J. Compos. Constr."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.compositesb.2016.03.085","article-title":"Mechanical properties and failure characteristics of CFRP under intermediate strain rates and varying temperatures","volume":"95","author":"Ou","year":"2016","journal-title":"Compos. Part B Eng."},{"key":"ref_47","unstructured":"Rocca, S. (2007). Experimental and Analytical Evaluation of FRP-Confined Large Size Reinforced Concrete Columns. [Ph.D. Thesis, University of Missouri]."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1016\/j.engstruct.2018.09.071","article-title":"Evaluation of large-size reinforced concrete columns strengthened for axial load using fiber reinforced polymers","volume":"178","author":"SayyarRoudsari","year":"2019","journal-title":"Eng. Struct."},{"key":"ref_49","unstructured":"(2003). Standard Test Methods and Definitions for Mechanical Testing of Steel Products (Standard No. ASTM A370-03a)."},{"key":"ref_50","unstructured":"(2021, December 15). Building Code Requirements for Structural Concrete: 2011. Available online: https:\/\/www.usb.ac.ir\/FileStaff\/5526_2020-1-25-11-12-7.pdf."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Campbell, F.C. (2010). Structural Composite Materials, ASM International.","DOI":"10.31399\/asm.tb.scm.9781627083140"},{"key":"ref_52","unstructured":"(2005). Iranian Code of Practice for Seismic Resistant Design of Buildings (Standard No. Standard No. 2800)."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/j.proeng.2013.03.020","article-title":"Determination the response modification factors of buckling restrained braced frames","volume":"54","author":"Mahmoudi","year":"2013","journal-title":"Procedia Eng."},{"key":"ref_54","unstructured":"Fajfar, P. (2002, January 9\u201313). Structural analysis in earthquake engineering\u2013a breakthrough of simplified non-linear methods. Proceedings of the 12th European Conference on Earthquake Engineering, London, UK."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.jcsr.2008.08.002","article-title":"BRBF response modification factor","volume":"65","author":"Asgarian","year":"2009","journal-title":"J. Constr. Steel Res."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Cican, G., Deaconu, M., Mirea, R., Ceatra, L., Cretu, M., and Dobre, T. (2020). Investigating the Use of Recycled Pork Fat-Based Biodiesel in Aviation Turbo Engines. Processes, 8.","DOI":"10.3390\/pr8091196"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"10833","DOI":"10.1016\/j.ijhydene.2019.02.140","article-title":"Nuclear hydrogen structure and dimensions","volume":"44","author":"Petrescu","year":"2019","journal-title":"Int. J. Hydrog. Energy"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"20740","DOI":"10.1016\/j.ijhydene.2020.05.253","article-title":"Hydrogen for aircraft power and propulsion","volume":"45","author":"Petrescu","year":"2020","journal-title":"Int. J. Hydrog. Energy"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.engfracmech.2017.04.018","article-title":"Extended MTSN criterion for fracture analysis of soda lime glass","volume":"178","author":"Mirsayar","year":"2017","journal-title":"Eng. Fract. Mech."},{"key":"ref_60","first-page":"193","article-title":"The Computer Algorithm for Machine Equations of Classical Distribution","volume":"4","author":"Petrescu","year":"2017","journal-title":"J. Mater. Eng. Struct."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"1392","DOI":"10.14807\/ijmp.v10i5.392","article-title":"An Algorithm to Determining the Gear Efficiency to a Simple Planetary Train","volume":"10","author":"Petrescu","year":"2019","journal-title":"Indep. J. Manag. Prod."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/1\/12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:54:19Z","timestamp":1760169259000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/1\/12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,27]]},"references-count":61,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["a15010012"],"URL":"https:\/\/doi.org\/10.3390\/a15010012","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2021,12,27]]}}}